Intervals in Turkish music

At 10:26 PM 3/3/00 -0800, you wrote:
>From: "Gerald Eskelin" <stg3music@earthlink.net>
>
>To Neil Haverstick's post:
>>>
>>> Blues has been popping up on the list lately, and I have a comment or
>>>two. First, after playing this style for over 30 years, I've come to
>>>believe that the so called "blue third" (or b5 or whatever note we are
>>>referring to) actually does not have one fixed position...the placement
>>>of the note is totally intuitive, and is done according to one's feeling
>>>at the time. When teaching, I can show my students how to do it, but I
>>>cannot intellectually tell them. It is a fluid situation, and is one of
>>>the things that gives blues it's charm and mystery...it's very difficult
>>>to learn to negotiate those bends in a truly convincing way.
>
>Dr. Can Akkoc added:
>>
>> This is precisely the phenomenon that prompted me into research on the
>> sound structures of Turkish music. My gut feeling is 'the placement of the
>> note' at any step is a non-deterministic function of the progression of
>> pitches that precede the said 'note'. That is, the melody line has a 'fuzzy
>> memory' that calls for variations in the actual pitches used, requiring a
>> fluid underlying scale as a whole. When put in these terms, I am inclined
>> to think there must be a mathematical pattern, waiting to be captured, that
>> will accomodate such fuzzy scales together with the memory mechanism
>> driving the deviations from a set of 'anchor' sounds. Such a mathematic
>> should accomodate the performer's 'feeling at the time' by determining the
>> proper pitch bends at every instant as the musical journey evolves in the
>> spiritual universe of the musician.
>
>Your post is very timely for me, Dr. Akkoc. I had said, in a recent book,
>that it seemed logical to me that the expressive tuning of Middle Eastern
>and Indian styles were, to a large extent, deviations from a norm. Since
>these styles seem to have roots in basic acoustic simple ratios (the 2:3
>"fifth" seems rather universal--except for Balinese type artificial
>divisions of the octave), it seems appropriate to assume that simple
>acoustical intervals were likely the _original "norms." Through the
>centuries, the stylistic deviations themselves have likely become second
>degree "norms" which provide the bases for further expressive deviation.
>
>Does this in any way relate to your idea of "fuzzy memory"?

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Dr Eskelin, thank you for your kind note and question. First of all, I like
the term you have used, "expressive tuning" for describing the 'dergah'
tradition in Turkish music. I have not come across this terminology before.

What you are suggesting in your comment could certainly be one way of
explaining the evolution in tuning that might have taken place over the
course of roughly two milleniums. Your idea of 'multi-layered norms' does
make a lot of sense to me. The term 'fuzzy memory' is based on and is
certainly an intrinsic part of the said evolution.

I was thinking more of the progression of sounds, the so called 'seyir'
issue, when I used the term fuzzy memory. During the course of a taksim,
master musicians seem to be drawing pitches from a set of sound clusters
making up the underlying 'scale' for the maqam on hand. The pattern as to
which particular pitch is going to be drawn from a given cluster at any
given time seems quite fuzzy to a layperson like myself. Since different
pitches are selected from these clusters for different 'visits' during the
course of the musical journey, the actual intervals are constantly changing
in time. This dynamic scale pattern could be linked to your term
"expressive tuning".

My problem is to find quantitative characterizations for such tuning norms
and the governing memory mechanisms that drive the seyir in different
maqams. Despite the 'chaotic' picture I might have drawn above, I strongly
believe, there are invariants, however fuzzy they might be, that keep
things from getting out of control while moving the spiritual ecstacy to
new heights and dimensions. I hope I have not cluttered the issue beyond
repair!

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>Needless to say, my reason for being here on the List also began with the
>notion that "there must be a mathematical pattern, waiting to be captured,
>that will accommodate" the phenomenon I have called the "high third." At
>this point, I'm not nearly so confident that such an explanation is there
>"waiting to be captured."
>
>There are so many variables at work here--not the least of which are
>personal taste, poor intonation, wild imagination, and who know's what
>else--that I suspect that art will win out over science in both of these
>regards. (However, check with me in the morning after I've had a good
>night's sleep.)
>
>Dr. Gerald R. Eskelin
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I would say don't give up. If there is a pattern, there must be a
mathematic that can model it. Have you looked at 'symbolic dynamics'? This
mathematic is currently being used quite heavily in speech recognition
along with 'hidden Markov models'.

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