Re: About the major 2nd. (Digest 132 Message 6)

Bonjour David,

On Sun, 4 Apr 1999 19:57:44 +0200, you wrote:
> From: "David Mezquita" <DMEZQUI@teleline.es>
>Subject: About the major 2nd.
>...
>I have some doubts about the the major 2nd of a major scale. It seems clear
to me, that a chord of "sixte ajout�e" (in C Major: F,A,C,D) should have the
following intervals:
>
>A/F=5/4
>C/A=6/5
>D/C=10/9
>---> C/F=3/2, D/F=5/3, D/A=4/3
>
>It also seems clear that a Dominant chord (G-B-D) should be:
>
>B/G=5/4
>D/B=6/5
>---> D/G=3/2
>
>The chord of "sixte ajout�e" is often followed by the Dominant, so that, if
we assume that G/C=3/2, then we get two different D's! The first one is
D1/C=10/9, and the second one D2/C=9/8.
>
>So, what would be the best solution? Sacrifying one chord by using only one
of the D's? Sacrifying both chords by using a D3 that is in the middle of
the other two? Sacrifying a melodic line by using both D1 and D2? Any other
solution?

I vote for using both D1 and D2. I don't think it sacrifices the melodic
line. I play trombone in symphonies, jazz bands, etc., and often need to
move the slide a little when playing a tied note through a modulation.

I have a web page that discusses almost exactly the same modulation:

http://www.pacificnet.net/~nowitzky/justint/somemath.htm

The page addresses the tuning of D (when in the key of C). An example on
the web page recommends how to tune the D in a "ii V I" (Dm, G, C)
progression. So instead of a "fa sixte ajout�e" (F with added sixth) chord,
it uses a D minor chord. Quoting myself from the bottom of the web page:

"See how when going from the first chord (D minor) to the
second chord (the G Major), the bottom note (D 2000 Hz)
has to move up a little (to D 2025 Hz)."

If the second (dominant) chord was a G7 (G,B,D,F) instead of a plain G, I'd
still move the D up, and leave the common F alone, when coming from the
first (F6 or Dm) chord:

1st chord 2nd chord 3rd chord
--------- --------- ---------
F 2400 Hz F 2400 Hz E 2250 Hz
D 2000 Hz D 2025 Hz C 1800 Hz

But here's a twist - if the first chord were a D MAJOR chord (instead of D
minor), I'd put the first D at 2025 Hz, which would match the second chord's
D. The idea is that if there is no F in the first chord, it loses its
subdominant flavor.

Anyway, gracias,

--Mark (nowitzky@alum.mit.edu, AKA tuning-owner@onelist.com)
+------------------------------------------------------+
| Mark Nowitzky |
| email: nowitzky@alum.mit.edu AIM: Nowitzky |
| www: http://www.pacificnet.net/~nowitzky |
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