hi lev36 and paul,


> From: "paulerlich" <paul@s...>
> Date: Wed Feb 27, 2002 2:33 pm
> Subject: Re: Middle-eastern tunings: Arabic, Turkish, Saz
>
>
> --- In tuning@y..., "lev36" <lev@h...> wrote:
> > --- In tuning@y..., "paulerlich" <paul@s...> wrote:
> > > --- In tuning@y..., "lev36" <lev@h...> wrote:
> > > > or to an older, somewhat
> > > > Pythagorean system devised by al-Farabi (c.f. Touma,
> > > > 1995, pp.18-28), which includes tones close to 24-TET
> > > > quartertones.
> > >
> > > are you sure about that? the medieval arabic system, which
> > > consists of an extended chain of pure 3/2 fifths, does not
> > > resemble 24-equal quartertones at all, but rather is
> > > extremely close to a subset of the turkish koma system.
> >
> > 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.
>
> the whole thing is very close to a subset of 24-equal.
>
> ok, i was thinking of something different, then, not
> al-farabi . . . i'll have to look it up . . . it's the one
> in partch's and helmholtz's books . . .
>
> > Of the above, 162/149 clocks in at 145 cumulative cents,
> > and 27/22 at 355 cents. Touma goes as far as saying of this
> > 355 cent interval that the approximately three-quarter tone
> > interval is what gives Arabian music its particular character,
> > as early as the 10th century.
>
> that's fine by me. there is a 17-tone chain of 3/2 fifths,
> though, that's often called the 'medieval arabic' system,
> and some have claimed (erroneously, i feel) that it continues
> to govern arabic music to this day. it doesn't have any neutral
> thirds in it (355 cents, or 345 cents, or anything in the
> vicinity), so it seems to be far removed from any arabic music
> i've heard.


i have a couple of webpages touching on this:


Arab Lute Frettings
http://www.ixpres.com/interval/monzo/arablute/arablute.htm

the fretting originally gave a typical Pythagorean scale.
Zalzal moved some frets so that his fretting produced some
Notes that are approximately ¼-tones:

String, fret ~cents ~ratio ~cents
1,3 558 11:8 551
2,3 1057 11:6 1049
3,3 355 11:9 347

(hmm... i see that i left some frets off the graph...
and in general there's not much numerical data...
someday I'll have to do a lot more work on that page.)

and others (actually more) that are approximately 1/6-tones.

String,fret ~cents
1,1 372
2,1 870
3,1 168
4,1 666


An Examination of Partch's comparison of Equal Temperaments
http://www.ixpres.com/interval/monzo/partch/et/partch-on-et.htm

Partch got the data for the Arabic scale from Helmholtz's book.
i illustrate it about 2/3 of the way down the page. it's a
Pythagorean system tuned 3^(-12…4).


also, list-member Can Akkoc has done some interesting research
into Turkish classical music.



-monz