Re: High Primes in Greek Music

Monz and Kraig: It was Archytas who is credited with saying that "there
are 3 means in music" and who renamed the subcontrary mean, the
harmonic. Actually, Greek mathematicians give about 8 more-- see Heath,
"A History of Greek Mathematics" for details. I used all of them and a
couple I invented myself to generate tetrachords in "Divisions."

I don't recall seeing much use of the geometric mean in Greek music
theory. The only JI contexts where it might occur are in sequences such
as 1/1 4/3 16/9 and 1/1 3/2 9/4, though the fact that the geometric mean
lies between the harmonic and the arithmetic was known. One might
interpret most of Aristoxenos's genera as being based conceptually on
the geometric mean to aurally divide the pyknotic interval into two
parts.

I've never been able to get a completely clear idea from Jim French what
the scales of his auloi are. He is a believer in Schlesinger, or was the
last time we discussed the subject at one of Mark Miner's Homer
recitations some years ago at UCSD, but he also states that the reed has
an enormous effect on the tuning. Lou Harrison told me that the Korean
equivalent, the piri, is very hard to play in tune and that once he
inadvertently played a passage a fifth too high without realizing it.
However, he never said anything about the harmoniai, with which he was
acquainted. I can easily believe that KS played what she wanted to hear
or heard what she wanted to hear on her home-built replicas.

However, other than making it possible, I don't see how these
experiments settle whether the Greeks actually used the Harmoniai as she
interprets them. Barring new archeological discoveries, I don't see how
the question can be answered on the basis of the data we have.

I can make little sense out of her notational claims, especially since
the scales she derives from the notation are different from those she
considers canonical. Also, the idea that the primary mode, the Dorian,
was retuned to sub-21 from 22 seems hard to accept in the absence of any
literary references. Likewise, lowering the Lydian M.D. 26 to 27 is
doubtful, though one can make up a nice sub-27 scale.

Her theory breaks down completely in the chromatic and enharmonic
genera- I devoted a large part of a chapter in "Divisions" to the kind
of scales one gets when her theories are applied to these forms of the
harmoniai. Suffice it to say, that although all the diatonic forms are
modes of the Dorian and each other, the chromatic and enharmonic forms
of the harmoniai are not.

As I said, though, the system is fascinating in its own right as a set
of xenharmonic scales and quite extensible. If we can get good
monophonic recordings of the harmoniai on played on replica instruments
or better, performances by master musicians on their own instruments in
their own styles, I think Can Akkoc's software would answer the
questions of whether they are easily and naturally playable on auloi (or
flutes) and whether they are in fact played in extant non-European
music.

The question of the roots of Greek civilization and its relation to
Africa and Western Asia is complex. Historians are virtually unanimous
in rejecting extreme views such as those in "Stolen Legacy," but some
feel that many of the points raised in "Black Athena" are valid, though
the African origin of Athena and the other Greek gods is not generally
accepted. The relation of Greek culture to Babylonian and Western
Semitic has also been underappreciated.

Greek mathematics is closer to Babylonian than to Egyptian. Since
nothing is known about Egyptian music, little can be said about the
influence.The claim that the Egyptians used the semitonal pentatonic
cannot be verified by any historical reference, though it is not
unlikely since this scale is very common in South India, Japan, and
Ethiopia.

BTW, the common Ethiopian lyre is called a Krar in Amharic and a Kissar
(s = sh?) in other language(s). These terms are probably derived from
kithara, but I don't know if Kora is related or not. Ethiopian music
also uses the whole-tone pentatonic and in Muslim areas, the usual kind
of 1/4-tone inflected Arabo-Persian diatonic scales are found.

While the Ethiopian alphabet (a syllabary of some 280 or so characters)
is derived apparently from South Arabia, the numerals are derived from
Greek letters (the arithmetic notation is decimal).Ethiopia also uses
the only logical calendar-- 12 months of 30 days plus a 5 or 6 day
holiday at the end to make up the 365 or 366 day solar year. Apparently
it derives from the old Egyptian calendar. Ethiopian Airlines advertises
"13 Months of Sunshine" to tourists.

--John