Brian is a true

conversationalist of the old school:
He seems to say things because they are putative, not because
he is trying to win some special contest.

He said in Tuning 809:

<<
Many cultures think musically in terms of adding
constant Herz intervals, disregarding whether the sum
comes out to a 2:1 or not. In fact the Banda Linda,
Banda Ndopka, Ngaka-Manza and Banda Gbambiya
peoples of Central Africa prefer an "octave" of
1150 cents. Lou Harrison has not explained how
to reconcile these facts with the notion that just
intonation forms the basis of world music.
>>

I think this objection is interesting, and I believe I can answer it.

I am not arguing here that just intonation forms the basis of all
musics (though I do tend to agree with that supposition). I am
arguing only that an arbitrary octave of 1150 cents does not
preclude reference to a just standard.

The music I've listened to from central Africa (mostly from
Zimbabwe) relies on a "gamut" (perhaps in adapting these terms
"tessitura" would be better) of a major third, which is different
from the characteristically European tetrachord. Tetrachords carry
inevitably a potential toward modulation, so that restraining from
modulation can be as forceful as a modulation would have been.
European thirds must remain chastely just in order to avoid
becoming leading tones.

Nevertheless, sharping thirds can be pleasant. That is exactly why
Frescobaldi sounds better in meantone.

The central African musics aren't concerned about melodic
modulatory implications, because their excursions tend to be
rhythmic, and therefore they are free to indulge in extravagently
wide thirds. The very extravagence, however, would be meaningless
without reference to a just standard.

Therefore, I do not see that the specific use of wide octaves can be
used to discredit the theoretical notion of a just standard.


Will



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