Full Name of Work: Neutral Thirds and Sixths in 17/33 System
Author: iNANÇ, Ertugrul (1976 - ), Turkish
Creator: iNANÇ, Ertugrul (1976 - ), Turkish
Instruments:    Clarinet

Comments:
(This article has been cross-posted to rec.music.compose, rec.music.early 
and rec.music.theory groups as well as the NWC forum, with a few nuances 
and lacking the attachment, under the title of "Notes on Eastern Tone 
System III.")

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'.

A NWC file for print and playback is available. 

Credit: Fred Nachbaur, for Harmonic Analyser.

Ertuğrul İnanç