Notes from an intuitive programmer

`My song is love unknown' (hymn)

2012-01-17T10:14:00.006-05:00

Recently, I heard a moving hymn, `My song is love unknown' (1664) by Samuel Crossman (1624-1683) and w/s found this post by Rupert Christiansen (in U.K.'s The Telegraph) for a story behind it.

Actually, what moved me was its tune, Love Unknown (1918) by John Ireland (1879-1962). Set to it, some contemporary churches know better the words, `Oft when of God we ask' by English Congregational minister Thomas Toke Lynch (1818-1871, more here).

During the 254 years that passed before Ireland wrote his, I wonder which tune the Crossman hymn used? There's currently no answer in Wikipedia's article. I found a list of alternate tunes for the text, but all are of poorer quality IMO for the words compared to Ireland's; it seems no wonder he was inspired to compose it, perhaps!

Crossman as a family name would seem to suggest to a boy, BTW, thinking about religion. However, that speculation remains unconfirmed by Wikipedia's article on Crossman.

Copyright (c) 2012 Mark D. Blackwell.

Lisp & Ruby metaprogramming

2012-01-10T23:30:00.016-05:00

I just reread Paul Graham's article, Beating the Averages, on Lisp being the most powerful computer programming language because of Lisp macros (which, BTW, are not like assembly language macros). It led me to the obvious perception that because Ruby lacks Lisp macros, metaprogramming in it is weaker than in Lisp.

He explains the essence of Lisp macros: '[I]n general, for application software, you want to be using the most powerful ...language you can get, and using anything else is a mistake. ...Lisp code, after it's read by the parser, is made of data structures that you can traverse. If you understand how compilers work, [in Lisp you] write programs in the parse trees that get generated within the compiler when other languages are parsed. But these parse trees are fully accessible to your programs. You can write programs that manipulate them. In Lisp, these programs are called macros. [P]ower ...refers to features you could only get in [a] less powerful language by writing an interpreter for [a] more powerful language in it.'

So, for someone who wants to know where to go next after Ruby, and thinks that, in a Ruby code base, having a high proportion of metaprogramming code, like some say Rails 3 has these days, results in awkwardness, the next step is Lisp. Lisp apparently is perhaps a better metaprogramming language.

Copyright (c) 2012 Mark D. Blackwell.

Chrome browser cookie exceptions, howto

2011-12-16T11:27:00.012-05:00

Google's `fast, new' Chrome browser has a development process that seems to fix problems rapidly.

An unmet need in the user interface, however, is explicating (right on the page) how to enter domains for cookie handling exceptions.

The proper way to be secure (although you may think differently) IMO follows:

Wrench-Options-Under the Hood-Content Settings-Cookies.
Select, `Block sites from setting any data'.
Check, `Block third party cookies from being set'.
Check, `Clear cookies and other site and plug-in data when I close my browser'.
Click, `Manage Exceptions...'.
Add and delete hostname patterns until you see what you like.

The problem is, it gives no subdomain examples. Per one bug report, `the user cannot...figure out...the right' syntax to enter them. Without adding the right subdomains, navigating to blogger.com mysteriously redirects us in a loop.

Its unusual wildcard syntax, for Google blogging, is:

[*.]blogger.com
[*.]google.com

The brackets must be entered explicitly. In other words, they do not merely indicate optional content.

Some kind of, `"Learn more" link about the pattern syntax would be awesome'.

Explicitly also, one could enter all the relevant subdomains (which is appropriate for some domains):

blogger.com
www.blogger.com
markdblackwell.blogspot.com
google.com
accounts.google.com

Copyright (c) 2011 Mark D. Blackwell.

Lean Startup book thoughts

2011-12-13T12:29:00.002-05:00

Have you read The Lean Startup by Eric Ries yet? good summary.

EVERYWHERE

Entrepreneurs are everywhere, he says, even in large, stolid, companies -- true even of IBM! I hope they exist, where you are now. Disruptive innovation might come from competitors.

WASTE

Just now, in the Amazon preview, I read the book's introduction. I see the book's epilogue: 'Waste Not'. That is so key! (to me, also).

Paraphrasing Ries: startup success, thus changing the world, is exciting. Let's not waste vision, passion and energy.

ACCOUNTING

'A new kind of accounting, designed for startups.' Like any accounting, it's good for measuring categories we want to watch, like how much is devoted to experimentation on customers.

TEAMS

Good to have '[c]ross-functional teams ... accountable to learning milestones ... instead of [specializing people in] ... functional departments.' Good to suggest things across functions. Good to set up a Lean Startup culture and systems.

SOCIAL

Lean Startup circle
Lean Startup at Meetup.com
Lean Startup Wiki

Good to connect socially with the Lean Startup people.

SUMMER

The book's graphs show manufacturing trending downward greatly these last ten years. With much borrowed money, he says we have been throwing our excess effort into many failed products. Hm, a recent Ries post says we are in a software development 'summer', but sometime a 'winter' will come.

LEARN

'Startups exist to *learn* how to build a sustainable business.'

With 'Build-Measure-Learn', steering to the 'destination[:] creating a thriving and world-changing business.' What a good idea!

Are we developing our own companies on Lean Startup principles?

BUSINESS

Like 'Zappos' [experiment,] ... a clear, quantifiable outcome: either a sufficient number of customers would buy or they would not.'

We might 'put [ourselves] in a position to interact with real customers and learn[.]' Right now, we could put a question on a website (and publicize it): are you (anyone browsing) interested in an app (of any kind) to do this?

LEGACY

He says plausible-sounding management theories, even seemingly reasonable (including legacy ones derived from manufacturing), are only as good as how well their predictions work.

Legacy practices (of 'good market research', even 'solid strategy') don't work when there is extreme 'uncertainty'. '[C]haos ... doesn't work either.'

'[N]ew product development ... routinely [and obviously now] requires ... [that which from a manufacturing perspective is] failure to plan adequately[,] failure properly to execute [the plan and a temporary] failure to deliver results ... on the way to greatness.' In other words, people (who learned the manufacturing paradigm) do resist.

Ries, quoting Scott Cook, 'Moving leaders from playing Ceasar with their thumbs up and down on every idea to --instead --putting in the culture and systems so that teams can move and innovate at the speed of the innovation system.'

Emphasizes he does not (just) do whatever customers say, interestingly, but focuses 'on what customers want (without asking them)'. That jibes with (my) experience: customers usually aren't good (naturally) doing breakthrough, useful, product imagining and creating.

SCIENCE

'Validated learning.' 'Scientific method.' It's great to see actual science entering into business management. BTW, science in general took a long time to overcome human nature and be adopted, just as (in particular) it did in business management.

'[O]ne ... lesson ... of the scientific method: if you cannot fail, you cannot learn.'

BOOK

Ries highly recommends The Four Steps to the Epiphany, 'the original book about customer development': dog-eared in his IMVU days.

Copyright (c) 2011 Mark D. Blackwell.

One-click registration on websites belonging to phone apps

2011-12-08T12:01:00.005-05:00

Recently, gmail passed me this advert (just for example). It is for a programming competition site that (incidentally) offers one-click registration (you know, while signed into other prestigious sites).

In most websites created for phone apps, user registration is better if it's one-click (in addition to signin). Sites (as above) do this in order to facilitate acting on impulse. (I'm not telling you anything you already don't know.)

In just two clicks (total!), users can register at the new website (even before buying the phone app) while they are skimming (or reading) posts or articles about the phone app's general topic (or smartphone technology), from a link which mentions some jazzy, new, tech feature. Generating this kind of news is something popular bloggers love to do. And it increases the phone app's mindshare.

Plausibly, in this way (huge) numbers of people would have an emotional commitment for trying-and-buying that phone app, and some would do so. If they are browsing in their smartphone, in one click they can purchase (and download) the app. Synergy! because websites are linked in ... well, a web.

People who use information aggregators (some generated by grassroots online communities, like my friend M) would (in their instream) see links to this new website, and inform their friends the same way. Thus will social synergy cause an explosive chain reaction!

One-click registration transfers (part of) the reputation of a very popular website, onto the new website.

After a person has gone through the effort of deciding to register themselves (and their personal information) on a popular website, and thus trust it, they desire also to trust (on the web) wherever else that (particular) website automatically allows them to register.

With the first website, we are in a 'community,' or have established a relationship. This leverages the natural human tendency to trust anyone referred to us, by a trusted other. Communities are a strong part of (genetically programmed) human nature.

This level of referral trust seems even to exceed the trust from (simple) hyperlink clicking. Perhaps what is called, 'cognitive dissonance' also plays a part.

Copyright (c) 2011 Mark D. Blackwell.

Webmaster gallery

2011-12-02T15:24:00.003-05:00

I made a picture gallery application for webmasters who use plain-vanilla web-hosting services (particularly those with cPanel).

The webmaster uploads pictures, thumbnails and CSS to a directory, then runs the app in order to create and modify the picture descriptions. It handles later uploaded pictures just as well.

It has been installed and run successfully (using cPanel).

An art gallery (of the app's first client) is visible (actually the static pages generated).

It is written in Rails 3.

Copyright (c) 2011 Mark D. Blackwell.

Bach-Lehman (and Young #1) using electronic tuner, howto

2011-11-17T18:06:00.015-05:00

Here's how to use an electronic tuner to tune a harpsichord in Bradley Lehman's Bach temperament, as well as Thomas Young's. They sound so much better than equal temperament (even better than Vallotti)--everyone should try them!

I found Lehman-Bach instructions (taking Vallotti as a starting point) in the section, `Easy way to tune it accurately and mostly electronically' (search for it) of his homepage.

Yet, there is another way. His section, `Electronic device instructions for the Bach' at the bottom
of `Practical temperament instructions by ear' also recommends we, `See the interesting method by David Hitchin', who says his method is useful if one has the `Korg-OT12 or a similar tuner which provides for ET and the Pythagorean, Werkmeister III and Vallotti temperaments.'

Dr. Lehman says the Thomas Young temperament he recommends (Young #1) `is not the more familiar "Young #2"; it is his first and better one...entirely symmetrical, and very simple...Young's #2 [the worse one] is technically [just] a transposition of the entire VALLOTTI temperament upward by a 5th.'

I found these instructions in the `YOUNG #1 1799/1800' section of his `Practical temperament instructions by ear':

1. Tune all of VALLOTTI first.
2. Nick F downward slightly so it's equally tempered between C and Bb.
3. Nick B upward slightly so it's equally tempered between E and F#.

Copyright (c) 2011 Mark D. Blackwell.

Text-label your measures in LilyPond with YAML

2011-11-14T06:57:00.014-05:00

Some music (especially some choral music) is somewhat irregular of measure length. Naturally with this kind of music, while entering (and editing, following one's musical sense), often measures will join or split. Then half of the measure numbers are thrown off. This is especially true of early music, and recent music whose source documents were prepared somewhat in a free way.

Often, given multiple voice parts (or instruments), each, for various purposes, necessitates several source files in parallel (if working in LilyPond): such as for adjustments to piano or organ reductions. Many features not yet done (completely and automatically) well by LilyPond necessitate these additional parallel files.

Whenever information is parallel, it requires careful synchronizing of all the measures (and measure lengths). What a bother!

Obviously, if humans are checking and synchronizing something (with difficulty), this is a good opportunity for computers to do the work instead. In that situation, I wrote a computer program allowing measures to be labeled by (text) strings, instead of (only) by measure numbers.

The program fills each measure (completely) with spacer rests (unless told otherwise). This eases synchronization, because you need only include measures with actual content.

The program uses YAML as its data entry format. YAML's noise (the extra characters you enter) is very spare. It seems cleanest for entering LilyPond source (it interferes only minimally) yet allows measures to be labeled easily by text strings.

Available on my GitHub (and written in Ruby), the program is called, 'yaml2lilypond'. Recently, I successfully used it to engrave (typset) a large work--and it helped a lot!

Copyright (c) 2011 Mark D. Blackwell.

Lean startup

2011-11-12T09:10:00.007-05:00

Recently, a project owner I know read with interest the new book, The Lean Startup: How Today's Entrepreneurs Use Continuous Innovation to Create Radically Successful Businesses, by Eric Ries. It just came out September, 2011; his blog is Startup Lessons Learned. Web searching for "lean startup" found:

From `Taking the guesswork out of startup success' (by Anne Fisher):

`“[S]tart...with a very basic, sloppy site, and...continually change it according to what users tell [you] they like and don’t like.” [E]very single week[,] invite customers in, plunk them down in front of computers, watch them use the site, and ask them questions about it. The (often surprising) answers then get built into the product.'

From Jeff Shuman's comment #40 in `Teaching a “Lean Startup” Strategy' (by Carmen Nobel):

`In Peter Drucker's 1985 book Innovation and Entrepreneurship, he noted that “When a new venture does succeed, (more often than not) it is in a market other than the one it was originally intended to serve, with products or services not (quite) those with which it had set out, bought in large part by customers it did not even think of (when started), and used for a host of purposes besides the ones for which the products were first designed.”'

From `Four myths about the Lean Startup' (by Eric Ries):

`Lean Startups...do not blindly do what customers tell them, nor do they mechanically attempt to optimize numbers. They use...actionable analytics as vehicles for learning...how to make their vision successful.'

From `Top 5 myths about the lean startup' (by Eric Ries):

`Lean startups are driven by a compelling vision, and they are rigorous about testing each element of this vision against reality...with every tool available...They use customer development, split-testing, and in-depth analytics as vehicles for learning about how to make their vision successful. Along the way, they pivot away from the elements of the vision that are delusional [emphasis added].'

`Lean...refers to a process of building companies and products based on lean manufacturing principles, but applied to innovation. That process involves rapid hypothesis testing, learning about customers, and a disciplined approach to product development.'

`[A] startup is [any] human institution creating a new product or service under conditions of extreme uncertainty.'

From Brian Mcfarlane's comment:
`getting out from behind you[r] computer and talking to real people will reward you with unresolved problems you may not of thought of to help you get to a product-market fit sooner.'

From `The Promise of the Lean Startup' (by Eric Ries):

`In parallel to [the] work by the “solution team”...there is a new kind of “problem team”...that is asking the bigger questions, such as: Who will our customers be? What problem does our product solve for them? How many of them are there? And how will we reach them?'

`The promise of the lean startup is that instead of building our companies according to myths, we can guide them with facts and the knowledge required to use those facts well. Or put another way, that we won’t waste our time building products or services that nobody wants.'

`The ultimate goal of a lean startup is to identify where its vision intersects with what reality can accommodate...It tries out new ideas with a fraction of customers in order to prioritize using facts, not opinions. Its unit of progress is that of validated learning about its customers. [Thus] the practice of entrepreneurship can be put on solid, rigorous, footing.'

`Instead of seeing process as a synonym for bureaucracy, it sees it as a synonym for discipline. Focusing all of its energy on only those activities that matter, it frees up time and energy for true productivity.'

Other references:
Why Lean Startups are Hard Part 1 – Our Genes Aren’t Lean - Kevin Dewalt
Perfection By Subtraction – The Minimum Feature Set - Steve Blank

Copyright (c) 2011 Mark D. Blackwell.

IPv6 aware, Linux iptables cloud hand firewall for Debian lenny, howto

2011-11-09T15:14:00.007-05:00

Recently, I set up a Linux software firewall by hand for a virtual machine instance running Debian lenny.

Reasonable, now or in the future, is concern about IPv6 traffic. 'Is your firewall aware?' speaks of some danger: 'You might think that [using iptables to] disallow incoming connections to your server on port 22[,] except from a single trusted IP[,] is sufficient to stop connections hitting your machine, but if it is accessible over IPv6 you'll soon discover this isn't the case.'

Many VM providers have not so far (completely) enabled IPv6. However, for anyone who has written their own firewall script, it is a good idea to be prepared beforehand for the event.

The latest VM's, running on recent kernels, can use regular, IPv6-capable firewalls, though they are somewhat hard to find. For instance, the Debian package, 'shorewall6' implements an IPv6 firewall, which 'requires kernel 2.6.24 or later'. Per their FAQ, 'Linux kernels before 2.6.20 didn't support connection tracking for IPv6'.

My particular VM provider allows me only kernel 2.6.18. So, for my old kernel, I developed a fairly simple firewall script, with goals to:

* Restrict sole use of my VM to a list of authorized, remote IP's
* Block tunneling of IPv6 through IPv4, inbound and outbound
* Ease establishing the same rules for IPv6 as for IPv4
* Learn more about iptables firewalls, and
* Learn something about IPv6

This modular firewall script allows full and easy control over IP addresses, protocols and ports. It was derived, with additions, from James Turnbull's 'Bastion Host Iptables Script' (see References).

In order to simplify, it leaves out denial of service (DOS) protection, because that seems unlikely in casual VM use. And, it assumes your VM's IP address is IPv4.

It is impossible accidentally to be locked out, because VM providers naturally offer direct console access, independent of services running on the VM.

The script is available free of charge from my GitHub account.

References:
Bastion Host Iptables Script: Appendix A (or chapter 2) of James Turnbull's book, _Hardening Linux_. For download, see http://www.apress.com.

/etc/default/iptables
/usr/src/linux/Documentation/filesystems/proc.txt
/usr/src/linux/Documentation/networking/ip-sysctl.txt

6in4 - Wikipedia
6to4 - Wikipedia
Adding proper IPv6 to my home network - Martin F. Krafft
After installation - Securing Debian manual - Debian
Anything in anything - Wikipedia
Basic iptables - howtos - 5dollarwhitebox
Basic iptables - Debian/RedHat (see comments) - HowToForge
Collection of basic Linux firewall iptables rules - LinuxConfig
Debian firewall - Debian
Druidic firewall - I)ruid
Easy firewall generator for iptables - Scott Morizot
Entries in /proc/sys/net/ipv6/ - Linux IPv6 howto - TLDP
Firewalling with netfilter/iptables - Shane Tzen
Firewalls - Debian
Firewalls resources - Center for Education and Research in Information Assurance and Security (CERIAS)
Firewalls tag - DebianAdministration
Getting IPv6 connectivity under Linux - Juliusz Chroboczek
Guidelines for firewall vendors regarding MIPv6 traffic - Internet Engineering Task Force
Internet firewalls: frequently asked questions- Paul D. Robertson, et al
The Internet is a dirty, dirty mistress - Dustin D. Trammell
Invisible IPv6 traffic poses serious network threat - Carolyn Duffy Marsan - Network World
Ip6tables: IPv6 firewall for Linux - Vivek Gite
Iptables - Wikipedia
Iptables(8) - Linux man page - Linux die.net
Iptables firewall - Thomas Pircher - TTY1
Iptables firewall script & configuration files for Linux 2.4.x-2.6.x - Bob Sully
Iptables/firewall setup for clusters - Richard Benson - Dixcart
Iptables howto - Community documentation - Ubuntu
Iptables rules - TheGeekStuff
Iptables tag - DebianAdministration
Iptables tutorial - Oskar Andreasson - Frozentux
IPv6 - Wikipedia
IPv6 & Linux howto - Peter Bieringer
IPv6: Configuration for Debian - lenehan
IPv6 firewalling - Sixxs.net
IPv6 firewalls - GetIPv6
IPv6-ready kernel - Linux IPv6 howto - TLDP
IPv6 security considerations and recommendations - Microsoft
IPv6 with Debian - Martin F. Krafft
Is your firewall IPv6 aware? - Debian administration - Steve Kemp
ISATAP - Wikipedia
Learn how to use IPp6tables - TLDP
Links2World howto - Links2World Firewall
Linux 2.4 packet filtering howto - Rusty Russell
Linux iptables avoid IP spoofing & bad addresses attacks - LinuxTitli
Linux iptables block common attacks howto - LinuxTitli
Linux iptables: how to specify a range of IP addresses or ports - Vivek Gite
Linux: IPv6 - Peter Bieringer
Linux IPv6 howto - TLDP
List of IP protocol numbers - Wikipedia
Local area network - Wikipedia
Miredo(8) - Linux man page - Linux die.net
Restoring iptables automatically on boot - Jawnsy - DebianAdministration
Running IPv6 in practice - Gribozavr - DebianAdministration
Securing network access - Securing Debian manual - Debian
Set up Ubuntu server in the cloud howto - dambrosio
The settings statement - Links2world Firewall
Shorewall firewall installation, configuration & understanding - Stephen P. Edwards
System run levels and init.d scripts - Debian
Teredo may render your firewall useless - René Pfeiffer
The Teredo protocol: tunneling past network security & other security implications (PDF) - James Hoagland - Symantec
Teredo tunneling - Wikipedia
Top 5 best Linux firewalls - Ramesh Natarajan - TheGeekStuff
Using iptables to secure your virtual machine - Cloud hosting applications - eApps
Why you want IPv6 - LinuxReviews

Copyright (c) 2011 Mark D. Blackwell.Copyright (c) 2011 Mark D. Blackwell.

Debian squeeze VM experiment

2011-10-28T09:36:00.008-04:00

This is regarding upgrading Debian on TekTonic.net, which has a Xen VM plan. See my post for lenny.

In squeeze, the failure of shell job control was debilitating, so I am sticking with lenny. Other things appeared to be okay, but did not actually work. Per:

http://www.debian.org/releases/squeeze/i386/release-notes/ch-upgrading.en.html#upgrading-udev

'The udev version in squeeze requires a kernel of version 2.6.26 ... Booting the 2.6.26 kernel from lenny with the udev from squeeze may result in a failure to correctly assign names to network devices, and will also fail to apply certain additional permissions to block devices (such as access by the disk group). The software itself will appear to be working, but some rules (for example, network-based rules) will not be loaded properly. It is therefore strongly recommended that you upgrade the kernel on its own at this point, to ensure a compatible kernel is available before upgrading udev.'

This is just experimental.

Upgrade lenny to squeeze, per:

http://www.debian.org/releases/squeeze/i386/release-notes/ch-upgrading.en.html

$ script -t 2>/root/upgrade/lenny-to-squeeze.time -a /root/upgrade/lenny-to-squeeze.script

Okay if package, 'locales' is not installed:

$ dpkg-reconfigure locales
$ dpkg --audit
$ aptitude search "~ahold"
$ dpkg --get-selections | grep hold

Change lenny to squeeze:

$ nano /etc/apt/sources.list

Fetch new list:

$ apt-get update
$ apt-get upgrade
$ exit

File is /root/upgrade/lenny-to-squeeze.script

Because squeeze seems scary, see if reboot works beforehand; got:

/etc/network/options still exists and it will be IGNORED! README.Debian of netbase. ... (warning)
FATAL: Could not load /lib/modules/2.6.18.8-xenU/modules.dep: No such file or directory

Rebooted okay.

$ script -t 2>/root/upgrade/lenny-to-squeeze-2.time -a /root/upgrade/lenny-to-squeeze-2.script
$ apt-get dist-upgrade

Got:

The following packages have unmet dependencies:
insserv : Breaks: sysv-rc (< 2.87dsf-3) but 2.86.ds1-61 is installed

$ apt-get remove insserv
$ exit

File is /root/upgrade/lenny-to-squeeze-2.script

Rebooted okay.

$ login root

Worked!

Backup:

$ cd /
$ tar --create --one-file-system --file=/backup/full/upgraded-to-squeeze.tar bin boot etc home initrd lib opt root sbin selinux usr
$ tar --list --file=/backup/full/upgraded-to-squeeze.tar root
$ cd /backup/full
$ gzip --best upgraded-to-squeeze.tar

Shut down and offload the file, /backup/full/upgraded-to-squeeze.tar.gz.

The next day, I did more.

Good on upgrading to squeeze:

http://mrngm.com/xen-on-debian-lenny-to-squeeze.html
http://library.linode.com/troubleshooting/upgrade-to-debian-6-squeeze
http://www.cyberciti.biz/faq/apt-get-upgrade-debian-lenny-5-to-debian-6-squeeze/

Good to get the files first, per:

http://www.howtoforge.com/upgrade-debian-lenny-to-squeeze-in-a-few-simple-steps#comment-27131

$ apt-get dist-upgrade -d

before doing:

$ apt-get dist-upgrade

'The udev version in squeeze requires a kernel of version 2.6.26 or newer', per:

http://www.debian.org/releases/squeeze/i386/release-notes/ch-upgrading.en.html

Tektonic uses Lilo, so Xen 3.2 doesn't have the grub2 problem (with a squeeze DomU).

To do apt-get hold and unhold:

http://forums.debian.net/viewtopic.php?t=240

$ script -t 2>/root/upgrade/lenny-to-squeeze-3.time -a /root/upgrade/lenny-to-squeeze-3.script

Resolve upgrade conflict:

$ apt-get remove initrd-tools

Hold udev to lenny version for lenny's kernel:

$ echo "udev hold" | dpkg --set-selections
$ aptitude hold udev
$ apt-get update
$ apt-get upgrade

Regarding obtaining Debian updates to squeeze, beyond the release:

http://permalink.gmane.org/gmane.linux.debian.user.news/417

and security updates:

http://www.debian.org/security/

Add to sources.list:

deb http://ftp.us.debian.org/debian/ squeeze-updates main contrib non-free
deb http://security.debian.org/ squeeze/updates main contrib non-free

$ nano /etc/apt/sources.list

$ apt-get update
$ apt-get upgrade

Mark upgradable and (g)o:

$ aptitude
$ exit

File is /root/upgrade/lenny-to-squeeze-3.script

To test bootability:

$ shutdown -rf now

This problem is caused by combining squeeze's udev with a too-old kernel:

No bash job control, because, 'cannot set terminal process group (-1): Inappropriate ioctl for device'.

Copyright (c) 2011 Mark D. Blackwell.

Upgrade Xen VM Debian from sarge to lenny, howto

2011-10-25T21:21:00.013-04:00

Here's how to upgrade a Debian Linux distribution to 'lenny', on a cheap Xen VM plan such as TekTonic.net's, which (of Debian) offers only version 3.1 ('sarge').

Upgrading to Debian 'squeeze' is inadvisable on TekTonic (until they offer an upgraded Linux kernel); please see my experimental blog post.

MISCELLANEOUS

I used Tektonic's shell access (through SSH), without logging in further to the account, 'root'.

One cannot change the date or time (apparently, as a DomU) under Xen. The command, 'date' appeared to work, but the time wasn't actually changed:

$ date --set=HHMM

My CPU is a 32-bit, dual-core AMD Opteron 242 (per, '/proc/cpuinfo').

WITHIN SARGE

First, upgrade within sarge, per '[Sarge] upgrades from previous releases', '[Etch] upgrading your sarge system' and 'Distribution archives':

$ mkdir /root/upgrade
$ script -t 2>/root/upgrade/sarge-to-sarge-latest.time -a /root/upgrade/sarge-to-sarge-latest.script
$ cd /

Edit (see the command, below):
1. Make sure the word, 'stable' is not in there. (If it is, change it to, 'sarge'.)

2. Change http.us.debian.org/debian to archive.debian.org/debian/ .

3. Comment out (with a leading '#', or remove) the non-us.debian.org/debian-non-US line.

4. Comment out the security.debian.org line.

$ nano /etc/apt/sources.list

Here is the desired result:

deb http://archive.debian.org/debian/ sarge main contrib non-free

Do this twice, to see error messages go away:

$ aptitude update

Then:

$ aptitude install aptitude
$ aptitude -f upgrade
$ exit

One should see the message, 'File is /root/upgrade/sarge-to-sarge-latest.script'.

SARGE TO ETCH

Next, upgrade from sarge to etch, per 'Upgrades from previous releases' and 'Upgrading the rest of the system':

$ script -t 2>/root/upgrade/sarge-to-etch.time -a /root/upgrade/sarge-to-etch.script

Edit, changing 'sarge' to 'etch':

$ nano /etc/apt/sources.list

Twice fetch the new list:

$ aptitude update

Then:

$ aptitude install aptitude
$ aptitude upgrade
$ aptitude install initrd-tools
$ aptitude --download-only dist-upgrade
$ aptitude dist-upgrade
$ exit

One should see the message, 'File is /root/upgrade/sarge-to-etch.script'.

ETCH TO LENNY

Next, upgrade from etch to lenny, per 'Upgrades from previous releases':

$ script -t 2>/root/upgrade/etch-to-lenny.time -a /root/upgrade/etch-to-lenny.script
$ dpkg --audit
$ dpkg --get-selections | grep hold
$ aptitude search "~ahold" | grep "^.h"

Edit:
1. Change 'etch' to 'lenny'.

2. Change, 'archive.debian.org/debian/' to, 'ftp.us.debian.org/debian/'.

$ nano /etc/apt/sources.list

Fetch the new list:

$ aptitude update

To fix an error saying, 'public key is not available':

$ aptitude install debian-archive-keyring
$ aptitude install aptitude apt dpkg

Make a request (in order to start aptitude working):

$ aptitude search "?false"

Then:

$ aptitude update
$ aptitude --download-only safe-upgrade

Thrice, till nothing changes:

$ aptitude safe-upgrade

Then:

$ aptitude --download-only dist-upgrade
$ aptitude dist-upgrade

POST-RELEASE & SECURITY

Per:
Updates & backports - Debian Reference - Debian.org
Debian volatile replaced by new updates suite - News - Debian.org

Edit:
1. Uncomment and change the security line (use '/', not '-'):

deb http://security.debian.org/ lenny/updates main contrib non-free

2. Add post-release updates:

deb http://volatile.debian.org/debian-volatile/ lenny/volatile main contrib non-free

$ nano /etc/apt/sources.list

Fetch the new list:

$ aptitude update

Repeat till nothing changes:

$ aptitude safe-upgrade

Remove a now-unused, old file:

$ rm -i /etc/network/options

Then:

$ exit

One should see the message, 'File is /root/upgrade/etch-to-lenny.script'.

BACKUP

Back up:

$ dpkg --get-selections "*" > /root/upgrade/dpkg-get-selections.txt
$ cd /
$ mkdir /backup
$ mkdir /backup/full
$ tar --create --one-file-system --file=/backup/full/upgraded-to-lenny.tar bin boot etc home lib opt root sbin selinux usr var/lib/apt/extended_states var/lib/aptitude/pkgstates var/lib/dpkg
$ cd /backup/full
$ gzip --best upgraded-to-lenny.tar

Shut down:

$ shutdown -h now

One must, on HyperVM, also click, 'shutdown' in order for its File Manager to see any files. Navigate (in it) to, '/backup/full' and click the icon under, 'Dn' to offload the corresponding, '.gz' file, made by gzip.

Copyright (c) 2011 Mark D. Blackwell.

Node.js frontend to Rails

2011-09-28T23:35:00.002-04:00

I have an intuition that Node.js can fruitfully front-handle user web requests, then pass them to Ruby/Rails, when doing this:

* In the case that processing requests (from users) requires collecting information from elsewhere, like various web service APIs (very common, now!).

Node.js would handle the (long) event queue thus generated, then send HTTP requests to Ruby/Rails, forging the sender in the header like the users'.

Then, Ruby/Rails won't block for very long, only long enough for the database.

Node.js could put the info anywhere, like the URL or in a fast database.

Copyright (c) 2011 Mark D. Blackwell.

Dice.com user data insecure

2011-09-26T14:57:00.004-04:00

I've just signed up (again) to Dice.com, and noticed that Dice only checks the first 8 password characters.

There is no description of a Dice password on the site, I believe.

However, a good feature is that Dice passwords can contain:
* Special characters like ! $ % & (etc., except backticks `)
* Bracket characters like ? [ ] { } ( ) < > (etc.)
* Underline and minus: _ -

in addition to the (more) usual digits and to distinguishing upper- and lower-case letters.

Using these, (Keepass informs me) Dice attains '53 bits of [password] quality,' which is not very much, in addition to a certain cleartext sniffing problem (see below).

But who cares?

EDIT: Dice confirmed they only use the first 8 characters of the password. They also pointed out (correctly) that their login form has an action which is https, so it normally uses SSL encryption.

However, some people say that corporate or other sniffers can see, block, rewrite (using Perl or something) and resend to a Dice user the packets in their login page as Dice sends it out unsecured, making its form action contain (sometimes) another address, other than the https address their software intends!

When the form is submitted (to the wrong address) they can see the Dice username or email, and the password. Then they can log into Dice using these credentials, and see whose resume it really is. If they want to.

They say some banks even have this problem!

References:

http://ask.metafilter.com/48531/are-http-forms-posted-thru-https-secure?
http://www.perlmonks.org/?node_id=542038?

Copyright (c) 2011 Mark D. Blackwell.

Learn You a Haskell for Great Good!

2011-09-22T10:39:00.002-04:00

Following is a note I wrote to the author of a wonderful book:

Hi, Miran Lipovača,

Thanks for your wonderful, _Learn You a Haskell for Great Good!_. Just now, I am resuming reading it, after completing a project (in another language).

For many people, it is important to be refreshed by beauty, as of mathematics in your book!

Copyright (c) 2011 Mark D. Blackwell.

Meantone tuning systems

2011-09-16T09:24:00.004-04:00

As you may know, interestingly, the tuning systems called quarter (1/4) and sixth (1/6) comma meantone differ, not only in their fractions, but also because their two commas (from which they calculate the fractions) are of different sizes (albeit somewhat close). To wit:

The comma in 1/6-comma meantone has one size (the well-known difference between 12 pure fifths and 7 octaves: about 23.46 cents: called the Pythagorean comma), per:

http://en.wikipedia.org/w/index.php?title=Pythagorean_comma&oldid=431111470

However, the comma in 1/4-comma meantone has another size (it is the difference between four pure fifths, C-G-D-A-E and two octaves, plus a pure major third, C-C-C-E: about 21.51 cents: called the syntonic comma). In other words,

'The syntonic comma... is the difference between four justly tuned perfect fifths, and two octaves plus a justly tuned major third', per:

http://en.wikipedia.org/w/index.php?title=Syntonic_comma&oldid=440411458

Interesting (linguistically, furthermore) is that 'mean-tone' is so-called, precisely because in that system, as you may remember, any major second (a 'tone') is found to be the 'mean' (the ordinary average, logarithmically) between the two notes of whatever size of major third it is we have, per p. (?) of Ross W. Duffin's _How Equal Temperament Ruined Harmony_.

The interesting, following book quotation admittedly differs in meaning from the Wikipedia article, quoted next following.

'[The] ratio between the major [whole] tone [is] 9:8 and the minor [whole] tone [is] 10:9[.] In meantone temperaments, the major and minor tones are made equal. In Pythagorean tuning, the minor tone is replaced by the major tone of 9:8. In quarter-comma meantone, the major and minor tones are made equal to the square root of 5:4.

'In the previous, Pythagorean tuning, a major third was 5:4 (C3 to E3 in the harmonic series, based on the piano note, C1) and there were two whole tones. The major semitone was 9:8 (C4 to D4) and the minor semitone was 10:9 (D4 to E4). These two semitones are not the same size.

'In any mean-tone tuning, however, these two semitones are averaged. This means that the two semitones have the same size, of 1/2 * sqrt( 5). This means that equal-temperament is a mean-tone tuning. Also, at first, people were rather shocked when the irrational square root of five disrupted the mathematically pure, small-whole number world of musical consonance.'

Now, for the Wikipedia article:

'In general, because the two semitones can be viewed as the difference between major and minor thirds, and the difference between major thirds and perfect fourths, tuning systems that match these just intervals closely will also distinguish between the two types of semitones and match their just intervals closely', per:

http://en.wikipedia.org/w/index.php?title=Semitone&oldid=450607863

Another interesting and relevant Wikipedia article is:

http://en.wikipedia.org/wiki/Meantone_temperament

Copyright (c) 2011 Mark D. Blackwell.

SoundCloud promotes your music compositions

2011-08-28T13:50:00.004-04:00

Recently, I discovered a nice website, SoundCloud which promotes (aurally, visually and socially) music that you compose.

Or, you can use it to play a stream of compositions, by typing tags and search words.

I searched for tag, 'classical', and keyword, 'experimental', and the resulting hits sound pretty nice!

It's been out since 2007: recently 5 million registered users.

Copyright (c) 2011 Mark D. Blackwell.

Cygwin, msysGit and native Windows apps, howto

2011-08-24T07:51:00.023-04:00

I use Debian and Windows XP -- the latter sometimes on a netbook, but principally on a fast desktop computer (it has a nice monitor). On Debian, I develop software in the normal way. But, when I'm on Windows, I have to resort to a variety of techniques.

On a fast desktop computer, I use many native Windows apps (e.g. 7-Zip instead of Tar with compression; in the Windows way). I use Cygwin apps where a good native Windows version is lacking.

For example, previously I ran Cygwin's LilyPond till I noticed the niceness of the Windows version.

But mostly on Cygwin I enjoy the Bash command line interface and its filesystem.

My desktop's Git is through Cygwin, but the netbook has msysGit (with its own version of Bash).

With msysGit, so far, Bash's symbolic links aren't good -- if you make one, it actually copies the whole folder!

I could try alternatives (suggested on MinGW's MSYS page) such as Interix (also known as Microsoft's SFU or SUA).

Paths

In order to maintain only one copy on the desktop of things like SSH keys (used by Git) I followed instructions to move my Cygwin user home directory to the same place as my Windows user home directory -- which worked just fine! (Additionally, I set LANG to en_US.UTF-8, as suggested.)

Now, this command works just fine for me:

ruby app/hello.rb

I seem to recall that, for a while, it gave me an error, 'no such file'. Perhaps when I cleaned and upgraded my Cygwin installation (including my .bash* files) and then did a couple of reboots, the problem went away. (Don't you hate that?)

Cygwin can run both Cygwin apps, and native Windows apps. For speed and maintainability reasons, it's good to minimize the programs installed into Cygwin, doing so only if no native Windows version will succeed there (or can conveniently be run outside it). For example, my RubyGems installation is a native Windows one.

In Cygwin, the command, 'rake' (e.g.) might give you:

No such file or directory -- /cygdrive/c/progra/ruby/1.8.7-p352/bin/rake (LoadError)

even though it is found by, 'which rake':

/cygdrive/c/progra/ruby/1.8.7-p352/bin/rake

The solution (in Cygwin) is to type, 'rake.bat' (gem.bat, irb.bat, pik.bat, etc.).

If desired, you can alias rake, gem, irb and pik as with Robert Wahler's Stack Overflow answer, but just on the command line -- it doesn't normally work in Bash scripts. (E.g., 'alias rake=rake.bat' -- to reverse it: 'unalias rake'.)

If you are having problems with native Windows programs still not finding files in Cygwin, you might want to look at one aspect of Cygwin filesystems (some sources say) which requires special handling.

The documentation says (although sometimes I don't have to) passing filesystem paths (in Cygwin Bash) to native Windows apps (such as Ruby) is done one of two ways:

One is to use native 'Win32' paths -- two examples follow, for which I made a Ruby test program ('app/hello.rb' containing only, 'p __FILE__'). They require at least one, escaped backslash:

In (Cygwin's) current directory (using native Win32 paths):

ruby '.\hello.rb'
ruby .\\hello.rb

Or in 'app', relative to the current directory:

ruby 'app\hello.rb'
ruby app\\hello.rb

The other is to use cygpath:

In the current directory (add, '-a' for the full path):

ruby "`cygpath -m hello.rb`"

Or in the relative directory, 'app' (recently, with one long path, I had to do it this way):

ruby "`cygpath -m app/hello.rb`"

Permissions

Developing with both msysGit and Cygwin normally generates Unix permissions problems. Their Gits flip-flop the permission bits between '100777' (Cygwin) and '100644' (msysGit) on most files! Those with certain typically-executable extensions like .exe and .bat alternate between '100777' (Cygwin) and '100755' (msysGit).

To avoid most of this problem, you can mount your Cygwin user home directory close to the msysGit method:

/cygdrive/c/Documents\040and\040Settings/[user name] /home/[user name] ntfs binary,noacl,bind 0 0

'noacl' tells Cygwin not to use the Access Control Lists found in Microsoft's NT tree. (BTW, as of Cygwin 1.7.9-1, 'posix=1' and 'nouser' are ignored here.)

The exception is that Cygwin will look for '#!' at the beginning of files to set the executable bit; msysGit, as mentioned above, will look at extensions like .exe and .bat.

In a development project, it might be useful to set write- and execute-permissions (at least the 'user' bits). If you want to manipulate permission bits further in your repository, you can tell msysGit (or even Cygwin Git) to ignore permission bit differences. Then you can set (see Jakub Narębski's answer) the (user?) execute bits:

git update-index --chmod=+x [file paths]

and reset them:

git update-index --chmod=-x [file paths]

before you do, 'git commit'.

(Tested with Ruby 1.8.7 (2011-06-30 patchlevel 352) [i386-mingw32], Cygwin 1.7.9-1.)

BTW, to see what Cygwin version you are running:

cygcheck -c cygwin

References

file modes - Cygwin
NT Security - Cygwin
file modes - msysGit
discussion

Copyright (c) 2011 Mark D. Blackwell.

BASH (GNU shell for Unix) cheat sheet

2011-08-13T09:34:00.009-04:00

While using the command-line shell, BASH (for Unixen, part of GNU (GNU's Not Unix), developed by FSF (Free Software Foundation), quite popular and superior), for a long time I employed just a few of its manipulation features for command lines -- just these, in fact:
!$ - last command's last argument
(C-r) - reverse search, through command history

Recently, I have wanted to combine multiple arguments from multiple commands. To help me remember how, I used the technique of making a cheat sheet. Interestingly, BASH is similar to the text editor, Emacs (as well as Nano). Here is a sample:

Key abbreviations:
(C-) - Ctrl
(M-) - Alt
(newline) - Enter
(rubout) - Backspace

Move the cursor:
(C-a) - beginning-of-line
(C-e) - end-of-line
(M-f) - forward-word
(M-b) - backward-word

Change text:
(M-t) - transpose-words

Kill and yank:
(C-k) - kill-line
(C-x rubout) - backward-kill-line
(M-d) - kill-word
(C-y) - yank

Completing:
(tab) - complete
(M-/ M-/) - complete-filename
(M-g) - glob-complete-word
(M-?) - possible-completions
(C-x /) - possible-filename-completions

Miscellaneous:
(C-_) - undo

Event designators:
(!-2) - command previous to last
(!-2:1-2) - second previous commands's first and second arguments
(!-2:0 !:3* !-2:2) - second previous command word plus its second argument, the last command's third and following arguments intervening

There's more on GitHub.

Copyright (c) 2011 Mark D. Blackwell.

CSS selector objects and methods for testing in Ruby

2011-08-08T11:23:00.008-04:00

Let's say, for a given web page, you are writing some tests. And, supposing, you want to test whether the page contains a single DIV, of CSS class, 'only'.

And, you want to know whether the DIV (or the page) contains a single FORM, of CSS class, 'good-form'.

And further, you want to know whether the FORM (or the page) contains (among other things) a single INPUT, of CSS class, 'my-input'.

And further, whether that INPUT has CSS attribute, 'type=text'.

So, a CSS selector, useful for finding that on a web page, would be:

div.only > form.good-form > input.my-input [type=text]

Right?

Maybe (in your test) specifying descendents instead of children would have a better flexibility, allowing later intervening DIV's (for instance). With this difference, the new CSS selector would be:

div.only form.good-form input.my-input [type=text]

How might one like to specify these selectors, speculatively and ideally? Even better than the CSS selector strings in Ruby above might be... what?

(A.) HTML elements

Well, it might be nice if code for DIV's could work simply like this:

D.class 'only'

(Unfortunately, this would clobber Object#class, probably interfering with essential Ruby functionality elsewhere in our application.) We could compromise and give it a longer method name:

D.css_class 'only'

(B.) HTML Attributes

A web page might also, in addition to an INPUT element carrying all of the desired attributes, supply some other INPUT with fewer of them, or indeed another kind of INPUT entirely.

So, obviously, it is good to test for:

o The desired number of INPUT's (in total), and
o The presence of each INPUT, carrying all the attributes desired.

In light of this, wouldn't it be nice if one easy method invocation could assert the unique presence of exactly one INPUT, plus its unique presence carrying a specific set of attributes?

Another thing possibly useful might be checking the attributes one at a time; I don't know.

The same would probably apply also to any other kind of HTML element having attributes.

A seemingly good way to invoke the method would be:

attribute 'type', 'text', 'value', 'your name here'

And, for unpaired attributes:

attribute 'hidden'

So: how could these semantics really work? Here's an example, carrying the idea further:

(C.) An implementation

# Fuller Example of Web Page Testing, Using CSS Selector Objects and Methods:

module CssSelectorConstants; D,F,I = %w[ div form input ].map{|e| CssString e} end

class SomeTestClass

extend CssSelectorConstants

def test_web_page
d_o = D. css_class 'only'
fg = d_o.descend(F).css_class 'good-form'
im = fg. descend(I).css_class 'my-input'

a_t = im.attribute 'type', 'text'
atv = im.attribute 'type', 'text', 'value', 'your name here'
av = im.attribute 'value', 'your name here'

# There should be exactly one DIV, 'div.only':
assert_select d_o, 1 do

# And within that, exactly one FORM, 'form.good-form':
assert_select fg, 1 do
# I.e., exactly one:
# div.only form.good-form

# And within that, exactly one INPUT, 'input.my-input':
assert_select im, 1
# I.e., exactly one:
# div.only form.good-form input.my-input

# And exactly one INPUT, 'input.my-input[type=text]':
assert_select a_t, 1
# I.e., exactly one:
# div.only form.good-form input.my-input
# [type=text]

# And exactly one INPUT, 'input.my-input[value=your name here]':
assert_select av, 1
# I.e., exactly one:
# div.only form.good-form input.my-input
# [value=your name here]

# And exactly one INPUT, 'input.my-input[type=text,value=your name here]':
assert_select atv, 1
# I.e., exactly one:
# div.only form.good-form input.my-input
# [type=text,value=your name here]
end #form
end #div
end #def
end #class

See also:
CSS selector objects & methods (for Rails; GitHub)

Copyright (c) 2011 Mark D. Blackwell.

Open letter re: error in my post

2011-07-27T13:41:00.016-04:00

I sent this letter to a friend, but others might find it interesting. [Elided name for privacy -- the letter starts ...] Hi!

Thanks again for (verbally) informing me that I misspelled Brandenburg in a post.

As George Soros (left-wing hedge fund owner and subsequent philanthropist) says, learning we have made a specific mistake causes joy and hope, because this knowledge is an opportunity to improve future outcomes. :)

It's been a while (I know) but I have corrected the post -- indeed, thanks!

With warm regards,
Mark D. Blackwell

Copyright (c) 2011 Mark D. Blackwell.

Brandenburg 5 in Bach-Lehman tuning

2011-07-27T13:24:00.005-04:00

The following is a re-post.

Please click to listen before reading further. Today, w/s Brandenburg MIDI turned up a top-page (Google) result, the fifth Brandenburg concerto, in D major, ('[o]ne of the lushest and most thrilling pieces ever written'--quotations are from Wikipedia), by (Johann Sebastian) Bach, 'now regarded as the supreme composer of the Baroque [period, and] one of the greatest of all time', produced by Alan Kennington, moderately, clearly and with great unity on a (single) MIDI instrument, the harpsichord.

According to the artist, '[T]he performer needs to be able to bring out the music comprehensibly. When the music is at the right speed, it resonates in the listener. It generates a kind of excitement and pleasure... I believe that Baroque composers wanted their audience to feel pleasure... Bach was more interested in giving gentle pleasure[,] rather than a sudden rush of breathless excitement.'

For this very purpose I adjusted its tuning to Bach- Lehman 1722 temperament using Scala, whose 'motto is INVENIT ET PERFICIT which means, "it finds and perfects"'. The result? My friend M agrees that this is a:

much more beautiful, second movement (Affettuoso), in B minor.

For this, it is essential to use some good wave-table MIDI synthesizer software like Microsoft GS Wavetable SW Synth which is based on Roland wavetables.

The Creative SoundBlaster SoundFont Synth and the QuickTime Music Synthesizer (at least on PC's) somehow blot out temperaments' emotional content, and they make this listening comparison meaningless.

For comparison, the original:

equal-tempered version

I predict you shall be uncomfortable with it, now. As my friend M said, it seems 'like a terribly out of tune MIDI file'. Now we know it wasn't the MIDI system's fault.

Also available are the

first and third

movements (both Allegro) fully adjusted to Bach- Lehman 1722 tuning.

(I have emailed Alan U. Kennington, Ph.D., and he granted permission for this use. His website states, 'All original material on the topology.org web site is Copyright (C) 1999-2009, Alan U. Kennington. Permission is hereby granted for non-commercial reproduction of small portions of this material under the Artistic Licence, provided that this copyright notice is attached.')

Copyright (c) 2010 Mark D. Blackwell.

Prevent accidental drag and drop on touchpad laptops in Windows Explorer, howto

2011-07-25T11:48:00.027-04:00

For convenience on many laptops, the touchpad functions like (left) clicking a mouse. However, in Windows Explorer, a classic problem occurs. We can drag and drop folders by mistake into other folders--they can get lost that way, or mess up our carefully organized tree.

The solution is a distance, a threshold before accepting a drag (of a clicked mouse). We don't want natural hand jitter (visible at small resolutions) or accidental motion (while clicking) to be interpreted as a request to drag graphical objects around. This is well known--Windows has such a threshold. However, their default is 4 pixels!

Some people's jitter is greater than others' (viz. Parkinson's disease); this default may be way too small to avoid the problem for touchpads, too.

Using 40 pixels, I move past first two folders (or files, in Windows Explorer). Then before releasing the mouse, I pull back wherever, even the adjacent folder.

There are two settings: horizontal and vertical. I set both the same--the horizontal is important, too, to prevent inadvertent mouse drags.

HKEY_CURRENT_USER\Control Panel\Desktop
DragHeight = "40"
DragWidth = "40"

Restart the computer for it to take effect.

This setting allows windows also to be dragged conveniently. Drag a centimeter (half an inch) then back to your new, desired, fine location. The feeling is like a momentary slow response.

If you wish, you can use Microsoft's TweakUI (a free-of-charge Windows XP download) to set these.

You might enjoy playing with click-lock (on the mouse) for this problem, though it changes the user interface in a deep way, globally.

I wonder if someone in the leadership structure of Microsoft might be big enough to admit--to themselves--they are continuing a mistake (whether small or important) that occurred some time in the past but was correct at one time, caused by an increase in monitor resolution (as others have said) and respond to some users' cries for help by changing this 4-pixel default? Because the key difficulty is in admitting a mistake. Already they have enabled us to change our setting; it's merely avoiding a redecision about the default which is causing a problem in the wider world.

The current state on this issue seems one of drifting inertia and big-company self-insulation. (Some of their attitude about it is visible on their Developer Network.)

Ref:
Disable Drag And Drop In Windows Explorer? (from Scot's Newsletter's Forum, editor of ComputerWorld)
Stop Windows copying files accidentally when Ctrl-click selecting (How-To Geek: more)
Prevent folder moving (see R. McCarty's answer)
Click lock (see S. Goodkin's answer)

Copyright (c) 2011 Mark D. Blackwell.

Installing Leo (Outlining Editor) on Windows, howto

2011-07-23T13:48:00.083-04:00

An introduction to Leo

Looking at text editors recently, I found a recommendation for Leo ('Leonine Editor with Outlines', developed by Edward K. Ream).

The (free) programmer's text editor and outliner (see Joe Orr's slideshow, or w/s Leo tutorial) improves software project readability, excitingly -- but it's not only for programmers. Leo is a feature-rich, productivity-increasing tool.

Using outlining is a fresh approach for the world of Literate Programming. It resolves the awkwardness, but easily fulfills the essence: it provides more readability, along with program code colocation with additional explanations, which helps prevent obsolescence.

To start, all you have to do (A) is enter an idea about any section of your text and (B) incrementally develop (in Leo) an outline of your ideas, referring to sections of the text.

Programmers need only (A) enter an idea about any (freely-chosen) section of their source code (e.g., its purpose) and (B) incrementally develop (in Leo) an outline of thoughts, referring to sections of the code.

Additions you make, no matter how few, are a kind of Easy Literate Programming.

Even while using Leo, no other team members will feel impacted, even if they edit the same source files without it. In no way does it hide the project source files inside its own folders or files, and it's compatible with version control systems, such as Git.

How can Leo accomplish this? Leo in a Nutshell explains. Ream's view is worth reading also, on Slashdot.

Leo is fairly mature and ready for use, long having had a 'small but extremely loyal group of users'^[1] in addition to the developer's personal use. Its architecture is extensible by scripting; upwards of 75 interesting plugins have been written. It has borrowed much from Emacs. Some of its voluminous documentation seems obsolete (however) or merely implementation-oriented.

Presumably all Leo needs to know about the languages (even if obscure) used on your project is the syntax of how to form block- and single-line comments.

Leo opens a file by default (normally ~/.leo/workbook.leo, even on Windows) so if you want you can use it as a personal outlining planner.

Clones

Leo's outlines have cloneable nodes (and subtrees), and therefore multiple views. This might be a simple idea; I'll give you two examples.

For any given bug, a tree of relevant files can be collected (and cloned) and focused on without distraction. In the bug tree, as you edit those files, the ordinary hierarchy of files is being updated also (but not by special software). Since the nodes are cloned, you are editing the same files, not merely in essence but in actuality.

Insofar as you make notes briefly while puzzling out a problem or solving a bug, naturally they are entered right there in the place provided: in the bug's file tree (or associated with it). Afterward, you collapse the bug's tree, left behind to help explain the solved bug to future readers (developers) whenever they might need it -- Easy Literate Programming.

To explain something special to developers (readers) of the project, any files or folders (even sections of files) can be clone-arranged into a new tree structure (regardless of the layout of a project's filesystem).

In particular, if you have written about several cross-cutting (e.g., aspect-oriented) concerns (say, a, b and c), or wish to explain them to other developers, then it's good to clone-arrange the relevant files (unless that's all the files) into trees belonging to those concerns, though the files actually reside elsewhere in the project's main organizational filesystem folders (say, w, x, y and z).

It's an alternative to tagged filesystems in a way, but with explanations that grow organically -- it naturally produces a kind of manual, with an outlined table of contents.

Here's how to install Leo on Windows XP in detail (for the non Python-familiar) the way I did, using some installation instructions (or a fuller version) on the website as a basis:

Leo prerequisites

Leo requires Python 3 (or 2). Download and install minimally the latest Python-3 for Windows from Python's official website--I used 'python-3.2.1.msi'--to 'C:\progra\Python32'.

For Python, and Register Extensions, Tcl/Tk and Utility Scripts, pick 'Will be installed on local hard drive'. For Documentation and Test Suite, pick 'Entire feature will be unavailable'.

Download and install minimally the latest binary package for Windows containing QT-4, the 'cross-platform application and UI framework' and Python bindings, PyQT-4 from its developer's website; I used 'PyQt-Py3.2-x86-gpl-4.8.4-1.exe'.

Leo requires 'Qt runtime'. To ease uninstalling later, select 'Start Menu shortcuts'. Unselect everything else, including Documentation, Examples, QScintilla and the developer tools Developer, Qt, and SIP.

When PyQt asks you to specify a 'Python installation folder', give the same folder as above, 'C:\progra\Python32'; the library goes there, in a subfolder.

Installing Leo

Download and install the latest one-click installer for Windows (.exe) of Leo from its download page or possibly here. Click where it says, 'Looking for the latest version'. I used 'LeoSetup-4.9-final-a.exe'.

Leo may complain, 'Python not found,' but that's okay; we'll tell it later.

Leave selected 'Leo', '.leo File Association' and 'Leo Start Menu' and click Next. For 'Destination Folder', give 'C:\progra\Leo-4.9-final' or the equivalent. For Python Folder, give the same folder as above, 'C:\progra\Python32'. Keeping the default Start Menu folder, 'Leo', click Install and Finish.

Open a command line window with Win+ R and go to the Leo program directory with 'cd \progra\leo*'. Type launchLeo.py. It should say something like, 'is Python 3: True', and a little while later (possibly a window) will ask you for, 'an id that identifies you uniquely'. After that, Leo's graphical window should pop up.

From now on, you should be able to start Leo using the Windows Start menu.

Improving usability of Leo

With any folder menu in Windows Explorer, do Tools-Folder Options. Pick the File Types tab; move down and select the row that contains LEO in the Extensions column. Click the Advanced button; uncheck 'Confirm open after download'. Under Actions, make sure 'open' is selected and click the Edit button. Uncheck 'Use DDE' and into the box, 'Application used to perform action', paste:

C:\progra\Python32\pythonw.exe C:\progra\Leo-4.9-final\launchLeo.py "%1"

and click OK. (Double-quotes fix file and folder names that have embedded spaces, e.g. as you know, 'My Documents'.) Click OK again.

Now if you click any Leo file, an instance should be loaded to edit it.

The best documentation to read first is available by means of Menu-Help-Open quickstart.leo.

^[1]Leo (Text editors wiki)

Further introduction

o Leo

Testimonial
Why I love Leo (Dan Rahmel)
What makes Leo special
Manual introduction
Blogpost: Using Leo as a personal information manager (PIM) (J.Tauber)
Leo (text editor) (Wikipedia)
Ream's thoughts on Joe Orr's slideshow
Leo website slideshow
Introductory tutorial

o Solved by Leo

Outliners, trees and meshes (Scott Rosenberg, author of Dreaming in Code, etc.)
Outlines and meshes (Taking Note, an anonymous blog)

o Background: Outliners

Outliners then and now (Scott Rosenberg)
MORE outliner (retrospective/review, ATPM.com)
MORE, dinosaur (retrospective/review, Matt Neuburg)

o Background: Literate Programming

LP (Ward Cunningham wiki)
[LP].com
Software design for engineers and scientists (J.A. Robinson, GoogleBooks from w/s literate programming editor)
LP (PyLit website)
Lightweight LP with example (J.W.Shipman)
LP Workshop (Mac program)
LP is a terrible idea (Matt Giuca)
LP, why? (Bart Childs)
LP to enhance agile methods (Vreda Pieterse: publications)

o Related, vaguely

Tabulator: RDF semantic web browser (Tim Berners-Lee)
Bacon on instruments of the mind (Taking Note)

For more information

o On Leo

All about Leo
More Leo resources
Joe Orr's Leo resource page
Installing Leo on Windows (Matt Wilkie)
Develop in Haskell with Leo

o General

Outliner editor family (Text editors wiki)
Outliners: comparison (Mark Wieczorek)
XP/agile universe (conferences)

Copyright (c) 2011 Mark D. Blackwell.

Unfamiliar Windows keyboard shortcuts

2011-07-11T15:17:00.066-04:00

I like to open folders sometimes in a new window, sometimes the same window. It's difficult to right-click my particular computer mouse. Also, generally I prefer keyboard shortcuts.

First I tried using Microsoft Windows Explorer's option which always opens a new window; soon I was frustrated, closing the many windows. (See Windows Explorer-Menu-Tools-Folder Options-General-Browse Folders.)

To open the other view (folder or explorer) in a new window, I was motivated to find a shortcut: either with the keyboard or a left mouse click. Some research found many that were unfamiliar and quite useful.

Here are my select keyboard and mouse shortcuts for Windows XP and later. You might not know all of them--I think you will find at least one excitingly useful!

Abbreviations:
App = Application key (AKA Menu key, context menu key)
Win = Windows key (AKA Flag key, Meta key, MOD4, Start key, Super key, Windows logo key, WinKey)

General:
Alt+ Esc: Cycle programs in starting order
Alt+ F6: Cycle windows of active program
Alt+ PrintScreen: Capture program window (paste into Paint)
Alt+ Shift+ Esc: Cycle programs in starting order, backward
Alt+ Spacebar M Arrow: Move active window
Alt+ Spacebar S Arrow: Resize active window
App: Show context menu
Ctrl+ Shift+ Esc: Task manager
F6: Cycle screen elements (e.g., in SeaMonkey, go to address bar)
Win: Show start menu
Win+ Break: Show system properties
Win+ D: Show desktop (toggle)
Win+ E: Explore My Computer
Win+ L: Lock/logon screen (switch user)
Win+ M: Minimize all windows
Win+ R: Run
Win+ Shift+ M: Undo minimize all windows (also undo show desktop)
Win+ Shift+ Tab Enter: Cycle programs in taskbar, backward
Win+ Tab Enter: Cycle programs in taskbar
Win+ U: Utility manager (accessibility)
(Shift+ F10: same as App)

Command-line window:
Alt+ Spacebar E K (make selection) Enter: Select text
Alt+ Spacebar E L Arrow: Scroll
Alt+ Spacebar E P: Paste text

Desktop:
Alt+ Double-click: Show properties (single folder or file)
Alt+ Enter: Show properties (multiple folders & files)
Enter: Open single selection in folder view (or last-selected)
Shift+ Enter: Explore single selection (or last-selected)
(App O: same as Enter; App X: same as Shift+ Enter)

Multi-document program:
Ctrl+ F4: Close active document

... Icon of non-maximized document:
Double-click: Close

Windows Explorer (file chooser in other programs):
Alt+ Double-click: Show properties (of single folder or file; except explore-view navigation pane)
Alt+ Enter: Show properties (multiple folders & files)
Alt F W Enter: Create new folder
Alt V E O: Show navigation pane (toggle)
Ctrl+ Keypad '+': Fit columns
F4: Show folder trail (toggle)
Shift+ Click: Select from top to pointer

Finally, to avoid right-clicking, here are the shortcuts I was looking for:

... In explore view:
App O: New folder-view window(s)
Enter: Change to single selection; explore (some of) multiple selection in new windows
(App X, Click Shift+ Double-click: same as Enter)

... In folder view:
Ctrl+ Enter: Open single (or some of multiple) selection in new window(s)
Enter: Change to first-selected
Shift+ Enter: Explore in new window(s)
(App X, Click Shift+ Double-click: same as Shift+ Enter)

Sources:
http://www.computerhope.com/shortcut/windows.htm
http://support.microsoft.com/kb/301583
http://support.microsoft.com/kb/126449
http://en.wikipedia.org/wiki/Windows_key
http://en.wikipedia.org/wiki/Menu_key

Mass, songs I composed

2011-06-11T13:33:00.066-04:00

I composed some music!

Also, I engraved its sheet music. (Good-looking, if I say so myself. I would be happy to engrave anyone's music! Please email me [click my profile] for reasonable rates.)

The following are free of charge (with the Creative Commons license):

A mass setting in Latin. Its title is, `Missa Brevis, Thomas Young'; its subtitle, `In a Sequence of Chords Inspired by His Harpsichord Temperament No. 1 of 1799, For Choir of Four Parts, Unaccompanied' (with optional organ). (Opus 1: May 2010, improved December 2011.)

I attempted, with music, to express the emotions naturally present in the mass text (for a wide audience, not necessarily Christian).

PDF sheet music and MIDI are available. The movements are Antiphon (Asperges Me & Vidi Aquam--Latin & English), Kyrie (Sixfold & Ninefold), Gloria, Sanctus & Benedictus and Agnus Dei.

Two songs, both on Roman Catholic/Anglican/Episcopal Church Lectionary texts (in English) for the Feast of the Sacred Heart (among other occasions, or for general use). (Opus 2: June 2010, improved December 2011.)

My aim was to approximate the pitches of natural speech, as well as to express the emotion of the texts.

They are for alto solo with tenor solo accompaniment (and optional keyboard):

1. `Jesus Addressed' (from Lk. 15:3-5) with PDF sheet music and MIDI, with piano accompaniment and without.

2. `It Is Rare' (from Rom. 5:7-8) with PDF sheet music and MIDI, with piano accompaniment and without.

I improved the print layout of the songs December, 2011.

The mass setting was inspired by (and is an homage to) Young's 1799 system of well-temperament (Young #1, called `ideal' by Owen H. Jorgensen in his classic book Tuning of 1991). It follows his temperament order of major thirds (which have roots C G=F D=Bb A=Eb E=Ab B=Db Gb), with CE purest-sounding and GbBb (in a sense, farthest away) the least pure-sounding (albeit the mass was written for equal-temperament).

Thus the (mass's) overall sequence of chords is actually two simultaneous circles of fifths. You can see an annotation of the chords in the sheet music (their roots, as well as major or minor), revolving (usually) in both directions. The movements are thus unified, and I added harmonic coloration (and inversion) to make them enjoyable.

Here is how I devised the mass's chord roots, in order of composition:

The Kyrie sections (of the two Kyrie settings) revolve from C to Gb; the Christe sections are the reverse. (The Sixfold one was composed after Agnus Dei.)

The Sanctus & Benedictus setting (considered as a unit) offers Young's equalized third roots the other way: C F G Bb D Eb A Ab E Db B Gb.

In the Gloria setting, the entire circle of fourths first revolves upward (on major chords) feeling like classical resolution, then downward (with some text-appropriate, minor chords) feeling like Plagal hymn resolution.

In the Agnus Dei setting, two arcs of fifths intertwine, though one breaks order slightly (and is reversed): C G D A E B Gb and Ab Eb Bb F (Db). Thus there (emotionally) is a regular falling pattern: C Ab G Eb D Bb A F E Db B Gb. Interestingly, the last four match the (chord) roots of the Benedictus, which inspired me.

Young's equalized third roots are presented simultaneously in the Antiphon setting, which revolves from C to Gb then reverses.

To the Gloria, Sanctus, Benedictus and Agnus Dei settings (previously Anglican chant: full-measure chords) I added rhythm (as well as improving the overall print layout) December, 2011.

Copyright (c) 2011 Mark D. Blackwell.

Install Rails 3 application to cPanel in sub-URI, howto

2011-03-23T17:00:00.007-04:00

Recently, I successfully installed a Rails 3.0.3 application (using Ruby 1.8.7) on a plain-vanilla webhost with cPanel (which normally is restricted to Rails 2).

It can be managed in the normal way (started and stopped) on cPanel's webpage, 'Manage Ruby on Rails Applications', because of additional code I wrote in the Rails app.

Here's how I did it:

o See the webhost's current Ruby version and gem environment (for your_user_name) with:

cron> gem env

(If shell access is unavailable, command lines can be run as one-time cron jobs by specifying (year) month, day, hour and minute.)

o Ask the webhost to update if they don't have the latest RubyGems system software:

root> gem update --system

o Create a Ruby on Rails application (on the cPanel Ruby on Rails page) specifying application path, 'rails_apps/your_app_name'.

o In cPanel's File Manager (with the option to show hidden files) navigate to $HOME/rails_apps/your_app_name and delete the contents just made. Upload your Rails 3 application (there, compressing with 'zip' gives the relative pathnames required by cPanel) and extract it.

o Correct your cPanel user's gem environment by uploading to $HOME/.gemrc the following:

---
gem: --no-rdoc --no-ri

# Note: a non-default value adds another gempath.
# Is default for rubygems 1.5.2:
gemhome: /home/your_user_name/.gem/ruby/1.8

gempath:
# Is default for rubygems 1.5.2:
- /home/your_user_name/.gem/ruby/1.8
# Your app's vendor bundle:
- /home/your_user_name/rails_apps/your_app_name/vendor/bundle/ruby/1.8
# Change this to the webhost's gem repository location:
- /usr/lib/ruby/gems/1.8

o The webhost's cPanel Software/Services RubyGems page might be incorrect:

oo It might say the location of your ruby gems is '/home/your_user_name/ruby/gems'. This is wrong; Rubygems software currently uses, '/home/your_user_name/.gem/ruby/1.8'.

oo It might recommend adding a gem repository to the include path. This is unnecessary; don't add either of the following:

$:.push("/home/your_user_name/ruby/gems")
$:.push("/home/your_user_name/.gem/ruby/1.8")

o Install the bundler gem:

cron> gem install bundler

o Generate Gemfile.lock with:

cron> cd $HOME/rails_apps/your_app_name; bundle install --path vendor/bundle

o Ask the webhost to install (in the system gem repository) any gems Bundler failed to install, for instance, when Bundler tries to compile native extensions, which fails for cPanel users. For me, this was:

root> gem install mysql2

o Replace the Bundler code in config/boot.rb with a fixed list of gems:

=begin
# Set up gems listed in the Gemfile.
gemfile = File.expand_path('../../Gemfile', __FILE__)
begin
ENV['BUNDLE_GEMFILE'] = gemfile
require 'bundler'
Bundler.setup
rescue Bundler::GemNotFound => e
STDERR.puts e.message
STDERR.puts "Try running `bundle install`."
exit!
end if File.exist?(gemfile)
=end

o To make the list, sort Gemfile.lock and keep only its highest version of each gem. My fixed list was:

require 'rubygems'

require 'mysql2'

# Moved arel up, because otherwise got error:
## /usr/lib/ruby/site_ruby/1.8/rubygems.rb:274:in `activate': can't activate arel (= 2.0.7, runtime) for [], already activated arel-2.0.8 for ["activerecord-3.0.3"] (Gem::LoadError)

gem 'arel', '=2.0.7'

gem 'abstract', '=1.0.0'
gem 'actionmailer', '=3.0.3'
gem 'actionpack', '=3.0.3'
gem 'activemodel', '=3.0.3'
gem 'activerecord', '=3.0.3'
gem 'activeresource', '=3.0.3'
gem 'activesupport', '=3.0.3'
gem 'builder', '=2.1.2'
gem 'erubis', '=2.6.6'
gem 'i18n', '=0.5.0'
gem 'mail', '=2.2.15'
gem 'mime-types', '=1.16'
gem 'polyglot', '=0.3.1'
gem 'rack', '=1.2.1'
gem 'rack-mount', '=0.6.13'
gem 'rack-test', '=0.5.7'
gem 'rails', '=3.0.3'
gem 'railties', '=3.0.3'
gem 'rake', '=0.8.7'
gem 'thor', '=0.14.6'
gem 'treetop', '=1.4.9'
gem 'tzinfo', '=0.3.24'

o Seamonkey's caching causes problems in testing. The setting, 'Menu-Edit-Preferences-Advanced-Cache-Compare the page in the cache to the page on the network', should be 'Every time I view the page'. This still did not prevent all old, cached pages even with page reloads. I recommend using another browser, such as Opera to test your application.

o For my Rails 3 application, I used port 12009, one higher than cPanel's Mongel port for Rails (12008).

o Besides the cPanel button, you can start the application yourself in the cPanel way by:

cron> cd $HOME/rails_apps/your_app_name; /usr/bin/ruby /usr/bin/mongrel_rails start -p cPanel_Mongel_port; -d -e development -P log/mongrel.pid

o When troubleshooting, you can also start the application yourself by:

cron> cd $HOME/rails_apps/your_app_name; $HOME/.gem/ruby/1.8/bin/rails server webrick --port=Rails_3_port

o In config/environment.rb, add this line at the top:

unless (STARTED_BY_CPANEL='script/rails' != $PROGRAM_NAME)

o and these lines at the bottom:

else
load File.expand_path '../../monkey_patch_mongrel_1.1.5/start_webrick.rb', __FILE__
end

o Make a directory at the app root called, 'monkey_patch_mongrel_1.1.5'. Into it, place a file called 'dispatcher.rb' containing:

## Work around Mongrel source file: mongrel-1.1.5/lib/mongrel/rails.rb: 148
## require 'dispatcher'

module ActionController
class AbstractRequest
def relative_url_root=
end
end
end

o Also place a file there called 'start_webrick.rb' containing:

p Time.now, 'in '+__FILE__

# Versions tested on:
# Apache: 2.2.15
# Architecture: x86_64
# cPanel: 11.28.86
# cPanel Pro: 1.0 (RC1)
# Hosting package: Starter
# Kernel: 2.6.9-89.31.1.ELsmp (Linux)
# Mongrel: 1.1.5 (cPanel's)
# MySQL: 5.1.45
# Rails: 3.0.3
# Ruby: 1.8.7 patchlevel 330

module MyStartup
require 'pathname'

MY_RAILS_ENV=ENV['RAILS_ENV'] # Set by cPanel's Mongrel.

PROGRAM_FILE=Pathname(__FILE__).realpath
pfd=[]; PROGRAM_FILE.descend{|e| pfd << e}
USER_HOME=pfd.at 1
APP_ROOT= pfd.at -3
SERVER='webrick'
PORT='12009'

ARGUMENTS="--environment=#{MY_RAILS_ENV} --port=#{PORT}"
# For debugging, change to '':
REDIRECT_OUTPUT='> /dev/null'

class GemPathEntry
SYSTEM = Pathname('/').join *%w[ usr lib ruby gems 1.8 ]
USER = USER_HOME .join *%w[ .gem ruby 1.8 ]
APP_BUNDLE = APP_ROOT .join *%w[ vendor bundle ruby 1.8 ]
end
MY_GEM_HOME= GemPathEntry::USER
MY_GEM_PATH=[GemPathEntry::APP_BUNDLE, GemPathEntry::USER, GemPathEntry::SYSTEM].join ':'

# We might need Bundler in system gems. Or, as working now, in user (.gem) gems; I don't remember.

# The following line doesn't work because Bundler (1.0.10) "bundle install --binstubs" rewrites gem executables to invoke Bundler:
## r = APP_ROOT.
r = GemPathEntry::APP_BUNDLE
RAILS_COMMAND=['exec',r.join(*%w[bin rails]),'server',SERVER,ARGUMENTS,REDIRECT_OUTPUT].join ' '

REQUIRED_ENVIRONMENT_VARIABLES=[
"HOME=#{ USER_HOME }",
"RAILS_ENV=#{ MY_RAILS_ENV }",
"GEM_HOME=#{ MY_GEM_HOME }",
"GEM_PATH=#{ MY_GEM_PATH }",
].join ' '

def self.stop_process(name,pid,signal)
begin
p "I Stopping #{name} pid #{pid} at #{Time.now}"
Process.kill signal, pid
p "I #{Process.waitall.inspect}, #{name} finished at #{Time.now}"
rescue Errno::EINVAL, Errno::ESRCH
p "I No #{name} process #{pid}"
end
# Got error, undefined local variable or method `pwa' with:
## p pwa, "All child processes finished at #{Time.now}." unless (pwa=Process.waitall).empty?
# Sometimes there are other processes, I don't know why; so wait for them.
pwa=Process.waitall
p "I #{pwa.inspect}, all child processes finished at #{Time.now}" unless pwa.empty?
end

# Rack (1.2.1) fails with Rails 3.0.3 and any Mongrel, although Webrick works, per:
# https://github.com/rack/rack/issues/35

MONGREL_PID_FILE=APP_ROOT.join *%w[ log mongrel.pid ]

p Time.now
p "I Program name ($0) is #{$PROGRAM_NAME}"
p "I In #{PROGRAM_FILE}"
$LOAD_PATH.unshift APP_ROOT.join 'monkey_patch_mongrel_1.1.5'

unless WEBRICK_MONITOR_PID=Process.fork # Mongrel doesn't stop all threads, so we use a process.
p "I Starting Webrick monitor pid #{WEBRICK_MONITOR_PID} at #{Time.now} using command:"
p (c="export #{REQUIRED_ENVIRONMENT_VARIABLES}; cd #{APP_ROOT}; #{RAILS_COMMAND}")
Process.exec c unless WEBRICK_PID=Process.fork # Fork and replace another process.
p "I Starting Webrick pid #{WEBRICK_PID} at #{Time.now}"
Signal.trap 'TERM' do
stop_process 'Webrick', WEBRICK_PID, 'INT'
end
p "I #{Process.waitall.inspect}, Webrick finished (itself); stopping Mongrel at #{Time.now}"
unless File.exist? MONGREL_PID_FILE.to_s
p "I File '#{MONGREL_PID_FILE}' not found"
else
`#{s='mongrel_rails stop'}`
p "I '#{s}' finished at #{Time.now}"
end
Process.exit
end

Kernel.at_exit do # Handle being stopped by Mongrel.
stop_process 'Webrick monitor', WEBRICK_MONITOR_PID, 'TERM'
end

end

o The following rewrite rules require you to make this symlink:
/home/your_user_name/public_html/your_app_name ->
/home/your_user_name/rails_apps/your_app_name/public

ln -s $HOME/rails_apps/your_app_name/public $HOME/public_html/your_app_name

o At least in Rails 3.0.3, the following config/application.rb statement, which allows your application to generate the proper sub-URI URL's for its static assets such as images, requires an extra '/your_app_name' in the RewriteCond directive for most cached pages:

config.action_controller.asset_path=proc{|p| "/your_app_name#{p}"}

o Note that cPanel users cannot change Apache's system-level configuration file (/usr/local/apache/conf/httpd.conf), for instance to add Alias directives, so the following applies:

'The most common situation in which mod_rewrite is the right tool is when the very best solution requires access to the server configuration files, and you don't have that access. Some configuration directives are only available in the server configuration file. So if you are in a hosting situation where you only have .htaccess files to work with, you may need to resort to mod_rewrite.' --from http://httpd.apache.org/docs/current/rewrite/avoid.html

o The Pattern argument to RewriteRule must be without leading slash (it is stripped by Apache) or trailing slash. Its Substitution argument must have the leading slash.

o Apache's directive, DirectorySlash redirects bare sub-URI requests to '/your_app_name/', since 'your_app_name' is a symlink to your application's directory, 'public'. Similarly, Apache normally redirects bare HTTP_HOST requests to '/' because 'public_html' is a directory.

o Per: httpd-docs-2.2.14.en/mod/mod_rewrite.html#rewriterule
Per-directory Rewrites: When using the rewrite engine in .htaccess files the per-directory prefix (which always is the same for a specific directory) is automatically removed for the pattern matching and automatically added after the substitution has been done.

o My file, 'public_html/.htaccess' has these directives regarding cache expiration:

# Requires mod_expires to be enabled.
<IfModule mod_expires.c>
# Enable expirations.
ExpiresActive On
# Cache all files for 2 weeks after access (A).
ExpiresDefault A1209600
# Do not cache dynamically generated pages.
ExpiresByType text/html A1
</IfModule>

o Apache's <if> directive is unavailable until version 2.3, per:
http://serverfault.com/questions/238832/how-should-i-use-the-if-directive-in-htaccess

o Apache's FallbackResource directive is unavailable until version 2.2.16, per:
http://httpd.apache.org/docs/2.2/mod/mod_dir.html#fallbackresource

o Place this .htaccess file in your application's public directory:

#
# Rails 3.0.3 cPanel Apache settings.
#
# Don't show directory listings for URLs which map to a directory.
Options -Indexes
# Set the default handler to none.
DirectoryIndex
# Don't follow symbolic links in this directory or below.
Options -FollowSymLinks

# Rewrite module.
<IfModule mod_rewrite.c>
RewriteEngine on
# Per http://httpd.apache.org/docs/2.2/mod/mod_rewrite.html#rewriteoptions :
RewriteOptions inherit
RewriteBase /your_app_name

# 1. Simplify the rules for your sub-URI by redirecting a missing subdomain to 'www.':

RewriteCond %{HTTP_HOST} ^your_user_name\.com$ [NC]
RewriteRule ^(.*)$ http://www.your_user_name.com/your_app_name/$1 [L,R=301]

# 2. Rewrite your Rails application URI's to various files if they exist.

# 2.1. Rewrite its page-cached URI's:

# 2.1.1. Try to rewrite the sub-URI root URI to a file ('public/your_app_name.html') with path '/home/your_user_name/public_html/your_app_name/your_app_name.html':

RewriteCond %{HTTP_HOST} ^www\.your_user_name\.com$ [NC]
RewriteCond %{REQUEST_FILENAME}your_app_name.html -f
#SHOW RewriteRule ^$ /your_app_name/your_app_name.html?dr=%{DOCUMENT_ROOT}&rf=%{REQUEST_FILENAME} [L,R=301]
RewriteRule ^$ /your_app_name/your_app_name.html [L]

# 2.1.2. Try to rewrite a sub-URI, non-root URI to a file with extension '.html' (under tree, 'public/your_app_name/') by prefixing '/home/your_user_name/public_html/your_app_name' and suffixing '.html':

RewriteCond %{HTTP_HOST} ^www\.your_user_name\.com$ [NC]
RewriteCond %{DOCUMENT_ROOT}/your_app_name%{REQUEST_URI}.html -f
#SHOW RewriteRule ^(.+)$ /your_app_name/$1.html?dr=%{DOCUMENT_ROOT}&ru=%{REQUEST_URI}&rf=%{REQUEST_FILENAME} [L,R=301]
RewriteRule ^(.+)$ /your_app_name/your_app_name/$1.html [L]

# 3. Rewrite all other requests (except existing files) to the Rails port:

RewriteCond %{HTTP_HOST} ^www\.your_user_name\.com$ [NC]
RewriteCond %{REQUEST_FILENAME} !-f
#SHOW RewriteRule ^(.*)$ /your_app_name/your_app_name.html?rf=%{REQUEST_FILENAME} [L,R=301]
RewriteRule ^(.*)$ http://127.0.0.1:12009/your_app_name/$1 [L,P]

</IfModule>

o References:
http://httpd.apache.org/docs/2.2/
http://httpd.apache.org/docs/2.2/mod/quickreference.html
http://httpd.apache.org/docs/2.2/rewrite/
http://httpd.apache.org/docs/2.2/mod/mod_rewrite.html
http://httpd.apache.org/docs/1.3/mod/mod_rewrite.html (simpler)
http://httpd.apache.org/docs/2.2/rewrite/vhosts.html
http://wiki.apache.org/httpd/WhenNotToUseRewrite
http://borkweb.com/story/apache-rewrite-cheatsheet
http://www.askapache.com/htaccess/crazy-advanced-mod_rewrite-tutorial.html

o Then as a result, if you start your application, its cPanel Mongrel log in log/mongrel.log should look like this:

** Daemonized, any open files are closed. Look at log/mongrel.pid and log/mongrel.log for info.
** Starting Mongrel listening at 0.0.0.0:12008
** Starting Rails with development environment...
Wed Mar 23 12:29:15 -0700 2011
"in /home/your_user_name/rails_apps/your_app_name/config/environment.rb"
Wed Mar 23 12:29:15 -0700 2011
"in /home/your_user_name/rails_apps/your_app_name/monkey_patch_mongrel_1.1.5/start_webrick.rb"
Wed Mar 23 12:29:15 -0700 2011
"I Program name ($0) is /usr/bin/mongrel_rails"
"I In /home/your_user_name/rails_apps/your_app_name/monkey_patch_mongrel_1.1.5/start_webrick.rb"
"I Starting Webrick monitor pid at Wed Mar 23 12:29:15 -0700 2011 using command:"
"export HOME=/home RAILS_ENV=development GEM_HOME=/home/.gem/ruby/1.8 GEM_PATH=/home/your_user_name/rails_apps/your_app_name/vendor/bundle/ruby/1.8:/home/.gem/ruby/1.8:/usr/lib/ruby/gems/1.8; cd /home/your_user_name/rails_apps/your_app_name; exec /home/your_user_name/rails_apps/your_app_name/vendor/bundle/ruby/1.8/bin/rails server webrick --environment=development --port=12009 > /dev/null"
"I Starting Webrick pid 15175 at Wed Mar 23 12:29:15 -0700 2011"
** Rails loaded.
** Loading any Rails specific GemPlugins
** Signals ready. TERM => stop. USR2 => restart. INT => stop (no restart).
** Rails signals registered. HUP => reload (without restart). It might not work well.
** Mongrel 1.1.5 available at 0.0.0.0:12008
** Writing PID file to log/mongrel.pid
[2011-03-23 12:29:16] INFO WEBrick 1.3.1
[2011-03-23 12:29:16] INFO ruby 1.8.7 (2009-06-12) [x86_64-linux]
[2011-03-23 12:29:16] INFO WEBrick::HTTPServer#start: pid=15175 port=12009

o If you use the cPanel button to stop your application, it should look like this:

** TERM signal received.
"I Stopping Webrick monitor pid 22436 at Wed Mar 23 12:47:43 -0700 2011"
"I Stopping Webrick pid 22437 at Wed Mar 23 12:47:43 -0700 2011"
[2011-03-23 12:47:43] INFO going to shutdown ...
[2011-03-23 12:47:43] INFO WEBrick::HTTPServer#start done.
"I [[22437, #<Process::Status: pid=22437,exited(0)>]], Webrick finished at Wed Mar 23 12:47:43 -0700 2011"
"I [], Webrick finished (itself); stopping Mongrel at Wed Mar 23 12:47:43 -0700 2011"
"I File '/home/your_user_name/rails_apps/your_app_name/log/mongrel.pid' not found"

o If, from inside your application, you also want to stop cPanel's Mongrel server and Webrick (I did, because my application makes static pages), add this to one of your controllers:

WEBRICK_PID_PATH=App.root.join *%w[ tmp pids server.pid ]
WEBRICK_PID = begin
f=File.new WEBRICK_PID_PATH.to_s, 'r'
s=f.gets("\n").chomp "\n"
f.close
s.to_i if s.present?
rescue Errno::ENOENT
nil
end
application_PID=Process.pid

def stop_application(s)
logger.info "I #{s}; sending INT to application PID #{application_PID}"
Process.kill 'INT', application_PID
end

def stop_server
# Attempt to stop Webrick server gracefully by sending it SIGINT:
webrick_killed=false
if WEBRICK_PID.present? && WEBRICK_PID > 0
begin
logger.info "I sending INT to Webrick PID #{WEBRICK_PID}; application PID is #{application_PID}"
Process.kill 'INT', WEBRICK_PID
webrick_killed=true
rescue Errno::EINVAL, Errno::ESRCH
end
end
# Handle various unusual conditions:
s=case
when WEBRICK_PID.blank?
'No Webrick server.pid file found'
when (WEBRICK_PID <= 0)
"Bad value in Webrick server.pid file: #{WEBRICK_PID}"
when (WEBRICK_PID != application_PID)
"Server PID #{WEBRICK_PID} differs from application's: not Webrick?"
when (!webrick_killed)
"No process #{WEBRICK_PID}"
# TODO: Handle hung Webrick server?
end
stop_application s if s
end

o If you stop Mongrel from within your application, it should look like this:

[2011-03-23 12:30:46] INFO going to shutdown ...
[2011-03-23 12:30:47] INFO WEBrick::HTTPServer#start done.
"I [[15175, #<Process::Status: pid=15175,exited(0)>]], Webrick finished (itself); stopping Mongrel at Wed Mar 23 12:30:47 -0700 2011"
** TERM signal received.
"I Stopping Webrick monitor pid 15174 at Wed Mar 23 12:30:47 -0700 2011"
"I Stopping Webrick pid 15175 at Wed Mar 23 12:30:47 -0700 2011"
"I No Webrick process 15175"
"I [[16266, #<Process::Status: pid=16266,exited(0)>]], all child processes finished at Wed Mar 23 12:30:47 -0700 2011"
"I 'mongrel_rails stop' finished at Wed Mar 23 12:30:47 -0700 2011"
"I [[15174, #<Process::Status: pid=15174,exited(0)>]], Webrick monitor finished at Wed Mar 23 12:30:47 -0700 2011"

References:
Webmaster gallery - cPanel Rails 3 app - Mark D. Blackwell

Copyright (c) 2011 Mark D. Blackwell.

Installing Keepassx on Puppy Linux, howto

2011-03-11T12:25:00.016-05:00

Today I installed Keepassx, the 'open source password manager' (see http://www.keepassx.org/) on a computer running Puppy Linux (Quirky Retro 1.2).

Keepassx is compatible with KeePass for Windows, as long as you use the 1.x series. Ports of the 2.x series probably require .NET (or Mono) to run; both are quite large (per http://keepass.info).

Here's how I did it:
o From Debian.org, I downloaded this package from Debian, selecting the binary for my architecture (i386):

http://packages.debian.org/lenny/keepassx

o In ROX-Filer, I installed it by clicking the package file.

o Then I clicked 'console' on the desktop and typed, 'keepassx'. One by one, I got error messages for various missing libraries. Searching:

http://www.debian.org/distrib/packages#search_contents

I found the missing libraries in the following packages, which I then installed:

http://packages.debian.org/lenny/libqt4-xml
http://packages.debian.org/lenny/libqtgui4
http://packages.debian.org/lenny/libqtcore4
http://packages.debian.org/lenny/libaudio2

Copyright (c) 2011 Mark D. Blackwell.

Installing Prolog on Puppy Linux, howto

2011-02-20T19:37:00.028-05:00

From the book, Seven Languages in Seven Weeks, I notice a trend toward specialty languages being glued together by Ruby, or any scripting language. We can use the right tool for the right purpose instead of one "sledgehammer" only! Some examples are Prolog for rules (or logic) and Io (w/s "io language") for parsing.

Today I installed the package SWI Prolog, useful for developing in Prolog, the logic computer programming language, on a computer running Puppy Linux (Quirky Retro 1.2).

Here's how I did it:

o From Debian.org, download two 'lenny' packages:

swi-prolog_5swi-prolog_5.6.58-2_i386.deb
libgmp3c2_4.2.2+dfsg-3_i386.deb

o In the ROX-Filer file manager, click their icons to install them.

o Create a file, ~/.plrc containing the single line:

:- set_prolog_flag(editor,'geany').

o Within ~/my-documents, create and change to the directory, 'prolog'.

o Associate the file extension, '.pl' with SWI Prolog. Create a file like 'any.pl'. Right-click it in ROX-Filer and edit the run command to be:

urxvt -e swipl -s "$@"

Now you can click on a file with extension '.pl' and it will be loaded by the interpreter.

To make changes, type, 'edit.'. The interpreter will re-read the file when you close the editor. Type 'halt.' to end the session.

One example to get you started: if you type 'alice.' into a file, and in the interpreter type 'alice.', it will respond with, 'true'.

For further information, the SWI Prolog user manual is available off-line at:

file:///usr/lib/swi-prolog/doc/Manual/index.html

Their FAQ is:

http://www.swi-prolog.org/FAQ/

Some tutorials appropriate to beginners:

http://www.bitwisemag.com/copy/programming/prolog/intro/firststeps.html
http://www.learnprolognow.org/
http://www.csupomona.edu/~jrfisher/www/prolog_tutorial/contents.html
http://www.doc.gold.ac.uk/~mas02gw/prolog_tutorial/prologpages/

Copyright (c) 2011 Mark D. Blackwell.

Bach cello suites on viola da spalla

2010-08-05T21:17:00.004-04:00

My favorite way to hear the Bach cello suites is on the viola da spalla: http://www.youtube.com/watch?v=081JUQ7f6Yo
http://www.youtube.com/watch?v=VFZ0HHMIMn0#t=0m44s

For more information:

http://dictionary.die.net/viola da spalla
http://en.wikipedia.org/wiki/Giovanni_Battista_Vitali

Copyright (c) 2010 Mark D. Blackwell.

Swahili

2010-07-20T11:14:00.009-04:00

(January 20, 2010.) This morning, after leaving M's car to be worked on, I conversed with an INTP long-time slight acquaintance, who typically wears Moslem robes, while returning home by bus. He seated himself beside me, seemingly unawares.

After surprised greetings, observing him reading Latin and Arabic alphabetical writing, I asked politely, "What are you reading?"

He informed me, "Swahili", (the lingua franca of central East Africa).

I prompted him, "For long, I have wanted to learn Swahili. I just know one word: Uhuru."

Pleased, as I predicted, he said, "That means, 'Freedom!'"

I explained, "I have read the grammar is very interesting." He proceeded to teach, and from him, I learned:

Ni - I.
Ni na kula. - I am eating.
Ni na soma. - I am reading.
Ni da kula. - I will eat.
Ni li kula. - I ate.
Ni si na kula. - I am not eating.
Ni na kula chakula. - I am eating food.
Ni na kula chakula moto. - I am eating hot food.
Ni na kula chakula moto haraka. - I quickly am eating hot food.

Thus far, it follows Greenbergian word-order correlations, in that adverbs are placed on the same side of verbs, as adjectives are of nouns. (Here, both 'hot' and 'quickly' come afterward.)

More about Swahili and Word order.

I find it interesting, BTW, that we can communicate more easily with a fellow INTP, of limited English from Africa who is Moslem, than with a person from here, of some other Myers-Briggs type!

Copyright (c) 2010 Mark D. Blackwell.

Q2 radio

2010-06-29T11:18:00.005-04:00

I discovered an all new-music classical radio station, Q2, from New York City! To listen, click.

It just came online October, 2009 (Internet only) and streams a nice 128Kbps. A playlist is available. It has New York Philharmonic commissions from 12 to 4 o'clock.

Copyright (c) 2010 Mark D. Blackwell.

Bach Well-Tempered Clavier in Bach-Lehman temperament

2010-03-15T18:39:00.010-04:00

You might enjoy both books of Bach's Well-Tempered Clavier on harpsichord in Bach/Lehman 1722 temperament (from Bradley Lehman, A.Mus.D.), which feels to me like what Bach really used. You might like this temperament, too!

If there is an immediate emotional difference between the following two versions of Prelude in C major from Book I of The Well-Tempered Clavier by Bach then, good!

Bach in equal temperament

Bach in Bach-Lehman temperament

Otherwise, your MIDI setup is not right somehow. You shouldn't bother to download books I and II in their entirety.

Available zip formats:

the major keys (the order is F C G Bb D Eb Ab F# A C# B E)

the minor keys (the order is D A E G C B F Eb G# F# Bb C#)

To start playing after downloading, just open the folders, select all the MIDI files, and drag them en masse to a RealPlayer window.

Toward answering the question, 'Which keys sound brightest?' here the pieces in the Well-Tempered Clavier are in order of increasing 'brightness': the size of the tonic chord's major third, essentially, after dividing major keys from minor.

For sizes of major thirds and fifths in Bach-Lehman temperament, see this chart.

For the detailed sorting decisions, see 'readme.txt' inside the major and minor key zip files.

I tuned the MIDI files to Bach-Lehman temperament using the program, Scala.

(For this, it is essential to use good wave-table MIDI synthesizer software like the Microsoft GS Wavetable SW Synth (which is based on Roland wavetables). The Creative (SoundBlaster) SoundFont Synth and the QuickTime Music Synthesizer (at least on PC's) somehow blot out temperaments' emotional content, and thus they make meaningless this listening comparison.)

Alan Kennington and Yo Tomita have given me permission to reuse their MIDI realizations.

Copyright (c) 2010 Mark D. Blackwell.

Bach Contrapunctus (Art of Fugue)

2010-02-19T18:19:00.010-05:00

I tuned to Bach-Lehman 1722 temperament a MIDI from the Mutopia Project using harpsichord of most of Bach's The Art of Fugue.

To hear, expand this zip file. Drag the files en masse to RealPlayer's window (for example), sort its playlist of movements (perhaps putting inversus before rectus), and enjoy!

Copyright (c) 2010 Mark D. Blackwell.

Goldberg Variations in Bach-Lehman tuning

2010-02-09T19:36:00.031-05:00

I am listening excitedly to Bach's Goldberg Variations in G major (in a file I recently re-tuned) because they sound so good! They are now in the temperament used by Bach himself I believe, Bach-Lehman 1722.

I invite you to listen to:

Variation 25 - Andante espressivo

However, if you try the:

equal temperament version

I believe you shall hear significantly less beauty, even unpleasantness!

For this, it is essential to use some good wave-table MIDI synthesizer software like Microsoft GS Wavetable SW Synth which is based on Roland wavetables.

The Creative SoundBlaster SoundFont Synth and the QuickTime Music Synthesizer (at least on PC's) somehow blot out temperaments' emotional content, and they make this listening comparison meaningless.

Sometime, feast your ears and emotional system on the:

complete variations

on harpsichord, in Bach-Lehman 1722 temperament. (It may be better if you minimize the treble on your speakers or whatever. Credits:

Goldberg Variations - by J.S. Bach - BWV 988.
MIDI version by David J. Grossman, 1997.
Bach-Lehman 1722 temperament version by Mark D. Blackwell, 2010.

Interesting, from Mr. Grossman's website on the Art of MIDI: 'Listening to a clean sequence of a Bach work, it is possible for the mind to add [its] own interpretation[;] one is able to listen to the work in such a way that [one's] own realization of the work comes through.'

Following immediately at 1:09:21 are Bach's Fourteen Canons on the First Eight Notes of the Goldberg Ground in G major - BWV 1087, which sound better, interestingly, in

equal temperament.

More Bach from David J. Grossman.

(I have emailed David J. Grossman;, he granted permission for this use. His website states, 'All original material is copyrighted ©1999 (unpronounceable) Productions', and also states, 'All of these sequences were created with Cakewalk Pro Audio and are copyrighted ©1997. However, they are freely distributable and modif[i]able for any non-commercial purpose[,] as long as proper credit is given and the textual information in the files remains intact', and also states, 'The original MIDI sequences at this site [are] copyrighted by myself but may be modified and redistributed[,] if: I am asked permission first and have given it, I am given partial credit for my original work, and they are not sold. Redistribution of my sequences in their unmodified form is allowed without explicit permission as long as no money is charged for them.')

Copyright (c) 2010 Mark D. Blackwell.

Chopin mystery

2010-02-09T16:28:00.012-05:00

Here is a puzzle, involving a short piece by Chopin: Etude No. 3 in E [major] (Op. 10)

realized by Katsuhiro Oguri.

(For this, it is essential to use good wave-table MIDI synthesizer software like the Microsoft GS Wavetable SW Synth (which is based on Roland wavetables). The Creative (SoundBlaster) SoundFont Synth and the QuickTime Music Synthesizer (at least on PC's) somehow blot out temperaments' emotional content, and thus they make meaningless this listening comparison.)

Etude No. 3, but different

The first was better, right? but just how is it different? That is your problem to solve, ladies and gentlemen!

Especially note the chromatic passage, starting at 1:50.

How is it different? In other words, what makes it better?

You will see the answer in a forthcoming post!

If you still cannot put your finger on it, here is another piece:

Impromptu in Gb [major] (Op. 51)

realized by Robert Finley.

Impromptu in Gb, but different

Especially note the passage (in Bb minor, I think), from 2:11 through 3:26.

(Thanks to the The Classical MIDI Collection for the original Chopin MIDI's.)

Copyright (c) 2010 Mark D. Blackwell.

Brandenburg 5 in Bach-Lehman tuning

2010-02-06T15:01:00.047-05:00

I have re-posted this, correcting the URL spelling to 'Brandenburg'!

Bach tuning vs. equal temperament

2010-02-04T21:50:00.007-05:00

I am so enjoying this beautiful tuning! A commenter said, 'The difference this temperament makes[,] compared with equal temperament[,] is like unstopping your ears.'

Important especially for the fearful, as its video information says, 'the Bach/Lehman 1722... temperament sounds enough like equal [temperament] to fool just about anybody[.]'

Further, 'and yet...it brings both more intensity and more relaxation to the music...

'Equal temperament, by contrast, goes on and on with a relatively bland inoffensiveness...being less than inspiring, and encouraging "run-on"[,] uninflected performances... Why not tune instead with a subtle inequality, and let the intonation itself do part of the interpretive work?':

Copyright (c) 2010 Mark D. Blackwell.

Bach Endlessly Rising Canon

2010-02-04T15:06:00.008-05:00

Do you remember Douglas Hofstadter in Gödel, Escher, Bach: an Eternal Golden Braid writing that Shepard tones (notes an octave apart which fade, so motion ultimately goes nowhere) could be combined with Bach's 'modulation', or 'endlessly rising', canon (number 5 of The Musical Offering) to avoid its problematic downward octave leaps? On YouTube just now, I discovered in 2008, Michael Monroe created

just this!

on MIDI guitars, and it's beautiful: quite smooth with the 'repeat' option on Windows Media player.

Copyright (c) 2010 Mark D. Blackwell.

Refactoring switch-code to objects, howto

2010-01-27T17:03:00.035-05:00

Recently, I had an opportunity to suggest a refactoring of some switch-code (case-like statements) into objects. So... if the original source (in Ruby) were:

case condition_variable
when :condition_one
# This condition requires the most lines to handle, let us say.
<code for handling condition one>
when :condition_two
<code>
when :condition_three
<code>
end #case

The first increment of refactoring is as follows. See how it cleanly divides and documents the code for handling condition one? (An important part of refactoring-to-patterns is stopping when the ugliness no longer shouts!)

class ConditionOne
def handle( <parameters for handling condition one> )
<code for handling condition one>
end #def
end #class
case condition_variable
when :condition_one
ConditionOne.new().handle( <arguments>)
when :condition_two
<code>
when :condition_three
<code>
end #case

If later a need is felt to refactor conditions two and three, another increment of refactoring is:

condition = case condition_variable
when :condition_one
ConditionOne.new( <arguments for condition one>)
when :condition_two
ConditionTwo.new( <arguments for condition two>)
when :condition_three
ConditionThree.new( <arguments for condition three>)
end #case
condition.handle()

Some further refactoring leads to:

i = [ :condition_one,
:condition_two,
:condition_three].
index( condition_variable)
arguments = [ # For condition...
[<arguments>], # one.
[<arguments>], # two.
[<arguments>]] # three.
condition = [
ConditionOne,
ConditionTwo,
ConditionThree].at( i).new( arguments.at( i))
condition.handle()

If a need is felt, further refactoring could subclass a class called, Condition.

Actually, ConditionOne and its siblings want meaningful, specific names. See how this solves the problem of the code being too procedural?

Sources & further information:
AnalysisIsRefactoring
CaseStatementsConsideredHarmful
HistoryOfRefactoring
PolymorphismVsSelectionIdiom
RefactoringIsaRequirement
RefactoringToPatterns
RefactorLowHangingFruit
RefactorMercilessly
SafelyRefactoringLegacyCode
SwitchStatement
SwitchStatementsSmell
WhatIsaFactor
WhyDidYouRefactorThat
WhyNotEnoughRefactoringHappens

Copyright (c) 2010 Mark D. Blackwell.

_why the lucky stiff

2010-01-14T02:25:00.014-05:00

Suddenly I am struck with sadness for our loss of the highly creative _why the lucky stiff. (I discovered this while researching Ruby Shoes.) Not just in programming, but creative also in drawing and prose.

There is more here, here and here, and a cute sample of his early writing. Also, I found a _why-related, compilation blog post.

On last.fm, a radio station in his name contains some strange and intelligent things.

His June, 2009 talk on "Hackety Hack" at an ART && CODE Symposium shows his general aim of convincing others (besides his own creative work) to expand the learning opportunities available to children for programming. Perhaps this was the original basis for his pseudonym? Perhaps the reason for his disappearance was promotion: to generate large-scale publicity for this worthy cause.

Copyright (c) 2010 Mark D. Blackwell.

Old DOS games in Linux using DOSBox, howto

2009-09-08T14:27:00.015-04:00

My friend, M loves old computer games, and she loves running DOS games in her Windows XP system using the emulator, DOSBox. At a party with friends, I was inspired to remark that possibly these games could be played on a Linux system. Specifically, I wondered whether DOS games could be run on UNIX systems using DOSBox. Subsequently, I discovered Debian's package, 'dosbox'. Being an x86 emulator, it is available for many architectures beside i386.

I installed the lenny package, and I was pleased to find indeed that it ran well! Caveat: I do not have sound on my system at the moment, so I did not test that part. Following the advice of my friend, these are the steps I followed:

o Make a directory for all your DOSBox games:

mkdir ~/dos-box

o Download a DOS game. My friend recommended the site, Classic DOS games. (I downloaded Crystal Caves.)

o If the download is a zip file, decompress it (with 'unzip') into a subdirectory of dos-box.

o Start DOSBox from the Start menu or from an X terminal (with 'dosbox').

The following steps take place inside the DOSBox window, and are not UNIX commands:

o As DOSBox's C: drive, select your DOSBox directory:

mount c: ~/dos-box
c:

o Navigate (with 'cd') into the game's subdirectory.

o Run the game's installation program, if it has one.

o Follow the games's README instructions to run the game within DOSBox.

o Enjoy!

Copyright (c) 2009 Mark D. Blackwell.

Religion book notes

2009-08-25T21:13:00.004-04:00

For seekers today after religious solutions, a few relevant book notes: 'In most Western countries, people no longer like to speak much of "religion" (except at the difficult or symbolic moments of life) ...But the fashionable word is "spirituality," which has come to refer to a countless number of different realities, from relationship with God to simply the meaning one may give to life or to "things," including retreat from the world, the search for inner peace, overcoming the traps of the consumerist society, or even diving voluntarily and deliberately into the world of emotions. The Jewish or Christian origins have faded or simply disappeared and the idea of spirituality now covers almost everything imaginable that could "give a breath of life" or "give meaning."' -p.117

'At the heart of the West, whose rhythms of life and myriad opportunities for diversion may unsettle even the strongest determination, practice may become a mechanical ritual, lifeless and without spirituality. Memory repeats the invocations and prayers, the lips say the words, the body goes through the motions, the hand gives, but the soul is absent. The ritual is not enough: life must be liberated.' -p.121

'[Religious] education['s] first objective is the education of the heart, which links the consciousness with God and should awaken us to an awareness of our responsibilities toward ourselves, our bodies, our relatives, our communities, and the human family at large.' -p.129

'It is impossible to flourish independently without having the spiritual and intellectual means to discover who one is, where one lives, and how to plan one's way of faithfulness. [A religious] message ...is not adequately served by an intellectual hodgepodge ...To educate is to provide the tools that will enable individuals to grow into independence' -p.129

'A scattering of ...teachings, verses learned by heart, and values idealistically passed on do not necessarily forge a personality whose faith is deep, whose consciousness is alert, and whose mind is active and critical.' -p.132

'[S]ome schools continue to serve up an education that pushes children toward the development of two contradictory personalities --one within a school that tries to provide a happy environment and where [religious] teaching and behavior have been inculcated, and the other outside school, where they end up getting lost without knowing how to use ethical references to establish their own ethical guideposts because they have not really been prepared to face life in society and to interact with others in it. Having been given a solid education in an artificial environment, the students are deeply fragile in real life: how many young people live torn between the two, how many feel "bad" or "guilty" because, having received so much knowledge at school, they feel unworthy because of not knowing how to live an integrated everyday life? Whose fault is it? They have often been instructed in the ideal, but they feel so ill educated and ill equipped in the real world.' -p.132

'[T]oo many [religious people] behave rigidly and self-consciously and hide behind copying old models ...to prove their faithfulness to principles. But ...there is a great difference between historical models and universal principles, and today everything is proving that the formalistic imitation of models [from] an age other than one's own is in fact the betrayal of principles. In the area of education, this has serious consequences.' -p.133

'[A] complete education program ...is not only a matter ...of passing on a knowledge of the scriptural sources that will illumine the heart with faith and build the mind for an understanding of self, humankind, and creation, but it also concerns providing a very deep knowledge of the cultural and social environment, of history and human beings; and, more broadly, mastering the general disciplines and sciences that will give [religious people] the means of living at home in their environment. These are the necessary prerequisites for harmony among faith, morality, reason, and life in the world.' -p.133

'What is central ...is to understand the crucial importance of giving a sense of worth: to educate is to give all persons a sense both of their own value and of the value of what they do.' -p.137

The quotations (not for Muslims only) are from Western Muslims and the Future of Islam, Tariq Ramadan, 2004.

Copyright (c) 2009 Mark D. Blackwell.

All chords

2009-08-25T09:26:00.005-04:00

Recently, I wrote a computer program to generate all the 2048 possible musical chords (from any given root after collapsing transpositions) in any twelve-note, equal-tempered octave system. Each chord's notes transpose into fair consonance by excluding major and minor seconds, minor ninths, and tritones. The above chords completely cover the inversions of the 351 chords, available after collapsing transpositions and inversions. For more background on why 351, see Wikipedia, Necklace (combinatorics).

I provide details on all the chord necklaces and their inversions, including note names. A readable yet concise and rigorous scheme (that I created) was followed to provide a chord name for each inversion. A goal was matching common practice as much as possible. This provides a useful, searchable inversion chart. One might read a chord's description and play it manually, for instance on a piano.

A provided MIDI file of these chords is more consonant when played on a capable electronic piano than by the usual FM (frequency modulation) synthesis: than for instance on a SoundBlaster computer sound card. RealPlayer shows elapsed time; for the QuickTime player, General MIDI synthesis (which may sound better, depending on your sound card) is available at least on PC's by selecting, 'Plug-in Settings/Audio/Default Music Synthesizer.' For listenability, the (MIDI) chord roots are made to descend, alternately by major and minor thirds.

This is better than all the lists previously available of pitch-class (PC) sets because the process of finding and sorting normal forms is more computer-oriented: it is simply the largest binary number of all the (necklace) rotations. Along with this way of numbering notes, leftward from G, it collects similar-sounding PC sets (especially in their '0-inversion' chords) because this collation first looks at sevenths (F# and F) rather than seconds (Ab and A).

Copyright (c) 2009 Mark D. Blackwell.

Rare, select chamber music (sheet music and MP3)

2009-04-15T18:42:00.015-04:00

Here are some rare, excellent, beautiful, intelligent and select chamber music pieces of famous and once-famous old composers, culled by listening carefully to the sound samples on Edition Silvertrust's website. They also publish The Chamber Music Journal. I audited their full catalog of sheet music in two categories: quite a number of pieces! (I developed the list for some of my acquaintances with whom I play music, and have clarified the titles, somewhat. Originally, it may have been a recommendation from Delicious.com which led me to Edition Silvertrust, but I am not sure.)

All the best, excellent pieces, and only the best ones, are on this list. This is only my educated opinion; and yet, I believe you should enjoy them if you heard them! But merely let me mention my extensive classical music background. I invite you to judge for yourself!

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String and clarinet quintets:

Joseph Eybler (1765-1846), String Quintet for Violin & 2 Violas (or 2 Violins & Viola), Cello & Bass in D Major, Op.6 No.1 (1801)

Friedrich Dotzauer (1783-1860), String Quintet for 2 Violins, Viola & 2 Cellos in d minor, Op.134 (1835)

This one is operatic:
Luigi Cherubini (1760-1842), String Quintet for 2 Violins, Viola & 2 Cellos in e minor (1837)

Johan Svendsen (1840-1911), String Quintet in C Major, Op.5 (1867)

Charles Villiers Stanford (1852-1924), String Quintet No.1 in F Major, Op.85 (1903)

Alexander Krein (1883-1951), Three Sketches on Hebrew Themes for Clarinet Quintet Op.12 (1914)

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Piano quintets:

Camille Saint-Saëns (1835-1921), Piano Quintet in A Major, Op.14 (1853)

Elfrida Andrée (1841-1929), Piano Quintet in e minor (1865)

Giovanni Sgambati (1841-1914), Piano Quintet No.1 in f minor, Op.4 (1866)

Friedrich Kiel (1821-1885), Piano Quintet No.1 in A Major, Op.75 (1873-4)

Hermann Goetz (1840-1876), Quintet for Violin, Viola, Cello, Bass & Piano in c minor, Op.16 (1874)

Friedrich Gernsheim (1839-1916), Piano Quintet No.1 in d minor, Op.35 (1877)

Zdenek Fibich (1850-1950), Quintet for Violin, Clarinet & Horn (or 2 Violins & Viola), Cello & Piano in D Major, Op.42 (1893)

Carl Frühling (1868-1937), Piano Quintet in f sharp minor, Op.30 (1894)

Salomon Jadassohn (1831-1902), Piano Quintet No.3 in g minor, Op.126 (1895)

Ermanno Wolf-Ferrari (1876-1948), Piano Quintet in D flat Major, Op.6 (1900)

Wilhelm Berger (1861-1911), Piano Quintet in f minor, Op.95 (1904)

Théodore Dubois (1837-1924), Quintet for Oboe (or Clarinet or Violin), Violin, Viola, Cello & Piano in F Major (1904-5)

Giuseppe Martucci (1856-1909), Piano Quintet in C Major, Op.45 (year not found)

Sergei Taneyev (1856-1915), Piano Quintet in g minor, Op.30 (1910-11)

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Piano sextets:

This one is not hard for piano (unlike the usual Glinka), because he intended his Italian doctor's daughter to play it:
Mikhail Glinka (1804-57), Grand Sextet for Piano, String Quartet & Bass in E flat Major (1832)

William Sterndale Bennett (1816-1875), Sextet for Cello & Bass (or 2 Cellos), 2 Violins, Viola & Piano in f# minor, Op.8 (1838)

This one has fewer notes than usual for strings:
Ludwig Thuille (1861-1907), Sextet for Flute, Oboe, Clarinet, Horn, Bassoon & Piano in B flat Major, Op.6 (1888)

Paul Juon (1872-1940), Divertimento (Piano Sextet) for Flute, Oboe, Clarinet, Horn, Bassoon & Piano, Op.51 (1913)

Copyright (c) 2009 Mark D. Blackwell.

MP3 bit rates for various occasions

2009-04-15T14:04:00.016-04:00

After listening for a couple of days carefully to MP3's made from a WAV file, which I recorded of a brass, choir and organ rehearsal, I came up with some rules of thumb about bit rates. I concluded that the following minimums are indistinguishable from the WAV file in capturing the music of their various types. They are expressed in the the usual thousands of bits per second, Kbps. iTunes, by the way, uses 128:

Speech (without too many resulting artifacts) needs 56.
(Hymns with) descant need 64.
Brass instruments reduce the needed rate for choirs to 64.
Choir a capella (they are rather pure tones, or maybe it is the harmony) needs 80.
A single cantor (alto) needs 128.
Propers (increased because the choir response pitches are slightly clustered) need 160.
Hymns (depending on the organ stops) need 64 to 192.
Organ (because of reed and string stops) needs 192.

Copyright (c) 2009 Mark D. Blackwell.

All-chords analysis

2009-02-24T12:37:00.007-05:00

Interestingly, by the way, the set of all chords formable from the twelve Western tones, numbering almost 4096 (two to the twelfth power), collapses with the following method easily and automatically to the rather small size of 351 chords (see below).

Symbol key:
#: sharp
( ): alternative
,: and
-: visual spacing
=: same chord (collapsing transpositions and inversions)
aug: augmented
b: flat
d: diminished
d6: diminished, sixth chord
I: major chord
i: minor or diminished chord
s: suspension
x: without

Symbols for intervals from the root (in the list always G) in chord names, but not in normalized notation:
1,2,3,(4,5,6,7),9,11,13: unison, second, third, (fourth, fifth, sixth, seventh), ninth, eleventh, thirteenth
maj, min: major, minor

The default (i.e., without 'maj' or 'min') is the interval from G as found in the (blank) key signature of C major, because when C is the tonic, G chords are very prevalent. Thus sometimes we might need 'min2', 'min6', 'maj7', 'min9', 'maj11', or 'min13'. Minor thirds and augmented fourths (or diminished fifths) are respectively written as (Roman numerals in) lower case as well as 'd' for 'diminished'. Often ninths and elevenths are written 's2', 'smin2' or 's4'.

To name chords without suspensions:
Each chord has a root; otherwise, it can then be written as another chord. Here are the options for each variable, which is an interval upward from the root:
2 min2
3 min3 x3 null
4 maj4
5 min5 x5 null
6 min6
7 maj7 x7 null
9 min9 x9 null
10 min10
11 maj11 x11 null
12 min12
13 min13

Above, '-' indicates that the apparent option is unnecessary. Also, some variable options are implied: for any variable, N greater than the highest mentioned, 'null' means 'xN', otherwise it means 'N'. E.g., the name, i9 implies 7, but also x11.
What about diminished chords? This is answered by min5, but what about id6? It is min3-min5-x7-x9-x11-13 or id13x7,9,11.
It is simpler to say that all chords are 13th chords with various notes x'd out. Then, we would need x13 as well.
The computer program might display only the normalized notation.

For each root, the total number of combinations (outside of silence), the number of unique chord names, would be 3x3x3x3x2x3 (?) = 2 x 3^5 = 486. However, many of these are duplicates of chords with different roots.

An attempt has been made to select the chord names of the more beautiful -sounding inversions. For chord names with suspensions, to sound beautiful, some suspensions are in the bass, e.g., 0,1,7 - idx3s5.

Here are the number of chords for different numbers of tones evenly distributed in the octave:

note-space-size chord-space-size
1 1
2 2
3 3
4 5
5 7
6 13
7 19
8 35
9 59
10 107
11 187
12 351
13 631
14 1181
15 2191
16 4115
17 7711
18 14601
19 27595
20 52487

Here are the 351 transposition- and inversion -collapsed chords formable from the twelve Western tones:

The total number of whole-tone scale chords is 13; the Agnus Dei has 7.

Use maj11 instead of aug11; dim11 is okay; min5 instead of dim5. Change I...smin3 (except aug) to i...s3. Rooting all numbers covers pedal tones. Change all 'good's' into chords. Use 'Id' instead of 'idx3s3'?
M=Agnus Dei chord, P=polytonal, W=whole tone scale chord, H=harmonic series, S=symmetrical
normalized-notation - standard-name [(nonstandard-names)] - spelling [(nonstandard-spelling)] [ - (good: good-sounding spelling)]
0 - ix3,5 - M (H) - (WS)
0,6 - idx3 - M - (WS)
0,5 - ix3 - M (H)
0,4 - Ix5 - M (H) - (W)
0,4,8 - 0-Iaug (=0-G B D#) - (WS good: G D# B)
0,3 - ix5 - M (H)
0,3,8 - i - M
0,3,7 - I - M
0,3,6 - id - M
0,3,6,9 - id6 - M - (S)
0,2 - i7x3,5 - M - (W)
0,2,9 - i7x5 - M
0,2,8 - I7x5 - M - (W)
0,2,7 - ix3s4 - M
0,2,6 - id7x3 - M - (W)
0,2,6,9 - id7 - M
0,2,6,8 - 0-Imaj11x5,9 2-idmin13x3,7,11 (=0-G B F C# =2-G Db 0-A Eb) - (WS good: G Eb A Db)
0,2,5 - i7x3 - M
0,2,5,9 - i7 - M
0,2,5,8 - I7 - M (H)
0,2,5,7 - i7x3s4 - M
0,2,4 - 0-iaug7x3 2-i9x3,5 4-I9x5,7 (=0-G D# F =2-G F 0-A =4-G 0-B A) - (W good: F G D#)
0,2,4,9 - I9x7 - M
0,2,4,8 - Iaug7 - M - (W)
0,2,4,7 - 0-i7min13x3,5,9 2-i9x3 4-I13x5,7,11 7-i11x7,9 (=0-G F C Eb =2-G D F 0-A =4-G 0-B A E =7-G Bb 0-D C)
0,2,4,7,9 - 0-imin13x5,9 2-i11x3 4-I13x7,11 4-I96x7 7-i11x9 9-i13x3,7 (=0-G Bb F C Eb =2-G D F 0-A C =4-G 0-B D A E =4-G 0-B D E A =7-G Bb 0-D F C =9-G D A C 0-E)
0,2,4,6 - 0-idmin13x3,9,11 2-imin13x3,5,11 4-I9x5 6-Imaj11x5,7 (=0-G Db F Eb =2-G F 0-A Eb =4-G 0-B F A =6-G B A 0-C#) - (W good: G A B F)
0,2,4,6,9 - 0-idmin13x9,11 2-imin13x3,5 4-I9 6-Imaj1113x5,7 9-i13x7,9 (=0-G Bb Db F Eb =2-G F 0-A C Eb =4-G 0-B D F A =6-G B A C# E =9-G Bb D C 0-E)
0,2,4,6,8 - 0-idmin13x3,9,11s3 2-idmin13x3,11 4-Iaug9 6-Imaj11x5 8-idmin13x3,7,11s3 (=0-G B Db F Eb =2-G Db F A Eb =4-G 0-B D# F A =6-G B F A C# =8-G B Db A 0-Eb)
0,2,4,6,8,10 - 0-Iaug7maj11 (=0-G B D# F A C#) - (WS 'full whole tone scale' good: G B D# A C# F)
0,1 - 0-imaj7x3,5 1-imin9x3,5,7 (=0-G F# =1-G 0-Ab)
0,1,10 - 0-imaj79x3,5 1-imin9x5,7 10-id67x3,5 (=0-G F# A =1-G Bb 0-Ab =10-G E 0-F) - (good: F G E)
0,1,9 - 0-imaj7x5 1-Imin9x5,7 9-iaug13x3,7,9,11 (=0-G Bb F# =1-G B 0-Ab =9-G D# 0-E) - (good: G F# Bb)
0,1,8 - Imaj7x5 - M
0,1,8,10 - Imaj79x5 - M
0,1,7 - idx3s5 - M
0,1,7,10 - 0-imaj711x3,5 1-idmin9x7 7-imaj1113x3,7,9 10-id67x5 (=0-G F# A C =1-G Bb Db 0-Ab =7-G 0-D C# E =10-G Bb E 0-F) - (good: G E Bb F, F G Bb E, G Bb F E, F E Bb G)
0,1,7,9 - 0-imaj7x5s4 0-imaj711x5,9 1-idmin9x3,7s3 7-imaj11x3,9 9-iaug13x3,7,11 (=0-G Bb C F# =0-G Bb F# C =1-G B Db 0-Ab =7-G 0-D F C# =9-G D# A 0-E) - (good: G C Bb F#)
0,1,6 - 0-idmaj7x3 1-imin9x3,7 6-id11x3,7,9 (=0-G Db F# =1-G D 0-Ab =6-G 0-Db C) - (good: G F# Db)
0,1,6,10 - imin9x7 - M
0,1,6,9 - 0-idmaj7 1-Imin9x7 6-id611x3,7,9 9-id6min13x5,7,9,11 (=0-G Bb Db F# =1-G B D 0-Ab =6-G 0-Db E C =9-G Bb E Eb) - (good: G F# Bb Db)
0,1,6,8 - 0-Imaj7maj11x5,9 1-imin911x3,7 6-id11x3,9 8-imin13x3,7,11 (=0-G B F# C# =1-G D 0-Ab C =6-G 0-Db F C =8-G D A 0-Eb) - (good: G C# F# B, F# B G C#, F# B C# G)
0,1,6,8,10 - 0-Imaj7maj11x5 1-imin911x7 6-idmin13x3,9 8-imin13x3,11 10-I13x5,11 (=0-G B F# A C# =1-G Bb D 0-Ab C =6-G 0-Db F C Eb =8-G D F A 0-Eb =10-G B 0-F A E) - (good: G Ab Bb C D)
0,1,6,7 - 0-idmaj711x3,9 1-imin9maj11x3,7 1-idmin9x3,7s5 (=0-G Db F# C =1-G D 0-Ab C# =1-G Db D 0-Ab) - (S good: C Db F# G, F# Db C G)
0,1,5 - 0-imaj7x3 1-imin9min13x3,5,7,11 5-I11x5,7,9 (=0-G D F# =1-G 0-Ab Eb =5-G B 0-C) - (good: D G F#)
0,1,5,10 - 0-imaj79x3 1-imin9min13x5,7,11 5-I11x7,9 10-i13x3,5,9 (=0-G D F# A =1-G Bb 0-Ab Eb =5-G B D 0-C =10-G 0-F C E)
0,1,5,9 - 0-imaj7 1-Iaugmin9x7 5-Iaug11x7,9 9-Iaug13x7,9,11 (=0-G Bb D F# =1-G B D# 0-Ab =5-G B D# 0-C =9-G B D# 0-E) - (good: G D F# Bb)
0,1,5,8 - Imaj7 - M
0,1,5,8,10 - 0-Imaj79 1-imin9min13x5,7 5-I13x7,9 8-imin13x9,11 10-i13x3,5 (=0-G B D F# A =1-G Bb 0-Ab C Eb =5-G B D 0-C E =8-G Bb D F 0-Eb =10-G 0-F A C E)
0,1,5,7 - 0-imaj711x3,9 1-idmin9min13x3,7,11 5-I7x5s4 5-I11x5,9 7-imaj11x3,7 (=0-G D F# C =1-G Db 0-Ab Eb =5-G B 0-C F =5-G B F 0-C =7-G 0-D A C#)
0,1,5,7,10 - 0-imaj711x3 1-idmin9min13x7,11 5-I11x9 5-I7s4 7-imaj1113x3,7 10-i13x5,9 (=0-G D F# A C =1-G Bb Db 0-Ab Eb =5-G B D F 0-C =5-G B 0-C D F =7-G 0-D A C# E =10-G Bb 0-F C E)
0,1,5,7,9 - 0-imaj711x9 0-imaj7s4 1-idmin9min13x3,7,11s3 5-Iaug711x9 5-Iaug7s4 7-imaj11x3 9-Iaug13x7,11 (=0-G Bb D F# C =0-G Bb C D F# =1-G B Db 0-Ab Eb =5-G B D# F 0-C =5-G B 0-C D# F =7-G 0-D F A C# =9-G B D# A 0-E)
0,1,5,6 - 0-imaj7maj11x3,9 1-imin9min13x3,7,11 5-Imaj7x5s4 6-idmin911x3,7 (=0-G D F# C# =1-G D 0-Ab Eb =5-G B 0-C F# =6-G 0-Db Ab C)
0,1,5,6,10 - 0-imaj7maj11x3 1-imin9min13x7,11 5-Imaj711x9 5-Imaj7s4 6-idmin9min13x3,7 10-I13x5,9 (=0-G D F# A C# =1-G Bb D 0-Ab Eb =5-G B D F# 0-C =5-G B 0-C D F# =6-G 0-Db Ab C Eb =10-G B 0-F C E)
0,1,4 - 0-iaugmaj7x3 1-imin913x3,5,7,11 4-ix5s3 (=0-G D# F# =1-G 0-Ab E =4-G Bb 0-B) - (good: F# D# G)
0,1,4,10 - 0-iaugmaj79x3 1-imin913x5,7,11 4-ids3 10-id67x3 (=0-G D# F# A =1-G Bb 0-Ab E =4-G Bb 0-B Db =10-G Db E 0-F)
0,1,4,9 - 0-imaj7min13x5,9,11 1-Imin913x5,7,11 4-is3 9-iaug13x3,7,9 (=0-G Bb F# Eb =1-G B 0-Ab E =4-G Bb 0-B D =9-G D# C 0-E)
0,1,4,8 - 0-Iaugmaj7 1-imin913x3,5,7 4-imin13x5,7,9,11s3 8-Imin13x7,9,11 (=0-G B D# F# =1-G 0-Ab C E =4-G Bb 0-B Eb =8-G B D 0-Eb) - (good: F# D# B G)
0,1,4,8,10 - 0-Iaugmaj79 1-imin913x5,7 4-idmin13x7,9,11s3 8-Imin13x9,11 10-imaj1113x3,5 (=0-G B D# F# A =1-G Bb 0-Ab C E =4-G Bb 0-B Db Eb =8-G B D F 0-Eb =10-G 0-F A C# E)
0,1,4,7 - ids5 - M
0,1,4,7,10 - id6min9x7 - M
0,1,4,7,9 - 0-imaj7min13x5,9 1-id6min9x3,7s3 4-is3,6 4-i13x7,9,11s3 7-id7s5 9-iaug13x3,7 (=0-G Bb F# C Eb =1-G B Db E 0-Ab =4-G Bb 0-B D E =4-G Bb 0-B D E =7-G Bb Db 0-D F =9-G D# A C 0-E)
0,1,4,7,8 - 0-Iaugmaj711x9 1-id6min911x3,7 4-Iaug13x7,9,11smin3 7-idmaj7s5 8-Imin9x7smin6 (=0-G B D# F# C =1-G Db E 0-Ab C =4-G Bb 0-B D# E =7-G Bb Db 0-D F# =8-G B D 0-Eb Ab)
0,1,4,6 - 0-iaugmaj7maj11x3,9 1-imin9x3,7s6 1-imin913x3,7,11 4-i7x5s3 6-id11x3,7 (=0-G D# F# C# =1-G D E 0-Ab =1-G D 0-Ab E =4-G Bb 0-B F =6-G 0-Db A C)
0,1,4,6,10 - 0-iaugmaj7maj11x3 1-imin9x7s6 4-id7s3 6-idmin13x3,7 10-Imaj1113x5,9 (=0-G D# F# A C# =1-G Bb D E 0-Ab =4-G Bb 0-B Db F =6-G 0-Db A C Eb =10-G B 0-F C# E)
0,1,4,6,9 - 0-idmaj7min13x9,11 1-Imin9x7s6 4-i7s3 6-id611x3,7 9-id6min13x5,7,9 (=0-G Bb Db F# Eb =1-G B D E 0-Ab =4-G Bb 0-B D F =6-G 0-Db E A C =9-G Bb 0-E C Eb)
0,1,4,6,8 - 0-Iaugmaj7maj11x9 1-imin913x3,7 4-Iaug7smin3 6-id11x3 8-Imin13x7,11 (=0-G B D# F# C# =1-G D 0-Ab C E =4-G Bb 0-B D# F =6-G 0-Db F A C =8-G B D A 0-Eb)
0,1,4,6,8,10 - 0-Iaugmaj7maj11 1-imin913x7 4-idmin13x9,11s3 4-Iaugmaj11x9smin3 6-idmin13x3 8-Imin13x11 10-Imaj1113x5 (=0-G B D# F# A C# =1-G Bb D 0-Ab C E =4-G Bb 0-B Db F Eb =4-G Bb 0-B D# F C# =6-G 0-Db F A C Eb =8-G B D F A 0-Eb =10-G B 0-F A C# E)
0,1,4,6,7 - 0-idmaj7min13x3,9 1-id6min9x3,7s5 4-id67x5s3 6-idmaj711x3 7-idmin9x7s5 (=0-G Db F# C Eb =1-G Db D E 0-Ab =4-G Bb 0-B E F =6-G 0-Db F# A C =7-G Bb Db 0-D Ab)
0,1,4,6,7,10 - 0-idmaj7min13x3 1-id6min9x7s5 4-id67s3 4-imaj1113x5,9s3 (=0-G Db F# A C Eb =1-G Bb Db D E 0-Ab =4-G Bb 0-B Db E F =4-G Bb 0-B F C# E) - (S good: D G Bb Db E Ab)
0,1,4,5 - 0-imaj7min13x3,9,11 1-iaugmin913x3,7,11 4-imaj7x5s3 5-Imin911x5,7 (=0-G D F# Eb =1-G D# 0-Ab E =4-G Bb 0-B F# =5-G B Ab 0-C) - (good: G Ab B C)
0,1,4,5,10 - 0-imaj7min13x3,11 1-id6min9min13x5,7,11 4-idmaj7s3 5-Imin911x7 10-id611x3,9 (=0-G D F# A Eb =1-G Bb E 0-Ab Eb =4-G Bb 0-B Db F# =5-G B D Ab 0-C =10-G Db E 0-F C) - (good: C Ab D G B)
0,1,4,5,9 - 0-imaj7min13x9,11 1-Iaugmin913x7,11 4-imaj7s3 5-Iaugmin911x7 9-Iaugmaj1113x7,9 (=0-G Bb D F# Eb =1-G B D# 0-Ab E =4-G Bb 0-B D F# =5-G B D# Ab 0-C =9-G B D# C 0-E)
0,1,4,5,8 - 0-Imaj7min13x9,11 0-Imaj7min13x3,9,11s10 1-imin9min13x3,5,7s6 4-Iaugmaj7smin3 5-Imin913x5,7 8-imin13x7,9,11s3 (=0-G B D F# Eb =0-G D F# B Eb =1-G E 0-Ab C Eb =4-G Bb 0-B D# F# =5-G B Ab 0-C E =8-G Bb B D 0-Eb)
0,1,4,5,8,10 - 0-Imaj7min13x11 1-id6min9min13x5,7 4-idmaj7min13x5,9,11s3 4-Iaugmaj7maj11x9smin3 5-Imin913x7 8-imin13x9,11s3 10-id611x3 (=0-G B D F# A Eb =1-G Bb E 0-Ab C Eb =4-G Bb 0-B Db F# Eb =4-G Bb 0-B D# F# C# =5-G B D Ab 0-C E =8-G Bb B D F Eb =10-G Db E 0-F A C)
0,1,4,5,8,9 - 0-imaj7min13x9,11s3 1-Iaugmin913x7 (=0-G Bb B D F# Eb =1-G B D# 0-Ab C E) - (S)
0,1,3 - 0-id6maj7x3,5 1-imin9x3,5 3-i9x5,7 (=0-G E F# =1-G F 0-Ab =3-G 0-Bb A) - (good: Ab G F)
0,1,3,10 - 0-imaj713x3,5,11 1-imin9x5 3-i11x5,7 10-i13x3,9,11 (=0-G F# A E =1-G Bb F 0-Ab =3-G 0-Bb A C =10-G D 0-F E)
0,1,3,9 - 0-id6maj7x5 1-Imin9x5 3-id9x7 9-id6min13x3,7,9,11 9-iaugmaj1113x3,7,9 (=0-G Bb E F# =1-G B F 0-Ab =3-G 0-Bb Db A =9-G Db 0-E Eb =9-G D# C# 0-E) - (good: G F B Ab, G F Ab B)
0,1,3,8 - 0-Imaj713x5,9,11 1-imin911x3,5 3-i9x7 8-imin13x3,7,9 (=0-G B F# E =1-G F 0-Ab C =3-G 0-Bb D A =8-G D C 0-Eb)
0,1,3,8,10 - 0-Imaj713x5,11 1-imin911x5 3-i11x7 8-imin13x3,9 10-i13x3,11 (=0-G B F# A E =1-G Bb F 0-Ab C =3-G 0-Bb D A C =8-G D F C 0-Eb 10-G D 0-F A E)
0,1,3,8,9 - 0-id6maj7s3 0-imaj713x5,9,11s3 1-Imin911x5 3-id9x7s5 3-imaj11x7 8-imaj7min13x3,9 9-id6min9min13x3,7,11 9-iaugmin9maj1113x3,7 (=0-G Bb B E F# =0-G Bb B F# E =1-G B F 0-Ab C =3-G 0-Bb Db D A =3-G 0-Bb D A C# =8-G D F# C 0-Eb =9-G Db 0-E Ab Eb =9-G D# Ab C# 0-E)
0,1,3,7 - 0-imaj713x3,5,9 1-idmin9x3 3-imin13x5,7,11 7-Imaj11x7,9 (=0-G F# C E =1-G Db F 0-Ab =3-G 0-Bb A Eb =7-G B 0-D C#)
0,1,3,7,10 - idmin9 - M
0,1,3,7,9 - 0-imaj713x5,9 1-idmin9x3s3 3-idmin13x7,11 7-Imaj11x9 9-iaugmaj1113x3,7 (=0-G Bb F# C E =1-G B Db F 0-Ab =3-G 0-Bb Db A Eb =7-G B 0-D F C# =9-G D# A C# 0-E) (good: G B C# D F)
0,1,3,7,8 - 0-Imaj713x5,9 1-idmin911x3 3-imin13x7,11 7-Imaj7maj11x9 8-imin9min13x3,7 (=0-G B F# C E =1-G Db F 0-Ab C =3-G 0-Bb D A Eb =7-G B 0-D F# C# =8-G D Ab C 0-Eb)
0,1,3,6 - imin9x3 - M
0,1,3,6,10 - imin9 - M
0,1,3,6,9 - 0-id6maj7 1-Imin9 3-id69 6-id611 9-id6min13 (=0-G Bb Db E F# =1-G B D F 0-Ab =3-G 0-Bb Db E A =6-G Bb 0-Db E C =9-G Bb Db 0-E Eb)
0,1,3,6,8 - 0-Imaj7maj1113x5,9 0-id6maj7x3s3 1-imin911x3 3-i13x7,11 6-id11x9 8-imin13x3,7 (=0-G B F# C# E =0-G B Db E F# =1-G D F 0-Ab C =3-G 0-Bb D A E =6-G Bb 0-Db F C =8-G D A C 0-Eb)
0,1,3,6,8,10 - 0-Imaj7maj1113x5 0-id6maj79x3s3 1-imin911 3-i13x7 6-idmin13x9 8-imin13x3 10-I13x11 (=0-G B F# A C# E =0-G B Db E F# A =1-G Bb D F 0-Ab C =3-G 0-Bb D A C E =6-G Bb 0-Db F C Eb =8-G D F A C 0-Eb =10-G B D 0-F A E)
0,1,3,6,8,9 - 0-imaj7maj1113x5,9s3 0-id6maj7s3 1-Imin911 3-imaj1113x7 6-id611x9 8-imaj7min13x3 9-id6min9min13x7,11 (=0-G Bb B F# C# E =0-G Bb B Db E F# =1-G B D F 0-Ab C =3-G 0-Bb D A C# E =6-G Bb 0-Db E F C =8-G D F# A C 0-Eb =9-G Bb Db 0-E Ab Eb)
0,1,3,6,7 - 0-id6maj711x3,9 1-imin9maj11x3 1-idmin9x3s5 3-iaug13x3,7,11smin3 6-idmaj711x9 7-Imin9maj11x7 (=0-G Db E F# C =1-G D F 0-Ab C# =1-G Db D F 0-Ab =3-G 0-Bb D# A E =6-G Bb 0-Db F# C =7-G B 0-D Ab C#)
0,1,3,6,7,10 - 0-id6maj711x3 1-idmin9s5 3-iaug13x3,7smin3 6-idmaj7min13x9 7-Imin9maj1113x7 7-id6min9x3s3,5,7 10-i13x9,11s3 (=0-G Db E F# A C =1-G Bb Db D F 0-Ab =3-G 0-Bb D# A C E =6-G Bb 0-Db F# C Eb =7-G B 0-D Ab C# E =7-G B Db 0-D E Ab =10-G Bb B D 0-F E)
0,1,3,6,7,9 - 0-id6maj711x3 1-Imin9maj11 3-id6min13x7,11 (=0-G Db E F# A C =1-G B D F 0-Ab C# =3-G 0-Bb Db E A Eb) - (S)
0,1,3,5 - i9x5 - M
0,1,3,5,10 - 0-imaj713x3,11 1-imin9min13x5,11 1-iaugmin9x3smin3 3-i11x5 5-I11x7 10-i13x3,9 (=0-G D F# A E =1-G Bb F 0-Ab Eb =1-G Bb D# F 0-Ab =3-G 0-Bb F A C =5-G B D A 0-C =10-G D 0-F C E)
0,1,3,5,9 - 0-imaj713x3,9,11 1-Iaugmin9 3-id9 5-Iaug11x7 9-Iaugmaj1113x7,9 (=0-G Bb D F# E =1-G B D# F 0-Ab =3-G 0-Bb Db F A =5-G B D# A 0-C =9-G B D# C# 0-E)
0,1,3,5,8 - 0-Imaj713x9,11 1-imin9min13x3,5 1-iaugmin911x3 3-i9 5-I13x5,7 8-imin13x7,9 (=0-G B D F# E =1-G F 0-Ab C Eb =1-G D# F 0-Ab C =3-G 0-Bb D F A =5-G B A 0-C E =8-G Bb D C 0-Eb) - (good: Bb G D F A, Bb F A D G, Bb D G A F)
0,1,3,5,8,10 - 0-Imaj713x11 1-imin9min13x5 1-iaugmin911x3smin3 3-i11 5-I13x7 8-imin13x9 10-i13x3 (=0-G B D F# A E =1-G Bb F 0-Ab C Eb =1-G Bb D# F 0-Ab C =3-G 0-Bb D F A C =5-G B D A 0-C E =8-G Bb D F C 0-Eb =10-G D 0-F A C E)
0,1,3,5,8,9 - 0-imaj713x9,11s3 1-Iaugmin911 3-id9s5 5-Iaug13x7 8-imaj7min13x9 9-Iaugmin9maj1113x7 9-id6min9min13x3,7,11s3 (=0-G Bb B D F# E =1-G B D# F 0-Ab C =3-G 0-Bb Db D F A =5-G B D# A 0-C E =8-G Bb D F# C 0-Eb =9-G B D# Ab C# 0-E =9-G B Db E Ab Eb)
0,1,3,5,7 - I11x5 - M
0,1,3,5,7,10 - 0-imaj713x3 1-idmin9min13x11 3-imin13x5 3-iaug11x3smin3 5-I11 7-Imaj1113x7 10-i13x9 (=0-G D F# A C E =1-G Bb Db F 0-Ab Eb =3-G 0-Bb F A C Eb =3-G 0-Bb D# F A C =5-G B D F A 0-C =7-G B 0-D A C# E =10-G Bb D 0-F C E)
0,1,3,5,7,9 - 0-imaj713x9 1-idmin9min13x3,11s3 1-Iaugmin9maj11 3-idmin13x11 5-Iaug11 7-Imaj11 9-Iaugmaj1113x7 (=0-G Bb D F# C E =1-G B Db F 0-Ab Eb =1-G B D# F 0-Ab C# =3-G 0-Bb Db F A Eb =5-G B D# F A 0-C =7-G B 0-D F A C# =9-G B D# A C# 0-E)
0,1,3,5,7,8 - 0-Imaj713x9 1-idmin9min13x3 3-imin13x11 5-I13x5 7-Imaj7maj11 8-imin9min13x7 (=0-G B D F# C E =1-G Db F 0-Ab C Eb =3-G 0-Bb D F A Eb =5-G B F A 0-C E =7-G B 0-D F# A C# =8-G Bb D Ab C 0-Eb)
0,1,3,5,6 - 0-imaj7maj1113x3,9 1-imin9min13x3,11 3-id69x5 3-i13x5,11 5-Imaj711x5 6-idmin911x7 (=0-G D F# C# E =1-G D F 0-Ab Eb =3-G 0-Bb E F A =3-G 0-Bb F A E =5-G B F# A 0-C =6-G Bb 0-Db Ab C)
0,1,3,5,6,10 - 0-imaj7maj1113x3 1-imin9min13x11 3-i13x5 5-Imaj711 6-idmin9min13x7 10-I13x9 (=0-G D F# A C# E =1-G Bb D F 0-Ab Eb =3-G 0-Bb F A C E =5-G B D F# A 0-C =6-G Bb 0-Db Ab C Eb =10-G B D 0-F C E)
0,1,3,5,6,9 - 0-imaj7maj1113x9 1-Imin9min13x11 3-id69 5-Iaugmaj711 6-id6min911x7 9-Iaugmaj1113x7,9smin3 9-id6min13x7,9,11s3 (=0-G Bb D F# C# E =1-G B D F 0-Ab Eb =3-G 0-Bb Db E F A =5-G B D# F# A 0-C =6-G Bb 0-Db E Ab C =9-G Bb B D# C# 0-E =9-G Bb B Db 0-E Eb)
0,1,3,5,6,8 - 0-Imaj7maj1113x9 1-imin9min13x3 3-i13x11 5-Imaj713x5 6-idmin911 8-imin13x7 (=0-G B D F# C# E =1-G D F 0-Ab C Eb =3-G 0-Bb D F A E =5-G B F# A 0-C E =6-G Bb 0-Db F Ab C =8-G Bb D A C 0-Eb)
0,1,3,5,6,8,10 - 0-Imaj7maj1113 1-imin9min13 3-i13 5-Imaj713 6-idmin9min13 8-imin13 10-I13 (=0-G B D F# A C# E =1-G Bb D F 0-Ab C Eb =3-G 0-Bb D F A C E =5-G B D F# A 0-C E =6-G Bb 0-Db F Ab C Eb =8-G Bb D F A C 0-Eb =10-G B D 0-F A C E)
0,1,3,4 - 0-iaugmaj713x3,9,11 1-imin913x3,5,11 3-imaj79x5 4-imin9x5,7s3 (=0-G D# F# E =1-G F 0-Ab E =3-G 0-Bb F# A =4-G Bb 0-B Ab)
0,1,3,4,10 - 0-iaugmaj713x3,11 1-id6min9x5 1-imin913x5,11 3-imaj711x5 4-idmin9dim11x7 4-idmin9x7s3 10-imaj1113x3,9 (=0-G D# F# A E =1-G Bb E F 0-Ab =1-G Bb F 0-Ab E =3-G 0-Bb F# A C =4-G Bb Db Ab 0-B =4-G Bb 0-B Db Ab =10-G D 0-F C# E)
0,1,3,4,9 - 0-iaugmaj713x3,9,11smin3 0-id6maj7min13x5,9,11 1-Imin913x5,11 3-idmaj79 4-imin9dim11x7 4-imin9x7s3 9-id6min13x3,7,9 (=0-G Bb D# F# E =0-G Bb E F# Eb =1-G B F 0-Ab E =3-G 0-Bb Db F# A =4-G Bb D Ab 0-B =4-G Bb 0-B D Ab =9-G Db 0-E C Eb)
0,1,3,4,8 - 0-Iaugmaj713x9,11 1-imin913x3,5 3-imaj79 4-imin9min13x5,7,11s3 4-Iaugmin9x7smin3 8-Imin13x7,9 (=0-G B D# F# E =1-G F 0-Ab C E =3-G 0-Bb D F# A =4-G Bb 0-B Ab Eb =4-G Bb 0-B D# Ab =8-G B D C 0-Eb)
0,1,3,4,8,10 - 0-Iaugmaj713x11 1-imin913x5 3-imaj711 4-idmin9min13x7,11s3 4-Iaugmin9maj11smin3 8-Imin13x9 10-imaj1113x3 (=0-G B D# F# A E =1-G Bb F 0-Ab C E =3-G 0-Bb D F# A C =4-G Bb 0-B Db Ab Eb =4-G Bb 0-B D# Ab C# =8-G B D F C 0-Eb =10-G D 0-F A C# E)
0,1,3,4,8,9 - 0-Iaugmaj713x9,11smin3 0-id6maj7min13x5,9,11s3 1-Imin913x5 3-imaj7maj11 3-idmaj79s5 4-imin9min13x7,11s3 8-Imaj7min13x9 9-id6min9min13x3,7 (=0-G Bb B D# F# E =0-G Bb B E F# Eb =1-G B F 0-Ab C E =3-G 0-Bb D F# A C# =3-G 0-Bb Db D F# A =4-G Bb 0-B D Ab Eb =8-G B D F# C 0-Eb =9-G Db 0-E Ab C Eb)
0,1,3,4,7 - 0-iaugmaj713x3,9 1-id6min9x3 3-imaj7min13x5,11 4-id6min9x5,7s3 7-ids3,5 (=0-G D# F# C E =1-G Db E F 0-Ab =3-G 0-Bb F# A Eb =4-G Bb 0-B E Ab =7-G Bb B Db 0-D)
0,1,3,4,7,10 - 0-iaugmaj713x3 1-id6min9 3-imaj7min13x5 4-id6min9x7s3 7-id6s3,5 10-id67s5 (=0-G D# F# A C E =1-G Bb Db E F 0-Ab =3-G 0-Bb F# A C Eb =4-G Bb 0-B Db E Ab =7-G Bb B Db 0-D E =10-G Bb Db D E 0-F)
0,1,3,4,7,9 - 0-iaugmaj713x3,9smin3 1-idmin913x3,11s3 3-idmaj7min13x11 4-imin913x7,11s3 7-id7s3,5 9-id6min13x3,7 (=0-G Bb D# F# C E =1-G B Db F 0-Ab E =3-G 0-Bb Db F# A Eb =4-G Bb 0-B D Ab E =7-G Bb B Db 0-D F =9-G Db 0-E A C Eb) - (P)
0,1,3,4,7,8 - 0-Iaugmaj713x9 1-idmin913x3 3-imaj7min13x11 4-Iaugmin913x7,11smin3 7-idmaj7s3,5 8-Imin9min13x7 (=0-G B D# F# C E =1-G Db F 0-Ab C E =3-G 0-Bb D F# A Eb =4-G Bb 0-B D# Ab E =7-G Bb B Db 0-D F# =8-G B D Ab C 0-Eb) - (P)
0,1,3,4,7,8,10 - 0-Iaugmaj713 1-idmin913 1-id67min911 3-imaj7min13 4-id6min9min13x7,11s3 7-imaj7maj1113x9s3 8-Imin9min13 10-imaj1113 10-id69s5 (=0-G B D# F# A C E =1-G Bb Db F 0-Ab C E =1-G Bb Db E F 0-Ab C =3-G 0-Bb D F# A C Eb =4-G Bb 0-B Db E Ab Eb =7-G Bb B 0-D F# C# E =8-G B D F Ab C 0-Eb =10-G Bb D 0-F A C# E =10-G Bb Db D E 0-F A) (P)
0,1,3,4,6 - 0-iaugmaj7maj1113x3,9 1-imin913x3,11 3-id6maj79x5 4-imin9x5s3 6-id11x7 (=0-G D# F# C# E =1-G D F 0-Ab E =3-G 0-Bb E F# A =4-G Bb 0-B F Ab =6-G Bb 0-Db A C)
0,1,3,4,6,10 - 0-iaugmaj7maj1113x3 1-imin913x11 3-id6maj711x5 4-idmin9s3 6-idmin13x7 10-Imaj1113x9 (=0-G D# F# A C# E =1-G Bb D F 0-Ab E =3-G 0-Bb E F# A C =4-G Bb 0-B Db F Ab =6-G Bb 0-Db A C Eb =10-G B D 0-F C# E)
0,1,3,4,6,9 - 0-id6maj7min13x9,11 1-Imin913x11 3-id6maj7maj11x5 4-imin9s3 6-id611x7 9-id6min13x7,9 (=0-G Bb Db E F# Eb =1-G B D F 0-Ab E =3-G 0-Bb E F# A C# =4-G Bb 0-B D F Ab =6-G Bb Db E A C =9-G Bb Db 0-E C Eb)
0,1,3,4,6,8 - 0-Iaugmaj7maj1113x9 1-imin913x3 3-imaj713x11 4-imin9min13x5,11s3 6-id11 8-Imin13x7 (=0-G B D# F# C# E =1-G D F 0-Ab C E =3-G 0-Bb D F# A E =4-G Bb 0-B F Ab Eb =6-G Bb 0-Db F A C =8-G B D A C 0-Eb)
0,1,3,4,6,8,10 - 0-Iaugmaj7maj1113 1-imin913 3-imaj713 4-idmin9min13x11s3 6-idmin13 8-Imin13 10-Imaj1113 (=0-G B D# F# A C# E =1-G Bb D F 0-Ab C E =3-G 0-Bb D F# A C E =4-G Bb 0-B Db F Ab Eb =6-G Bb 0-Db F A C Eb =8-G B D F A C 0-Eb =10-G B D 0-F A C# E)
0,1,3,4,6,8,9 - 0-Iaugmaj7maj1113x9smin3 1-Imin913 3-imaj7maj1113 4-imin9min13x11s3 6-id611 8-Imaj7min13 9-id6min9min13x7 (=0-G Bb B D# F# C# E =1-G B D F 0-Ab C E =3-G 0-Bb D F# A C# E =4-G Bb 0-B D F Ab Eb =6-G Bb 0-Db E F A C =8-G B D F# A C 0-Eb =9-G Bb Db 0-E Ab C Eb)
0,1,3,4,6,7 - 0-id6maj7min13x3,9 1-imin9maj1113x3 3-iaugmaj713x3,11smin3 3-id6maj7min13x5,11 4-id6min9x5s3 4-imin913x5,11s3 6-idmaj711 7-imin9maj11x7s3 7-idmin9x7s3,5 (=0-G Db E F# C Eb =1-G D F 0-Ab C# E =3-G 0-Bb D# F# A E =3-G 0-Bb E F# A Eb =4-G Bb 0-B E F Ab =4-G Bb 0-B F Ab E =6-G Bb 0-Db F# A C =7-G Bb B 0-D Ab C# =7-G Bb B Db 0-D Ab)
0,1,3,4,6,7,10 - 0-id6maj7min13x3 1-imin9maj1113 1-id6min9s5 3-iaugmaj713x3smin3 3-id6maj7min13x5 4-imin9maj1113x5s3 4-id6min9s3 6-idmaj7min13 7-imin9maj1113x7s3 7-id6min9x7s3,5 10-imaj1113x9s3 10-id67s3,5 (=0-G Db E F# A C Eb =1-G Bb D F 0-Ab C# E =1-G Bb Db D E F 0-Ab =3-G 0-Bb D# F# A C E =3-G 0-Bb E F# A C Eb =4-G Bb 0-B F Ab C# E =4-G Bb 0-B Db E F Ab =6-G Bb 0-Db F# A C Eb =7-G Bb B 0-D Ab C# E =7-G Bb B Db 0-D E Ab =10-G Bb B D 0-F C# E =10-G Bb B Db D E 0-F)
0,1,3,4,6,7,9 - 0-id6maj7min13x9 1-Imin9maj1113 3-id6maj7min13x11 4-imin913x11s3 6-id6maj711 7-idmin9s3,5 7-imin9maj11s3 9-id6min13x7 (=0-G Bb Db E F# C Eb =1-G B D F 0-Ab C# E =3-G 0-Bb Db E F# A Eb =4-G Bb 0-B D F Ab E =6-G Bb 0-Db E F# A C =7-G Bb B Db 0-D F Ab =7-G Bb B 0-D F Ab C# =9-G Bb Db 0-E A C Eb)
0,1,3,4,6,7,9,10 - 0-id6maj7min13 1-imin9maj1113s3 1-id6min9s3,5 (=0-G Bb Db E F# A C Eb =1-G Bb B D F 0-Ab C# E =1-G Bb B Db D E F 0-Ab) - (S 'sawtooth')
0,1,2 - 0-imaj7x3,5s7 1-imaj7min9x3,5 2-imin9x3,5,7s9 (=0-G F F# =1-G F# 0-Ab =2-G Ab 0-A)
0,1,2,10 - 0-imaj79x3,5s7 1-imaj7min9x5 2-Imin9x5,7s9 10-id6min13x3,5,9,11 (=0-G F F# A =1-G Bb F# 0-Ab =2-G B Ab 0-A =10-G E 0-F Eb) - (good: F# Ab G Bb)
0,1,2,9 - 0-imaj7x5s7 1-Imaj7min9x5 2-imin911x3,5,7s9 9-imin13x3,7,9,11s13 (=0-G Bb F F# =1-G B F# 0-Ab =2-G Ab 0-A C =9-G D Eb 0-E)
0,1,2,9,10 - 0-imaj79x5s7 1-imaj7min9x5s3 2-Imin911x5,7s9 9-imaj7min13x3,9,11s13 10-id6min9min13x3,5,11 (=0-G Bb F F# A =1-G Bb B F# 0-Ab =2-G B Ab 0-A C =9-G D F# Eb 0-E =10-G E 0-F Ab Eb)
0,1,2,8 - 0-Imaj7x5s7 1-imaj7min911x3,5 2-idmin9x3,7s9 8-imaj11min13x3,7,9 (=0-G B F F# =1-G F# 0-Ab C =2-G Db Ab 0-A =8-G D C# 0-Eb)
0,1,2,8,10 - 0-Imaj79x5s7 1-imaj7min911x5 2-Imin9maj11x5,7s9 8-imaj11min13x3,9 10-id6min13x3,5,11 (=0-G B F F# A =1-G Bb F# 0-Ab C =2-G B Ab 0-A C# =8-G D F C# 0-Eb =10-G E 0-F A Eb)
0,1,2,8,9 - 0-imaj7x5s3,7 1-Imaj7min911x5 2-idmin911x3,7s9 8-imaj7maj11min13x3,9 9-imin9min13x3,7,11s13 (=0-G Bb B F F# =1-G B F# 0-Ab C =2-G Db Ab 0-A C =8-G D F# C# 0-Eb =9-G D Ab Eb 0-E)
0,1,2,7 - 0-imaj711x3,5,9s7 1-idmaj7min9x3 2-imin9x3,7s9 7-imin13x3,7,9,11s13 (=0-G F F# C =1-G Db F# 0-Ab =2-G D Ab 0-A =7-G D Eb 0-E)
0,1,2,7,10 - 0-imaj711x3,5s7 1-idmaj7min9 2-Imin9x7s9 7-id611x3,7,9s5 10-id6min13x5,9,11 (=0-G F F# A C =1-G Bb Db F# 0-Ab =2-G B D Ab 0-A =7-G Db 0-D E C =10-G Bb E 0-F Eb)
0,1,2,7,9 - 0-imaj711x5,9s7 1-idmaj7min9x3s3 2-imin911x3,7s9 7-id11x3,9s5 9-imin13x3,7,11s13 (=0-G Bb F F# C =1-G B Db F# 0-Ab =2-G D Ab 0-A C =7-G Db 0-D F C =9-G D A Eb 0-E)
0,1,2,7,9,10 - 0-imaj711x5s7 1-idmaj7min9s3 2-Imin911x7s9 7-id611x3,9s5 9-imaj7min13x3,11s13 10-id6min9min13x5,11 (=0-G Bb F F# A C =1-G Bb B Db F# 0-Ab =2-G B D Ab 0-A C =7-G Db 0-D E F C =9-G D F# A Eb 0-E =10-G Bb E 0-F Ab Eb)
0,1,2,7,8 - 0-Imaj711x5,9s7 1-idmaj7min911x3 2-imin9maj11x3,7s9 7-idmaj711x3,9s5 8-idmin9min13x3,7,11s5 (=0-G B F F# C =1-G Db F# 0-Ab C =2-G D Ab 0-A C# =7-G Db 0-D F# C =8-G Db D Ab 0-Eb)
0,1,2,7,8,10 - 0-Imaj711x5s7 1-idmaj7min911 2-Imin9maj11x7s9 7-id6maj711x3,9s5 8-idmin9min13x3,11s5 10-id6min13x5,11 (=0-G B F F# A C =1-G Bb Db F# 0-Ab C =2-G B D Ab 0-A C# =7-G Db 0-D E F# C =8-G Db D F Ab 0-Eb =10-G Bb E 0-F A Eb)
0,1,2,6 - 0-idmaj7x3s7 1-imaj7min9x3 2-iaugmin9x3,7s9 6-id11x3,7,9s3 (=0-G Db F F# =1-G D F# 0-Ab =2-G D# Ab 0-A =6-G B 0-Db C)
0,1,2,6,10 - 0-idmaj79x3s7 1-imaj7min9 2-Iaugmin9x7s9 6-idmin13x3,7,9s3 10-id6min13x3,5,9,11s3 (=0-G Db F F# A =1-G Bb D F# 0-Ab =2-G B D# Ab 0-A =6-G B 0-Db C Eb =10-G B E 0-F Eb)
0,1,2,6,9 - 0-idmaj7s7 1-Imaj7min9 2-iaugmin911x3,7s9 6-id611x3,7,9s3 9-imin13x7,9,11s13 (=0-G Bb Db F F# =1-G B D F# 0-Ab =2-G D# Ab 0-A C =6-G B Db E C =9-G Bb D Eb 0-E)
0,1,2,6,9,10 - 0-idmaj79s7 1-imaj7min9s3 2-Iaugmin911x7s9 6-id6min13x3,7,9s3 9-imaj7min13x9,11s13 10-id6min9min13x3,5,11s3 (=0-G Bb Db F F# A =1-G Bb B D F# 0-Ab =2-G B D# Ab 0-A C =6-G B 0-Db E C Eb =9-G Bb D F# Eb 0-E =10-G B E 0-F Ab Eb)
0,1,2,6,8 - 0-idmaj7x3s3,7 1-imaj7min911x3 2-idmin9min13x3,7,11s9 6-id11x3,9s3 8-idmin13x3,7,11s5 (=0-G B Db F F# =1-G D F# 0-Ab C =2-G Db Ab 0-A Eb =6-G B 0-Db F C =8-G Db D A 0-Eb)
0,1,2,6,8,10 - 0-idmaj79x3s3,7 1-imaj7min911 2-Iaugmin9maj11x7s9 6-Iaugmaj11x9,11s11 8-imaj11min13x3 10-id6min13x3,5,11s3 (=0-G B Db F F# A =1-G Bb D F# 0-Ab C =2-G B D# Ab 0-A C# =6-G B D# F C 0-C# =8-G D F A C# 0-Eb =10-G B E 0-F A Eb)
0,1,2,6,8,9 - 0-idmaj7s3,7 1-Imaj7min911 2-idmin9min13x3,7s9 6-id611x3,9s3 8-idmaj7min13x3,11s5 9-imin9min13x7,11s13 (=0-G Bb B Db F F# =1-G B D F# 0-Ab C =2-G Db Ab 0-A C Eb =6-G B 0-Db E F C =8-G Db D F# A 0-Eb 9-G Bb D Ab Eb 0-E)
0,1,2,6,7 - 0-idmaj711x3,9s7 1-imaj7min9maj11x3 2-imin9min13x3,7,11s9 6-idmaj711x3,9s3 7-idmin911x3,7s5 (=0-G Db F F# C =1-G D F# 0-Ab C# =2-G D Ab 0-A Eb =6-G B 0-Db F# C =7-G Db 0-D Ab C)
0,1,2,6,7,10 - 0-idmaj711x3s7 1-imaj7min9maj11 2-Imin9min13x7,11s9 6-idmaj7min13x3,9s3 7-idmin9min13x3,7s5 10-id6min13x5,9,11s3 (=0-G Db F F# A C =1-G Bb D F# 0-Ab C# =2-G B D Ab 0-A Eb =6-G B 0-Db F# C Eb =7-G Db 0-D Ab C Eb =10-G Bb B E 0-F Eb)
0,1,2,6,7,9 - 0-idmaj711x9s7 1-Imaj7min9maj11 2-imin9min13x3,7s9 6-id6maj711x3,9s3 7-idmin911x3s5 9-imin13x7,11s13 (=0-G Bb Db F F# C =1-G B D F# 0-Ab C# =2-G D Ab 0-A C Eb =6-G B 0-Db E F# C =7-G Db 0-D F Ab C =9-G Bb D A Eb 0-E)
0,1,2,6,7,9,10 - 0-idmaj711s7 1-imaj7min9maj11s3 2-Imin9min13x7s9 6-id6maj7min9x3,9s3 7-id6min911s5 9-imaj7min13x11s13 10-id6min9min13x5,11s3 (=0-G Bb Db F F# A C =1-G Bb B D F# 0-Ab C# =2-G B D Ab 0-A C Eb =6-G B 0-Db E F# C Eb =7-G Db 0-D E F Ab C =9-G Bb D F# A Eb 0-E =10-G Bb B E 0-F Ab Eb) - (good: G B D F# Bb C# Ab)
0,1,2,6,7,8 - 0-idmaj711x3,9s3,7 1-idmaj7min911x3s5 2-imin9maj11min13x3,7s9 (=0-G B Db F F# C =1-G Db D F# 0-Ab C =2-G D Ab 0-A C# Eb) - (S)
0,1,2,5 - 0-imaj7x3s7 1-imaj7min9min13x3,5,11 2-imin913x3,5,7,11s9 5-i11x5,7,9s3 (=0-G D F F# =1-G F# 0-Ab Eb =2-G Ab 0-A E =5-G Bb B 0-C)
0,1,2,5,10 - 0-imaj79x3s7 1-imaj7min9min13x5,11 2-Imin913x5,7,11s9 5-i11x7,9s3 10-id6min13x3,5,9 (=0-G D F F# A =1-G Bb F# 0-Ab Eb =2-G B Ab 0-A E =5-G Bb B D 0-C =10-G E 0-F C Eb)
0,1,2,5,9 - 0-imaj7s7 1-Imaj7min9min13x5,11 2-imin913x3,5,7s9 5-imin13x5,7,9s3 9-Imin13x7,9,11s13 (=0-G Bb D F F# =1-G B F# 0-Ab Eb =2-G Ab 0-A C E =5-G Bb B 0-C Eb =9-G B D Eb 0-E)
0,1,2,5,9,10 - 0-imaj79s7 1-imaj7min9min13x5,11s3 2-Imin913x5,7s9 5-imin13x7,9s3 9-Imaj7min13x9,11s13 10-id6min9min13x3,5 (=0-G Bb D F F# A =1-G Bb B F# 0-Ab Eb =2-G B Ab 0-A C E =5-G Bb B D 0-C Eb =9-G B D F# Eb 0-E =10-G E 0-F Ab C Eb)
0,1,2,5,8 - 0-Imaj7s7 1-imaj7min9min13x3,5 2-id6min9x3,7s9 5-i13x5,7,9s3 8-idmin13x7,9,11s5 (=0-G B D F F# =1-G F# 0-Ab C Eb =2-G Db E Ab 0-A =5-G Bb B 0-C E =8-G Bb Db D 0-Eb)
0,1,2,5,8,10 - 0-Imaj79s7 1-imaj7min9min13x5 2-id6min9x3,7s3,9 5-i13x7,9s3 8-idmin13x9,11s5 10-id6min13x3,5 (=0-G B D F F# A =1-G Bb F# 0-Ab C Eb =2-G B Db E Ab 0-A =5-G Bb B D 0-C E =8-G Bb Db D F 0-Eb =10-G E 0-F A C Eb)
0,1,2,5,8,9 - 0-imaj7s3,7 1-Imaj7min9min13x5 2-id6min911x3,7s9 5-Iaug13x7,9smin3 8-idmaj7min13s5 9-Imin9min13x7,11s13 (=0-G Bb B D F F# =1-G B F# 0-Ab C Eb =2-G Db E Ab 0-A C =5-G Bb B D# 0-C E =8-G Bb Db D F# 0-Eb =9-G B D Ab Eb 0-E)
0,1,2,5,7 - 0-imaj711x3,9s7 1-idmaj7min9min13x3,11 2-imin913x3,7,11s9 5-i11x5,9s3 7-id11x3,7s5 (=0-G D F F# C =1-G Db F# 0-Ab Eb =2-G D Ab 0-A E =5-G Bb B F 0-C =7-G Db 0-D A C)
0,1,2,5,7,10 - 0-imaj711x3s7 1-idmaj7min9min13x11 2-Imin913x7,11s9 5-i11x9s3 7-id611x3,7s5 10-id6min13x5,9 (=0-G D F F# A C =1-G Bb Db F# 0-Ab Eb =2-G B D Ab 0-A E =5-G Bb B D F 0-C =7-G Db 0-D E A C =10-G Bb E 0-F C Eb)
0,1,2,5,7,9 - 0-imaj711x9s7 1-idmaj7min9min13x3,11s3 2-imin913x3,7s9 5-Iaug11x9smin3 7-id11x3s5 9-Iaug13x7,11s5 (=0-G Bb D F F# C =1-G B Db F# 0-Ab Eb =2-G D Ab 0-A C E =5-G Bb B D# F 0-C =7-G Db 0-D F A C =9-G B D D# A 0-E)
0,1,2,5,7,9,10 - 0-imaj711s7 1-idmaj7min9min13x11s3 2-Imin9x7s9 5-imin13x9s3 7-id611x3s5 9-Imaj7min13x11s13 10-id6min9min13x5 (=0-G Bb D F F# A C =1-G Bb B Db F# 0-Ab Eb =2-G B D Ab 0-A C E =5-G Bb B D F 0-C Eb =7-G Db 0-D E F A C =9-G B D F# A Eb 0-E =10-G Bb E 0-F Ab C Eb)
0,1,2,5,7,8 - 0-Imaj7x9s7 1-idmaj7min9min13x3 2-imin9maj1113x3s9 5-i13x5,9s3 7-idmaj711x3s5 8-imin9maj11min13x7 (=0-G B D F F# C =1-G Db F# 0-Ab C Eb =2-G D Ab 0-A C# E =5-G Bb B F 0-C E =7-G Db 0-D F# A C =8-G Bb D Ab C# 0-Eb)
0,1,2,5,7,8,10 - 0-Imaj711s7 1-idmaj7min9min13 2-Imin9maj1113x7s9 5-i13x9s3 7-id6maj711x3s5 8-idmin9min13x11s5 10-id6min13x5 (=0-G B D F F# A C =1-G Bb Db F# 0-Ab C Eb =2-G B D Ab 0-A C# E =5-G Bb B D F 0-C E =7-G Db 0-D E F# A C =8-G Bb Db D F Ab 0-Eb =10-G Bb E 0-F A C Eb)
0,1,2,5,6 - 0-idmaj7x3s5,7 1-imaj7min9min13x3,11 2-iaugmin913x3,7,11s9 5-imaj711x5,9s3 6-idmin911x3,7s3 (=0-G Db D F F# =1-G D F# 0-Ab Eb =2-G D# Ab 0-A E =5-G Bb B F# 0-C =6-G B 0-Db Ab C)
0,1,2,5,6,10 - 0-imaj7maj11x3s7 1-imaj7min9min13x11 2-Iaugmin913x7,11s9 5-imaj711x9s3 6-idmin9min13x3,7s3 10-id6min13x3,5,9s3 (=0-G D F F# A C# =1-G Bb D F# 0-Ab Eb =2-G B D# Ab 0-A E =5-G Bb B D F# 0-C =6-G B 0-Db Ab C Eb =10-G B E 0-F C Eb)
0,1,2,5,6,9 - 0-imaj7maj11x9s7 1-Imaj7min9min13x11 2-iaugmin913x3,7s9 5-Iaugmaj711x9smin3 6-id6min911x3,7s3 9-imin13x7,9,11s3,13 (=0-G Bb D F F# C# =1-G B D F# 0-Ab Eb =2-G D# Ab 0-A C E =5-G Bb B D# F# 0-C =6-G B 0-Db E Ab C =9-G Bb B D Eb 0-E)
0,1,2,5,6,9,10 - 0-imaj7maj11s7 1-imaj7min9min13x11s3 2-Iaugmin913x7s9 5-imaj7min13x9s3 6-id6min9min13x3,7s3 9-imaj7min13x9,11s3,13 10-id6min9min13x3,5s3 (=0-G Bb D F F# A C# =1-G Bb B D F# 0-Ab Eb =2-G B D# Ab 0-A C E =5-G Bb B D F# 0-C Eb =6-G B 0-Db E Ab C Eb =9-G Bb B D F# Eb 0-E =10-G B E 0-F Ab C Eb)
0,1,2,5,6,8 - 0-Imaj7maj11x9s7 1-imaj7min9min13x3 2-id6min9min13x3,7,11s9 5-imaj713x5,9s3 6-idmin911x3s3 8-imaj11min13x7 (=0-G B D F F# C# =1-G D F# 0-Ab C Eb =2-G Db E Ab 0-A Eb =5-G Bb B F# 0-C E =6-G B Db F Ab C =8-G Bb D A C# 0-Eb)
0,1,2,5,6,8,10 - 0-Imaj7maj11s7 1-imaj7min9min13 2-id6min9min13x3,7,11s3,9 5-imaj713x9s3 6-idmin9min13x3s3 8-imaj11min13 10-id6min13x3,5s3 (=0-G B D F F# A C# =1-G Bb D F# 0-Ab C Eb =2-G B Db E Ab 0-A Eb =5-G Bb B D F# 0-C E =6-G B 0-Db F Ab C Eb =8-G Bb D F A C# 0-Eb =10-G B E 0-F A C Eb)
0,1,2,5,6,8,9 - 0-imaj7maj11x9s3,7 1-Imaj7min9min13 2-id6min9min13x3,7s9 5-Iaugmaj713x9smin3 6-id6min911x3s3 8-imaj7maj11min13 9-imin9min13x7,11s3,13 (=0-G Bb B D F F# C# =1-G B D F# 0-Ab C Eb =2-G Db E Ab 0-A C Eb =5-G Bb B D# F# 0-C E =6-G B 0-Db E F Ab C =8-G Bb D F# A C# 0-Eb =9-G Bb B D Ab Eb 0-E)
0,1,2,5,6,7 - 0-idmaj711x9s5,7 1-idmaj7min9min13x3,11s5 2-imin9min13x3,7,11s9,13 5-imaj711x5,9s3,7 6-idmin911x3s3 7-imin9maj11x3,7s9,11 (=0-G Db D F F# C =1-G Db D F# 0-Ab Eb =2-G D Ab 0-A Eb E =5-G Bb B F F# 0-C =6-G B 0-Db F Ab C =7-G 0-D Ab A C C#)
0,1,2,5,6,7,10 - 0-imaj7maj11x3s7,11 1-idmaj7min9min13x11s5 2-Imin9min13x7,11s9,13 5-imaj711x9s3,7 6-idmaj7min9min13x3s3 7-id6min911x3,7s5,9 10-id6min13x5,9s3 (=0-G D F F# A C C# =1-G Bb Db D F# 0-Ab Eb =2-G B D Ab 0-A Eb E =5-G Bb B D F F# 0-C =6-G B 0-Db F# Ab C Eb =7-G Db 0-D E Ab A C =10-G Bb B E 0-F C Eb)
0,1,2,4 - 0-iaugmaj7x3s7 1-imaj7min913x3,5,11 2-imin9x3,5s9 4-i9x5,7s3 (=0-G D# F F# =1-G F# 0-Ab E =2-G F Ab 0-A =4-G Bb 0-B A)
0,1,2,4,10 - 0-iaugmaj79x3s7 1-imaj7min913x5,11 2-Imin9x5s9 4-id9x7s3 10-id6min13x3,9,11 (=0-G D# F F# A =1-G Bb F# 0-Ab E =2-G B F Ab 0-A =4-G Bb 0-B Db A =10-G Db E 0-F Eb)
0,1,2,4,9 - 0-iaugmaj7x3smin3,7 1-Imaj7min913x5,11 2-imin911x3,5s9 4-i9x7s3 9-imin13x3,7,9s13 (=0-G Bb D# F F# =1-G B F# 0-Ab E =2-G F Ab 0-A C =4-G Bb 0-B D A =9-G D C Eb 0-E)
0,1,2,4,9,10 - 0-iaugmaj79smin3 1-imaj7min913x5,11s3 2-Imin911x5s9 4-imaj11x7s3 9-imaj7min13x3,9s13 10-id6min9min13x3,11 (=0-G Bb D# F F# A =1-G Bb B F# 0-Ab E =2-G B F Ab 0-A C =4-G Bb 0-B D A C# =9-G D F# C Eb 0-E =10-G Db E 0-F Ab Eb)
0,1,2,4,8 - 0-Iaugmaj7s7 1-imaj7min913x3,5 2-idmin9x3s9 4-Iaug9x7smin3 8-Imaj11min13x7,9 (=0-G B D# F F# =1-G F# 0-Ab C E =2-G Db F Ab 0-A =4-G Bb 0-B D# A =8-G B D C# 0-Eb)
0,1,2,4,8,10 - 0-Iaugmaj79s7 1-imaj7min913x5 2-idmin9x3s3,9 4-idmin13x7,11s3 9-Imaj11min13x9 10-id6min13x3,11 (=0-G B D# F F# A =1-G Bb F# 0-Ab C E =2-G B Db F Ab 0-A =4-G Bb 0-B Db A Eb =9-G B D F C# 0-Eb =10-G Db E 0-F A Eb)
0,1,2,4,8,9 - 0-Iaugmaj7smin3,7 1-Imaj7min913x5 2-idmin911x3s9 4-imin13x7,11s3 8-Imaj7maj11min13x9 9-imin9min13x3,7s13 (=0-G Bb B D# F F# =1-G B F# 0-Ab C E =2-G Db F Ab 0-A C =4-G Bb 0-B D A Eb =8-G B D F# C# 0-Eb =9-G D Ab C Eb 0-E)
0,1,2,4,7 - 0-iaugmaj711x3,9s7 1-idmaj7min913x3,11 2-imin9x3s9 4-id69x5,7s3 7-id11x7,9s5 (=0-G D# F F# C =1-G Db F# 0-Ab E =2-G D F Ab 0-A =4-G Bb 0-B E A =7-G Bb Db 0-D C)
0,1,2,4,7,10 - 0-iaugmaj711x3s7 1-idmaj7min913x11 2-Imin9s9 4-id69x7s3 7-id611x7,9s5 10-id6min13x9,11 (=0-G D# F F# A C =1-G Bb Db F# 0-Ab E =2-G B D F Ab 0-A =4-G Bb 0-B Db E A =7-G Bb Db 0-D E C =10-G Bb Db E 0-F Eb)
0,1,2,4,7,9 - 0-iaugmaj711x3,9smin3,7 1-idmaj7min913x3,11s3 2-imin911x3s9 4-i13x7,11s3 7-id11x9s5 9-imin13x3,7s13 (=0-G Bb D# F F# C =1-G B Db F# 0-Ab E =2-G D F Ab 0-A C =4-G Bb 0-B D A E =7-G Bb Db 0-D F C =9-G D A C Eb 0-E)
0,1,2,4,7,9,10 - 0-iaugmaj711x3smin3,7 1-idmaj7min913x11s3 2-Imin911s9 4-imaj1113x7s3 7-id611x9s5 9-imaj7min13x3s13 10-id6min9min13x11 (=0-G Bb D# F F# A C =1-G Bb B Db F# 0-Ab E =2-G B D F Ab 0-A C =4-G Bb 0-B D A C# E =7-G Bb Db 0-D E F C =9-G D F# A C Eb 0-E =10-G Bb Db E 0-F Ab Eb)
0,1,2,4,7,8 - 0-Iaugmaj711x9s7 1-idmaj7min913x3 2-imin9maj11x3s9 4-iaug13x7,11smin3 7-idmaj711x9s5 8-Imin9maj11min13 (=0-G B D# F F# C =1-G Db F# 0-Ab C E =2-G D F Ab 0-A C# =4-G Bb 0-B D# A E =7-G Bb Db 0-D F# C =8-G B D Ab C# 0-Eb)
0,1,2,4,7,8,10 - 0-Iaugmaj711s7 1-idmaj7min913 2-Imin9maj11s9 4-id6min13x7,11s3 4-Iaugmaj1113x7smin3 7-id6maj711x9s5 8-Imin9maj11min13 10-id6min13x11 (=0-G B D# F F# A C =1-G Bb Db F# 0-Ab C E =2-G B D F Ab 0-A C# =4-G Bb 0-B Db E A Eb =4-G Bb 0-B D# A C# E =7-G Bb Db 0-D E F# C =8-G B D F Ab C# 0-Eb =10-G Bb Db E 0-F A Eb)
0,1,2,4,7,8,9 - 0-Iaugmaj711x9smin3 1-idmaj7min913x3s3 2-idmin911x3s5,9 4-imin13x7,11s3,13 7-idmaj711x9s5,7 8-Imaj7min9maj11min13 9-imin9min13x3,7s9,13 (=0-G Bb B D# F F# C =1-G B Db F# 0-Ab C E =2-G Db D F Ab 0-A C =4-G Bb 0-B D A Eb E =7-G Bb Db 0-D F F# C =8-G B D F# Ab C# 0-Eb =9-G D Ab A C Eb 0-E)
0,1,2,4,6 - 0-idmaj7min13x3,9,11s7 0-iaugmaj7maj11x3,9s7 1-imaj7min913x3,11 2-iaugmin9x3s9 4-i9x5s3 6-id11x3,7s3 (=0-G Db F F# Eb =0-G D# F F# C# =1-G D F# 0-Ab E =2-G D# F Ab 0-A =4-G Bb 0-B F A =6-G B 0-Db A C)
0,1,2,4,6,10 - 0-idmaj7min13x3,11s7 0-iaugmaj7maj11x3s7 1-imaj7min913x11 2-Iaugmin9s9 4-id9s3 6-Iaugmaj11x7s11 6-idmin13x3,7s3 10-id6min13x3,9,11s3 (=0-G Db F F# A Eb =0-G D# F F# A C# =1-G Bb D F# 0-Ab E =2-G B D# F Ab 0-A =4-G Bb 0-B Db F A =6-G B D# A C 0-C# =6-G B Db A C Eb =10-G B Db E 0-F Eb)
0,1,2,4,6,9 - 0-idmaj7min13x9,11s7 1-Imaj7min913x11 2-iaugmin911x3s9 4-i9s3 6-id611x3,7s3 9-imin13x7,9s13 (=0-G Bb Db F F# Eb =1-G B D F# 0-Ab E =2-G D# F Ab 0-A C =4-G Bb 0-B D F A =6-G B 0-Db E A C =9-G Bb D C Eb 0-E)
0,1,2,4,6,9,10 - 0-idmaj7min13x11s7 1-imaj7min913x11s3 2-Iaugmin911s9 4-imaj11s3 6-id6min13x3,7s3 9-imaj7min13x9s13 10-id6min9min13x3,11s3 (=0-G Bb Db F F# A Eb =1-G Bb B D F# 0-Ab E =2-G B D# F Ab 0-A C =4-G Bb 0-B D F A C# =6-G B 0-Db E A C Eb =9-G Bb D F# C Eb 0-E =10-G B Db E 0-F Ab Eb)
0,1,2,4,6,8 - 0-idmaj7min13x3,9,11s3,7 0-Iaugmaj7maj11x9s7 1-imaj7min913x3 2-idmin9min13x3,11s9 2-Iaugmin9maj11x3s9 4-Iaug9smin3 6-id11x3s3 8-idmin13x3,7,11s3,5 8-Imaj11min13x7 (=0-G B Db F F# Eb =0-G B D# F F# C# =1-G D F# 0-Ab C E =2-G Db F Ab 0-A Eb =2-G D# F Ab 0-A C# =4-G Bb 0-B D# F A =6-G B 0-Db F A C =8-G B Db D A 0-Eb =8-G B D A C# 0-Eb)
0,1,2,4,6,8,10 - 0-Iaugmaj7maj11s7 0-idmaj7min13x3,11s3,7 1-imaj7min913 2-Iaugmin9maj11s9 2-idmin9min13x3,11s3,9 4-Iaugmaj11smin3 4-idmin13x11s3 6-idmin13x3s3 8-Imaj11min13 10-id6min13x3,11s3 (=0-G B D# F F# A C# =0-G B Db F F# A Eb =1-G Bb D F# 0-Ab C E =2-G B D# F Ab 0-A C# =2-G B Db F Ab 0-A Eb =4-G Bb 0-B D# F A C# =4-G Bb 0-B Db F A Eb =6-G B 0-Db F A C Eb =8-G B D F A C# 0-Eb =10-G B Db E 0-F A Eb)
0,1,2,4,6,8,9 - 0-idmaj7min13x9,11s3,7 0-Iaugmaj7maj11x9smin3,7 1-Imaj7min913 2-idmin9min13x3s9 4-imin13x11s3 6-id611x3s3 8-Imaj7maj11min13 9-imin9min13x7s13 (=0-G Bb B Db F F# Eb =0-G Bb B D# F F# C# =1-G B D F# 0-Ab C E =2-G Db F Ab 0-A C Eb =4-G Bb 0-B D F A Eb =6-G B 0-Db E F A C =8-G B D F# A C# 0-Eb =9-G Bb D Ab C Eb 0-E)
0,1,2,4,6,7 - 0-idmaj7min13x3,9s7 1-idmaj7min913x3,11s5 2-imin9min13x3,11s9 4-i13x5,11s3 6-idmaj711x3 7-idmin911x7s5 (=0-G Db F F# C Eb =1-G Db D F# 0-Ab E =2-G D F Ab 0-A Eb =4-G Bb 0-B F A E =6-G B 0-Db F# A C =7-G Bb Db 0-D Ab C)
0,1,2,4,6,7,10 - 0-idmaj7min13x3s7 1-idmaj7min913x11s5 2-Imin9min13x11s9 4-id69s3 6-idmaj7min13x3s3 7-id6min911x7s5 10-id6min13x9,11s3 (=0-G Db F F# A C Eb =1-G Bb Db D F# 0-Ab E =2-G B D F Ab 0-A Eb =4-G Bb 0-B Db E F A =6-G B 0-Db F# A C Eb =7-G Bb Db 0-D E Ab C =10-G Bb B Db E 0-F Eb)
0,1,2,4,6,7,9 - 0-idmaj7min13x9s7 1-idmaj7min913x3,11s3,5 2-imin9min13x3s9 4-i13x11s3 6-id6maj711x3s3 7-idmin911s5 9-imin13x7s13 (=0-G Bb Db F F# C Eb =1-G B Db D F# 0-Ab E =2-G D F Ab 0-A C Eb =4-G Bb 0-B D F A E =6-G B 0-Db E F# A C =7-G Bb Db 0-D F Ab C =9-G Bb D A C Eb 0-E)
0,1,2,4,6,7,9,10 - 0-idmaj7min13s7 1-idmaj7min913x11s3,5 2-Imin9min13s9 4-imaj1113s3 6-id6maj7min13x3s3 6-Iaugmaj7maj1113s11 7-id6min911s5 7-imin9maj1113s11 9-imaj7min13s13 10-id6min9min13x11s3 (=0-G Bb Db F F# A C Eb =1-G Bb B Db D F# 0-Ab E =2-G B D F Ab 0-A C Eb =4-G Bb 0-B D F A C# E =6-G B 0-Db E F# A C Eb =6-G B D# F# A C C# E =7-G Bb Db 0-D E F Ab C =7-G Bb 0-D F Ab C C# E =9-G Bb D F# A C Eb 0-E =10-G Bb B Db E 0-F Ab Eb) - (good: G B D F# Bb Db E Ab)
0,1,2,4,6,7,8 - 0-idmaj7min13x3,9s3,7 0-Iaugmaj7maj11x9s7,11 1-idmaj7min913x3s5 2-imin9maj11min13x3s9 4-Iaug13x11smin3 6-idmaj711x3s3,7 7-idmaj7min911s5 -Imin9maj11min13x7s9 (=0-G B Db F F# C Eb =0-G B D# F F# C C# =1-G Db D F# 0-Ab C E =2-G D F Ab 0-A C# Eb =4-G Bb 0-B D# F A E =6-G B 0-Db F F# A C =7-G Bb Db 0-D F# Ab C =8-G B D Ab A C# 0-Eb)
0,1,2,4,6,7,8,10 - 0-Iaugmaj7maj11s7,11 0-idmaj7min13x3s3,7 1-idmaj7min913s5 1-id6maj7min911s5 1-imaj7min9maj1113s11 2-Imin9maj11min13s9 4-id6min13x11s3 (=0-G B D# F F# A C C# =0-G B Db F F# A C Eb =1-G Bb Db D F# 0-Ab C E =1-G Bb Db D E F# 0-Ab C =1-G Bb D F# 0-Ab C C# E =2-G B D F Ab 0-A C# Eb =4-G Bb 0-B Db E F A Eb) (S)
0,1,2,4,5 - 0-imaj7min13x3,9,11s7 1-iaugmaj7min913x3,11 2-imin913x3,5,11s9 4-imaj79x5s3 5-imin911x5,7s3 (=0-G D F F# Eb =1-G D# F# 0-Ab E =2-G F Ab 0-A E =4-G Bb 0-B F# A =5-G Bb B Ab 0-C)
0,1,2,4,5,10 - 0-imaj7min13x3,11s7 1-iaugmaj7min913x3,11smin3 2-Imin913x5,11s9 4-idmaj79s3 5-imin911x7,11s3 10-id6min13x3,9 (=0-G D F F# A Eb =1-G Bb D# F# 0-Ab E =2-G B F Ab 0-A E =4-G Bb 0-B Db F# A =5-G Bb B D Ab 0-C =10-G Db E 0-F C Eb)
0,1,2,4,5,9 - 0-imaj7min13x9,11s7 1-Iaugmaj7min913x11 2-imin913x3,5s9 4-imaj79s3 5-Iaugmin911x7smin3 9-Imin13x7,9s13 (=0-G Bb D F F# Eb =1-G B D# F# 0-Ab E =2-G F Ab 0-A C E =4-G Bb 0-B D F# A =5-G Bb B D# Ab 0-C =9-G B D C Eb 0-E)
0,1,2,4,5,9,10 - 0-imaj7min13x11s7 1-Iaugmaj7min913x11smin3 2-Imin913x5s9 4-imaj7maj11s3 5-imin9min13x7s3 9-Imaj7min13x9s13 10-id6min9min13x3 (=0-G Bb D F F# A Eb =1-G Bb B D# F# 0-Ab E =2-G B F Ab 0-A C E =4-G Bb 0-B D F# A C# =5-G Bb B D Ab 0-C Eb =9-G B D F# C Eb 0-E =10-G Db E 0-F Ab C Eb)
0,1,2,4,5,8 - 0-Iaugmaj7s5,7 0-Imaj7min13x9,11s7 1-iaugmaj7min913x3 2-id6min9x3s9 4-Iaugmaj79smin3 5-imin913x5,7s3 8-idmin13x7,9,11s3,5 8-imaj11min13x7,9s3 (=0-G B D D# F F# =0-G B D F F# Eb =1-G D# F# 0-Ab C E =2-G Db E F Ab 0-A =4-G Bb 0-B D# F# A =5-G Bb B Ab 0-C E =8-G Bb B Db D 0-Eb =8-G Bb B D C# 0-Eb)
0,1,2,4,5,8,10 - 0-Imaj7min13x11s7 1-iaugmaj7min913x3smin3 2-id6min9x3s3,9 4-idmaj7min13x11s3 4-Iaugmaj7maj11smin3 5-imin913x7s3 8-imaj11min13x9s3 8-Iaugmaj11x9smin3,5 8-idmin13x9,11s3,5 10-id6min13x3 (=0-G B D F F# A Eb =1-G Bb D# F# 0-Ab C E =2-G B Db E F Ab 0-A =4-G Bb 0-B Db F# A Eb =4-G Bb 0-B D# F# A C# =5-G Bb B D Ab 0-C E =8-G Bb B D F C# 0-Eb =8-G Bb B D 0-D# F C# =8-G Bb B Db D F 0-Eb =10-G Db E 0-F A C Eb)
0,1,2,4,5,8,9 - 0-Iaugmaj7smin3,5,7 0-imaj7min13x9,11s3,7 1-Iaugmaj7min913 2-id6min911x3s9 4-imaj7min13x11s3 4-Iaugmaj79smin3,5 5-Iaugmin913x7smin3 8-idmaj7min13x9,11s3,5 8-imaj7maj11min13x9s3 9-Imin9min13x7s13 9-Iaugmin913x7s5 (=0-G Bb B D D# F F# =0-G Bb B D F F# Eb =1-G B D# F# 0-Ab C E =2-G Db E F Ab 0-A C =4-G Bb 0-B D F# A Eb =4-G Bb 0-B D D# F# A =5-G Bb B D# Ab 0-C E =8-G Bb B Db D F# 0-Eb =8-G Bb B D F# C# 0-Eb =9-G B D Ab C Eb 0-E =9-G B D D# Ab C 0-E)
0,1,2,4,5,7 - 0-imaj7min13x3,9s7 0-iaugmaj711x3,9s5,7 1-id6maj7min9min13x11 1-iaugmaj7min9maj1113x3 2-imin913x3,11s9 4-imaj713x5,11s3 5-imin911x5s3 7-id11x7s5 7-imaj11x7s11 (=0-G D F F# C Eb =0-G D D# F F# C =1-G Db E F# 0-Ab Eb =1-G D# F# 0-Ab C# E =2-G D F Ab 0-A E =4-G Bb 0-B F# A E =5-G Bb B F Ab 0-C =7-G Bb Db 0-D A C =7-G Bb 0-D A C C#)
0,1,2,4,5,7,10 - 0-imaj7min13x3s7 1-id6maj7min9min13x11 1-iaugmaj7min9maj1113x3smin3 2-Imin913x11s9 4-id6maj79s3 5-imin911s3 7-id611x7s5 7-imaj1113x7s11 10-id6min13x9 (=0-G D F F# A C Eb =1-G Bb Db E F# 0-Ab Eb =1-G Bb D# F# 0-Ab C# E =2-G B D F Ab 0-A E =4-G Bb 0-B Db E F# A =5-G Bb B D F Ab 0-C =7-G Bb Db 0-D E A C =7-G Bb 0-D A C C# E =10-G Bb Db E 0-F C Eb)
0,1,2,4,5,7,9 - 0-imaj7min13x9s7 1-Iaugmaj7min9maj1113 1-id6maj7min9min13x3,11s3 2-imin913x3s9 4-imaj713x11s3 5-Iaugmin911smin3 7-id11s5 9-Imin13x7s13 9-Iaug13x7s5 (=0-G Bb D F F# C Eb =1-G B D# F# 0-Ab C# E =1-G B Db E F# 0-Ab Eb =2-G D F Ab 0-A C E =4-G Bb 0-B D F# A E =5-G Bb B D# F Ab 0-C =7-G Bb Db 0-D F A C =9-G B D A C Eb 0-E =9-G B D D# A C 0-E)
0,1,2,4,5,7,9,10 - 0-imaj7min13s7 1-id6maj7min9min13x11s3 1-Iaugmaj7min9maj1113smin3 2-Imin913s9 4-id6maj79s3,5 4-imaj7maj1113s3 5-imin9min13s3 7-id611s5 7-imaj1113s11 9-Imaj7min13s13 9-Iaugmaj713s5 10-id6min9min13 (=0-G Bb D F F# A C Eb =1-G Bb B Db E F# 0-Ab Eb =1-G Bb B D# F# 0-Ab C# E =2-G B D F Ab 0-A C E =4-G Bb 0-B Db D E F# A =4-G Bb 0-B D F# A C# E =5-G Bb B D F Ab 0-C Eb =7-G Bb Db 0-D E F A C =7-G Bb 0-D F A C C# E =9-G B D F# A C Eb 0-E =9-G B D D# F# A C 0-E =10-G Bb Db E 0-F Ab C Eb)
0,1,2,4,5,7,8 - 0-Imaj7min13x9s7 1-id6maj7min9min13x3 2-imin9maj1113x3s9 4-Iaugmaj713x11smin3 5-imin913x5s3 7-idmaj711s5 7-imaj7maj11s11 8-idmin9min13x7,11s3,5 8-imin9maj11min13x7s3 8-Iaugmin9maj11x7smin3,5 (=0-G B D F F# C Eb =1-G Db E F# 0-Ab C Eb =2-G D F Ab 0-A C# E =4-G Bb 0-B D# F# A E =5-G Bb B F Ab 0-C E =7-G Bb Db 0-D F# A C =7-G Bb 0-D F# A C C# =8-G Bb B Db D Ab 0-Eb =8-G Bb B D Ab C# 0-Eb =8-G Bb B D 0-D# Ab C#)
0,1,2,4,5,7,8,10 - 0-Imaj7min13s7 1-id6maj7min9min13 2-Imin9maj1113s9 4-id6maj7min13x11s3 4-Iaugmaj7maj1113smin3 5-imin913s3 7-id6maj711s5 8-idmin9min13x11s3,5 8-Iaugmin9maj11smin3,5 8-imin9maj11min13s3 10-id6min13 10-iaugmaj1113x3smin3,11 (=0-G B D F F# A C Eb =1-G Bb Db E F# 0-Ab C Eb =2-G B D F Ab 0-A C# E =4-G Bb 0-B Db E F# A Eb =4-G Bb 0-B D# F# A C# E =5-G Bb B D F Ab 0-C E =7-G Bb Db 0-D E F# A C =8-G Bb B Db D F Ab 0-Eb =8-G Bb B D 0-D# F Ab C# =8-G Bb B D F Ab C# Eb =10-G Bb Db E 0-F A C Eb =10-G Bb D# 0-F A C C# E)
0,1,2,4,5,7,8,9 - 0-imaj7min13x9s3,7 1-id6maj7min9min13x3s3 1-Iaugmaj7min9maj1113s11 2-id6min911x3s5,9 2-imin9maj1113x3s9,11 4-imaj7min13x11s3,13 4-Iaugmaj713x11smin3,5 5-Iaugmin913smin3 7-idmaj711s5,7 7-imaj7maj11s7,11 8-idmaj7min9min13x11s3,5 8-imaj7min9maj11min13s3 9-Imin9min13x7s9,13 9-Iaugmin913x7s5,9 (=0-G Bb B D F F# C Eb =1-G B Db E F# 0-Ab C Eb =1-G B D# F# 0-Ab C C# E =2-G Db D E F Ab 0-A C =2-G D F Ab 0-A C C# E =4-G Bb 0-B D F# A Eb E =4-G Bb 0-B D D# F# A E =5-G Bb B D# F Ab C E =7-G Bb Db 0-D F F# A C =7-G Bb 0-D F F# A C C# =8-G Bb B Db D F# Ab 0-Eb =8-G Bb B D F# Ab C# 0-Eb =9-G B D Ab A C Eb 0-E =9-G B D D# Ab A C 0-E)
0,1,2,4,5,6 - 0-idmaj7min13x3,9,11s5,7 0-imaj7maj11min13x3,9s7 0-iaugmaj7maj11x3,9s5,7 1-imaj7min9min13x3,11s13 1-iaugmaj7min913x3,11s5 2-iaugmin913x3,11s9 4-imaj79x5s3,7 5-imaj7min911x5s3 6-idmin911x3,7s3,9 (=0-G Db D F F# Eb =0-G D F F# C# Eb =0-G D D# F F# C# =1-G D F# 0-Ab Eb E =1-G D D# F# 0-Ab E =2-G D# F Ab 0-A E =4-G Bb 0-B F F# A =5-G Bb B F# Ab 0-C =6-G B 0-Db Ab A C)
0,1,2,4,5,6,10 - 0-idmaj7min13x3,11s5,7 0-iaugmaj7maj11x3s5,7 0-imaj7maj11min13x3s7 1-iaugmaj7min913x3,11smin3,5 1-imaj7min9min13x11s13 2-Iaugmin913x11s9 4-idmaj79s3,7 5-imaj7min911s3 6-idmin9min13x3,7s3,9 6-iaugmin9maj11x7s9,11 10-id6min13x3,9s3 10-iaugmaj1113x9s11 (=0-G Db D F F# A Eb =0-G D D# F F# A C# =0-G D F F# A C# Eb =1-G Bb D D# F# 0-Ab E =1-G Bb D F# 0-Ab Eb E =2-G B D# F Ab 0-A E =4-G Bb 0-B Db F F# A =5-G Bb B D F# Ab 0-C =6-G B 0-Db Ab A C Eb =6-G B D# Ab A C 0-C# =10-G B Db E 0-F C Eb =10-G B D# 0-F C C# E)
0,1,2,4,5,6,9 - 0-idmaj7min13x9,11s5,7 0-imaj7maj11min13x9s7 1-Iaugmaj7min913x11s5 1-Imaj7min9min13x11s13 2-iaugmin913x3s9 4-imaj79s3,7 5-Iaugmaj7min911smin3 6-id6min911x3,7s3,9 9-Iaug13x7,9smin3,5 9-imin13x7,9s3,13 (=0-G Bb Db D F F# Eb =0-G Bb D F F# C# Eb =1-G B D D# F# 0-Ab E =1-G B D F# 0-Ab Eb E =2-G D# F Ab 0-A C E =4-G Bb 0-B D F F# A =5-G Bb B D# F# Ab 0-C =6-G B 0-Db E Ab A C =9-G Bb B D D# C 0-E =9-G Bb B D C Eb 0-E)
0,1,2,4,5,6,9,10 - 0-idmaj7min13x11s5,7 0-imaj7maj11min13s7 1-Iaugmaj7min913x11smin3,5 1-imaj7min9min13x11s3,13 2-Iaugmin913s9 4-imaj7maj11s3,7 5-imaj7min9min13s3 6-id6min9min13x3,7s3,9 6-Iaugmin9maj1113x7s9,11 9-imaj7min13x9s3,13 9-Iaugmaj713x9smin3,5 10-id6min9min13x3s3 10-Iaugmin913s11 (=0-G Bb Db D F F# A Eb =0-G Bb D F F# A C# Eb =1-G Bb B D D# F# 0-Ab E =1-G Bb B D F# 0-Ab Eb E =2-G B D# F Ab 0-A C E =4-G Bb 0-B D F F# A C# =5-G Bb B D F# Ab 0-C Eb =6-G B 0-Db E Ab A C Eb =6-G B D# Ab A C 0-C# E =9-G Bb B D F# C Eb 0-E =9-G Bb B D D# F# C 0-E =10-G B Db E 0-F Ab C Eb =10-G B D# 0-F Ab C C# E)
0,1,2,4,5,6,8 - 0-idmaj7min13x3,9,11s3,5,7 0-Iaugmaj7maj11x9s5,7 0-Imaj7maj11min13x9s7 1-iaugmaj7min913x3s5 1-imaj7min9min13x3s13 2-id6min9min13x3s9 2-iaugmin9maj1113x3s9 4-Iaugmaj79smin3,7 5-imaj7min913x5s3 6-idmin911x3s3,9 8-idmin13x7,11s3,5 8-Iaugmaj11x7smin3,5 8-imaj11min13x7s3 (=0-G B Db D F F# Eb =0-G B D D# F F# C# =0-G B D F F# C# Eb =1-G D D# F# 0-Ab C E =1-G D F# 0-Ab C Eb E =2-G Db E F Ab 0-A Eb =2-G D# F Ab 0-A C# E =4-G Bb 0-B D# F F# A =5-G Bb B F# Ab 0-C E =6-G B 0-Db F Ab A C =8-G Bb B Db D A 0-Eb =8-G Bb B D 0-D# A C# =8-G Bb B D A C# 0-Eb)
0,1,2,4,5,6,8,10 - 0-idmaj7min13x3,11s3,5,7 0-Iaugmaj7maj11s5,7 0-Imaj7maj11min13s7 1-Iaugmaj7min913x3smin3,5 1-imaj7min9min13s13 2-id6min9min13x3,11s3,9 2-Iaugmin9maj1113s9 4-idmaj7min13x11s3,7 4-Iaugmaj7maj11smin3,7 5-imaj7min913s3 6-idmin9min13x3s3,9 6-Iaugmin9maj11s9,11 8-idmin13x11s3,5 8-Iaugmaj11smin3,5 8-imaj11min13s3 10-id6min13x3s3 10-Iaugmaj1113s11 (=0-G B Db D F F# A Eb =0-G B D D# F F# A C# =0-G B D F F# A C# Eb =1-G Bb D D# F# 0-Ab C E =1-G Bb D F# 0-Ab C Eb E =2-G B Db E F Ab 0-A Eb =2-G B D# F Ab 0-A C# E =4-G Bb 0-B Db F F# A Eb =4-G Bb 0-B D# F F# A C# =5-G Bb B D F# Ab 0-C E =6-G B 0-Db F Ab A C Eb =6-G B D# F Ab A C 0-C# =8-G Bb B Db D F A 0-Eb =8-G Bb B D 0-D# F A C# =8-G Bb B D F A C# 0-Eb =10-G B Db E 0-F A C Eb =10-G B D# 0-F A C C# E)
0,1,2,4,5,6,8,9 - 0-idmaj7min13x9,11s3,5,7 0-Iaugmaj7maj11x9smin3,5,7 0-imaj7maj11min13x9s3,7 1-Iaugmaj7min913s5 1-Imaj7min9min13s13 2-id6min9min13x3s9 2-iaugmin9maj1113x3s9,11 4-imaj7min13x11s3,7 5-Iaugmaj7min913smin3 6-id6min911x3s3,9 8-imaj7maj11min13s3 9-Iaugmin913x7smin3,5 9-imin9min13x7s3,13 (=0-G Bb B Db D F F# Eb =0-G Bb B D D# F F# C# =0-G Bb B D F F# C# Eb =1-G B D D# F# 0-Ab C E =1-G B D F# 0-Ab C Eb E =2-G Db E F Ab 0-A C Eb =2-G D# F Ab 0-A C C# E =4-G Bb 0-B D F F# A Eb =5-G Bb B D# F# Ab 0-C E =6-G B 0-Db E F Ab A C =8-G Bb B D F# A C# 0-Eb =9-G Bb B D D# Ab C 0-E =9-G Bb B D Ab C Eb 0-E)
0,1,2,4,5,6,8,9,10 - 0-imaj7maj11min13s3,7 1-Iaugmaj7min913smin3,5 1-imaj7min9min13s3,13 2-id6min9min13x3s3,9 2-Iaugmin9maj1113s9,11 (=0-G Bb B D F F# A C# Eb =1-G Bb B D D# F# 0-Ab C E =1-G Bb B D F# 0-Ab C Eb E =2-G B Db E F Ab 0-A C Eb =2-G B D# F Ab 0-A C C# E) - (S)
0,1,2,3 - - 1-G F F# 0-Ab - (good: G F# Ab F)
0,1,2,3,10 - -
0,1,2,3,9 - -
0,1,2,3,9,10 - -
0,1,2,3,8 - -
0,1,2,3,8,10 - -
0,1,2,3,8,9 - -
0,1,2,3,8,9,10 - - - (good: G Bb D Ab C A C#)
0,1,2,3,7 - -
0,1,2,3,7,10 - -
0,1,2,3,7,9 - -
0,1,2,3,7,9,10 - -
0,1,2,3,7,8 - -
0,1,2,3,7,8,10 - -
0,1,2,3,7,8,9 - -
0,1,2,3,6 - -
0,1,2,3,6,10 - -
0,1,2,3,6,9 - -
0,1,2,3,6,9,10 - -
0,1,2,3,6,8 - -
0,1,2,3,6,8,10 - -
0,1,2,3,6,8,9 - -
0,1,2,3,6,8,9,10 - -
0,1,2,3,6,7 - -
0,1,2,3,6,7,10 - -
0,1,2,3,6,7,9 - -
0,1,2,3,6,7,9,10 - - - (good: G B D F# Bb Db F Ab)
0,1,2,3,6,7,8 - -
0,1,2,3,6,7,8,10 - -
0,1,2,3,6,7,8,9 - - - (S)
0,1,2,3,5 - -
0,1,2,3,5,10 - -
0,1,2,3,5,9 - -
0,1,2,3,5,9,10 - -
0,1,2,3,5,8 - -
0,1,2,3,5,8,10 - -
0,1,2,3,5,8,9 - -
0,1,2,3,5,8,9,10 - -
0,1,2,3,5,7 - -
0,1,2,3,5,7,10 - -
0,1,2,3,5,7,9 - -
0,1,2,3,5,7,9,10 - -
0,1,2,3,5,7,8 - -
0,1,2,3,5,7,8,10 - -
0,1,2,3,5,7,8,9 - -
0,1,2,3,5,6 - -
0,1,2,3,5,6,10 - -
0,1,2,3,5,6,9 - -
0,1,2,3,5,6,9,10 - -
0,1,2,3,5,6,8 - -
0,1,2,3,5,6,8,10 - - - (H)
0,1,2,3,5,6,8,9 - -
0,1,2,3,5,6,8,9,10 - -
0,1,2,3,5,6,7 - -
0,1,2,3,5,6,7,10 - -
0,1,2,3,5,6,7,9 - -
0,1,2,3,5,6,7,9,10 - -
0,1,2,3,5,6,7,8 - -
0,1,2,3,5,6,7,8,10 - -
0,1,2,3,4 - -
0,1,2,3,4,10 - -
0,1,2,3,4,9 - -
0,1,2,3,4,9,10 - -
0,1,2,3,4,8 - -
0,1,2,3,4,8,10 - -
0,1,2,3,4,8,9 - -
0,1,2,3,4,8,9,10 - -
0,1,2,3,4,7 - -
0,1,2,3,4,7,10 - -
0,1,2,3,4,7,9 - -
0,1,2,3,4,7,9,10 - -
0,1,2,3,4,7,8 - -
0,1,2,3,4,7,8,10 - -
0,1,2,3,4,7,8,9 - -
0,1,2,3,4,7,8,9,10 - -
0,1,2,3,4,6 - -
0,1,2,3,4,6,10 - -
0,1,2,3,4,6,9 - - - (good: G Bb D F Ab B A)
0,1,2,3,4,6,9,10 - -
0,1,2,3,4,6,8 - -
0,1,2,3,4,6,8,10 - -
0,1,2,3,4,6,8,9 - -
0,1,2,3,4,6,8,9,10 - -
0,1,2,3,4,6,7 - -
0,1,2,3,4,6,7,10 - -
0,1,2,3,4,6,7,9 - -
0,1,2,3,4,6,7,9,10 - -
0,1,2,3,4,6,7,8 - -
0,1,2,3,4,6,7,8,10 - -
0,1,2,3,4,6,7,8,9 - -
0,1,2,3,4,6,7,8,9,10 - - - (S)
0,1,2,3,4,5 - -
0,1,2,3,4,5,10 - - - (good: G Bb D Ab B A C, G Bb Db F# A Ab B, G Bb D A C Ab B)
0,1,2,3,4,5,9 - - - (good: G Bb Db F Ab F# A, G Bb D F# A Ab B)
0,1,2,3,4,5,9,10 - -
0,1,2,3,4,5,8 - - - (good: G Bb D F# A F Ab, G Bb D F Ab F# A)
0,1,2,3,4,5,8,10 - -
0,1,2,3,4,5,8,9 - -
0,1,2,3,4,5,8,9,10 - -
0,1,2,3,4,5,7 - - - (good: G B D A# C# A C)
0,1,2,3,4,5,7,10 - -
0,1,2,3,4,5,7,9 - -
0,1,2,3,4,5,7,9,10 - -
0,1,2,3,4,5,7,8 - -
0,1,2,3,4,5,7,8,10 - -
0,1,2,3,4,5,7,8,9 - -
0,1,2,3,4,5,7,8,9,10 - -
0,1,2,3,4,5,6 - - - (good: G Bb Db A C Ab B)
0,1,2,3,4,5,6,10 - -
0,1,2,3,4,5,6,9 - -
0,1,2,3,4,5,6,9,10 - -
0,1,2,3,4,5,6,8 - -
0,1,2,3,4,5,6,8,10 - -
0,1,2,3,4,5,6,8,9 - -
0,1,2,3,4,5,6,8,9,10 - -
0,1,2,3,4,5,6,7 - -
0,1,2,3,4,5,6,7,10 - -
0,1,2,3,4,5,6,7,9 - -
0,1,2,3,4,5,6,7,9,10 - -
0,1,2,3,4,5,6,7,8 - -
0,1,2,3,4,5,6,7,8,10 - -
0,1,2,3,4,5,6,7,8,9 - -
0,1,2,3,4,5,6,7,8,9,10 - -
0,1,2,3,4,5,6,7,8,9,10,11 - - - (S)

Copyright (c) 2009 Mark D. Blackwell.

An harmonic analysis of Mozart's Agnus Dei from Missa Brevis in D (K.194)

2009-01-16T13:22:00.014-05:00

I am pleased to have created and to post here a complete analysis of the harmony of Mozart's interesting Agnus Dei movement from Missa Brevis in D (K.194). 'Complete' means every note is included; no passing tones are excluded. However, trills are excluded.

Explanation of notation:
o In '(chord)/N', the component, '/N' indicates the bass note. E.g., 'b: F#/3' says the bass is A#. This is true even though b minor contains A-natural. Of course, all default accidentals are like the G chord in C major. The key determines the default roots of the chords, but not any other notes of the chords.
o No interval from the root higher than a seventh appears in the bass; e.g., a hypothetical notation of 'G9/9' is replaced with, 'G9/2'.
o Symbols:
Raised or lowered from the current, major or minor scale:
+: root is raised a half-step.
-: root is lowered a half-step.
( ): combines chords over time; e.g., in the notation, '(F G) C', the chord, 'C' consumes the same amount of time as the chord sequence, 'F G'.
;: a separator for human readability; use in the center of measures.
_: continue the latest chord.
~: continue the latest chord.
|: measure separator
0: measure separator
dim: diminished chord (the fifth from the root is diminished).
m: minor chord. (Note that 'm' (e.g., Bm) is used only for minor thirds and only in letter-name chord names; the chord symbol, 'min' (e.g., Gmmin9, vmin9) is used only for other minor intervals both in the letter-name and in the roman-numeral chord names.)
rest: silence.

The harmony:
The following measures are in 3/4 time:
Adagio, solo (religious mood), 'Agnus Dei, Agnus Dei, qui tollis peccata, peccata mundi:'
1-8: Bm 0 F#7/A# 0 Bm 0 F#7/A# 0 Bm G/B ~ 0 Gdim/A# F#/A# F#m/A 0 G#dim7 G#dim6 G7 0 Bdimx3s5/F# F#x5/A# REST 0
| 1-8: b: i | V7/3 | i | V7/3 | i VI/3 _ | vid/3 V/3 v/3 | +vid7 +vid6 VI7 | idx3s5/5 Vx5/3 rest |

tutti (crowd mood), 'miserere, miserere,'
9-12: D 0 A7/C# 0 D 0 A7/C# 0
9-12: D: I | V7/3 | I | V7/3 |

13 beat 2 (group mood), 'miserere nobis.'
13-16: D ~ Am/C 0 B7 ~ A#dim6 0 ~ Bx3s4 B 0 Ex3 ~ Cx5 Am F#dim7 D#dim6min9x7 0
13-16: D: I _ v/3 | VI7 _ +vd6 | _ vix3s4 VI | iix3 _ -VIIx5 v iiid7 +id6min9x7 |
13-16: D: I _ e: iv/3 | V7 _ +ivd6 | _ vx3s4 V | ix3 _ VIx5 iv iid7 +viid6min9x7 |

letter A, solo (religious mood), 'Agnus Dei, Agnus Dei, qui tollis peccata, peccata mundi,'
17-24: Em 0 B7/D# 0 Em 0 B7/D# 0 Em C/E ~ 0 Cdim/D# B/D# Bm/D 0 C#dim7 C#dim6 C7 0 Edimx3s5/B Bx5/D# REST 0
17-24: e: i | V7/3 | i | V7/3 | i VI/3 _ | vid/3 V/3 v/3 | +vid7 +vid6 VI7 | idx3s5/5 Vx5/3 rest |

tutti (crowd mood), 'miserere, miserere,'
25-28: G 0 D7 ~ (Bmmin9 D7/A) 0 (G ~ ~ G9x7/A) G G/D 0 D7 ~ (Bmmin9 D7/A) 0
25-28: G: I | V7 _ (iiimin9 V7/5) | (I _ _ I9x7/2) I I/5 | V7 _ (iiimin9 V7/5) |

29 beat 2 (group mood), 'miserere nobis.'
29-32: (G ~ ~ G9x7/A) G Dm/F 0 E7 ~ Adim/D# 0 D#dim6 Ex3s4 E 0 Ax3 ~ Fx5 Dm Bdim7 G#dim6min9x7 0
29-32: G: (I _ _ I9x7/2) I v/3 | VI7 _ iid/5 | +vd6 vix3s4 VI | iix3 _ -VIIx5 v iiid7 +id6min9x7 |
29-32: G: (I _ _ I9x7/2) I a: iv/3 | V7 _ id/5 | +ivd6 vx3s4 V | ix3 _ VIx5 iv iid7 +viid6min9x7 |

letter B, solos (religious mood), 'Agnus Dei, Agnus Dei,' 36 beat 3 (group mood), 'qui'
33-36: Am Am/E ~ ~ Am ~ 0 E7/G# 0 Am/E ~ Am 0 E7/G# ~ ~ ~ ~ E7 0
33-36: a: i i/5 _ _ i _ | V7/3 | i/5 _ i | V7/3 _ _ _ _ V7 |

'tollis peccata mundi,'
37-40: Ax3s4/E Am/E ~ ~ ~ G7/F 0 F# ~ F#7 0 ~ ~ Bdim/F 0 F# ~ Gdim Gdim/Db Edim6 A#dim6 0
37-40: a: ix3s4/5 i/5 _ _ _ VII7/7 | +VI _ +VI7 | _ _ iid/5 | +VI _ viid viid/5 vd6 +id6 |
37-40: a: ix3s4/5 i/5 _ _ _ b: VI7/7 | V _ V7 | _ _ id/5 | V _ vid vid/5 ivd6 +viid6 |

tutti (combined religious and (41 beat 2) crowd moods), 'Agnus Dei, Agnus Dei,'
41-44: Bm Bm/F# ~ 0 F#7 ~ ~ F#7/E F#aug7 F#7/C# 0 Bm Bm/F# ~ 0 F#7 ~ ~ F#7/E F#aug7 F#7/C# 0
41-44: b: i i/5 _ | V7 _ _ V7/7 Vaug7 V7/5 | i i/5 _ | V7 _ _ V7/7 Vaug7 V7/5 |

45 beat 3 (group mood), 'qui tollis peccata mundi:'
45-48: Bm ~ G/B 0 A#dim6 F#/A# F#m 0 G#dim6 ~ G7 0 Bdims5/F# F# REST 0
45-48: b: i _ VI/3 | +viid6 V/3 v/3 | +vid6 _ VI7 | ids5/5 V rest |

The following measures are in 4/4 time:
Allegro moderato, letter C, solo (religious mood), 'dona nobis pacem, pacem,'
49-50: Ax3,5 D F#mx5 Dx5 ; Ax3s4 ~ C#dim/G Dx5/F# 0 Em7x5/G ~ D/A G/B ; C#dim A7x3 Dx5 ~ 0
49-50: D: vx3,5 I iiix5 Ix5 ; vx3s4 _ viid/5 Ix5/3 | ii7x5/3 _ I/5 IV/3 ; viid v7x3 Ix5 _ |

tutti (religious mood, still), 'dona, dona nobis pacem,'
51-52: G D A7/G D/F# 0 A7/C# D ; (D/A A) (_ A7/G ~ A7/E) 0
51-52: D: IV I V7/7 I/3 | V7/3 I ; (I/5 V) (_ V7/7 _ V7/5) |

solo (religious mood), 'dona nobis pacem, pacem,'
53-54: Dx3 D F#mx5 Dx5 ; Ax3s4 ~ C#dim/G Dx5/F# 0 Em7x5/G ~ D/A G/B ; C#dim A7x3 Dx5 ~ 0
53-54: D: ix3 I iiix5 Ix5 ; vx3s4 _ viid/5 Ix5/3 | ii7x5/3 _ I/5 IV/3 ; viid v7x3 Ix5 _ |

tutti (group mood), 'dona nobis,'
55: D A/C# E7/B A 0
55: D: I V/3 A: V7/5 I |
55: D: I A: I/3 V7/5 I |

'dona nobis pacem,'
56: (E7/D A/C#) (E7/B A) ; (A/E E) REST 0
56: A: (V7/7 I/3) (V7/5 I) ; (I/5 V) rest |

solos (person mood), 'dona pa-/dona'
57: Ex3,5 ~ ; (Ex5/G# Ex3,5) (Ex5/G# E7x5/G# C#m/E E) 0
57: A: vx3,5 _ ; (Vx5/3 vx3,5) (Vx5/3 V7x5/3 iii/3 V) |

'(pa-)/nobis, nobis pacem, dona'
58: A A/E E7x5/G# (C#mmin9x7/E E7) ; A A/E E7x5/G# (C#mmin9x7/E E7) 0
58: A: I I/5 V7x5/3 (iiimin9x7/3 V7) ; I I/5 V7x5/3 (iiimin9x7/3 V7) |

'-cem,/nobis, nobis'
59: A ~ D/F# A/E ; Bm/D G#dim/B E/G# E7 0
59: A: I _ IV/3 I/5 ; ii/3 viid/3 V/3 V7 |

'pacem,'
60: A Bm/D A/E E ; A A/E A/C# A 0
60: A: I ii/3 I/5 V ; I I/5 I/3 I |

tutti (crowd mood), 'dona pa-/dona'
61: Ex3,5 ~ ; (E7x5/G# E7x3,5) (E7x5/G# ~ C#mmin9x7/E E7) 0
61: A: vx3,5 _ ; (V7x5/3 v7x3,5) (V7x5/3 _ iiimin9x7/3 V7) |

'(pa-)/nobis, nobis pacem, dona/nobis pa-'
62: A A/E E7x5/G# (C#mmin9x7/E E7) ; A A/E E7x5/G# (C#mmin9x7/E E7) 0
62: A: I I/5 V7x5/3 (iiimin9x7/3 V7) ; I I/5 V7x5/3 (iiimin9x7/3 V7) |

'-cem,/dona nobis'
63: A (Ax3 ~ Ex3s4/A A) D/F# Amaj7/E ; Bm7/D (G#dim ~ C#7min9x3/G# G#dim) E/G# E7 0
63: A: I (ix3 _ vx3s4/4 I) IV/3 Imaj7/5 ; ii7/3 (viid _ iii7min9x3/5 viid) V/3 V7 |

'pacem, dona'
64: (Ax5 A) (D Bm/D) A/E E ; A (Ax3 ~ Ex3s4/A A) D/F# Amaj7/E 0
64: A: (Ix5 I) (IV ii/3) I/5 V ; I (ix3 _ vx3s4/4 I) IV/3 Imaj7/5 |

'nobis pa-'
65: Bm7/D (G#dim ~ C#min9x3/G# G#dim) E/G# E7 ; (Ax5 A) (D Bm/D) A/E E 0
65: A: ii7/3 (viid _ iiimin9x3/5 viid) V/3 V7 ; (Ix5 I) (IV ii/3) I/5 V |

letter D, '-cem,' solos, 66 beat 3 (religious mood), 'dona nobis pa-'
66-67: Ax3 Ax3/E Ax3,5 ~ ; Ax3 C#mx5 Ax5/C# Ax3/E 0 Ddimx3 Ex5 Ax5/C# Ax3/E ; (Dx5 Dmaj7x5/C#) (Bm D/A) G#dim7x3 ~ 0
66-67: A: ix3 ix3/5 ix3,5 _ ; ix3 iiix5 Ix5/3 ix3/5 | ivdx3 Vx5 Ix5/3 ix3/5 ; (IVx5 IVmaj7x5/7) (ii IV/5) viid7x3 _ |

'-cem,/' (person mood), 'dona nobis pacem, pacem,'
68-69: A ~ C#mx5 Ax5 ; Ex3s4 ~ G#dim/D Ax5/C# 0 Bm7x5/D ~ A/E D/F# ; G#dim E7x3 A F#7/A# 0
68-69: A: I _ iiix5 Ix5 ; vx3s4 _ viid/5 Ix5/3 | ii7x5/3 _ I/5 IV/3 ; viid v7x3 I VI7/3 |

(religious mood: sad), 'dona nobis pa-' 71 beat 3 '-cem,/' (person mood: sad) 'dona'
70-71: Bm Dx5 Bmx5 Bx3 ; A#dimx3 F#x5/A# Bmx5 Bx3 0 (Emx5/G Em7x5/G) (C#dim/G Em/G) Edim/G ~ ; Bm/F# Bm Dx5 Bmx5 0
70-71: b: i IIIx5 ix5 ix3 ; +viidx3 Vx5/3 ix5 ix3 | (ivx5/3 iv7x5/3) (iid/5 iv/3) ivd/3 _ ; i/5 i IIIx5 ix5 |

'nobis pacem,'
72: F#x3s4 ~ A#dim/E Bmx5/D ; C#m7x5 ~ Bm/D Em 0
72: b: vx3s4 _ +viid/5 ix5/3 ; iid7x5 _ i/3 iv |

'pacem,' tutti, 73 beat 3 (group mood), 'pacem,'
73: (A#dim/E F#7x3/E Bmx5/D Bmx5) ; tutti: D7 0
73: b: (+viid/5 v7x3/7 ix5/3 ix5) ; tutti: G: V7 |

letter E (crowd mood), 'dona nobis pacem,/dona nobis pa-/dona nobis/dona'
74-75: Dx3,5 ~ ~ Gx3 ; Gx3s4 (!) ~ D7x5/F# G 0 D7x3s4/A ~ D7/A Gx5/B ; D7x3s4 ~ D7 Gx5 0
74-75: G: vx3,5 _ _ ix3 ; ix3s4 (!) _ V7x5/3 I | v7x3s4/5 _ V7/5 Ix5/3 ; v7x3s4 _ V7 Ix5 |

'dona, dona/(pa-)cem, do-/pacem, dona/nobis, dona'
76: Am7/G ~ D7/F# G ; (Am7x5 Am9x5) (F#dim/A Am7x5) (Bmin9x3 Gmaj79x5/B) (F#dim/C F#dimmin9/C) 0
76: G: ii7/7 _ V7/3 I ; (ii7x5 ii9x5) (viid/3 ii7x5) (iiimin9x3 Imaj79x5/3) (viid/5 viidmin9/5) |

'(do-)/nobis pa-,' 77 beat 4 (group mood), '-na,/-cem,'
77: D7/C (D11x5/C D7/C) G/B E7/D ; ~ (E11x5/D E7/D) A/C# A7/E 0
77: G: V7/7 (V11x5/7 V7/7) I/3 VI7/7 ; _ (VI11x5/7 VI7/7) II/3 II7/5 |
77: G: V7/7 (V11x5/7 V7/7) D: IV/3 II7/7 ; _ (II11x5/7 II7/7) V/3 V7/5 |

'dona nobis pacem,'
78: D (A7x3s4/E D/F#) Em/G G#dim7 ; D/A A (Ax3,5 A7x3,5/G) (F#mx5 A7x3/E) 0
78: D: I (v7x3s4/5 I/3) ii/3 +ivd7 ; I/5 V (vx3,5 v7x3,5/7) (iiix5 v7x3/5) |

solo (religious mood), 'dona nobis pacem, pacem,'
79-80: Dx3 D F#mx5 Dx5 ; Ax3s4 ~ C#dim/G Dx5/F# 0 Em7x5/G ~ D/A G/B ; C#dim A7x3 Dx5 ~ 0
79-80: D: ix3 I iiix5 Ix5 ; vx3s4 _ viid/5 Ix5/3 | ii7x5/3 _ I/5 IV/3 ; viid v7x3 Ix5 _ |

tutti (religious mood still), 'dona nobis pacem, pacem,'
81-82: G D A7/G D/F# 0 A7/C# D ; (D/A A) (Ax3,5 A7x3,5/G F#mx5 A7x3/E) 0
81-82: D: IV I V7/7 I/3 | V7/3 I ; (I/5 V) (vx3,5 v7x3,5/7 iiix5 v7x3/5) |

solo (religious mood), 'dona nobis pacem, pacem,'
83-84: Dx3 Dm Fx5 Dmx5 ; Ax3s4 ~ C#dim/G Dmx5/F 0 Em7x5/G ~ Dm/A G/B ; C#dim A7x3 Dm ~ 0
83-84: d: ix3 i IIIx5 ix5 ; vx3s4 _ +viid/5 ix5/3 | ii7x5/3 _ i/5 IV/3 ; +viid v7x3 i _ |

tutti (group mood), 'dona nobis, dona nobis pacem,'
85-86: A G#dim6 Gdim6 Dm/F 0 A7/C# (_ Dm) ; (Dm/A A) REST 0
85-86: d: V +ivd6 ivd6 i/3 | V7/3 (_ i) ; (i/5 V) rest |

solo (person mood), 'dona pa-/dona'
87: Ax3,5 ; (Ax5/C# Ax3,5 (Ax5/C# A7x5/C#) (F#m/A A)) 0
87: finally D: vx3,5 ; (Vx5/3 vx3,5 (Vx5/3 V7x5/3) (iii/3 V)) |

'(pa-)/nobis, nobis pacem, dona'
88: D D/A A7x5/C# (F#mmin9x7/A A7) ; D D/A A7x5/C# (F#mmin9x7/A A7) 0
88: D: I I/5 V7x5/3 (iiimin9x7/3 V7) ; I I/5 V7x5/3 (iiimin9x7/3 V7) |

'-cem,/dona nobis'
89: D ~ G/B D/A ; Em/G C#dim/E A/C# A7 0
89: D: I _ IV/3 I/5 ; ii/3 viid/3 V/3 V7 |

'pacem,'
90: Dx5 Emx5/G D/A A ; Dx3,5 Dx3/A F#mx5 D 0
90: D: Ix5 iix5/3 I/5 V ; ix3,5 ix3/5 iiix5 I |

tutti (combined person and (91 beat 3) crowd moods), 'dona pa-/dona'
91: Ax3,5 ~ ; (A7x5/C# A7x3,5) (A7x5/C# ~ F#mmin9x7/A A7) 0
91: D: vx3,5 _ ; (V7x5/3 v7x3,5) (V7x5/3 _ iiimin9x7/3 V7) |

'(pa-)/nobis pa-/nobis, nobis pacem, dona'
92: D D/A A7x5/C# (F#mmin9x7/A A7) ; D D/A A7x5/C# (F#mmin9x7/A A7) 0
92: D: I I/5 V7x5/3 (iiimin9x7/3 V7) ; I I/5 V7x5/3 (iiimin9x7/3 V7) |

'-cem,/dona nobis'
93: D (Dx3 ~ Ax3s4/D D) G/B Dmaj7/A ; Em7/G (C#dim/E ~ F#min9x3/E C#dim/E) A/C# A7 0
93: D: I (ix3 _ vx3s4/4 I) IV/3 Imaj7/5 ; ii7/3 (viid/3 _ iiimin9x3/7 viid/3) V/3 V7 |

'pacem do-/dona'
94: D Em/G D/A A ; Dx3 (Dx3 ~ Ax3s4/D D) G/B Dmaj7/A 0
94: D: I ii/3 I/5 V ; ix3 (ix3 _ vx3s4/4 I) IV/3 Imaj7/5 |

'-na/nobis pacem,' 96 beat 3 (group mood), 'dona'
95-96: Em7/G (C#dim/E ~ F#min9x3/E C#dim/E) A/C# A7x5 ; D Bm Em7/G A 0 (Dx3 D (Ax3,5 A7x3,5) (F#mx5 A7x3/E)) ; D 0
95-96: D: ii7/3 (viid/3 _ iiimin9x3/7 viid/3) V/3 V7x5 ; I vi ii7/3 V | (ix3 I (vx3,5 v7x3,5) (iiix5 v7x3/5)) ; I |

'nobis pacem,'
97: D/A ~ A7/G D/F# ; Em7/G ~ D/A G 0
97: D: I/5 _ V7/7 I/3 ; ii7/3 _ I/5 IV |

rit., 'pacem,' 98 beat 3 (religious mood), 'do-'
98: A7/C# D A7 ~ 0
98: D: V7/3 I V7 _ |

'-na', a tempo, 99 beat 3 (group mood), 'pa-'
99: G#dim7 REST Ax3s4 A7 0
99: D: +ivd7 rest vx3s4 V7 |

'-cem,' rit., 100 beat 3 (religious mood), 'do-'
100: Bm REST A7 ~ 0
100: D: vi rest V7 _ |

'-na', a tempo, 101 beat 3 (group mood), 'pa-'
101: G#dim7 REST Ax3s4 A 0
101: D: +ivd7 rest vx3s4 V |

'-cem, pa-', 102 beat 3 (religious mood in soprano, holding as others drop out) '-cem.'
102: Dx3 A D REST ~/
102: D: ix3 V I rest |/

Comparisons of the harmony of various measures:
i:
25: G: I |
60+: A: ; I I/5 I/3 I |
66: A: ix3 ix3/5 ix3,5 _ ;
i ii i v:
60: A: I ii/3 I/5 V ;
94: D: I ii/3 I/5 V ;
90: D: Ix5 iix5/3 I/5 V ;
i iii i:
66+: A: ; ix3 iiix5 Ix5/3 ix3/5 |
90+: D: ; ix3,5 ix3/5 iiix5 I |
70: b: i IIIx5 ix5 ix3 ;
71+: b: ; i/5 i IIIx5 ix5 |
53-54: D: ix3 I iiix5 Ix5 ; vx3s4 _ viid/5 Ix5/3 | ii7x5/3 _ I/5 IV/3 ; viid v7x3 Ix5 _ |
79-80: D: ix3 I iiix5 Ix5 ; vx3s4 _ viid/5 Ix5/3 | ii7x5/3 _ I/5 IV/3 ; viid v7x3 Ix5 _ |
83-84: d: ix3 i IIIx5 ix5 ; vx3s4 _ +viid/5 ix5/3 | ii7x5/3 _ i/5 IV/3 ; +viid v7x3 i _ |
68-69: A: I _ iiix5 Ix5 ; vx3s4 _ viid/5 Ix5/3 | ii7x5/3 _ I/5 IV/3 ; viid v7x3 I VI7/3 |
i iv i:
59: A: I _ IV/3 I/5 ; ii/3 viid/3 V/3 V7 |
89: D: I _ IV/3 I/5 ; ii/3 viid/3 V/3 V7 |
i iv ii:
64: A: (Ix5 I) (IV ii/3) I/5 V ;
i v:
13: D: I _ v/3 |
33-34: a: i i/5 _ _ i _ | V7/3 |
35-36: a: i/5 _ i | V7/3 _ _ _ _ V7 |
41-42: b: i i/5 _ | V7 _ _ V7/7 Vaug7 V7/5 |
43-44: b: i i/5 _ | V7 _ _ V7/7 Vaug7 V7/5 |
i v i:
102: D: ix3 V I rest |
97: D: I/5 _ V7/7 I/3 ;
74+: G: ; ix3s4 (!) _ V7x5/3 I |
i v i ii:
78: D: I (v7x3s4/5 I/3) ii/3 +ivd7 ;
i v i iv:
63: A: I (ix3 _ vx3s4/4 I) IV/3 Imaj7/5 ; ii7/3 (viid _ iii7min9x3/5 viid) V/3 V7 |
93: D: I (ix3 _ vx3s4/4 I) IV/3 Imaj7/5 ; ii7/3 (viid/3 _ iiimin9x3/7 viid/3) V/3 V7 |
64+: A: ; I (ix3 _ vx3s4/4 I) IV/3 Imaj7/5 |
94+: D: ; ix3 (ix3 _ vx3s4/4 I) IV/3 Imaj7/5 |
i v i v:
1-4: b: i | V7/3 | i | V7/3 |
17-20: e: i | V7/3 | i | V7/3 |
9-12: D: I | V7/3 | I | V7/3 |
i v iii v:
78+: D: ; I/5 V (vx3,5 v7x3,5/7) (iiix5 v7x3/5) |
96: D: (ix3 I (vx3,5 v7x3,5) (iiix5 v7x3/5)) ; I |
58: A: I I/5 V7x5/3 (iiimin9x7/3 V7) ; I I/5 V7x5/3 (iiimin9x7/3 V7) |
62: A: I I/5 V7x5/3 (iiimin9x7/3 V7) ; I I/5 V7x5/3 (iiimin9x7/3 V7) |
88: D: I I/5 V7x5/3 (iiimin9x7/3 V7) ; I I/5 V7x5/3 (iiimin9x7/3 V7) |
92: D: I I/5 V7x5/3 (iiimin9x7/3 V7) ; I I/5 V7x5/3 (iiimin9x7/3 V7) |
i vi iv:
16: e: ix3 _ VIx5 iv iid7 +viid6min9x7 |
32: a: ix3 _ VIx5 iv iid7 +viid6min9x7 |
i vi v:
5-8: b: i VI/3 _ | vid/3 V/3 v/3 | +vid7 +vid6 VI7 | idx3s5/5 Vx5/3 rest |
21-24: e: i VI/3 _ | vid/3 V/3 v/3 | +vid7 +vid6 VI7 | idx3s5/5 Vx5/3 rest |
i vi vii:
45-48: b: i _ VI/3 | +viid6 V/3 v/3 | +vid6 _ VI7 | ids5/5 V rest |
i vii:
37: a: ix3s4/5 i/5 _ _ _ VII7/7 |
ii i:
50: D: ii7x5/3 _ I/5 IV/3 ;
97+: D: ; ii7/3 _ I/5 IV |
72+: b: ; iid7x5 _ i/3 iv |
ii v:
77+: D: ; II7/7 (II11x5/7 II7/7) V/3 V7/5 |
ii v i:
76: G: ii7/7 _ V7/3 I ;
ii vii ii:
76+: G: ;(ii7x5 ii9x5) (viid/3 ii7x5) (iiimin9x3 Imaj79x5/3) (viid/5 viidmin9/5) |
ii vii iii:
65: A: ii7/3 (viid _ iiimin9x3/5 viid) V/3 V7 ; (Ix5 I) (IV ii/3) I/5 V |
95: D: ii7/3 (viid/3 _ iiimin9x3/7 viid/3) V/3 V7x5 ; I vi ii7/3 V |
ii vii v:
16: D: iix3 _ -VIIx5 v iiid7 +id6min9x7 |
32: G: iix3 _ -VIIx5 v iiid7 +id6min9x7 |
iv i:
51: D: IV I V7/7 I/3 |
81: D: IV I V7/7 I/3 |
iv ii iv:
71: b: (ivx5/3 iv7x5/3) (iid/5 iv/3) ivd/3 _ ;
iv ii iv vii:
67+: A: ; (IVx5 IVmaj7x5/7) (ii IV/5) viid7x3 _ |
iv v:
67: A: ivdx3 Vx5 Ix5/3 ix3/5 ;
+iv
15: e: +ivd6 vx3s4 V |
31: a: +ivd6 vx3s4 V |
99: D: +ivd7 rest vx3s4 V7 |
101: D: +ivd7 rest vx3s4 V |
v:
38: b: V _ V7 |
v i:
30: a: V7 _ id/5 |
39: b: V7 _ id/5 |
74: G: vx3,5 _ _ ix3 ;
75: G: v7x3s4/5 _ V7/5 Ix5/3 ;
75+: G: ; v7x3s4 _ V7 Ix5 |
v i iii:
49: D: vx3,5 I iiix5 Ix5 ;
v i v:
98: D: V7/3 I V7 _ |
52: D: V7/3 I ; (I/5 V) (_ V7/7 _ V7/5) |
86: d: V7/3 (_ i) ; (i/5 V) rest |
v i v i:
56: A: (V7/7 I/3) (V7/5 I) ; (I/5 V) rest |
v i v iii:
82: D: V7/3 I ; (I/5 V) (vx3,5 v7x3,5/7 iiix5 v7x3/5) |
v iii v:
57: A: vx3,5 _ ; (Vx5/3 vx3,5) (Vx5/3 V7x5/3 iii/3 V) |
87: D: vx3,5 ; (Vx5/3 vx3,5 (Vx5/3 V7x5/3) (iii/3 V)) |
61: A: vx3,5 _ ; (V7x5/3 v7x3,5) (V7x5/3 _ iiimin9x7/3 V7) |
91: D: vx3,5 _ ; (V7x5/3 v7x3,5) (V7x5/3 _ iiimin9x7/3 V7) |
v iii v i:
26-27: G: V7 _ (iiimin9 V7/5) | (I _ _ I9x7/2) I I/5 |
28-29: G: V7 _ (iiimin9 V7/5) | (I _ _ I9x7/2) I v/3 |
28-29: G: V7 _ (iiimin9 V7/5) | (I _ _ I9x7/2) I a: iv/3 |
v +iv:
14: e: V7 _ +ivd6 |
v +iv iv:
85: d: V +ivd6 ivd6 i/3 |
v vi:
40: b: V _ vid vid/5 ivd6 +viid6 |
v vii:
49+: D: ; vx3s4 _ viid/5 Ix5/3 |
72: b: vx3s4 _ +viid/5 ix5/3 ;
+v:
15: D: +vd6 vix3s4 VI |
31: G: +vd6 vix3s4 VI |
vi:
38: a: +VI _ +VI7 |
vi ii:
30: G: VI7 _ iid/5 |
39: a: +VI7 _ iid/5 |
vi v:
100: D: vi rest V7 _ |
vi +v:
14: D: VI7 _ +vd6 |
vi vii:
40: a: +VI _ viid viid/5 vd6 +id6 |
vii:
50+: D: ; viid v7x3 Ix5 _ |
70+: b: ; +viidx3 Vx5/3 ix5 ix3 |

Mid-measure key changes:
13: D: I _ e: iv/3 |
29: G: (I _ _ I9x7/2) I a: iv/3 |
37: a: ix3s4/5 i/5 _ _ _ b: VI7/7 |
55: D: I V/3 A: V7/5 I |
55: D: I A: I/3 V7/5 I |
77: G: V7/7 (V11x5/7 V7/7) D: IV/3 II7/7 ;
73: b: (+viid/5 v7x3/7 ix5/3 ix5) ; G: V7 |

Copyright (c) 2009 Mark D. Blackwell.

A normalized chord notation & naming based on Mozart's Agnus Dei from Missa Brevis in D (K.194)

2009-01-16T13:16:00.019-05:00

This Christmas (2008), I sang Mozart's 'Missa Brevis in D (K.194)' and greatly enjoyed it! I am pleased now to be able to present the following, detailed and complete list I have created of the chords in the Agnus Dei movement. 'Complete' means every note is included; no passing tones are excluded. However, trills are excluded. I intend to write a computer program in some way involving these chords.

The chords, harmonic function agnostic, are in a notation that automatically collapses all transpositions and inversions, which I created for the list. The twelve adjacent tones in an octave are numbered backward with this method, 0 to 11. Each chord is transposed until (in a computer sense) its combination of numbers is as low as possible ('normalized'). This collapses the transpositions and inversions. The number, '0' in the normalized notation does not necessarily mean the root of the chord. Sorting these chords, as you can see in the list, conveniently collects the categories of basic triads, diminished, and seventh chords.

Here are the thirty-three (33) transposition- and inversion -collapsed chords of the Agnus Dei ordered by their normalized notation:

normalized-notation - standard-name [(nonstandard-names)] - example
0 - ix3,5 - G
0,6 - idx3 (=I7x1,5) - G Db
0,5 - ix3 - G D
0,4 - Ix5 (=ix1) - G B
0,3 - ix5 (=Ix1) - G Bb
0,3,8 - i - G Bb D
0,3,7 - I - G B D
0,3,6 - id (=id6x3) - G Bb Db
0,3,6,9 - id6 (=id13x7,9,11) - G Bb Db E
0,2 - i7x3,5 - G F
0,2,9 - i7x5 - G Bb F
0,2,8 - I7x5 - G B F
0,2,7 - ix3s4 (=i11x3,7,9 =i9x3,7 =ix3s2) - G C D
0,2,6 - id7x3 - G Db F
0,2,6,9 - id7 - G Bb Db F
0,2,5 - i7x3 - G D F
0,2,5,9 - i7 - G Bb D F
0,2,5,8 - I7 - G B D F
0,2,5,7 - i7x3s4 (=i11x3,9 =ix3s2,4 =ix3s2,6) - G C D F
0,2,4,9 - I9x7 (=Is2) - G B D A
0,2,4,8 - Iaug7 (=Iaug9x7) - G B D# F
0,1,8 - Imaj7x5 - G B F#
0,1,8,10 - Imaj79x5 - G B F# A
0,1,7 - idx3s5 (=idmin9x3,7 =imaj711x3,5,9 =imaj7x3,5s4) - G Db D
0,1,6,10 - imin9x7 (=I7x5s6) - G Bb D Ab
0,1,5,8 - Imaj7 - G B D F#
0,1,4,7 - ids5 (=id6min9x3,7) - G Bb Db D
0,1,4,7,10 - id6min9x7 (=id13min9x7,11) - G Bb Db E Ab
0,1,3,7,10 - idmin9 - G Bb Db F Ab
0,1,3,6 - imin9x3 (=id6maj7x3 =ids4) - G D F Ab
0,1,3,6,10 - imin9 - G Bb D F Ab
0,1,3,5 - i9x5 (=i7x5s2) - G Bb F A
0,1,3,5,7 - I11x5 - G B F A C

Also, I created a (variant) system of chord naming which I believe suits the above list. For an example of the small difference, in the chord, G Bb Db E (which is 0,3,6,9) to avoid interpreting the interval G to E as a diminished seventh, because '6' is not needed for inversions which in this system go unnotated, the whole chord is called a 'd6, diminished sixth chord'. (This can be interpreted as a diminished triad, plus a major sixth above the root.) This naming as a diminished sixth chord avoids collisions with other seventh-chord nomenclature, and it more simply shows how to combine them with the major and minor seventh intervals (and higher) from the root. (However, when lacking a diminished fifth of the chord, sixths are written as the suspensions, 's6' and 'smin6'.)

The chord symbols, 'I' and 'i' are exemplary here without attaching their roots to any degree of the scale.

Following are the transposition- and inversion -collapsed chord names applicable to the Agnus Dei. Here are the standard chord names, arranged alphabetically:

standard-name [(nonstandard-names)] - example - normalized-notation
I - G B D - 0,3,7
i - G Bb D - 0,3,8
I11x5 - G B F A C - 0,1,3,5,7
I7 - G B D F - 0,2,5,8
i7 - G Bb D F - 0,2,5,9
i7x3 - G D F - 0,2,5
i7x3,5 - G F - 0,2
i7x3s4 (=i11x3,9 =ix3s2,4 =ix3s2,6) - G C D F - 0,2,5,7
I7x5 - G B F - 0,2,8
i7x5 - G Bb F - 0,2,9
i9x5 (=i7x5s2) - G Bb F A - 0,1,3,5
I9x7 (=Is2) - G B D A - 0,2,4,9
Iaug7 (=Iaug9x7) - G B D# F - 0,2,4,8
id (=id6x3) - G Bb Db - 0,3,6
id6 (=id13x7,9,11) - G Bb Db E - 0,3,6,9
id6min9x7 (=id13min9x7,11) - G Bb Db E Ab - 0,1,4,7,10
id7 - G Bb Db F - 0,2,6,9
id7x3 - G Db F - 0,2,6
idmin9 - G Bb Db F Ab - 0,1,3,7,10
ids5 (=id6min9x3,7) - G Bb Db D - 0,1,4,7
idx3 (=I7x1,5) - G Db - 0,6
idx3s5 (=idmin9x3,7 =imaj711x3,5,9 =imaj7x3,5s4) - G Db D - 0,1,7
Imaj7 - G B D F# - 0,1,5,8
Imaj79x5 - G B F# A - 0,1,8,10
Imaj7x5 - G B F# - 0,1,8
imin9 - G Bb D F Ab - 0,1,3,6,10
imin9x3 (=id6maj7x3 =ids4) - G D F Ab - 0,1,3,6
imin9x7 (=I7x5s6) - G Bb D Ab - 0,1,6,10
ix3 - G D - 0,5
ix3,5 - G - 0
ix3s4 (=i11x3,7,9 =i9x3,7 =ix3s2) - G C D - 0,2,7
Ix5 (=ix1) - G B - 0,4
ix5 (=Ix1) - G Bb - 0,3

Some nonstandard alternative (discouraged) names for the same normalized chord might be included. Here are the twenty-two (22) nonstandard chord names, arranged alphabetically:

nonstandard-name [['nonstandard'] (standard-name)] - example - normalized-notation
i11x3,7,9 nonstandard (=ix3s4) - G D C - 0,2,7
i11x3,9 nonstandard (=i7x3s4) - G D F C - 0,2,5,7
I7x1,5 nonstandard (=idx3) - B F - 0,6
i7x5s2 nonstandard (=i9x5) - G A Bb F - 0,1,3,5
I7x5s6 nonstandard (=imin9x7) - G B E F - 0,1,6,10
i9x3,7 nonstandard (=ix3s4) - G D A - 0,2,7
Iaug9x7 nonstandard (=Iaug7) - G B D# A - 0,2,4,8
id13min9x7,11 nonstandard (=id6min9x7) - G Bb Db Ab E - 0,1,4,7,10
id13x7,9,11 nonstandard (=id6) - G Bb Db E - 0,3,6,9
id6maj7x3 nonstandard (=imin9x3) - G Db E F# - 0,1,3,6
id6min9x3,7 nonstandard (=ids5) - G Db E Ab - 0,1,4,7
id6x3 nonstandard (=id) - G Db E - 0,3,6
idmin9x3,7 nonstandard (=idx3s5) - G Db Ab - 0,1,7
ids4 nonstandard (=imin9x3) - G Bb C Db - 0,1,3,6
imaj711x3,5,9 nonstandard (=idx3s5) - G F# C - 0,1,7
imaj7x3,5s4 nonstandard (=idx3s5) - G C F# - 0,1,7
Is2 nonstandard (=I9x7) - G A B D - 0,2,4,9
Ix1 nonstandard (=ix5) - B D - 0,3
ix1 nonstandard (=Ix5) - Bb D - 0,4
ix3s2 nonstandard (=ix3s4) - G A D - 0,2,7
ix3s2,4 nonstandard (=i7x3s4) - G A C D - 0,2,5,7
ix3s2,6 nonstandard (=i7x3s4) - G A D E - 0,2,5,7

Copyright (c) 2009 Mark D. Blackwell.

Obama's landslide ranking among U.S. Electoral College first-term votes

2009-01-10T11:01:00.027-05:00

Obama's 2008 landslide election achievement ranks a good 16th-best among the 34 first-term U.S. presidents. Over all 56 elected presidential terms, Obama ranks 32nd-best.

The rankings seem important in measuring the 'mood of the country' regarding the immediately-previous president's policies. The size of the landslide may give some insight into how dissatisfied we were at the time. The rankings are expressed here as ratios formed from the number of Electoral College votes received, and the votes needed to win, rounded to three decimal places.

Obama ranks below only the presidents: Washington, Reagan, Roosevelt (1932), Pierce, Monroe, Hoover, Eisenhower, Wilson, Harrison (1840), Bush (1988), Harding, Grant, Madison, Clinton, and Jackson.

Obama ranks above the presidents: Taft, Polk, McKinley, Lincoln, Buchanan, Harrison (1888), Garfield, Van Buren, Kennedy, Taylor, Nixon, Carter, Cleveland, Jefferson, Adams (1796), Bush (2000), Hayes, and Adams (1824).

On December 15, 2008, the Electoral College, comprising electors selected by each state, met together and voted. On January 8, 2009, "Vice President Dick Cheney, in his role as Senate president,"(A) "led a Senate delegation into the House chamber, along with teenage pages carrying two mahogany boxes containing the certified vote totals of each state."(B)

"'Pursuant to the Constitution and laws of the United States, the Senate and House of Representatives are meeting in joint session to verify the certificates and count the votes of the electors of the several states,' Cheney intoned in opening the session."(B) He then "sat on the podium next to"(B) House Speaker Nancy Pelosi and "handed the certificates from each state's electors to the"(B) "four 'tellers,' two members each from the House and Senate,"(B) "to be read and tallied,"(B) who "then commenced reading the votes from each state."(B) After 30 minutes, Cheney announced that Congress had certified and tallied, finally, the Electoral College's votes from each state as reflected here.

Here are the landslide rankings for all the elected, first-term presidents:

year received needed-to-win name ratio rank
1789 69 35 Washington 1.971 1
1980 489 270 Reagan 1.811 2
1932 472 266 Roosevelt 1.774 3
1852 254 149 Pierce 1.705 4
1816 183 109 Monroe 1.679 5
1928 444 266 Hoover 1.669 6
1952 442 266 Eisenhower 1.662 7
1912 435 266 Wilson 1.635 8
1840 234 148 Harrison 1.581 9
1988 426 270 Bush 1.578 10
1920 404 266 Harding 1.519 11
1868 214 148 Grant 1.446 12
1808 122 88 Madison 1.386 13
1992 370 270 Clinton 1.370 14
1828 178 131 Jackson 1.359 15
2008 365 270 Obama 1.352 16
1908 321 242 Taft 1.326 17
1844 170 138 Polk 1.232 18
1896 271 224 McKinley 1.210 19
1860 180 152 Lincoln 1.184 20
1856 174 149 Buchanan 1.168 21
1888 233 201 Harrison 1.159 22
1880 214 185 Garfield 1.157 23
1836 170 148 Van Buren 1.149 24
1960 303 269 Kennedy 1.126 25
1848 163 146 Taylor 1.116 26
1968 301 270 Nixon 1.115 27
1976 297 270 Carter 1.100 28
1884 219 201 Cleveland 1.090 29
1800 73 70 Jefferson 1.043 30
1796 71 69 Adams 1.029 31
2000 271 270 Bush 1.004 32
1876 185 185 Hayes 1.000 33
1824 84 131 Adams 0.641 34

Here are the landslide rankings of all the elected, presidential terms:

year received needed-to-win name ratio rank
1789 69 35 Washington 1.971 1
1792 132 67 Washington 1.970 2
1936 523 266 Roosevelt 1.966 3
1820 231 118 Monroe 1.958 4
1984 525 270 Reagan 1.944 5
1972 520 270 Nixon 1.926 6
1804 162 89 Jefferson 1.820 7
1864 212 117 Lincoln 1.812 8
1980 489 270 Reagan 1.811 9
1964 486 270 Johnson 1.800 10
1932 472 266 Roosevelt 1.774 11
1956 457 266 Eisenhower 1.718 12
1852 254 149 Pierce 1.705 13
1940 449 266 Roosevelt 1.688 14
1816 183 109 Monroe 1.679 15
1928 444 266 Hoover 1.669 16
1952 442 266 Eisenhower 1.662 17
1912 435 266 Wilson 1.635 18
1944 432 266 Roosevelt 1.624 19
1872 286 177 Grant 1.616 20
1840 234 148 Harrison 1.581 21
1988 426 270 Bush 1.578 22
1832 219 144 Jackson 1.521 23
1920 404 266 Harding 1.519 24
1868 214 148 Grant 1.446 25
1924 382 266 Coolidge 1.436 26
1904 336 239 Roosevelt 1.406 27
1996 379 270 Clinton 1.404 28
1808 122 88 Madison 1.386 29
1992 370 270 Clinton 1.370 30
1828 178 131 Jackson 1.359 31
2008 365 270 Obama 1.352 32
1908 321 242 Taft 1.326 33
1900 292 224 McKinley 1.304 34
1892 277 223 Cleveland 1.242 35
1844 170 138 Polk 1.232 36
1896 271 224 McKinley 1.210 37
1860 180 152 Lincoln 1.184 38
1812 128 109 Madison 1.174 39
1856 174 149 Buchanan 1.168 40
1888 233 201 Harrison 1.159 41
1880 214 185 Garfield 1.157 42
1836 170 148 Van Buren 1.149 43
1948 303 266 Truman 1.139 44
1960 303 269 Kennedy 1.126 45
1848 163 146 Taylor 1.116 46
1968 301 270 Nixon 1.115 47
1976 297 270 Carter 1.100 48
1884 219 201 Cleveland 1.090 49
2004 286 270 Bush 1.059 50
1800 73 70 Jefferson 1.043 51
1916 277 266 Wilson 1.041 52
1796 71 69 Adams 1.029 53
2000 271 270 Bush 1.004 54
1876 185 185 Hayes 1.000 55
1824 84 131 Adams 0.641 56

Here is the raw data about all of the presidential elections:

year received needed-to-win name ratio
1789 69 35 Washington 1.971
1792 132 67 Washington 1.970
1796 71 69 Adams 1.029
1800 73 70 Jefferson 1.043
1804 162 89 Jefferson 1.820
1808 122 88 Madison 1.386
1812 128 109 Madison 1.174
1816 183 109 Monroe 1.679
1820 231 118 Monroe 1.958
1824 84 131 Adams 0.641
1828 178 131 Jackson 1.359
1832 219 144 Jackson 1.521
1836 170 148 Van Buren 1.149
1840 234 148 Harrison 1.581
1844 170 138 Polk 1.232
1848 163 146 Taylor 1.116
1852 254 149 Pierce 1.705
1856 174 149 Buchanan 1.168
1860 180 152 Lincoln 1.184
1864 212 117 Lincoln 1.812
1868 214 148 Grant 1.446
1872 286 177 Grant 1.616
1876 185 185 Hayes 1.000
1880 214 185 Garfield 1.157
1884 219 201 Cleveland 1.090
1888 233 201 Harrison 1.159
1892 277 223 Cleveland 1.242
1896 271 224 McKinley 1.210
1900 292 224 McKinley 1.304
1904 336 239 Roosevelt 1.406
1908 321 242 Taft 1.326
1912 435 266 Wilson 1.635
1916 277 266 Wilson 1.041
1920 404 266 Harding 1.519
1924 382 266 Coolidge 1.436
1928 444 266 Hoover 1.669
1932 472 266 Roosevelt 1.774
1936 523 266 Roosevelt 1.966
1940 449 266 Roosevelt 1.688
1944 432 266 Roosevelt 1.624
1948 303 266 Truman 1.139
1952 442 266 Eisenhower 1.662
1956 457 266 Eisenhower 1.718
1960 303 269 Kennedy 1.126
1964 486 270 Johnson 1.800
1968 301 270 Nixon 1.115
1972 520 270 Nixon 1.926
1976 297 270 Carter 1.100
1980 489 270 Reagan 1.811
1984 525 270 Reagan 1.944
1988 426 270 Bush 1.578
1992 370 270 Clinton 1.370
1996 379 270 Clinton 1.404
2000 271 270 Bush 1.004
2004 286 270 Bush 1.059
2008 365 270 Obama 1.352

Sources:
http://www.archives.gov/federal-register/electoral-college/votes/index.html
(A) http://www.boston.com/news/nation/washington/articles/2009/01/09/\
its_official_congress_certifies_obamas_victory/
(B) http://news.yahoo.com/s/ap/20090108/ap_on_go_pr_wh/electoral_votes
http://en.wikipedia.org/wiki/Electoral_College_(United_States)
See also:
http://www.electoral-vote.com/evp2008/Pres/ec_graph-2008.html
http://www.outsidethebeltway.com/archives/obamas_landslide/
http://www-personal.umich.edu/~mejn/election/2008/
http://en.wikipedia.org/wiki/\
List_of_United_States_presidential_elections_by_Electoral_College_margin

Copyright (c) 2009 Mark D. Blackwell.