Mohajira

Mohajira (stressed on the "ha"), 24 & 7, is an extension to Rastmatic (Neutral) that is a Meantone temperament. In other words, the generator is a neutral third representing 11/9, which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: 5/4). Thus, 243/242 and 81/80 are both tempered out. Mohajira, due to its neutral third generator, is a 7 cluster temperament, and its main MOS scale is 3L 4s ("mosh", LsLsLss), with the notable MODMOS ssLLssL (which is associated with the maqam Rast and (perhaps not coincidentally) the result of applying Mohajira tempering to the just equiheptatonic). Mohajira equates 11/10 with 12/11 and 9/8 with 10/9, and by this distinguishes itself from other temperaments of the just equiheptatonic such as Flattone and Porcupine.

As a tuning generated by the unstable interval 11/9, it is perhaps viable to directly map 11/9 to edos and determine the tuning of 11 from there, instead of vice versa.

Generally, Mohajira is also extended to include prime 7 as the semidiminished seventh, though an alternate mapping also available in 31edo shares septimal Meantone's mapping of 7 (and contributes much to 31edo's 7-limit structure).

Interval table

Generator step table:

# up	Cents	Just interval	Neutral diatonic notation	# down	Cents	Just interval	Neutral diatonic notation
0	0	1/1	P1	0	1200	2/1	P8
1	348	11/9, 27/22	n3	-1	852	18/11, 44/27	n6
2	696	3/2	P5	-2	504	4/3	P4
3	1044	11/6, 20/11	n7	-3	156	11/10, 12/11	n2
4	192	10/9, 9/8	M2	-4	1008	9/5, 16/9	m7
5	540	11/8, 15/11	sA4	-5	660	16/11, 22/15	sd5
6	888	5/3	M6	-6	312	6/5	m3
7	36	33/32	sA1	-7	1164	64/33	sd8
8	384	5/4	M3	-8	816	8/5	m6

Patent vals

Mohajira patent vals are tunings of Meantone for which 11 is mapped to the semiaugmented fourth. As such, they are a subset of possible Meantone tunings. In fact, the space is rather limited due to how necessarily flat 11/8 is (most Meantone tunings have an 11/9 sharp of neutral). Unless otherwise stated, these also support the 7-limit version of the temperament.

EDO	Generator tuning	Fifth tuning
24	350c	700c
55	349.1c	698.2c
31	348.4c	696.8c
38	347.4c	694.7c
7	342.9c	685.7c

2.3.5.11/9 "patent" vals

It may also be desirable to optimize equal temperament mappings for 11/9 instead of 11 itself. Mohajira tunings that do this and are not mentioned above are the following, and usually utilize the second-best 11/8:

EDO	Fifth tuning	Generator tuning	11/8 tuning*
134	698.51	349.25	546.27
86	697.67	348.84	544.19
117	697.44	348.72	543.59
100	696.00	348.00	540.00
69	695.65	347.83	539.13
45*	693.33	346.67	533.33
52*	692.31	346.15	530.77

**The 11/8 tuning is not the best 11/8.

*45e and 52e do not support septimal Mohajira.