Choirs need electronic temperament keyboard

Choirs which perform early music need, for rehearsal purposes, an electronic keyboard capable of playing in various temperaments. All these temperaments should be adjustable by a simple slider bar, so that the choir's listening experience will fall at a point which lies anywhere (at the director's discretion) from hearing each temperament fully, to hearing merely a barely-detectable taste of the "flavor" of that temperament. This slider bar must range from 100% (for full engagement of the selected temperament) to 0% (for Equal Temperament).

This aspect of the keyboard would thus follow the advice of the best experts on temperament, who generally believe that, in history, always and actually, practice has been to use no temperament only in its pure form: but instead, that the timeline of historical practice constitutes a gradual drift from one temperament to another. Further, they believe it is historically accurate for us to duplicate today these same practices from the past, by means of any degree of alteration from Equal Temperament which we desire, using our own good taste.

Since the last century represents the triumph of Equal Temperament, perhaps our use of other temperaments should remain fairly close to it. The slider would enable this.

In order to perform early music, choirs need these temperaments:

• Bradley Lehman/J.S. Bach
• Equal Temperament
• Meantone
• Pythagorean
• Valotti
• Victorian

Some facility to load in new temperaments would be desirable as well.

Copyright (c) 2015 Mark D. Blackwell.

Thomas Young mass setting open letter

Subject: Thomas Young mass setting by Mark D. Blackwell

TYC Administrator
Thomas Young Centre
The London Centre For Theory And Simulation Of Materials

Dear madam:

Since your website:

http://www.thomasyoungcentre.org/about-tyc/contacts/

indicates you as the first point of contact, I write to announce with pleasure that I have composed a mass setting in honor of your own Thomas Young, the famous polymath.

This entire mass setting was inspired by Thomas Young's list of major thirds in his own Young Temperament (a well-temperament for keyboards). He arranged these thirds in order of increasing size (thus increasing distance from purity). In his design, this order matches the key signatures with increasing numbers of sharps and flats. His temperament (I assume you know) is described here:

http://en.wikipedia.org/w/index.php?title=Young_temperament&oldid=505261244

To be more explicit, the chord roots in this mass setting exactly follow Thomas Young's ordered sequence (or otherwise relate to it): C, G, F, D, Bb, A, Eb, E, Ab, B, Db, Gb.

You might find it amusing to inform your membership of this connection to your namesake, perhaps in a note in a publication. At least, I hope so!

The "Thomas Young" mass setting can be heard here (click the icons which depict two notes on a staff):

http://www.bakerartistawards.org/nominations/view/MarkDBlackwell/#project_10581_detail

Copyright (c) 2013 Mark D. Blackwell.

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

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.

Meantone tuning systems

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.