Re: Ekrem Karadeniz's 41 tone system

I had assumed that Karadeniz's system was either 41tet or a pure
pythagorean series. In, fact, according to Ioannis Zannos (_Ichos und
Makam_, Bonn 1994), in order to make 41 pure fifths come byck to an octave
multiple, two fifths, the 5th and the 17th are altered by a half komma. OUt
of this assymmetry, the accidental signs for sharpening and flattening
represent different quantities (sharps are provided for 1.5, 3, 4, and 5.5
kommas, flats for 1, 2, 3.5, and 5 kommas). 1.5. kommas are identified with
the ratio 51/50, 2.5 kommas the ratio 31/30.

Here, then, are are Karadeniz's intervals within a tone, his terminology is
partially neological:

name cents ratio size in kommas
koma 22.63 77/76 1
irha 34.28 51/50 1.5
sagir 56.76 31/30 2.5
bakiyye 88.80 20/19 4
kucuk mucennep 11.73 16/15 5
buyuk mucennep 182.40 10/9 8
tanini 203.91 9/8 9

For another curiosity, Karadeniz uses his own logarithmic measure, "turkish
cents", each of which is 1/200 of a komma, or 1/10600 of an octave, or
0.1132 usual cents. Yet more evidence that: neologisms are really a
universal endemic among tuning theorists!

At 12:44 3/18/99 -0500, you wrote:
>From: Daniel Wolf <DJWOLF_MATERIAL@compuserve.com>
>
>I had assumed that Karadeniz's system was either 41tet or a pure
>pythagorean series. In, fact, according to Ioannis Zannos (_Ichos und
>Makam_, Bonn 1994), in order to make 41 pure fifths come byck to an octave
>multiple, two fifths, the 5th and the 17th are altered by a half komma. OUt
>of this assymmetry, the accidental signs for sharpening and flattening
>represent different quantities (sharps are provided for 1.5, 3, 4, and 5.5
>kommas, flats for 1, 2, 3.5, and 5 kommas). 1.5. kommas are identified with
>the ratio 51/50, 2.5 kommas the ratio 31/30.
>
>Here, then, are are Karadeniz's intervals within a tone, his terminology is
>partially neological:
>
>name cents ratio size in kommas
>koma 22.63 77/76 1
>irha 34.28 51/50 1.5
>sagir 56.76 31/30 2.5
>bakiyye 88.80 20/19 4
>kucuk mucennep 11.73 16/15 5
>buyuk mucennep 182.40 10/9 8
>tanini 203.91 9/8 9
>
>For another curiosity, Karadeniz uses his own logarithmic measure, "turkish
>cents", each of which is 1/200 of a komma, or 1/10600 of an octave, or
>0.1132 usual cents. Yet more evidence that: neologisms are really a
>universal endemic among tuning theorists!
>
>
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Dear Mr. Wolf,

Thank you for your post on Ekrem Karadeniz's model of 41et and your
comments regarding the model. Having tried my hand on learning the 'kanun'
long time ago I am a bit familiar with the terminology used for small
intervals. I can also understand the frantic search for a deterministic
scale that will explain everything under the sun. After endless
frustrations in learning the kanun and not being able to produce
consistently the scales used by legendary masters such as Tanburi Cemil Bey
I began
questioning the theoretical models that were being used at the time. This
led me to the research I am conducting currently. The distributions I am
referring to are sometimes 80 cents wide, which would be considered
significantly beyond a vibrato or a coloration of any sort. My perception
that Turkish music has memory is endorsed by people of respect in the
musical arena in Turkey. This seemingly stochastic pattern certainly
contains intrinsic just intervals at the local/micro level, as suggested by
Karadeniz, Arel, and others in different forms. However, the situation at
the macro level seems to be much more involved than a simple just scale. I
would be very much interested in hearing your expert opinion on my
pedestrian ideas in looking for non-deterministic models that might
characterize the scales for various 'maqam's in a 'fuzzy' yet realistic
manner. Sincerely.
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/

> I would be very much interested in hearing your expert opinion on my
pedestrian ideas in looking for non-deterministic models that might
characterize the scales for various 'maqam's in a 'fuzzy' yet realistic
manner. Sincerely.
Dr. Can Akkoc<

Your ideas sound far from pedestrian: please let us know more about what
you are doing! The one thing that I could suggest at the moment is to
include something like Barlow's scale step property, where the acceptance
of one interval identity does not conflict with the identification of other
scale members by crowding the tolerance space around them. (Now that I
write that, it does sound very much like a 'fuzzy' system). Barlow assigned
an arbitrary number of cents to his function, but I am certain that the
width of this tolerance space is highly dependent on the underlying scale
structure, _whether it is exactly intoned or not_. If we could get a better
picture of the extent and limits of this element of tolerance, we would be
in a better position to talk about the variations that individual musicians
put on intonation. This would be helpful to understand what the Javanese
call _embat_, the Japanese _embai_, and some of the rest of us 'expressive
intonation'.

On Thu, 18 Mar 1999, Daniel Wolf wrote:

> From: Daniel Wolf <DJWOLF_MATERIAL@compuserve.com>
>
> > I would be very much interested in hearing your expert opinion on my
> pedestrian ideas in looking for non-deterministic models that might
> characterize the scales for various 'maqam's in a 'fuzzy' yet realistic
> manner. Sincerely.
> Dr. Can Akkoc<
>
> Your ideas sound far from pedestrian: please let us know more about what
> you are doing! The one thing that I could suggest at the moment is to
> include something like Barlow's scale step property, where the acceptance
> of one interval identity does not conflict with the identification of other
> scale members by crowding the tolerance space around them. (Now that I
> write that, it does sound very much like a 'fuzzy' system). Barlow assigned
> an arbitrary number of cents to his function, but I am certain that the
> width of this tolerance space is highly dependent on the underlying scale
> structure, _whether it is exactly intoned or not_. If we could get a better
> picture of the extent and limits of this element of tolerance, we would be
> in a better position to talk about the variations that individual musicians
> put on intonation. This would be helpful to understand what the Javanese
> call _embat_, the Japanese _embai_, and some of the rest of us 'expressive
> intonation'.
>
>
*************************************************************************
Dr. Wolf,

Thank you for your comments. It is a wonderful feeling to hear from a
professional ethnomusicologist of your stature given that I am just the
man on the street grappling with ideas way over my head.

How can I educate myself efficiently and effectively on the work of
Barlow? Any recommendation will help. Thank you.

Can Akkoc
Alabama School of Mathematics and Science
Mobile, Alabama 36604-2519
Phone: (334) 441-2126
Fax : (334) 441-3290