Mohajira: Difference between revisions
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'''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_family#Mohajira|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. | '''Mohajira'''<ref group="note">(/mʊˈhɑːdʒɪɹə, -hæ-/ ''muu-HA(H)-jirr-ə'' or /məˈhɑːdʒɪɹə, -hæ-/ ''mə-HA(H)-jirr-ə'', named by Jacques Dudon from Arabic مهاجرة ''Muhājirah'')</ref> is a [[Meantone_family#Mohajira|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. | ||
The simplest form of this temperament, in 2.3.5.11, is sometimes called '''mohaha'''. To extend mohaha into full 11-limit mohajira, 7 is found at 11 neutral thirds down, tempering out the [[valinorsma]] such that 14/11 is equated with 32/25. Mohaha is tuned best sharp of 31edo's neutral third. An alternate extension, ''migration,'' is optimized for flatter tunings and finds 7 at 20 generators up, the same mapping as in [[septimal meantone]] which tempers out [[225/224]]. | |||
As mohajira is a neutral third system, 13 also has a reasonable mapping at -1 generator, equating 11/9 and 16/13. Subsequently, 17 is mapped to -10 generators (the diatonic semitone) and 19 to -6 generators (the minor third). | |||
For temperament data see [[Meantone family #Mohajira]]. | For temperament data see [[Meantone family #Mohajira]]. | ||
| Line 24: | Line 28: | ||
|0 | |0 | ||
|0 | |0 | ||
|1/1 | |'''1/1''' | ||
|0 | |0 | ||
|1200 | |1200 | ||
|2/1 | |'''2/1''' | ||
|- | |- | ||
|1 | |1 | ||
|348. | |348.7 | ||
|11/9, 27/22 | |11/9, 27/22 | ||
| -1 | | -1 | ||
|851. | |851.3 | ||
|44/27, 18/11 | |44/27, 18/11 | ||
|- | |- | ||
|2 | |2 | ||
| | |697.4 | ||
|3/2 | |'''3/2''' | ||
| -2 | | -2 | ||
| | |502.6 | ||
|4/3 | |4/3 | ||
|- | |- | ||
|3 | |3 | ||
| | |1046.1 | ||
|20/11, 11/6 | |20/11, 11/6 | ||
| -3 | | -3 | ||
| | |153.9 | ||
|11/10, 12/11 | |11/10, 12/11 | ||
|- | |- | ||
|4 | |4 | ||
| | |194.8 | ||
|9/8, 10/9 | |9/8, 10/9 | ||
| -4 | | -4 | ||
| | |1005.2 | ||
|9/5, 16/9 | |9/5, 16/9 | ||
|- | |- | ||
|5 | |5 | ||
| | |543.5 | ||
|11/8 | |'''11/8''' | ||
| -5 | | -5 | ||
| | |656.5 | ||
|16/11 | |16/11 | ||
|- | |- | ||
|6 | |6 | ||
| | |892.2 | ||
|5/3 | |5/3 | ||
| -6 | | -6 | ||
| | |307.8 | ||
|6/5 | |6/5 | ||
|- | |- | ||
|7 | |7 | ||
| | |40.9 | ||
|33/32 | |33/32 | ||
| -7 | | -7 | ||
| | |1159.1 | ||
|64/33 | |64/33 | ||
|- | |- | ||
|8 | |8 | ||
| | |389.6 | ||
|5/4 | |'''5/4''' | ||
| -8 | | -8 | ||
| | |810.4 | ||
|8/5 | |8/5 | ||
|- | |- | ||
|9 | |9 | ||
| | |738.3 | ||
| | |32/21 | ||
| -9 | | -9 | ||
| | |461.7 | ||
| | |21/16 | ||
|- | |- | ||
|10 | |10 | ||
| | |1087 | ||
| | |15/8 | ||
| -10 | | -10 | ||
| | |113 | ||
| | |16/15 | ||
|- | |- | ||
|11 | |11 | ||
| | |235.7 | ||
| | |8/7 | ||
| -11 | | -11 | ||
| | |964.3 | ||
| | |'''7/4''' | ||
|- | |- | ||
|12 | |12 | ||
| | |584.4 | ||
| | |45/32 | ||
| -12 | | -12 | ||
| | |615.6 | ||
| | |64/45 | ||
|- | |- | ||
|13 | |13 | ||
| | |933.1 | ||
| | |12/7 | ||
| -13 | | -13 | ||
| | |266.9 | ||
| | |7/6 | ||
|- | |- | ||
|14 | |14 | ||
| | |81.8 | ||
| | |25/24 | ||
| -14 | | -14 | ||
| | |1118.2 | ||
| | |48/25 | ||
|- | |||
|15 | |||
|430.5 | |||
|9/7 | |||
| -15 | |||
|769.5 | |||
|14/9 | |||
|- | |||
|16 | |||
|779.2 | |||
|11/7 | |||
| -16 | |||
|420.8 | |||
|14/11 | |||
|} | |} | ||
== Scales and harmony == | == Scales and harmony == | ||
: {{main|Mohajira/Scales}} | |||
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. | 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. | ||
== Notes == | |||
<references group="note" /> | |||
[[Category:Mohajira| ]] <!-- main article --> | [[Category:Mohajira| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Meantone family]] | [[Category:Meantone family]] | ||