Traditional Turkish Music

Dr. Akkoc is probably describing the same statistical situation you will
find in most music cultures. A very few musicians will insist on the best
intonation and maintain their instruments to play in that intonation while
the vast majority either get by without giving the matter a lot of thought
or even could care less. I would wager that the Siberian piano tuning
recently described is closer to the norm than one of Ed Foote's
masterpieces. This, coupled with the fact that the tuning apparatus on a
Kanun or a Tanbor is incredibly fragile when compared with that of a piano
or a bronze gender, makes measuring the intended tuning especially
difficult.

The tuning that has served as a common basis for Arab, Persian, and Turkish
classical musics, as well as for Greek Orthodox liturgical music is the
17-tone scale of Safi al-Din, in which the octave is divided into a series
of Leimmas (256/243) and pythagorean Kommas (531441/524288):

L L k - L L k - L - L L K - L L K - L - L L K

This system remains prevalent in the Arab world, although a 24tet
approximation is widely used in Urban commercial music. In the Ottoman
Empire and today in Turkey, there have been various variations on this
model. The 'official' system in Turkey today is an expansion of the Safi
al-Din system in that within the L L k subdivided wholetone, an additional
tone is added an apotome above the lower tone (= a leimma below the upper
tone). This processes in repeated to yield a system of 24 pitches. In the
popular Arabesque repertoire, some saz players get by with a 14-tone subset
of the 17, although this is generally heard as a restriction. Neither 14,
17, nor 24 is sufficient, however, to present all of the intervals actually
used in current practice. The system of Ekrem Karadeniz (_Turk Musikisinin
Nazariye ve Esaslari_ ca. 1981) is considered by many to be an improvement
over that of Ezgi-Arel, and has 41 tones in the octave, but has not been
put into general use.

Can Akkoc wrote:

> From: Can Akkoc <akkoc@asms.net>
>
> At 16:07 3/17/99 -0500, you wrote:
> >From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
> >
> >Kraig Grady wrote:
> >
> >>>It seems the only places that Wolf saw these instruments was
> >>place adjacent to 12ET countries. I<
> >
> >Daniel Wolf wrote,
> >
> >>Kraig Grady:
> >
> >>I think your geography is a bit skewed. It is only in Turkey -- the
> >major
> >>Islamicate country closest culturally to Europe -- where non-tempered
> >>tunings have maintained their monopoly in both classical, folk, and
> >>arabesque repertoires.
> >
> >Though I think Daniel's right, it should be mentioned that Turkish
> >theory recognizes a division of the octave into 53 equal parts. However,
> >the difference between 53-equal and Just/Pythagorean versions of Turkish
> >scales is exceedingly small -- on the order of 0.1 to 1 cent -- far
> >smaller than the deviations that would occur in even the most ideal
> >musical circumstances. I've played on a Turkish saz with very unevenly
> >spaced frets but the smallest intervals were eighth-tones (approximately
> >1/53 octave) and these tended to occur in pairs, dividing in half the
> >second smallest interval (quartertones or 2/53 octave). The placing of
> >these frets was surely too approximate to distinguish between 53-equal
> >and JI/Pythagorean (by the latter I could mean either JI extended much
> >farther along the 3-axis than the 5-axis, or Pythagorean with schismatic
> >approximations to 5-limit intervals).
> >
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> Gentlemen,
>
> It is true that for the past 150 years or so 'theoreticians' in traditional
> Turkish music have tried to divide an octave into 53 equal sub-intervals.
> Various models have been constructed with the intent of modeling all modal
> scales (around 120+ modes) in deterministic form. The most recent model was
> proposed by Huseyin Sadettin Arel where the octave is partitioned into 24
> unequal sub-intervals.
>
> I am trying to determine the nature of the modal scales by making direct
> measurements
> on improvisations given by indisputable master musicians coming from the
> 'dergah' tradition.

As I stated in another post I have been told that there are regional tuning
differences of all kinds despite the fact that the tunings share the same
theoretical scale

> My findings are several light years away from the 24
> unequally tempered deterministic model suggested by Arel and company . The
> 'scales' that are emerging from my research are not even deterministic.
> Instead, they are sound clusters along the pitch axis in the form of
> distributions with statistical characteristics. In view of my findings so
> far, I am inclined to think a search for a 'magic' deterministic scale is
> going to be a futile attempt on the part of the researchers.
> Dr. Can Akkoc
> Alabama School of Mathematics and Science
> 1255 Dauphin Street
> Mobile, AL 36604
> USA

-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

At 18:22 3/17/99 -0500, you wrote:
>From: Daniel Wolf <DJWOLF_MATERIAL@compuserve.com>
>
>Dr. Akkoc is probably describing the same statistical situation you will
>find in most music cultures. A very few musicians will insist on the best
>intonation and maintain their instruments to play in that intonation while
>the vast majority either get by without giving the matter a lot of thought
>or even could care less. I would wager that the Siberian piano tuning
>recently described is closer to the norm than one of Ed Foote's
>masterpieces. This, coupled with the fact that the tuning apparatus on a
>Kanun or a Tanbor is incredibly fragile when compared with that of a piano
>or a bronze gender, makes measuring the intended tuning especially
>difficult.
>
>The tuning that has served as a common basis for Arab, Persian, and Turkish
>classical musics, as well as for Greek Orthodox liturgical music is the
>17-tone scale of Safi al-Din, in which the octave is divided into a series
>of Leimmas (256/243) and pythagorean Kommas (531441/524288):
>
> L L k - L L k - L - L L K - L L K - L - L L K
>
>This system remains prevalent in the Arab world, although a 24tet
>approximation is widely used in Urban commercial music. In the Ottoman
>Empire and today in Turkey, there have been various variations on this
>model. The 'official' system in Turkey today is an expansion of the Safi
>al-Din system in that within the L L k subdivided wholetone, an additional
>tone is added an apotome above the lower tone (= a leimma below the upper
>tone). This processes in repeated to yield a system of 24 pitches. In the
>popular Arabesque repertoire, some saz players get by with a 14-tone subset
>of the 17, although this is generally heard as a restriction. Neither 14,
>17, nor 24 is sufficient, however, to present all of the intervals actually
>used in current practice. The system of Ekrem Karadeniz (_Turk Musikisinin
>Nazariye ve Esaslari_ ca. 1981) is considered by many to be an improvement
>over that of Ezgi-Arel, and has 41 tones in the octave, but has not been
>put into general use.
>
>
>
>
>------------------------------------------------------------------------
>Start a new hobby. Meet a new friend.
>http://www.onelist.com
>Onelist: The leading provider of free email list services
>------------------------------------------------------------------------
>You do not need web access to participate. You may subscribe through
>email. Send an empty email to one of these addresses:
> tuning-subscribe@onelist.com - subscribe to the tuning list.
> tuning-unsubscribe@onelist.com - unsubscribe from the tuning list.
> tuning-digest@onelist.com - switch your subscription to digest mode.
> tuning-normal@onelist.com - switch your subscription to normal mode.
>
>

Mr. Daniel Wolf's note on scales used in traditional Turkish music is
describing what most people in the music business in Turkey recite when
pressed for a mathematical model for the underlying modal scales.
Unfortunately the reality is significantly different from such models which
invariably suggest 'magical' DETERMINISTIC scales in some form. In a
typical improvisation the musician seems to be using scales that are
inspired at the spur of the moment depending, among others, on the
spiritual state he/she is in, where the music has been before coming to
that particular point in the improvisation, the evolution the improvisation
has gone through since the beginning, etc. It appears musical scales have
'memory' which allows them to evolve in time. However, the situation is not
chaotic at all. There seems to be non deterministic (stochastic) patterns
which carry the 'finger print' or 'genetic code' for the underlying maqam.
A master musician is capable of recognizing the finger print after hearing
a few sounds no matter how chaotic or random they may sound to a pedestrian.

Since the musicians seem to be creating their own non-deterministic
stochastic scales in the form of distributions, why not make an attempt to
construct mathematical characterizations in a stochastic setting? An
analogy could be that of someone trying very hard to make a stream flow in
a user-prescribed river bed, while the rives wants to meander and deviate
from the pre-assigned bed, sometimes displaying significant variations,
while trying to carve its own.

I appreciate Mr. Wolf taking time to inform the people in this circle about
trends in Turkish music, and look forward to more interaction along this
venue. Since music is a universal endeavour, there must be interconnections
linking all musics on this planet in some mysterious way.

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

Phone: (334) 441-2126
Fax: (334) 441-3290
Web: http://199.20.31.100/GIFT/