lev36 wrote:

> Touma (p. 21) gives an example of one of the tone rows devised by al-
> Farabi in the 10th c. CE. Expressed in cents:
> C 0
> D 204
> E 355
> F 498
> G 702
> A 853
> B 996
> C 1200
>
> As you can see, the third and the 6th are very neary quarter-tones,
> while the rest resemble Pythagorean values.

I haven't seen a full list of al Farabi's tunings. You can get some from
Manuel's scale archive, somewhere at http://www.xs4all.nl/~huygensf

Probably the idea with that scale is to express quartertones with simple
integer ratios. They didn't have cents in those days. There's a strong
Greek influence in all this -- al-Farabi was well read in Greek texts,
more so than European scholars of his day as more had been translated to
Arabic than Latin. The first part of al-Farabi's treatise is a list of
Ptolemy's scales, which must therefore include the equable diatonic, which
is essentially the one Touma gives on p.21.

The Pythagorean scale from al-Urmawi (Touma pp21-22) is what Paul was
thinking of. It is more recent than al-Farabi, but has less to do with
modern Arab tuning. It's a lot more like Persian tuning, and may have
been Persian influenced back then. Owen Wright's book (it's in Touma's
bibliography) is excellent for this. It seems that the
Pythagorean/schismic notation was intended to show neutral thirds although
if you take it literally it doesn't sound like that.

Incidentally, Farmer's "An Old Moorish Lute Tutor" happens to have fallen
into my lap. The subject, probably earlier than the late C16th Morocco,
describes a Pythagorean tuning and fretting.


Graham