F in G7 as 21/16 rather than 4/3...

>From: Robert C Valentine <bval@iil.intel.com>
>
>
>>
>> If you actually SANG an F in G7 as 16/9 relative to C then I suspect that
>> you wouldn't make the cut at an audition for Gerald Eskelin's L.A. Jazz
>> Choir, or any good barbershop quartet.
>>
>
>How about the Mormon Tabernacil Choir? I'm sure you are correct with
>the settings you site, and I am not against septimal intervals, but
>are (and others in this thread) you saying that 7/4 (21/16) is ALWAYS
>the right choice for the dominant seventh?

Absolutely not. In fact, there are cases where it would be clearly out of
tune, and I intend to write about some of these soon.

John Link
ALMOST ACAPPELLA

John Link (11 Nov 1999, 11:01) wrote
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
My view is that the 7/4 seventh is exactly the one used by good string
quartets in the dominant 7th chord leading to the tonic in e.g.,
Mozart's
music.

Let's remember that meantone tuning is a possible tuning for keyboards,
but
that singers and unfretted strings have never been constrained by such
tuning, except when accompanied by meantone instruments. Meantone
tuning,
like any system of fixed tuning, can never be the standard of
intonation.
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

DWolf (11 Nov 1999 12:15) wrote
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Meantone tunings were the dominant keyboard tunings in the common
practice
tonal era, a time when a capella repertoire was the exception rather
than the
rule. Singers would have been highly unlikely to sing in dissonace with
the
continuo instruments, i.e. organs -- mostly in 1/6 comma -- and other
keyboards -- mostly in 1/4 comma.
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

I think that 7/4 is really better when it's possible...
I mean that, in Mozart's quartets for example, it's more often than not
possible. But only if it's really a dominant chord, not for altered II
(D-#F-A-C in C major), in this case, I think that it will be
36-45-54-64.
An example of problem is in the first quartet (K.80, G major, mesure
12/13). The tonality is A major, the chord is E-#G-B-D (m.13), but just
before there is this chord : A-#F-D, then, if both A are the same (m.12
and 14), both D can't be the same if the second is 7/4 of E (and E 3/2
of A).

I'm actually working to play (with my violin) the double concerto in D
minor (Bach... BWV 1043). If I play alone first or second soloist part,
there is note which seams to be "7", but if I look accompaniment, or if
I play with an other violonist, it becomes very compicated.
In the Largo, m.2, in F, 2d violin has a B flat and an A. just before
the A it's a dominant chord
(C-E-G-bB), but before, under the same B flat there is a II� chord
(G-bB-D-F).
I think that we must do 4/3 (for bB/F) at this place.
In the same movement, m.27, the B flat is above just one dominant chord,
then bB/C=7/4 don't make problem (even if the second violin plays
G-F-G-E-C-E, with a 21/16 bB/F between both violins).

I don't think that playing violin (or singing) with a piano or an
harpsichord makes so hard problems that Dwolf wrote. When the sound is
so different, our ears are more tolerant, a french acoustic theorist
(Emile LEIPP)had point over this fact few years ago with a clarinet and
a piano. But I am'not sure that it's better to play together with
different intonations...
For flute and organ, I suppose that the problem is quite stronger.

Let me remind you that I try(...) to play JI with the help of difference
tones, when I play B flat and C together, I hear an C when it's 7/4, a B
flat when it's 16/9, and a A flat when it's 9/5. But it's easier with a
second than a 7th : when I play C/bB as 8/7, I hear a C, for 9/8 I hear
a bB, for 10/9 I hear a bA.
When I play long chords it's easy, but when I play really a piece of
music it's more difficult...

Xavier wrote,

>Let me remind you that I try(...) to play JI with the help of difference
>tones, when I play B flat and C together, I hear an C when it's 7/4, a B
>flat when it's 16/9, and a A flat when it's 9/5. But it's easier with a
>second than a 7th : when I play C/bB as 8/7, I hear a C, for 9/8 I hear
>a bB, for 10/9 I hear a bA.

That's an excellent strategy for trying to play JI. But I would argue that
if you are trying to play Bach or Mozart and interpret every major second as
one of the above, you are doing a disservice to these composers. All the
"problems" you mention vanish in meantone tuning, and yet meantone goes most
of the way in correcting the deviations from pure consonance found in
12-tET. I would suggest that your best approach for this music is to use
meantone as your starting point, and then make very small adjustments at
each moment in time so that the simulateneities will be tuned in JI (however
you define that). Then instead of having notes shifting by a comma, you'd
have notes shifting by no more than 3 or 4 cents, and your level of
consonance would be undisturbed.

>>Try as I might, I can't come up with any glitchy sound in the 5-limit
>>Bach file (b-b-bz5.mid, 10-19-99, 88540 bytes) at 00:22-00:23 or
>>2:44-2:45. Would one of the other list members who has this file (Carl?
>>Jay?) listen and see if you can help me understand what Paul is talking
>>about?
>
>It's not a glitchy sound but a slight but noticeable difference in tuning in
>two successive instances of a note.

00:22-00:23 - There seems to be a diminished chord resolving to a dominant.
It almost sounds like the bass note drops a comma, but it's very hard to
hear. There's no reason for it to drop, if diminished chords are tuned in
12tET; holding the treble notes constant, the 16:9 in the bass of the
dominant chord would be essentially the same pitch as the root of its
diminished forerunner. In any case, this segment is a prominant part of
the ground -- it wouldn't just bother you at 00:22!

2:44-2:45 - You must mean 45-46. There's an F# that gets sharper as the
augmented 5th of a Bb chord than it was as the major 3rd of a D chord.
Slightly annoying.

-Carl

>>Try as I might, I can't come up with any glitchy sound in the 5-limit
>>Bach file (b-b-bz5.mid, 10-19-99, 88540 bytes) at 00:22-00:23 or
>>2:44-2:45. Would one of the other list members who has this file (Carl?
>>Jay?) listen and see if you can help me understand what Paul is talking
>>about?
>
>2:44-2:45 - You must mean 45-46. There's an F# that gets sharper as the
>augmented 5th of a Bb chord than it was as the major 3rd of a D chord.
>Slightly annoying.

Hmm. In the 7-limit version there's a pronounced commatic shift in the
bass at 2:44-2:45, but I don't hear it in the 5-limit version.

-Carl