Text: NEUTRAL THIRDS and SIXTHS 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) --- Credit: Fred Nachbaur, for Harmonic Analyser.

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