Notes on Eastern Tone System III

2001-08-20 04:00 am

(This article has been posted to the newsgroup as well as rec.music.compose, rec.music.early and rec.music.theory groups)

APPENDIX 1: NEUTRAL THIRDS and SIXTHS
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Neutral thirds and sixths are as important and critical as seconds in the
melodic construction of music in 17 tone system; that's Eastern/Turkish
music.

They are, according to my observation, the basic key to the harmonic
tension-release mechanism of the mentioned musical tradition. In addition,
several genera (Segâh to name the most commonly used) are structured upon
neutral third, thus, it appears to be as important as the perfect fourth and
the perfect fifth.

Here is a table of neutral thirds and sixths, five of which are inversions
of thirds. Five of the thirds and three of the sixths aren't invertible
within the 33-overtone context.

The coloumns are read as follows;

Interval (Ratio) - notated pitch (relative to C, for MIDI applications) -
Pitch bending (negative if in brackets) - Cents value

A) Neutral Thirds

11/9 - Eb - 1942 - 347.41
16/13 - E - (1660) - 359.47
17/14 - Eb - 1480 - 336.13
21/17 - E - (1400) - 365.83
23/19 - Eb - 1260 - 330.76
26/21 - E - (1234) - 369.74
27/22 - E - (1862) - 354.55
28/23 - Eb - 1661 - 340.55
29/24 - Eb - 1132 - 327.62
31/25 - E - (1130) - 372.41

B) Neutral Sixths

13/8 (inv. 16/13) - Ab - 1660 - 840.53
18/11 (inv. 11/9) - A - (1942) - 852.59
21/13 (inv. 26/21) - Ab - 1239 - 830.26
23/14 (inv. 28/23) - A - (1661) - 859.45
28/17 (inv. 17/14) - A - (1480) - 863.87
29/18 - Ab - 1051 - 825.67
31/19 - Ab - 1947 - 847.52
33/20 - A - (1353) - 866.94

Note that, there is a difference of 44.79 c. between the maximum and minimum
values of the thirds (41.27 c. between the sixths). Remember that the
minimum available interval, 33/32, makes 46.73 c. Thus, smaller values than
that are treated within the 'range' of a single 'pitch'. (The same as we
treated E# as Gb in the Phythagorean Method)

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Credit: Fred Nachbaur, for Harmonic Analyser.
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Regards,
Ertugrul iNANC
Copyright © 2001

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Re: Notes on Eastern Tone System III

Reply #1 – 2001-08-24 04:00 am

Thnaks for the info (and the examples in the newsgroup). Wish I had more time to focus on music (Darn work! Unfortunately not talented enough to make a living as a musician). But, at least I'll keep the info in the back of my mind for a potential future application.

Re: Notes on Eastern Tone System III

Reply #2 – 2001-08-24 04:00 am

You're welcome. Btw, the NWC file containing the intervals can be found at the NWC Scriptorium.

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