AW.: Re: A7b9b13 in D minor

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

<<
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.

<<
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!