More to John Chalmer's post

The current school of thought regarding Turkish Art and Folk Musics is
based upon a tone of nine _koma_s - suggesting a 53 tone scale. (A good
introduction to contemporary Turkish music - albeit more cultural than
theoretical - is Martin Stokes' _The Arabesque Debate_, Oxford 1992).
However, the exact value of a _koma_ varies from theorist to theorist, and
it is more than likely that we are dealing with something akin to
Aristonexian units, or a more precise sruti-like unit. The centuries long
debate within the Byzantine theoretical tradition has largely been over
what is the most appropriate equal division to describe a practice that has
not been - until the advent of the latest technical resources - equally
divided.

I realize that that a large faction of the tuning community maintains that
the Aristoxenian units are/were units of an equal temperament. I am more
comfortable - and find Aristoxenus, as well as Sruti theorists, or writers
on Byzantine, Turkish, or Arabic musics easier and more useful to read -
when these units are viewed conceptually, as smallest bits of meaningful
pitch differences, with exact rational values left undetermined. It is
striking to me that, almost universally, musicians in these traditions who
are also familiar with methods for the accurate measurement of pitches and
intervals refrain from making such measurements, or find them of little
value in analysing their music making. (I have come to think of Aristoxenus
as the first cognitive scientist).

Since we spend a lot of time discussing exactitudes of pitch and interval,
it may be useful to discuss what we can learn about musical tunings without
reference to exact magnitudes. Certainly intonational tolerance is one
aspect of this discussion, but I am also interested in what may be called a
'topological' analysis of pitch materials, of properties that are unaltered
by elastic deformations.

Best wishes for the holidays -

Daniel Wolf
Frankfurt

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