Greek musical intervals, Partch

Gregg: Aristoxenos said that melody admits 1/4, 1/3 and 1/2 tones, but
nothing smaller and that no one can sing a sequence of more than
2 dieses, which can be any of these intervals. In his own genera, he
uses all of these intervals plus an interval of about 75 cents, the
hemiolic chromatic diesis.

Since we have several actual fragments of music written in the
enharmonic genus with quarter-tones, I think it is clear that they
were used in real Greek melodies and there is suggestive evidence from
Winnington-Ingram's analysis of the Spondeion scale that the 3/4
interval was also used. The interval 12/11 occurs in Ptolemy's scales
as well and may represent the practice of 2nd Century CE Alexandria.

There is some question as to how large the 1/4-tone diesis was.
It is thought that in the late 5th century BCE, the limma in the
original limmatal-ditonal enharmonic trichord was split into two
microtones of roughly 45 cents, though the ancient writers do not give
the exact measures. The earliest actual enharmonic tuning we have
is Archytas's (390 BCE) and his enharmonic tetrachord consists of an
approximate 1/3-tone, a 1/4-tone and a major third. The 28/27 first
interval is thought to have been chosen in order to make a 7/6 with
the note a 9/8 below the first note of the tetrachord (hyperhypate,
mese). The archaic enharmonic Dorian harmonia of Aristeides
Kointilianos has this note and it is used prominently in the
Orestes fragment. Bacchios calls this interval an ekbole or
eklysis and it apparently occurred in the chromatic genus as well.

Although the enharmonic genus fell into disuse in the 3rd century,
the theorists continued to describe enharmonic tunings with either
nearly equal quarter-tones such as Eratosthenes's 40/39 x 39/38 x
19/15, which is acoustically almost identical to the earlier
Pythagorean tuning (and close to Aristoxenos's theoretical 50 + 50
+ 400 cents), and Didymos's 32/31 x 31/30 x 5/4 or very unequal
microtones such as Ptolemy's 46/45 x 24/23 x 5/4.

What one sees is a gradual widening of the enharmonic diesis from a
very narrow quarter-tone though a third-tone and a 3/8-tone to a
semitone. While the Greek form of the chromatic genus eventually died
out as well, Hellenistic (and Roman) music was diatonic with some
chromaticism, sometimes of the modern Near Eastern type using
tetrachords of the form 1/2 3/2 1/2 (Winnington-Ingram).

I don't deny, though, that the 1/3 is a valid musical interval.
Greek Orthodox liturgical music uses intervals close to third
tones in some scales according to some authorities.

I feel you are somewhat misinformed about the popularity of Harry
Partch's music. I once heard a new listener come up to HP after
a concert and tell him that she had never heard real music before.
A national magazine once described his music as the only new music
that listeners really like. While no type of "experimental" music is
overwhelmingly popular with the general public, Partch's recordings
continue to sell well and his music continues to inspire composers,
theorists, and instrument builders. I would hazard that a significant
part of this List became interested in non-12 tone music because
of Harry Partch's music.

--John


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