Neutral Thirds

I saw some discussion on a facebook tuning group about neutral thirds in Persian music, attributed to Mansour Zalzal in the 9th Century. A neutral third is between a major third and a minor third. Since a major third and a minor third combine to form a perfect fifth, a neutral third should be about half of a perfect fifth. Zalzal evidently proposed 27:22 as a neutral third. Squaring this gives 729:484. A perfect fifth would be 726:484, so Zalzal's neutral third is quite accurate.

This looked worth exploring. What equal divisions of the octave work well with ratios involving the prime number 11? 87edo is very good, but it is a bit strange: it doesn't temper the schisma, it has three circles of fifths, etc. 65edo looks good, though!

The Persian scales discussed in the tuning group have 17 notes per octave. The neutral third corresponds to 19 steps of 65edo, or 19\65. A 17 note scale generated by neutral thirds has the Moment of Symmetry property, e.g. the scale has two different step sizes: 3\65 and 5\65.

This is a table of the 17 notes, in terms of cents.

Here's an example of what it sounds like: 65edo scale 17.