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'''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.
{{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]].
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).  
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 technical data, see [[Meantone family #Mohajira]].


== Interval chain ==
== Interval chain ==
In the following tables, odd harmonics 1–11 are shown in '''bold'''.  
In the following tables, odd harmonics 1–11 are shown in '''bold'''.  


<div><div style="display: inline-grid; margin-right: 25px;">
<div style="display: inline-grid; margin-right: 25px;">
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
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| 3
| 3
| 1045.5
| 1045.5
| 20/11, 11/6
| 11/6, 20/11
|-
|-
| 4
| 4
| 194.0
| 194.0
| 9/8, 10/9
| '''9/8''', 10/9
|-
|-
| 5
| 5
| 542.5
| 542.5
| '''11/8'''
| '''11/8''', 15/11
|-
|-
| 6
| 6
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| 7
| 7
| 39.4
| 39.4
| 33/32
| 33/32, 36/35, 45/44, <br>55/54, 64/63
|-
|-
| 8
| 8
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| 12
| 12
| 581.9
| 581.9
| 45/32
| 25/18, 45/32
|-
|-
| 13
| 13
Line 81: Line 94:
| 14
| 14
| 78.9
| 78.9
| 25/24
| 22/21, 25/24
|-
|-
| 15
| 15
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| 775.9
| 775.9
| 11/7
| 11/7
|-
| 17
| 1124.3
| 27/14, 40/21
|}
|}


Line 106: Line 123:
| -1
| -1
| 851.5
| 851.5
| 44/27, 18/11
| 18/11, 44/27
|-
|-
| -2
| -2
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| -5
| -5
| 657.5
| 657.5
| 16/11
| 16/11, 22/15
|-
|-
| -6
| -6
Line 130: Line 147:
| -7
| -7
| 1160.6
| 1160.6
| 64/33
| 35/18, 63/32, 64/33, <br>88/45, 108/55
|-
|-
| -8
| -8
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| -12
| -12
| 618.1
| 618.1
| 64/45
| 36/25, 64/45
|-
|-
| -13
| -13
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| -14
| -14
| 1121.1
| 1121.1
| 48/25
| 21/11, 48/25
|-
|-
| -15
| -15
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| 424.1
| 424.1
| 14/11
| 14/11
|-
| -17
| 75.7
| 21/20, 28/27
|}
|}
</div>
</div>
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== Scales and harmony ==
== Scales and harmony ==
: {{main|Mohajira/Scales}}
: {{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 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}}
|}


== Notes ==
== Notes ==
<references group="note" />
<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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