Octaves, Tetrachords

While there are indications that archaic Greek scales spanned less than
the octave, certainly the octave was known in practice by the 4th
century, if not the fifth. Aristoxenos mentions that Eratocles had
discussed the octave species (modes), without analysing them into
tetrachords and pentachords. A late writer, Aristides Quintilianus,
lists the harmonia he claimed Plato was referring to in The Republic and
four of these, including the preferred Dorian and Phrygian, span the
octave (the Dorian has a range of a major 9th) and the whole set spans
an 11th (Winnington-Ingram, Mode in Ancient Greek Music).

Pythagoras is credited with bringing the tetrachordal framework 6:8:9:12
from Babylon, where "Pythagorean" octave scales had been known since at
least the beginning of the 2nd millennium BCE.

The diatonic genus was considered the oldest genus in Greece and was
assuredly borrowed from Babylon. The full chromatic scale was known in
Babylon and the coastal Near East by 1800 BCE and the Greeks were in
close cultural contact withe these civilizations (and with the
Egyptians, though little is known of Egyptian music).

(Interestingly, I saw a program on PBS in San Diego last night on the
discovery of mummies with European features (blond and red hair, etc.)
in Turkestan, Western China. These date from the 2nd millennium BCE and
are likely to be ancestral to the later Tochars, who mediated trade
between China and the Near East along the Silk Road. (The Tochars spoke
a language related to Celtic in the Indo-European family.) Thus it is
even more likely that Babylonian tuning lore reached Western China,
where the Ling Lun (Master of Music) claimed that he obtained the tuning
of the Lu" (bamboo tubes tuned to a chromatic cycle by fifths/fourths)
from the voice of a Phoenix.)

As for scales with dissimilar tetrachords, Kraig is correct; the mixed
modes reported by Ptolemy consisted of a diatonic upper tetrachord and a
soft diatonic or chromatic one below. However, they are usually used in
different modes than the standard Dorian which has the disjunctive tone
between the two tetrachords.

--John