Re: Response to Dave Hill on JI and European composition [TD444.20]

On Fri, 17 Dec 1999 15:57:25 -0800, Gerald Eskelin
<stg3music@earthlink.net> wrote:
>>From: DWolf77309@cs.com
>>Date: Thu, Dec 16, 1999, 2:26 PM
>>
>> In einer Nachricht vom 12/16/99 9:20:03 PM (MEZ) Mitteleurop�ische
>> Zeitschreibt PErlich@Acadian-Asset.com:
>>
>> << (try, for example, Brahm's _In stiller Nacht_).

For those of you who, like myself, have never heard this piece, I found it at:
http://www.cpdl.org/composers/brahms.htm
Or you can go straight to the sound file (in good ol' equal-tempered MIDI
format), at:
http://www.newsbit.com/cpdl/sound/brahms/bra-stil.mid

>> Can you elaborate on what tuning problems this piece presents? >>
>>
>> For example the repeated alternating chords:
>>
>> S: g' f'
>> A: eb' eb'
>> T: bb cb'
>> B: eb Ab
>>
>> I really want to hear the second chord as a subharmonic harmonic seventh
>> chord with eb' as the one identity of both chords, sounding like something
>> right out of Partch:
>>
>> 5/4 8/7
>> 1/1 1/1
>> 3/2 8/5
>> 1/1 4/3

I'd suggest almost the same tuning, but I'd stick to 5-Limit JI. For the
F, I'd use 10/9 instead of 8/7. My F would be a minor 3rd below the Ab
(F:Ab = 5:6). Here's the ratios and their corresponding Nowitzkian Note
Names:

Ratios NNN
-------- --------
5/4 10/9 4G 4F
1/1 1/1 5Eb 5Eb
3/2 8/5 5Bb 6Cb
1/1 4/3 5Eb 5Ab

(More info on Nowitzkian Note Names at
<http://www.pacificnet.net/~nowitzky/justint/nnn.htm>.)

>> But the conventional analysis (e.g. Schoenberg) identify f as the second
>> chord's tonic, and there functional and motivic aspects in the piece as a
>> whole that make one not want to immediately give up these
interpretations as
>> well. Brahms rehearsed his choir from the piano, so I assume that the puns
>> available in temperament were intended.

You need not even go to 7-Limit JI to unveil a pun here. The F on Brahms'
piano could represent either of these 5-Limit tones:

Ratio Nowitzkian Note Name
----- ------------------------------
10/9 4F (down a minor 3rd from 5Ab)
9/8 5F (up a perfect 5th from 5Bb)

>Paul Hindemith, in his book "The Craft of Musical Composition" would call
>the Ab in the second chord the root, in that it is "root" of the most stable
>interval (Ab up to Eb). His point of view is very refreshing to any "jazzer"
>who knows very well that the root of a C6 chord is NOT "A."

I'd agree with Hindemith and Eskelin in the case of the second chord of the
aforementioned Brahms piece (the Ab minor triad with the added 6th) - the
Cb to F (tritone) is way less stable than the Ab to Eb.

And although I'd also agree that C is the root of a C6 chord, the case is a
little less cut-and-dried. A perfect 4th (E to A in the C6 chord) is a lot
more stable than a tritone. But the perfect 5th (C to G in the C6 chord)
still "wins".

+------------------------------------------------------+
| Mark Nowitzky |
| email: nowitzky@alum.mit.edu AIM: Nowitzky |
| www: http://www.pacificnet.net/~nowitzky |
| "If you haven't visited Mark Nowitzky's home |
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