source file: m1417.txt
Date: Sat, 16 May 1998 13:11:14 -0400

Subject: Re: TUNING digest 1416

From: monz@juno.com (Joseph L Monzo)

Paul Erlich wrote:

> I think the fact that the tritone in major nearly forms a 4:5:6:7
> with the dominant, and that the tritones in minor nearly form
> an 8:10:12:14:17 with the dominant, were not inconsequential
> for the development of tonal harmony.

I don't think the fact that the tritones are close to septimal
consonances has anything to do with the development of
tonal harmony.  Tonal harmony, as used during the so-called
"common practice" period 1600-1900, developed mainly out of
the fixing of pitches as absolute values (especially in notation),
the recognition of 5-limit ratios as consonances, and the intuitive
realization that because ratios have two terms, they are
related to other ratios in two different ways (Partch's
"Basic Monophonic Concept #2": "every ratio of a Monophonic
system is at least a dual identity"; "Genesis", p. 88), giving
rise to the major/ minor system.

In fact, assuming a tuning in 5-limit JI (or a meantone
which approximates 5-ratios well), the tritone could be one
of four ratios, all of which, while much less dissonant than
the Pythagorean tritones:
3^6		729/512		6.12	aug 4th
3^-6		1024/729	5.88	dim 5th
were pretty much at, if not beyond, the limit of what could
be considered consonant:
3^2 * 5^-2	36/25	6.31	dim 5th
3^-2 * 5^-1	64/45	6.10	dim 5th
3^2 * 5^1	45/32	5.90	aug 4th
3^-2 * 5^2	25/18	5.69	aug 4th

The 64/45 would normally be considered the tritone which appears
in the 5-limit Dominant 7th chord of 36:45:54:64.  4:5:6:7 is the
same as 36:45:54:63.
---------------------------------------------------------
> [Monzo:]
>> (I'd really like to see more feedback about microtonality in
>> the blues.)

> [Erlich:]
> I think this is a great topic, but I don't think ratios of large
numbers
> have much to do with it. I do think that many blues performers do
> distinguish between 6/5 and 7/6, however, as well as approaching a
> pentatonic scale in 7tET.

I'm certain that some blues vocalists distinguish between 6/5 and
7/6, and in Robert Johnson's vocals, I've heard a "sharp 9th" which
sounds to me like it starts as a 7/6 then slides upward to a 19/16 -
exactly the pitches we debated in the "Hendrix Chord", so my ears
are especially sensitive to this distinction.  Johnson in particular
exhibits
such minute pitch discrimination in his vocals that I'm sure his "odd
limit"
is _well_  above 7 or 9.
======================================
Mark Nowitzky wrote:

> P.S.:  Bassoons, on a sustained low note, also sometimes
> sound to me like some sort of electrical problem.

You should hear some of the sounds Johnny Reinhard
gets out of his axe!  I've dubbed him the "Hendrix of
the Bassoon".
 
   Joseph L. Monzo
    monz@juno.com
   

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