weekend listenning (altered scale, 17 and 19)

After last weeks exchange on the altered dominant scale,
I had a weekend to sit at the tuning table and try all
manner of experiment in. I'll summarize what I found.

John Link came up with an altered dominant scale to
fill in the blanks for the chord

A7b9b13

which is resolving to a D (I presume it was Dminor).
The following are the ratios he presented (shown both root
and target oriented).

A Bb B# C# Eb (E) F G A
A 1/1 17/16 19/16 5/4 11/8 3/2 13/8 21/16
D 3/2 51/32 57/32 15/8 33/32 9/8 39/32 21/16

To my ears...
the chord sound itself is weakened from the choice of the
harmonic series 13. I wouldn't call it a 'b13' even though
it is a flat thirteen. Part of this weakness comes from the
lack of identity vs the b9, where I would like to hear a P5.

In playing the scale, the 13/11 between the b13 and b5 is too
much of a 'minor third' when I want to hear a whole tone.

Although the 21/16 G sounds GREAT with the A7 triad, the
fact that it misses a bunch of good relationships with the
chord and scale under discussion make me want to hear it
(as well as the b13 and b5) a little sharper.

I presented a half-dozen alternatives last week which, John
correctly anticipated, would not work. Most of them tuned
the inter-relationships (getting the P5s and triads back)
but weakenning the identity a 'A'. So eventually, I adopted
his tuning from A to D, as it was more
pleasing an "A like" than any of my alternatives.

But then I 'corrected' the top of the scale for my ears by
getting the fifths and upper structure triads in tune.
(shown in its full chromatic glory).

A Bb B B# C# D Eb E F F# G G#
A 1/1 17/16 9/8 19/16 5/4 4/3 17/12 3/2 19/12 5/3 16/9 15/8
D 3/2 51/32 27/16 57/32 15/8 1 17/16 9/8 19/16 5/4 4/3 45/32

The only real sacrifice is the 16/9 rather than 7/4 seventh, which is
certainly 'spongier' on a plain A7, but to my ears worked better in
the "altered dominant" scale and chord.

It features the intriguing identity 51:64:76 ~= 4:5:6!

When I actually looked at the cents deviations, I realized that
I'm getting pretty close to reinventing 12tet (the hard way!).

a 2
bb 7
b 6
b# -1
c# -12
d 0
eb 5
e 4
f -2
f# -14
g -2
g# -10

Bob Valentine

> [Bob Valentine, TD 396.1]
>
> After last weeks exchange on the altered dominant scale,
> I had a weekend to sit at the tuning table and try all
> manner of experiment in. I'll summarize what I found.
>
> John Link came up with an altered dominant scale to
> fill in the blanks for the chord
>
> A7b9b13
>
> which is resolving to a D (I presume it was Dminor).
>
> <snip>
>
> But then I 'corrected' the top of the scale for my ears by
> getting the fifths and upper structure triads in tune.
> (shown in its full chromatic glory).
>
> A Bb B B# C# D Eb E F F# G G#
> A 1/1 17/16 9/8 19/16 5/4 4/3 17/12 3/2 19/12 5/3 16/9
15/8
> D 3/2 51/32 27/16 57/32 15/8 1 17/16 9/8 19/16 5/4 4/3
45/32
>
> The only real sacrifice is the 16/9 rather than 7/4 seventh, which is
> certainly 'spongier' on a plain A7, but to my ears worked better in
> the "altered dominant" scale and chord.
>
> It features the intriguing identity 51:64:76 ~= 4:5:6!
>
> When I actually looked at the cents deviations, I realized that
> I'm getting pretty close to reinventing 12tet (the hard way!).
>
> a 2
> bb 7
> b 6
> b# -1
> c# -12
> d 0
> eb 5
> e 4
> f -2
> f# -14
> g -2
> g# -10

Hmmm... that sounds suspiciously like Paul Erlich's
thesis (with which I basically agree) that 'certain'
chords are most in-tune when tuned in the 12-eq scale,
if by 'in-tune' one means that the various individual
chord-members are able to fulfill multiple different
harmonic-function roles simultaneously. (Paul's
usual example is a '6/9 chord'.)

What this kind of thing points out is that the entire
thought-process involved in analyzing and describing
chords is highly conditioned by the kind of tuning
system under consideration. Many types of chords
and descriptions of their progressions are really
only possible in 12-eq, and trying to make them
fit a certain rational implication is quite difficult,
and many different rational interpretations could be
argued with various degrees of success.

When listing chord-members as ratios they can certainly
be analyzed as having multiple functions, as Partch
pointed out so emphatically. But as Bob points out
these multiple functions are often hard to reconcile
with the types of multiple functions possible in 12-eq
or other types of tunings.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

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Joe Monzo wrote,

>Hmmm... that sounds suspiciously like Paul Erlich's
>thesis (with which I basically agree) that 'certain'
>chords are most in-tune when tuned in the 12-eq scale,
>if by 'in-tune' one means that the various individual
>chord-members are able to fulfill multiple different
>harmonic-function roles simultaneously. (Paul's
>usual example is a '6/9 chord'.)

I would rather say "meantone tuning" than "the 12-eq scale" here, but
whatever.