Happy 1000th,Aristoxenos

I'd like to second Adam's comments and express my appreciation to David
Madole (and Greg Higgs) for starting and administering the Tuning List
for the past three years. The accumulated digests, Bibliography, and
other FTP files, etc. are a unique resource containing information
accessible only with difficulty elsewhere, if at all.

Some comments on recent digests:

Plomp and Levelt's model is simpler to program and computes faster
than Kameoka and Kuriyagawa's. I'm told they give essentially the
same results as far as predicting the relative dissonance of intervals
in specific timbres.

As for the use of 5/4. Eratosthenes, who may be responsible for
the linear misinterpretation of Aristoxenos's parts, used 19/15 as his
enharmonic ditone. By Ptolemy's time, the enharmonic was no longer
used in popular music except as a semitonal pentatonic produced by
gapping the diatonic sequence (Winnington-Ingram, Mesomedes hymns,
etc.)

Frankly, I'm somewhat suspicious of Ptolemy's enharmonic and chromatic
genera as they have a rough 1:2 division of the pyknon (Barbera), even
if it meant that he had to reorder the intervals resulting from
"katapyknosis" to obtain usable superparticular ratios. But, I do
agree that the kithara and lyra tunings probably represent practice.
I also find his Equable Diatonic interesting as it resembles extant
3/4-tone Islamic diatonic tunings.

Aristoxenos's (or Cleonides's) parts are still used by the Eastern
Orthodox Churches to describe their tetrachords, though at one time
another system of 68 parts to the octave, 28 to the fourth was in use.
(Savas, Xenakis, Athanasopoulos, Tiby, etc.). I do not know the origin
of this system, however.

I would agree with Dan that Aristo was a cognitive (proto)scientist
more concerned with perception rather than mathematical niceties.
Whatever he might have met, his scales are certainly worth hearing
and using, even if we tune them to some 0 mod 12 ET or even try to
interpret them as Ptolemy and Eratosthenes did as linear division.
I think he may also be a witness for his own contemporary practice as
he gives scales plausibly interpretable as Archytas's and the old
Pythagorean forms. He may also have been documenting the various
tuning of the relatively new chromatic genus.

Kathleen Schlesinger also understood Aristoxenos to mean the 9/8 tone,
but she then fantasically interpreted his genera in terms of a
part of 17+ cents and a fourth of 510+ cents to try to make it agree
with theories.

Has anyone actually tried repeating his experiment on a replica kithara
without tuning machines? I suspect it wouldn't be hard to loose the
comma in the chain of intervals.

I don't have copies of Barker's books handy and I would appreciate
it very much if someone could send me (or post) the "planetary scales"
in the several genera. I would like to check them against a list of
correspondences with KS's harmoniai as used by the Anthroposophists,
including Elsie Hamilton. Winnington-Ingram states that Censorinus
and Pliny list planetary scales which resemble the Dorian and
Phrygian of Aristides Q. with chromatic, rather than enharmonic,
intervals. It would be interesting to see if Steiner's correspondences
are the same as the Greek theorists and writers, but I am unable to
get either the classical or Steiner's texts at the moment.

--John


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