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.
Friday, January 16, 2009
A normalized chord notation & naming based on Mozart's Agnus Dei from Missa Brevis in D (K.194)
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.
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.
Saturday, January 10, 2009
Obama's landslide ranking among U.S. Electoral College first-term votes
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.
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