“Mujannab zone” ratios

The neutral thirds of Maqam music are more diversified than the ratio 11:9 can encompass. As far as I can tell, middle second intervals roam the “mujannab zone” between 14:13 and 11:10. This is a region 37 cents wide. Then again, it is possible to broaden the zone and take 15:14 and 10:9 as the extremes. In that case, we acquire a zone that is 63 cents wide!

I conjecture that high prime-limit and relatively simple integer ratios such as 14:13, 27:25, 13:12, 12:11, 35:32, 11:10, 54:49 are at play. Then again, instead of middle seconds, we might be looking at neutral thirds, in which case, the performer could be searching for 17:14, 39:32, 11:9, 27:22, 16:13, 21:17 and 31:25.

So many ratios imply the necessity to temper pitches and represent diverse middle seconds as well as neutral thirds with few, yet, variegated microtones that are reasonably spaced apart. That is how I arrived at 79 MOS 159-tET. Check out page 95 of my doctorate dissertation. There, you will see how the 79-tone tuning approximates many such RI intervals.