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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's and the 6/5 into two 11/10's, thus equating 11/10 with 12/11 and 11/9 with 27/22. 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.
{{Infobox regtemp
| Title = Mohajira
| Subgroups = 2.3.5.7, 2.3.5.7.11
| Comma basis = [[81/80]], [[6144/6125]] (7-limit); <br>[[81/80]], [[121/120]], [[176/175]] (11-limit)
| Edo join 1 = 24 | Edo join 2 = 31
| Mapping = 1; 2 8 -11 5
| Generators = 11/9
| Generators tuning = 348.5
| Optimization method = CWE
| MOS scales = [[3L 4s]], [[7L 3s]], [[7L 10s]], [[7L 17s]]
| Odd limit 1 = 9 | Mistuning 1 = 10.8 | Complexity 1 = 24
| Odd limit 2 = 11-limit 21 | Mistuning 2 = 10.8 | Complexity 2 = 24
}}
'''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 11/9's reach [[5/4]], and five reach [[11/8]]. It [[tempering out|tempers out]] the biyatisma ([[121/120]]) and the [[rastma]] (along with meantone's [[syntonic comma]]). It can be thought of as meantone with [[quartertone]]s as it merely splits the generator 3/2 into two equally spaced neutral thirds. Among the most common is the 7-note mos Mohajira[7] which consists of the steps LsLsLss, as well as the [[modmos]] "Rast" which merely flats the fourth by one quartertone.
 
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]].


For temperament data see [[Meantone family #Mohajira]].
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 technical data, see [[Meantone family #Mohajira]].


== Interval chain ==
== Interval chain ==
{| class="wikitable"
In the following tables, odd harmonics 1–11 are shown in '''bold'''.
|+
 
! colspan="3" |Up from the tonic, and fifthward
<div style="display: inline-grid; margin-right: 25px;">
! colspan="3" |Down from the octave, and fourthward
{| class="wikitable center-1 right-2"
|-
|-
!#
! #
!Cents*
! Cents*
!Ratios
! Approximate ratios
!#
!Cents*
!Ratios
|-
|-
|0
| 0
|0
| 0.0
|1/1
| '''1/1'''
|0
|-
|1200
| 1
|2/1
| 348.5
| 11/9, 27/22
|-
| 2
| 697.0
| '''3/2'''
|-
| 3
| 1045.5
| 11/6, 20/11
|-
| 4
| 194.0
| '''9/8''', 10/9
|-
| 5
| 542.5
| '''11/8''', 15/11
|-
| 6
| 890.9
| 5/3
|-
| 7
| 39.4
| 33/32, 36/35, 45/44, <br>55/54, 64/63
|-
| 8
| 387.9
| '''5/4'''
|-
| 9
| 736.4
| 32/21
|-
| 10
| 1084.9
| 15/8
|-
| 11
| 233.4
| 8/7
|-
| 12
| 581.9
| 25/18, 45/32
|-
| 13
| 930.4
| 12/7
|-
| 14
| 78.9
| 22/21, 25/24
|-
| 15
| 427.4
| 9/7
|-
| 16
| 775.9
| 11/7
|-
| 17
| 1124.3
| 27/14, 40/21
|}
 
</div>
<div style="display: inline-grid; margin-right: 25px;">
{| class="wikitable center-1 right-2"
|-
! #
! Cents*
! Approximate ratios
|-
| 0
| 1200.0
| '''2/1'''
|-
|-
|1
|348.207
|11/9, 27/22
| -1
| -1
|851.793
| 851.5
|44/27, 18/11
| 18/11, 44/27
|-
|-
|2
|696.414
|3/2
| -2
| -2
|503.586
| 503.0
|4/3
| 4/3
|-
|-
|3
|1044.621
|20/11, 11/6
| -3
| -3
|155.379
| 154.5
|11/10, 12/11
| 11/10, 12/11
|-
|-
|4
|192.828
|9/8, 10/9
| -4
| -4
|1007.172
| 1006.0
|9/5, 16/9
| 9/5, 16/9
|-
|-
|5
|541.035
|11/8
| -5
| -5
|658.965
| 657.5
|16/11
| 16/11, 22/15
|-
|-
|6
|889.242
|5/3
| -6
| -6
|310.758
| 309.1
|6/5
| 6/5
|-
|-
|7
|37.449
|33/32
| -7
| -7
|1162.551
| 1160.6
|64/33
| 35/18, 63/32, 64/33, <br>88/45, 108/55
|-
|-
|8
|385.656
|5/4
| -8
| -8
|814.344
| 812.1
|8/5
| 8/5
|-
|-
|9
|733.863
|
| -9
| -9
|466.137
| 463.6
|
| 21/16
|-
|-
|10
|1082.07
|
| -10
| -10
|117.93
| 115.1
|
| 16/15
|-
|-
|11
|230.277
|
| -11
| -11
|969.723
| 966.6
|
| '''7/4'''
|-
|-
|12
|578.484
|
| -12
| -12
|621.516
| 618.1
|
| 36/25, 64/45
|-
|-
|13
|926.691
|
| -13
| -13
|273.309
| 269.6
|
| 7/6
|-
|-
|14
|74.898
|
| -14
| -14
|1125.102
| 1121.1
|
| 21/11, 48/25
|-
| -15
| 772.6
| 14/9
|-
| -16
| 424.1
| 14/11
|-
| -17
| 75.7
| 21/20, 28/27
|}
|}
</div>
<nowiki/>* In 11-limit CWE tuning, octave reduced


== Scales and harmony ==
== 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.
: {{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 24edo 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.
 
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~128/105 = 348.4374{{c}}
| CWE: ~128/105 = 348.4194{{c}}
| POTE: ~128/105 = 348.4149{{c}}
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~11/9 = 348.5608{{c}}
| CWE: ~11/9 = 348.4910{{c}}
| POTE: ~11/9 = 348.4767{{c}}
|}


For Kentaku's further exploration, see [[Mohajira/Scales]].
== 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]]
[[Category:Porwell temperaments]]
[[Category:Rastmic clan]]
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