Re: Digest Number 387

>
> Robert,
>
> I'll rephrase what I wrote in a previous post. In the key of D minor, I
> believe that A7b9b13 is taken from the following scale (the altered scale):
>
> A Bb B C# Eb (E) F G A
> 1/1 17/16 19/16 5/4 11/8 3/2 13/16 7/8 2/1
>
> And that #9 (B) and b5 (Eb) for that chord would also come from that same scale.
>

I would tend to tune the altered scale differently than that, but
part of it has to do with context.

Re-writing this scale in the target key

A Bb B# C# Eb (E) F G A
3/2 51/32 57/32 15/8 33/32 9/8 39/32 21/16

shows some notes which are trying to fall into very "weak" pockets and
are going to be tugged at by very strong local factors (the Bb Eb and
G are going to try to become a major triad if there is any simultaneous
usage of them).

But, I see that you are expecting the
overtone series to provide the gravity to make this tuning work. I
can agree with this assumption, but would use the overtone sereis of
the target and come up with a tuning like...

A Bb B# C# Eb (E) F G A
3/2 25/16 7/4 15/8 17/16 9/8 19/16 21/16

...which still has the the F drifting down on the D minor, or staying
where it is to let the D minor sizzle.

> Such a dominant 7th chord is loaded with tension waiting to be released (by
> the D minor triad to follow). It is not a pretty chord.

I'm sure thats true. I would tend to look for common tones between the
dominant and the tonic, if there doesn't HAVE to be drift (for instance
on the F) I don't see any reason to add it. That is why I would tend
towards...

A Bb B# C# Eb (E) F G A
3/2 8/5 9/5 15/8 16/15 6/5 4/3

which tunes the obvious triads in the altered dominant and is in tune
with the target.

But, since the Eb triad (with the B#) is independent, other tunings
could be considered. One that stresses the septimal seventh sound (if
that is what the context determines to be more "in tune" or otherwise
"more desireable")

A Bb B# C# Eb (E) F G A
3/2 63/40 7/4 15/8 21/20 6/5 21/16

...but another one that does this, with the stretched septimal major
chords (which gives a better leading tone) is...

A Bb B# C# Eb (E) F G A
3/2 14/9 7/4 27/14 28/27 7/6 4/3

...which looks like a Howler, plenty of tension.

Does your group have any recordings?

Bob Valentine

>From: Robert C Valentine <bval@iil.intel.com>
>
>>
>> Robert,
>>
>> I'll rephrase what I wrote in a previous post. In the key of D minor, I
>> believe that A7b9b13 is taken from the following scale (the altered scale):
>>
>> A Bb B C# Eb (E) F G A
>> 1/1 17/16 19/16 5/4 11/8 3/2 13/16 7/8 2/1
>>
>> And that #9 (B) and b5 (Eb) for that chord would also come from that
>>same scale.
>>
>
>I would tend to tune the altered scale differently than that, but
>part of it has to do with context.
>
>Re-writing this scale in the target key
>
> A Bb B# C# Eb (E) F G A
> 3/2 51/32 57/32 15/8 33/32 9/8 39/32 21/16
>
>shows some notes which are trying to fall into very "weak" pockets and
>are going to be tugged at by very strong local factors (the Bb Eb and
>G are going to try to become a major triad if there is any simultaneous
>usage of them).
>
>But, I see that you are expecting the
>overtone series to provide the gravity to make this tuning work.

Yes,that's right.

>I can agree with this assumption, but would use the overtone sereis of
>the target and come up with a tuning like...
>
> A Bb B# C# Eb (E) F G A
> 3/2 25/16 7/4 15/8 17/16 9/8 19/16 21/16
>
>...which still has the the F drifting down on the D minor, or staying
>where it is to let the D minor sizzle.
>
>> Such a dominant 7th chord is loaded with tension waiting to be released (by
>> the D minor triad to follow). It is not a pretty chord.
>
>I'm sure thats true. I would tend to look for common tones between the
>dominant and the tonic,

That means less movement from dominant to tonic, and also less resolution.

> if there doesn't HAVE to be drift

Not *drift*, flexibility, or adjustment.

(for instance
>on the F) I don't see any reason to add it. That is why I would tend
>towards...
>
> A Bb B# C# Eb (E) F G A
> 3/2 8/5 9/5 15/8 16/15 6/5 4/3
>
>which tunes the obvious triads in the altered dominant and is in tune
>with the target.

I doubt that anyone would recognize A as the root of this collecton of
pitches. If I've drawn the lattice diagram correctly then Eb at 16/15
relative to D is the fundamental (which is possible as the root of a
dominant chord in D minor, but I don't think it would tune as you
describe). In the tuning I describe A is unmistakeably the root.

>But, since the Eb triad (with the B#) is independent, other tunings
>could be considered. One that stresses the septimal seventh sound (if
>that is what the context determines to be more "in tune" or otherwise
>"more desireable")
>
> A Bb B# C# Eb (E) F G A
> 3/2 63/40 7/4 15/8 21/20 6/5 21/16
>
>...but another one that does this, with the stretched septimal major
>chords (which gives a better leading tone) is...
>
> A Bb B# C# Eb (E) F G A
> 3/2 14/9 7/4 27/14 28/27 7/6 4/3
>
>...which looks like a Howler, plenty of tension.

It looks like a howler, but it doesn't have A=3/2 as its root.

>Does your group have any recordings?

I'm planning to release a CD of a concert soon (maybe in the next few
months?). I will be sure to let all of you know when it is ready.

John Link
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