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

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)

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.