Mohajira

Mohajira (/mʊˈhɑːdʒɪɹə, -hæ-/ muu-HA(H)-jirr-ə or /məˈhɑːdʒɪɹə, -hæ-/ mə-HA(H)-jirr-ə, named by Jacques Dudon from Arabic مهاجرة Muhājirah) is a meantone temperament that splits 3/2 into two 11/9 generators and the 6/5 into two 11/10's, thus equating 11/10 with 12/11 and 11/9 with 27/22. As a result, eight 11/9s reach 5/4, and five reach 11/8. It tempers the biyatisma (121/120) and the rastma (along with meantone's syntonic comma). It can be thought of as meantone with quarter tones as it merely splits the generator 3/2 into two equally spaced neutral thirds. Among the most common is the seven note MOS mohajira[7] which consists of the steps LsLsLss, as well as the modMOS "Rast" which merely flats the fourth by one quarter tone.

For temperament data see Meantone family #Mohajira.

Interval chain

Up from the tonic, and fifthward			Down from the octave, and fourthward
#	Cents*	Ratios	#	Cents*	Ratios
0	0	1/1	0	1200	2/1
1	348.207	11/9, 27/22	-1	851.793	44/27, 18/11
2	696.414	3/2	-2	503.586	4/3
3	1044.621	20/11, 11/6	-3	155.379	11/10, 12/11
4	192.828	9/8, 10/9	-4	1007.172	9/5, 16/9
5	541.035	11/8	-5	658.965	16/11
6	889.242	5/3	-6	310.758	6/5
7	37.449	33/32	-7	1162.551	64/33
8	385.656	5/4	-8	814.344	8/5
9	733.863		-9	466.137
10	1082.07		-10	117.93
11	230.277		-11	969.723
12	578.484		-12	621.516
13	926.691		-13	273.309
14	74.898		-14	1125.102

Scales and harmony

There are seven modes of mohajira's 7-note MOS (named mosh due to being "mohajira-ish") which are structured in an analogous way to the seven modes of the major scale. They can be thought of as quarter tone altered modes in a 24 EDO setting, but also as microtonal altered scales in any equal temperament. While the Mohajira[7] MOS by itself is quite beautiful, the modMOS Rast tends to be more expressive as it contains a few major and minor thirds allowing for more contrast.

For Kentaku's further exploration, see Mohajira/Scales.