number 7 + minor

Hello
I'm a new french member of this list.

I'm interesting by just intonation, especially to analyse "classical"
music. I also practice violin and I try to play with just intonation
with the help of combination tones.
But I don't use traditionnal just intonation theories because, for
example, I think we must use number "7" in few situations, especially
for dominant chord. Usely number 7 isn't admitt in those theories.
What is your opinion for that subject?

There is an other point which doesn't satisfy me in just intonation
theories : the problem of the minor chord.

Xavier CHARLES

4:5:6:7 is a common tuning for the dominant seventh chord in barbershop
music, but is more controversial for classical music. I wouldn't use it
except for the augmented sixth chord, where it is historically appropriate.
John deLaubenfels is working on adaptively tuned, 5-limit and 7-limit
versions of Beethoven, and should have more to say (I haven't been able to
get his retuned sequences to work on my computer, though other microtonal
MIDI files have in the past).

My ears used to prefer 16:19:24 over 1/6:1/5:1/4 (10:12:15) for the
root-position tonic triad in a minor key, though the latter certainly wins
out for first-inversion minor triads (12:15:20 beats 19:24:32). Since having
my piano in meantone for a while, I've come to accept the (near-) 10:12:15
as a tonic minor, though it's a very different experience from what we're
used to from 12-tET.

Paul H. Erlich wrote:

> 4:5:6:7 is a common tuning for the dominant seventh chord in barbershop
> music, but is more controversial for classical music. I wouldn't use it
> except for the augmented sixth chord, where it is historically appropriate.

I'm actually working to analyse music of Mozart and Bach (and playing on
my violin) by the mean of whole numbers. For Mozart, I think it's nearly
always possible to play 4-5-6-7 for dominant chords. But for Bach, it
depends of the context.

I don't know what is "barbershop music"?

> My ears used to prefer 16:19:24 over 1/6:1/5:1/4 (10:12:15) for the
> root-position tonic triad in a minor key, though the latter certainly wins

I'm very happy to see those numbers for minor triads. After few years of
work, I find it was the only poosibility for this chord. I wrote it in
my "m�moire de DEA" (University of Paris Sorbonne, 1996, "Contribution a
l'�tude des probl�mes de la gamme et de la justesse dans la musique
occidentale, vers une autre th�orie des hauteurs?"), and I found few
elements wich "proove" that "16-19-24" is a very intersting solution for
minor chord. One element is the commbination tones, another is something
writen by Helmholtz.
Is this solution officially admit in USA? I have never read about it
before today!

Thank you for you very fast response...

Xavier CHARLES

First of all, I would like to say that I don't like the idea of using just
intonation for Mozart and Bach, and there is certainly no "official
solution" recognized by "USA". But anyway, I believe Mozart did occasionally
reinterpret German augmented sixths as dominant seventh, while Bach did not,
so that's one excuse for using 4:5:6:7 for Mozart but not Bach.

>One element is the commbination tones, another is something
>writen by Helmholtz.

Helmholtz preferred 16:19:24 for its combination tones. What is the other
element? (To be, having the root of the chord octave-equivalent to the
fundamental of the harmonic series seems important). However, in Bach's time
10:12:15 (nearly) would still have appeared on many instruments, so I
suggest you give it a chance.

>I have never read about it
>before today!

Besides Helmholtz, Van Eck makes a point of the 16:19:24 chord in his book,
_J. S. Bach's Critique of Pure Music_.

[Xavier Charles, TD 327.15:]
> Hello. I'm a new french member of this list. I'm interesting by
> just intonation, especially to analyse "classical" music. I also
> practice violin and I try to play with just intonation with the help
> of combination tones. But I don't use traditionnal just intonation
> theories because, for example, I think we must use number "7" in few
> situations, especially for dominant chord. Usely number 7 isn't
> admitt in those theories. What is your opinion for that subject?
> There is an other point which doesn't satisfy me in just intonation
> theories : the problem of the minor chord.

[Paul Erlich, TD 327.17:]
> 4:5:6:7 is a common tuning for the dominant seventh chord in
> barbershop music, but is more controversial for classical music. I
> wouldn't use it except for the augmented sixth chord, where it is
> historically appropriate. John deLaubenfels is working on adaptively
> tuned, 5-limit and 7-limit versions of Beethoven, and should have more
> to say.

I won't argue the point of whether past theory accepts 4:5:6:7 as the
dominant 7th, but to my ears, other options aren't even close in beauty.
I've used it, and love it, in sequences of Bach through Beethoven,
Schubert, Brahms, and other 19th century composers. I haven't yet found
a sequence in which I prefer any other tuning. I do recognize that ears
differ in what pleases them, so if you don't like it, don't use it (try
listening to a big dominant ninth before you decide!).

I don't really care if something is "historically appropriate" if it is
good music. I would make the appeal that faithfulness to the past is a
red herring that can thwart the pursuit of maximum musical enjoyment and
creativity. In saying this, I'm not trying to knock scholarly pursuits
which aim to record exactly how things were, nor even performances that
attempt maximum adherence to past practice; it's just that in my own
work, I don't want to be anywhere but where everything from the past has
the potential to be combined with the wonderful new tools we've just
been given in the present.

My guess is that 4:5:6:7 just takes getting used to (I didn't like it
for the first year or so that I was adaptively tuning), but I don't
mean that to sound arrogant - tastes may simply vary in this regard.

Minor chords I tune 10:12:15, and am reasonably happy. I've never tried
16:19:24, but I do like 6:7:9 (the "sub-minor").

JdL