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.
Letter M is used to denote a step halfway between L and s steps, A stands for "augmented", which is widening an individual step by a chroma (L - s).
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).
Ajnas
The beginning of one jins is ending of another (known as ghammaz), and it's a point where modulation occurs usually. As such, these notes are unchaged from the original mos pattern.
The three most common ajnas - hijaz, bayati, and rast, are based on their diatonic counterpart in pattern in the basic mos case, - sAs, MML, and LMM respectively.
In case where the mos is basic, variations derived with jins hijaz are entirely contained within the original temperament and do not require equal tuning twice the size, as L = s, which means A = L + (L - s) = L + s.
13-tone orwell example
Orwell[13], which amounts to 9L 4s, is an interesting case, as it has a subminor third as a generator and also it features 4 notes inclusive from generator to generator, meaning that each ghammaz of every jins there is one generator above the other, making it perfect for such variations.
This is a hardness 2:1 variation in 44edo, which doubles 22edo. Since we have a basic mos, the middle step is 3 steps.
Following scales were designated by Eliora and are based on the LLsLLsLLsLLLs mode of Orwell[13] in 22edo.
| Jins style | 44edo | |
|---|---|---|
| Original scale | - | 0-4-8-10-14-18-20-24-28-30-34-38-40-44 |
| Maqam Eurasia | Hijaz | 0-2-8-10-12-18-20-22-28-30-32-38-40-44 |
| Maqam Oceania | Bayati | 0-3-6-10-13-16-20-23-26-30-33-36-40-44 |
| Maqam Eastasia | Rast | 0-4-7-10-14-17-20-24-27-30-34-37-40-44 |
It is worth noting that Maqam Oceania and Maqam Eastasia are non-MOS variations of p-chro oneirotonic, where steps are rearranged.