Re: Digest Number 868 -Equable Diatonic

John,

thank you for your helpful post which I have just caught up with

Peter
www.midicode.com

John Chalmers wrote

> Unless we are deliberately archaizing, there is no reason for us not to
> permute the
> intervals of any historical scale if doing so suits our musical needs
> and purposes.
> The Islamic writers, particularly Safiyu-Din (transliterations vary)
> discussed all six
> forms of the general tetrachord, though it is not clear how many of
> these were actually
> used in Arabic musical practice. IIRC, after pages of tables of permuted
> tetrachords,
> S said that only those approximated by the 17-tone cycle of fifths scale
> were in use in
> his day.

> In general, the Greeks put the smallest intervals at the bottom of the
> tetrachord and the
> largest on top, though there are are exceptions such as Archytas's
> 28/27 x 8/7 x 9/8, 28/27 x 36/35 x 5/4, and Didymos's 16/15 x 25/24 x
> 6/5. In these cases, the choice of the first interval
> may have depended upon the interval it made with a note a 9/8 below the
> first note of the tetrachord (mese for the diezeugmenon tetrachord,
> proslambanomenos for hypaton, and an extra note, diatonic lichanos
> hypaton or hyperhypate, for the meson). The use of this composite
> interval appears to have been a standard stylistic feature of music in
> the enharmonic and chromatic genera.

> There is good reason to believe that the so-called "Pythagorean" tuning
> of the diatonic
> genus was the oldest scale in Greek art music (see Franklin's
> dissertation) and that the enharmonic derived from 5-toned folk scales
> of the semitone-Major third (ditone) type.
> This scale is derivable from the diatonic by gapping, of course. The
> chromatic genus developed
> from the enharmonic, which became heptatonic only around the end of the
> 4th century BCE and
> the beginning of the 3rd. Stopping half-way between the enharmonic and
> chromatic produces
> Aristoxenos's hemiolic chromatic (75 + 75 + 350 cents), giving another
> example of the neutral third.

> I suggest that the neutral diatonic type of scale such as Ptolemy's
> Equable or Even Diatonic, Al-Farabi's reduplicated 3/4-tone genera, etc.
> are not Greek, but possibly of African or Arabian origin. I think
> Ptolemy heard them in Alexandria, which was the most cosmopolitan city
> in the eastern Mediterranean area in the 2nd century CE. In addition to
> large Greek and Egyptian population, there were Romans, Jews, Arabs,
> Ethiopians, Persians, etc., and even Buddhist missionaries from India
> living and trading there.

> --John