31-tET and Persian tar/sehtar tuning

31-tET and Persian tar/sehtar tuning

Hi Paul, (et al,)

I played around a little with the 31-tET tar/sehtar tuning for Persian
music.

[Christopher Chapman, TD 549.11]:
>C Db Dp D Eb Ep E F F> Gp G Ab Ap A Bb Bp B C

[Paul Erlich, TD 549.12]:
>0 3 4 5 8 9 10 13 14 17 18 21 22 23 26 27 28 31 in 31-tET.

Here are some of my initial observations:

* It seems to modulate well between the main dastgah-ha and the
subsidiary dastgah-ha.

* The flats (b) and koron-ha (p) seem too small relative to the natural
note, or, said another way, the 3-step semitones seem too wide
(as you predicted in TD 549.12).

* The beating of C-G would probably drive me nuts if I left my sehtar
tuned to this.

For the uninitiated who may be reading this, the tar and sehtar have
three courses, tuned C,G,C and played such that two of the three
courses usually serve as drones while the third plays the melody.
When I tried playing with the G tuned to an ~697 cent fifth, some part
of my brain kept saying, "OK, time to tune again..." :-)

* The Db and Gp end up being about 77 cents flat on the G string. Using
the tuning given by Dariush Anooshfar in the Scala scale archives (1/1
256/243 27/25 9/8 32/27 243/200 81/64 4/3 25/18 36/25 3/2 128/81 81/50
27/16 16/9 729/400 243/128 2/1), the Db and Gp end up about 20 cents
flat on the G string (and F> ends up about 28 cents flat on the G
string), so I guess these are problematic notes either way. Sehtar
don't normally even have a Db fret (relative to the C string, though I
believe tar normally do, and I've actually added one to my sehtar),
and I normally I only play up to C on the G string anyway, so I think
this is really a non-issue. :-)

While we're on the topic:

In case you or anyone else is interested, I was recently given a copy
of Hormoz Farhat's dissertation, "The Dastgah Concept in Persian
Music" in which he wrote that his measurements in 1959 and some UCLA
students' measurements in 1964 of various tar and sehtar "showed that
the whole-tone and the semi-tone are relatively fixed in Persian
music, and they are very close to the Pythagorean whole-step (204 c.)
and half-step (90 c.). A neutral step which falls between these two,
and is the L+C of the scale of Barkeshli, was found to be very
flexible, varying anywhere from 125 to 150 cents. It was shown,
however, that most often it is in the vicinity of 135 cents."

Farhat goes on to give a tuning of steps (in cents): 90 45 70 90 45
70 90 65 65 70 90 45 70 90 45 70 90, which I think is basically the
same as Dariush Anooshfar's tuning (with intervals rounded to the
nearest five cents).

Cheers,
Christopher

p.s. It's about 1:00 am and I'm rather out-of-it, so I apologize for my
rambling and incoherence, but I didn't think I'd get another chance
to write much in the next few days, so I wrote just now. :-)