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Dominant 7th tuning again

🔗Tom Dent <stringph@gmail.com>

11/20/2006 7:11:30 AM

I remember an old (ish) thread about tuning the dom 7th... not sure
what the result of it, if any, was, but singing the Schumann Missa
Sacra has led to a few thoughts.

The particular relevant feature of this piece is the number of 7th
chords in 3rd inversion, with a tritone between the lower 2 parts. A
few diminished chords were also spaced this way. I suspect that a 7:5
tritone would be quite successful here (as distinct from the 7:5 dim
5th in barbershop 7th chords) and may have been what we got close to
in our a capella rehearsals.

The 7th chord would then be

28:35:42:50(:56)

using the 28:25 'septimal middle tone', 126:125 away from 10:9 and
225:224 from 9:8. Very natural for 'common practice', and even
difficult to avoid when the tenor & bass have the tritone and the
tenor is used to singing true thirds:

e.g. when the 7th is prepared by the dominant triad with spacing

G-B-d-g -> F-B-d-g.

This dom 7th tuning would be relatively easy to implement in adaptive
JI, for example, involving quite small fractional pitch shifts.

A justly tuned 'Tristan chord' F-B-D#-G# would then have the intervals

5:7, 4:5, 3:4

which is 60:84:105:140 or 1/7:1/5:1/4:1/3, as often discussed ...

... but one has to wonder if orchestral players possibly using 19th
century 'expressive intonation' (sharps sharp, etc.) would come
anywhere close to this 'choral' degree of justness, or even a good
meantone approximation, particularly since the chord is completely
unprepared and involves different orchestral sections.

~~~T~~~