re : G13#11

> Paul Ehrich wrote
>
> Anyway, the second chord sounds totally different to me than the first
> chord. I would expect 99% of jazz musicians to reject the
> second chord as a G13#11 in this context of coming right after a
> 12-tET version of the same chord.

I haven't listened to Monz' tuning, but when I first got a sound card
with tuning tables, I convinced myself that "everything is the overtone
series" is NOT going to work for the music I routinely play with exactly
this example. The jazz #11 and 13 are, to my ears, not remotely related
to the 11'th and 13'th harmonic. They should make 'as good' a major
triad with the 9 as the underlying G triad, since the polychord zing is
part of the sound (9:11:13 is quite distinguishable from 4:5:6).

Most jazzers see this chord as coming from the fourth mode of the
ascending melodic minor scale. This is also the chord that
flips over on its tritone for the much abused 'tritone substitution'
(which I balieve in Classical theory is referred to as the augmented
sixth?).

The relationships are shown below.

1 2 b3 4 5 6 7 melodic minor
1 2 3 #4 5 6 b7=#6 lydian b7
1 b2 b3=#2 b4=3 b5 b6=#5 b7 altered dominant

Of course, once we go into other temperments, things start
falling apart since the puns don't hold.

In meantones, we can keep things working out through proper spelling.
The melodic minor scale is comprised of WsWWWWs, and #=W-s (b=s-W). The
first option is to raise the seventh by the amount of the amount
higher that the 'next b' is above the 'current #' on a whole step.
I've designated this with a '^' sign.

1 2 b3 4 5 6 ^7 'melodic minor'
1 #1 #2 3 #4 #5 #6 'altered dominant'
1 2 3 b5 5 6 b7 'lydian b7'

The other technique lowers the third by the same amount and leaves
the seventh as is.

1 2 #2 4 5 6 7 'melodic minor'
1 b2 b3 3 b5 b6 b7 'altered dominant'
1 2 3 #4 5 6 #6 'lydian b7'

In 31tet, these corrections bring 'in tune' septimal intervals
into the scale. For instance,

#2 ~= 7/6 ( 2^(7/31) )
#4 ~= 7/5 ( 2^(15/31) )
b5 ~= 10/7 ( 2^(16/31) )
#6 ~= 7/4 ( 2^(25/31) )

The actual spelling I've been using in 'ascii 31tet research'
(some C programs I've written to generate scales given certain
constraints) is

C C^ C# C#^ CX D
Dbb Db. Db D. D D^ D# D#^
Ebb Eb. Eb (etc...)

Bob Valentine