Persian neutral thirds and other intervals

[Paul Erlich, TD 740.5]:
>Certainly the "neutral third" is found in many forms -- in Persian and
>Byzantine music, often around 367 cents. Remember, these musics are
>melodic, not harmonic, so the field of attraction of nearby simple
>ratios is not really an issue.

OK, first a disclaimer: the easiest way to get two Persian music
theorists in an argument is to ask them what the actual intervals
of Persian music are. :-)

That said, IMHO as a student of Persian classical music, my observation
has been that the neutral intervals tend to be closer to the minor
intervals than to the major intervals. 367 cents sounds too close to
the major third to me. Actually, even the 24 tET neutral third of 350
cents sounds too sharp to me. :-)

I think one of the things that does strongly influence the placement of
frets for Persian music is that in the course of playing a Dastgah one
modulates through many subsidiary Gusheh-ha by changing tonics. So, the
ability to change keys is a major factor. I think it was partly for
this reason that Vaziri was such a big fan of 24 tET -- since then one
can change to any key and still play all the intervals consistently. The
other two groups of fixed tunings that seem to be popular are tunings
built up of fifths (as promoted by theorists such as Barkechli) or of
fifths and thirds (based on observations by Farhat, et al).

Despite the above, most of what I have heard and read from Persian
musicians (as opposed to Persian music theorists) is that the ideal
intervals for all the Gusheh-ha of all the Dastgah-ha can not be reduced
to a fixed set, which is why there are moveable gut frets on those
Persian lutes which are not fretless. The musicians adjust their frets
depending on the sequence of Gusheh-ha they are about to play.

A note about the following notation:
Ep is "E koron"
F> is "F sori"

This is an ASCII-ified version of the symbols Vaziri introduced to allow
Persian classical music to be written in western classical notation.

Barkechli's Persian scale is basically a 17-tone Pythagorean scale
(this is from PYTH_17.SCL from Scala):

0: 1/1 0.000 cents C unison, perfect prime
1: 256/243 90.225 cents Db Pythagorean limma
2: 2187/2048 113.685 cents Db apotome
3: 9/8 203.910 cents D major whole tone
4: 32/27 294.135 cents Eb Pythagorean minor third
5: 19683/16384 317.595 cents Ep Pythagorean augmented second
6: 81/64 407.820 cents E Pythagorean major third
7: 4/3 498.045 cents F perfect fourth
8: 1024/729 588.270 cents F> Pythagorean diminished fifth
9: 729/512 611.730 cents Gp Pythagorean tritone
10: 3/2 701.955 cents G perfect fifth
11: 128/81 792.180 cents Ab Pythagorean minor sixth
12: 6561/4096 815.640 cents Ab Pythagorean augmented fifth
13: 27/16 905.865 cents A Pythagorean major sixth
14: 16/9 996.090 cents Bb Pythagorean minor seventh
15: 59049/32768 1019.550 cents Bp Pythagorean augmented sixth
16: 243/128 1109.775 cents B Pythagorean major seventh
17: 2/1 1200.000 cents C octave

Farhat, in his doctoral thesis, gives the following as the average of
several observed tar and sehtar tunings:

0: 1/1 C
1: 90.000 cents Db
2: 135.000 cents Dp
3: 205.000 cents D
4: 295.000 cents Eb
5: 340.000 cents Ep
6: 410.000 cents E
7: 500.000 cents F
8: 565.000 cents F>
9: 630.000 cents Gp
10: 700.000 cents G
11: 790.000 cents Ab
12: 835.000 cents Ap
13: 905.000 cents A
14: 995.000 cents Bb
15: 1040.000 cents Bp
16: 1110.000 cents B
17: 1200.000 cents C

The following (PERSIAN.SCL from Scala) is similar to Farhat's
observed tuning and is built up of fifths and thirds:

Persian Tar Scale, from Dariush Anooshfar, Internet Tuning List 2/10/94
0: 1/1 0.000 cents C unison, perfect prime
1: 256/243 90.225 cents Db Pythagorean limma
2: 27/25 133.238 cents Dp large limma
3: 9/8 203.910 cents D major whole tone
4: 32/27 294.135 cents Eb Pythagorean minor third
5: 243/200 337.148 cents Ep acute minor third
6: 81/64 407.820 cents E Pythagorean major third
7: 4/3 498.045 cents F perfect fourth
8: 25/18 568.717 cents F> classic augmented fourth
9: 36/25 631.283 cents Gp classic diminished fifth
10: 3/2 701.955 cents G perfect fifth
11: 128/81 792.180 cents Ab Pythagorean minor sixth
12: 81/50 835.193 cents Ap acute minor sixth
13: 27/16 905.865 cents A Pythagorean major sixth
14: 16/9 996.090 cents Bb Pythagorean minor seventh
15: 729/400 1039.103 cents Bp acute minor seventh
16: 243/128 1109.775 cents B Pythagorean major seventh
17: 2/1 1200.000 cents C octave

Vaziri's scale is just a subset of 24 tET:

0: 1/1 C
1: 100.000 cents Db
2: 150.000 cents Dp
3: 200.000 cents D
4: 300.000 cents Eb
5: 350.000 cents Ep
6: 400.000 cents E
7: 500.000 cents F
8: 550.000 cents F>
9: 650.000 cents Gp
10: 700.000 cents G
11: 800.000 cents Ab
12: 850.000 cents Ap
13: 900.000 cents A
14: 1000.000 cents Bb
15: 1050.000 cents Bp
16: 1100.000 cents B
17: 2/1 C

I believe Vaziri actually had more than 17 frets per octave on his tar,
but I can not remember if he had all 24 frets per octave or a subset
that was 17 < n < 24. If somebody really wants to know I can look it up
or send you a bibliography so you can look it up. :-)

Cheers,
Christopher

Christopher,

Thanks for the wonderfully informative post. I'm curious if you may
be able to answer the below question that I posted in message 11442:

From: <jacky_ekstasis@y...>
Date: Fri Aug 11, 2000 4:59pm
Subject: Another Maqam Question

Paul Erlich wrote:

"We had some debate about this here on the list, and there's really
too much
variety between different parts of the Arabic world, and too much
divergence
between theory and practice, for there to be one definitive answer to
your
question. As I see it, all kinds of creative deviations from the
modern
standard 24-tET can be justified on theoretical and/or cultural
grounds, but
I wouldn't automatically stuff everything into the nearest just ratios
unless I were going to make a significant use of harmony (which is
rare in
Arabic music). If I were, I'd make sure the ratios provided for simple
proportions in the intervals to be used as harmonies (rather than
worrying
about whether they looked simple on their own), and didn't run into
any
comma difficulties (such as the "wolf" fifth between 9/8 and 5/3 if I
planned to use the D-A harmony in the C major "just" scale).
Otherwise, I'd
see no real reason to choose just ratios over 24-tET, though in many
cases
(11/9, 3/2, etc.), it wouldn't make an audible difference."

Paul,

I will keep your suggestions in mind as I work with the scales.

I entered all of the Arabic scales into my spread sheet so that I
could see them as cents scales. I found that one of the scales had a
sequence that exceeded 1200 cents. It was the 3 1 2 1 4 4 2 4 4 Maqam
Jabburi, which added up to be 150, 200, 300, 350, 550, 750, 850,
1050, 1250 cents. Is this correct for this scale? All the others
terminated on 1200 cents.

Thanks,

Jacky

> 3 1 2 1 4 4 2 4 4 is exactly how it appears in Manuel's table. There must
be
> an error. Manuel?

Yes there's an error in that Maqam Jabburi, I've noticed it earlier but
can't
find the correct notes. Anyone, mr. Akkoc? Maybe I'll just remove it.

Manuel Op de Coul coul@ezh.nl

At 04:47 PM 08/18/2000 +0200, you wrote:
>
>> 3 1 2 1 4 4 2 4 4 is exactly how it appears in Manuel's table. There must
>be
>> an error. Manuel?
>
>Yes there's an error in that Maqam Jabburi, I've noticed it earlier but
>can't
>find the correct notes. Anyone, mr. Akkoc? Maybe I'll just remove it.
>
>Manuel Op de Coul coul@ezh.nl
>
>
>--------------------------------------------------------------------
Dear Manuel,

Thank you for referring to me on this issue. I referred your request to a
good friend of mine, Mr. Feridun Ozgoren in Boston for a sequence of
intervals as you have requested.

As I posted on various occasions on this list I do not believe in fixed,
deterministic intervals. I am still in the process of constructing
mathematical characterizations of scales in the form of distributions for
traditional Turkish music. Such characterizations
are going to be based entirely on a large data base created by making
direct measurements from improvisations by indisputable master musicians.
Basically I am trying to map the 'course' a music has evolved into by using
actual performances, as opposed to 'imposing' a speculative model.

Respectfully,

.
Dr. Can Akkoc
Alabama School of Mathematics and Science
1255 Dauphin Street
Mobile, AL 36604
USA

Phone: (334) 441-2126
Fax: (334) 441-3297

--- In tuning@egroups.com, Can Akkoc <akkoc@a...> wrote:

I am still in the process of constructing
> mathematical characterizations of scales in the form of
distributions for
> traditional Turkish music. Such characterizations
> are going to be based entirely on a large data base created by
making
> direct measurements from improvisations by indisputable master
musicians.
> Basically I am trying to map the 'course' a music has evolved into
by using
> actual performances, as opposed to 'imposing' a speculative model.
>
> Respectfully,
>
>
> .
> Dr. Can Akkoc
> Alabama School of Mathematics and Science
> 1255 Dauphin Street
> Mobile, AL 36604

Dear Dr. Akkoc,

Hello.

It is my sincere hope that you will share you findings about the
Turkish Scales on this list, as this is something that I feel many of
us would be greatly interested to learn about.

Thanks for your effort in trying to find out the intervals for the
Maqam Jabburi.

Regards,

Jacky Ligon

At 05:47 PM 08/18/2000 -0000, you wrote:
>--- In tuning@egroups.com, Can Akkoc <akkoc@a...> wrote:
>
>I am still in the process of constructing
>> mathematical characterizations of scales in the form of
>distributions for
>> traditional Turkish music. Such characterizations
>> are going to be based entirely on a large data base created by
>making
>> direct measurements from improvisations by indisputable master
>musicians.
>> Basically I am trying to map the 'course' a music has evolved into
>by using
>> actual performances, as opposed to 'imposing' a speculative model.
>>
>> Respectfully,
>>
>>
>> .
>> Dr. Can Akkoc
>> Alabama School of Mathematics and Science
>> 1255 Dauphin Street
>> Mobile, AL 36604
>
>Dear Dr. Akkoc,
>
>Hello.
>
>It is my sincere hope that you will share you findings about the
>Turkish Scales on this list, as this is something that I feel many of
>us would be greatly interested to learn about.
>
>Thanks for your effort in trying to find out the intervals for the
>Maqam Jabburi.
>
>Regards,
>
>Jacky Ligon
>
>
>--------------------------------------------------------------------

Dear Jacky,

I am working on a paper that hopefully will be published in JASA
in the not so distant future. This first paper will display the
mathematical approach and methodology involved as well as the philosophy
behind this work. I will inform the tuning_list
community as soon as it comes out.

Best regards,

.
Dr. Can Akkoc
Alabama School of Mathematics and Science
1255 Dauphin Street
Mobile, AL 36604
USA

Phone: (334) 441-2126
Fax: (334) 441-3297