A7b9b13 in D minor

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 included E and put it in parentheses because although it is not
considered part of the altered scale, it could be used as an alternative
for Eb. Note that in my previous post I mistakenly put a "5" rather than a
"3" under the "E".

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.

John Link
ALMOST ACAPPELLA

>From: Robert C Valentine <bval@iil.intel.com>
>
>
>I would think that singers would tune the chord to
>be both simple harmonically and to reflect the target.
>
>shown as
>
> relative interval within A7 chord
>note name
>absolute interval from D minor
>
>I would expect
>
> 5/4 6/5 32/27 6/5 3/2
>A C# E G Bb F
>3/2 15/8 9/8 4/3 8/5 6/5
>
>or
>
> 5/4 6/5 6/5 32/27 3/2
>A C# E G Bb F
>3/2 15/8 9/8 27/20 8/5 6/5
>
>One could think about
>
> 5/4 6/5 7/6 32/27 3/2
>A C# E G Bb F
>3/2 15/8 9/8 21/16 14/9 7/6
>
>but I doubt anyone would not feel that the G was flat, and
>having the F 'move up' to the F in the target would sound
>intriqueing as well.
>
>BUT... it depends on the voicing. Shown "straight up",
>I think the fifth Bb-F will be tuned. But in other
>voicings, the tuning of the diminshed seventh chord
>may dominate.
>
>Bob Valentine

John Link wrote:
>
> From: johnlink@con2.com (John Link)
>
> 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

Do you really want 19/16 for B/A?,
I suppose 19/16 is possible for C/A, or perhaps you made a mistake with
18/16?

Xavier

>From: "Xavier J.-P. CHARLES" <xcharles@club-internet.fr>
>
>John Link wrote:
>>
>> 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
>
>Do you really want 19/16 for B/A?,
>I suppose 19/16 is possible for C/A, or perhaps you made a mistake with
>18/16?

Thank you for your careful reading. I meant to write not B but B# for the
#9, and it IS 19/16:

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

John Link
ALMOST ACAPPELLA

John,
my reading is careful especially when I see "19/16"...
A few days ago, I write few words on this interval to say that, for me,
it's good third (the JI minor third?) for minor chords (but only if it's
really a minor chord, with the tonic for root note) in tonal music.
What do you think about that?
And what do others members of this list think?

Xavier

>my reading is careful especially when I see "19/16"...
>A few days ago, I write few words on this interval to say that, for me,
>it's good third (the JI minor third?) for minor chords (but only if it's
>really a minor chord, with the tonic for root note) in tonal music.
>What do you think about that?
>And what do others members of this list think?

That sounds exactly like what I said. Similarly, the 7b9b13 chord would be
tuned 8:10:12:14:17:26 if it were meant to be a stable tonic chord, which is
certainly not the case in jazz. Jazz harmony is very voicing-specific and is
more closely related to polyharmony than to extended overtone structures.

>From: "Xavier J.-P. CHARLES" <xcharles@club-internet.fr>
>
>John,
>my reading is careful especially when I see "19/16"...
>A few days ago, I write few words on this interval to say that, for me,
>it's good third (the JI minor third?) for minor chords (but only if it's
>really a minor chord, with the tonic for root note) in tonal music.
>What do you think about that?

Well, my initial response was negative, but then I understood by "really a
minor chord, with the tonic for the root note". That means that we'd have

D 1
F 19/16
A 5/3

Although D is clearly the root, as opposed to Bb (8/5 relative to D), I
don't think that that's what good singers would do, because of the large
third between F and A involving the primes 3, 5, and 19. Also, this tuning
does not have the property of the minor triad being formed by the swapping
of thirds of two different sizes (unless you think a D major triad would
tune as 1 80/57 3/2). Furthermore, the tuning you suggest would not easily
allow the addition of C and E to make D-7 and D-9, so I'm not convinced.

John Link
ALMOST ACAPPELLA

>From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
>>my reading is careful especially when I see "19/16"...
>>A few days ago, I write few words on this interval to say that, for me,
>>it's good third (the JI minor third?) for minor chords (but only if it's
>>really a minor chord, with the tonic for root note) in tonal music.
>>What do you think about that?
>>And what do others members of this list think?
>
>That sounds exactly like what I said.

Where? I can't find it.

>Similarly, the 7b9b13 chord would be
>tuned 8:10:12:14:17:26 if it were meant to be a stable tonic chord, which is
>certainly not the case in jazz.

Unless I've made a mistake, the tuning you wrote is the one that I consider
to be in tune. I agree that 7b9b13 is not meant to be a stable tonic chord.
But I don't think that the tuning I propose gives a such a chord. It DOES
have a well-defined root, and because each tone is represented by a single
prime (except for powers of 2), it has loads of tension, which makes it THE
prime (note the double meaning?) example of a dominant chord.

> Jazz harmony is very voicing-specific and is
>more closely related to polyharmony than to extended overtone structures.

I disagree with the second half of the statement. I believe the fact that
jazz harmony is sometimes taught that way (e.g., Cmaj7#11 = B-/C) is a
result of 12tet.

John Link
ALMOST ACAPPELLA

>From: DWolf77309@cs.com
>
>In einer Nachricht vom 11/11/99 12:18:58 AM (MEZ) Mitteleurop�ische
>Zeitschreibt johnlink@con2.com:
>
><< Well, my initial response was negative, but then I understood by "really a
> minor chord, with the tonic for the root note". That means that we'd have
>
> D 1
> F 19/16
> A 5/3
>>>
>
>You must mean:
>
>D 1/1
>F 19/16
>A 3/2
>

Of course. I think i must be spending too much time these days sending
email. I should probably spend more time practicing my singing or finishing
my CD.

><<
> Although D is clearly the root, as opposed to Bb (8/5 relative to D), I
> don't think that that's what good singers would do, because of the large
> third between F and A involving the primes 3, 5, and 19.
>>>
>
>The interval between F and A is 24/19. No 5's.

Yes. My mistake was due to my previous mistake of typing 5/3 for A.

><<
>Also, this tuning
> does not have the property of the minor triad being formed by the swapping
> of thirds of two different sizes (unless you think a D major triad would
> tune as 1 80/57 3/2). Furthermore, the tuning you suggest would not easily
> allow the addition of C and E to make D-7 and D-9, so I'm not convinced.
> >>
>
>While the minor triad 16:19:24 is very much more pleasant (it was either Lou
>Harrison or Tom Stone who called the 19:16 "nature's own minor third") than
>the Major triad found by inversion:
>38:48:57, the latter is extremely close to the 12tet and certainly better
>than the pythagorean 64:81:96!

So? I don't consider a major triad in 12tet a standard for intonation, and
the Pythagorean major triad is not one that I'd want my singers to produce,
either. Neither of them stacks up to a 4:5:6 major triad. Still, I'm
curious what 16:19:24 would sound like.

John Link
ALMOST ACAPPELLA

John Link wrote,

>Still, I'm
>curious what 16:19:24 would sound like.

John, I suggest you spend a lot of time with a tunable synthesizer or
something and investigate these things. No offense, but I'm getting the
feeling that you're basing a lot of things on an abstract "theory" that has
too little grounding in actual, precise experimentation.

I wrote,

>> Jazz harmony is very voicing-specific and is
>>more closely related to polyharmony than to extended overtone structures.

John Link wrote,

>I disagree with the second half of the statement. I believe the fact that
>jazz harmony is sometimes taught that way (e.g., Cmaj7#11 = B-/C) is a
>result of 12tet.

And I disagree strongly. For another example, in a G13b9 chord, voiced G f b
e' g#', the top three notes _must_ approximate a 3:4:5 in order for the
chord to sound good. No "overtones of G" interpretation will do.