Maqam variations of MOS

This page assumes that the reader is familiar with TAMNAMS mos interval and step ratio names.

Given a xL ys mos scale pattern, and also with the difference between L and s being an even number, it is possible to apply neutral and interordinal k-mossteps through methodology and notation of Middle Eastern music. Such phenomena produce some rather unique scales.

Implementation

Historically, maqam music made extensive use of neutral intervals, but less so interordinals like 5\24 semifourth. This is primarily due to the fact that a maqam is based on jins (plural: ajnas) from which a whole family derives.

There are different levels of maqam music with respect to their approximation by equal division to the octave, with the first being: an equal division must contain a neutral second, neutral third, and a diatonic-esque scale because that's how ajnas are in place. This means that to generalize this to an arbitrary xL ys mos pattern, we need the chroma, L - s, to be an even number.

In the diatonic scale, 17edo and 24edo are the smallest edos supporting level 1 maqam. Likewise, the smallest type of mos which can support maqam variations are hard (3:1) and basic pattern embedded in edo twice the size (4:2).

Orwell[13] example

This is a hardness 2:1 variation in 44edo, which doubles 22edo.

	Jins pattern	44edo
Maqam Eurasia	sAs	0-1-6-10-11-16-20-21-26-30-31-36-40-44
Maqam Oceania	msL	0-4-5-10-14-15-20-24-25-30-34-35-40-44
Maqam Eastasia	msL	0-4-6-10...