Ave Verum 1

Last month, Wim Hoogewerf told you about an analyse I did in my "memoire
de DEA" (1996).
The critics of the specialists of the Tuning-List would be helpful for
me.
Thanks, even if it's negatives critics!
:-)

It's an analysis of the Mozart's motet "Ave Verum Corpus" K.V.618.
Here is the first part:

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I consider, in this analysis, that major chords is reductible to 4-5-6,
minor chords to 16-19-24, and real dominant chords to 4-5-6-7 with a
7th, and to 4-5-6-7-9 with a major 9th. Others chords will be deduce of
the context in which they are, in particular diminished 7th chords and
secondary 7th chords. Obviously, the validity of this analysis depends
on the one of the postulates.

### Chords without problems

The first measure is to strings only (with organ), it presents notes of
the chord of D major, first violins ends it with an E (passing note).
First violin's melody is like 8-6-8-9 (D-A-D-E), 2d violin's melody is
4-5 (A-C#), viola's is 5-6 (F#-A), cellos made tonic "4".
If we want to reduce to the same denominator, we must start with sound 8
(cellos) because of the leading-note which is a 15 compare to the tonic,
which results :

* example 1 (first bar)

16 12 16 18 = D A D E

12_____________15 = A___________C#

10_____________12 = F#__________A

8________________ = D____________

In the same way, 3d measure (for the choir) may be analysed like this :

* example 2 (3d bar)

6________8___5___ = A________D___F#____

5________5_______ = F#_______F#________

3________3_______ = A________A_________

2________2_______ = D________D_________

All the measures which allowed only a major chord more or less spread
can be numbered like this (bars 1, 3, 7, 18, 21, 22, 30, 37, 43 and 46).
Second bar contains a G and an E passing notes, which will oblige us to
choose between 3 possibilities:

- Either we consider them like a part of a dominant chord, and, if we
allow number 7, E-G is equal to 6-7, thus a "false" 4th 21/16 between D
abd G.
- Or we prefer to keep the real 4th 4/3, minor 3d becoming pythagorus
(32/27).
- Or we want that E-G remain simple and conventional (6/5), which
involve either a false 4th D-G (27/20), or a false 5th A-E (40/27).
The first solution appear (to me...) more coherent.

### Dominant chords without problems

We'll consider as this dominant chords which the 7th major may be
number 7 (usually call 7th overtone) without conflict with an identical
note (on the score and with ET12), in particularly if this note is a
sub-dominant chord. It won't proove that 7 is the best solution, but
o,ly that's not impossible.
The 5th bar is in this case, and furthermore it's a major (dominant)
ninth chord. With numbering only soprano part, we have:
G-B-A-G = 7-9-8-7.
If we want to number all the measure with whome-numbers (except F#,
passing note, because it will still be more complicated), we obtain:

* example 3 (5th bar)

14 18 16 14 = G B A G

12 14 (40/3) 12 = E G (F#) E

8_________8______ = A_______A______

5_________5______ = C#______C#_____

Measures 8, 13, 24 and 38 can be analysed by the same way.

### Avoided complicated relations with the tonic

A suspension of the tonic on the third of a dominant chord involve a
false 5th 32/21 (bigger than 3/2) between this tonic and the 7th of the
dominant chord (always if we admit number 7 as the 7th of dominant
chords). Mozart avoid this 3 times. For example at 17th bar, there is a
7th dominant chord in A major, the sopranos sing an A for two
quarter-notes [crochets], the 7th happend only on the 3d quarter-note
and, at the same moment, the A is resolved on a G#. We have the same
proceeding bars 20 and 29. On the other hand, at the last but one bar
(45), the friction between the 7th G and the tonic D isn't avoid,
moreover, there is even a discord between the leading note and the
tonic.
As soon as 4th bar, we have an analogous discord, where a chord
traditionally analysed as a 7th chord on the second degree [supertonic]
may be a major dominant ninth chord without root whose leading note
would be delayed by the tonic. This interpretation a little convoluted
allows equality between the two G of 4th and 5th bar where there is
precisely a dominant chord. An analyse as a 2d degree would be quite
complex, and, it would implied, in particular, the appearance of false
"identical notes" [??? :-( "notes communes" in French...].
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End of first part.