Ave Verum II

Analyse of Ave Verum, part two.
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### False dominant chords

On the last quarter-note of 28th bar there is a diminished seventh
which may be consider as a transition (brief modulation) to A minor
before the return of main key of D major. Here, it would be audacious to
consider the D as a 7, because of its proximity with the real tonic D of
this motet. Perhaps, the notion of transition may be explained by this
impossibility to justify a 7, but we must proove this with different
scores. There is the same problem on 40th and 41th bar, also with a D.

### Chromatisms

In 4th bar, there is a chromatism which can be logically analised, if
the G is identified as a 7 : A-G#-G = 16-15-14. Trying to combine usual
semi-tones would be very complex (but not impossible, only incoherent).
The 39th bar is a lot more complex, if we want that the D of soprano
part to be at 9/8 under the E of 40th bar, while keeping usual semi-tone
16/15 between D# and E, the semi-tone D-D# becomes complex : 135/128.
Apparently, a simpler solution consist in considering that D-D#-E is
equivalent to 16-17-18, this hypothesis will be developped in the
chapter on the chromatism.

### Modulations

The problem of the correct ratio between the new and the old tonic is
rarely mentionned in theoretical works. At best, advocates (and
detractors) of just intonation scales consider that the new tonic is
necessarily a note of the main scale. This non-avowed postulat is really
not justifable, and it seems obvious that the way of the modulation
intervenes directly in the pitch of the new tonic. This point will be
also developped in a chapter of my future "Th�se de Doctorat" (~~
Dissertation). A foreseeable risk is that the return to the initial key
happens one or more commas higher or lower ["pump"?]. In that case, we
will have to prove that there is no mistake in the analyse, or if we may
consider that the composer hasn't modulate with the good way, or if it
is deliberately comlex. Also, we may decide that it prove the necessity
of Equal Temperament; but, at least, we must know how the modulation
will be perceived [and performed].
In our score, there is a problem like that between 36th and 41th bars.
After a surprising V-IV cadence there is a series of chords with a lot
of chromatisms, "landing", on the last quarter-note of 41th bar on the
same fourth degree arranging as the same way, it looks like a hole in
the score, where there is a short but daring coda. Here are the
different chords of this passage :

36th bar : A major
37th bar : G major
38th bar : D dominant seventh chord
39th bar : G minor, then a diminished seventh chord in E minor (without
the root B)
40th bar : E major turning into a (false?) seventh dominant chord.
41th bar : a seventh dominant chord in D major, then the first degree of
D major (as a sixth), then the return of the IVth degree of D (G major).

A first attempt of numbering analyse gives this calculation :

bar ! 36 ! 37 ! 38 ! 39 ! 39 ! 40
! 41 !
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chord! A x 8/9 = ! G x 3/4 =! D x 4/3 =! G x 5/4 =! B x 3/2 =! E x 3/2 =
! A !

(the B is the estimated root of the diminished seventh chord of 39th
bar).
The fractions are those which are deducted "logically" from the melody
formed by the root of each chord. With this logic, we found that the
chord of A (dominant seventh) of 41th bar is one comma syntonic (81/80)
lower than the one of 36th bar. As we have already consider, either it's
voluntary, or it's a mistake of Mozart, or an error of the analyst. The
critical place, where an other solution is possible is the progression
of 39th bar, may be it must be considered most melodically than
harmonically? The previous solution gives for the chromatism of the
sopranos (39th and 40th bar) : D-D# = 24-25, and D#-E = 15-16, hence D-E
= 9-10. We can "decide" that D-E is equal to 8-9, what permits precisely
to recuperate the 81/80 comma which exist between minor whole tone
(10/9) and major whole tone (9/8). In this case we must fix the pitch of
the intermediate D#, we have already consider 16-17-18 for this
chromatism D-D#-E, this choice imply, as we have supposed it, a most
melodic than harmonic reading of this progression. This approach is, for
the moment, a simple hypothesis, but this problem of the modulations
mustn't be neglected since we make up our's mind to analyse a score with
the "simple" fractions ["Just intonation" in U.S.].
An other very complex progression - which we won't study here - is at
14th bar. It's an interrupted cadence with a diminished seventh chord
coming between the Vth and the VIth degree.

### Speculations and intonation

The previous analysis are rather daunting, I hope that other analysis
as the same principle will contribute to return them more convivial.
Nevertheless, those analysis will be able, more or less punctually, help
to detect, even to correct, some problems of intonation, of pitch, for
strings or voices. The 22th and 23th bar provide us a typical example of
this approach. We can see a quite daring progression from an A major
chord towards a dominant chord in F major. If we consider the A as a
really "equal note" (without any comma) between A and F major, and if,
as well, we allow that Ist, IId and IId degree in major scale are equal
to 8-9-10, then bass must sing a whole tone 10/9 between A and G of 23th
bar. When voices work separately, it may happen that, because of the key
of 20th to 22th bars (A major), the G may be sing too low, as a 7th in D
major, which is 8/7 (if we allow, I have already say, the hypothesis of
the "7th harmonic").
After I done this hypothesis, I asked a chorus master if he has any
problems of pitch in this score. He answered that there are a lot of
problems, and precisely on 23th bar where "bass are too low".

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End of analysis of Ave Verum (part II/II)
Xavier CHARLES