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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
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| de = Mohajira
: This revision was by author [[User:cookiemeows|cookiemeows]] and made on <tt>2014-08-20 20:30:29 UTC</tt>.<br>
| en = Mohajira
: The original revision id was <tt>519125874</tt>.<br>
| es =
: The revision comment was: <tt></tt><br>
| ja =
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
}}
<h4>Original Wikitext content:</h4>
'''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.
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Mohajira is a meantone temperament that splits 3/2 into two 11/9's and the 4/3 into two 11/10's. It can be thought of as meantone with quarter tones as it merely spits 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.


=Modes and MOS=
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]].
There are seven diatonic modes of mohajira which are structured in an analogous way to the seven church 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 contain a few major and minor thirds allowing for more contrast.


Because there are too many possible Mohajira Mos and Modmos, Kentaku has organized a way to think of the progression of accidentals in the modes of 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).  
The scales are organized based on evoking slightly different colors and categorized by different levels of alteration from a meantone scale. A Mos of Mohajira[10] can be used in order to improvise on all the common Modmos of mohajira.


Here are the scales with 1 2 3 4 5 6 7 being the major scale.
For temperament data see [[Meantone family #Mohajira]].
==Level 0 - Mohajira MOS - The Neutral Diatonic scale==
1 2 v3 ^4 5 6 v7 1 or C D Ed Ft G A Bd C


==Level 1 - Mohajira ModMOS by 1 alteration==
== Interval chain ==
Rast - 1 2 v3 4 5 6 v7 1 or C D Ed F G A Bd C
{| class="wikitable"
|+
! colspan="3" |Up from the tonic, and fifthward
! colspan="3" |Down from the octave, and fourthward
|-
!#
!Cents*
!Ratios
!#
!Cents*
!Ratios
|-
|0
|0
|'''1/1'''
|0
|1200
|'''2/1'''
|-
|1
|348.7
|11/9, 27/22
| -1
|851.3
|44/27, 18/11
|-
|2
|697.4
|'''3/2'''
| -2
|502.6
|4/3
|-
|3
|1046.1
|20/11, 11/6
| -3
|153.9
|11/10, 12/11
|-
|4
|194.8
|9/8, 10/9
| -4
|1005.2
|9/5, 16/9
|-
|5
|543.5
|'''11/8'''
| -5
|656.5
|16/11
|-
|6
|892.2
|5/3
| -6
|307.8
|6/5
|-
|7
|40.9
|33/32
| -7
|1159.1
|64/33
|-
|8
|389.6
|'''5/4'''
| -8
|810.4
|8/5
|-
|9
|738.3
|32/21
| -9
|461.7
|21/16
|-
|10
|1087
|15/8
| -10
|113
|16/15
|-
|11
|235.7
|8/7
| -11
|964.3
|'''7/4'''
|-
|12
|584.4
|45/32
| -12
|615.6
|64/45
|-
|13
|933.1
|12/7
| -13
|266.9
|7/6
|-
|14
|81.8
|25/24
| -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
|}


==Level 2 - Mohajira ModMOS by 2 alteration==  
== Scales and harmony ==
Altered Melodic Minor - 1 2 b3 4 5 6 v7 1 or C D Eb F G A Bd C
: {{main|Mohajira/Scales}}
Turkish Minor - 1 2 b3 4 5 b6 7 1 or C D Ed F G A Bd C
Bayati - 1 d2 b3 4 5 b6 b7 1
==Level 3 - Meantone by 3 alterations==


[[image:altered mohajira levels.PNG]]
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.


=Harmonization of Mohajira=  
== Notes ==
While the structure of mohajra[7] may seem similar to the shape of meantone, because of there being only one size of thirds, it's better to harmonize the scale
<references group="note" />
with a combination of various voicings of 1-5-7-4 and 1-5-7-3 as well as other combinations of chords such as quartal tetrads. The Rast scales generally have more variety as they contain major and minor thirds as well as neutral thirds.
[[Category:Mohajira| ]] <!-- main article -->
 
[[Category:Rank-2 temperaments]]
To introduce more interest into harmony involving mohajira, a 10 note Mos can be used to incorporate various synthetic versions of traditional turkish and middle eastern scales.
[[Category:Meantone family]]
 
The intervals of Mohajira and Neutral harmony work in an almost reverse manner from meantone. The most consonant is 3/2 and 4/3 followed by 11/6, 11/9 and 11/8. In context of a chord with a perfect fifth, 11/9's tend to produce a rather rough chord that sounds good in many context but is quite rough as a tonic chord. It can be good to think of the neutral seventh 11/6 and 3/2 as the base intervals of a chord with 11/8 and 4/3 acting almost in an analogous way to the major and minor third in meantone. This is why 11/8 can be called the major fourth in 24 ET.
 
See also [[Meantone family#Mohajira]].</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Mohajira&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Mohajira is a meantone temperament that splits 3/2 into two 11/9's and the 4/3 into two 11/10's. It can be thought of as meantone with quarter tones as it merely spits 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 &amp;quot;Rast&amp;quot; which merely flats the fourth by one quarter tone.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Modes and MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Modes and MOS&lt;/h1&gt;
There are seven diatonic modes of mohajira which are structured in an analogous way to the seven church 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 contain a few major and minor thirds allowing for more contrast.&lt;br /&gt;
&lt;br /&gt;
Because there are too many possible Mohajira Mos and Modmos, Kentaku has organized a way to think of the progression of accidentals in the modes of Mohajira.&lt;br /&gt;
The scales are organized based on evoking slightly different colors and categorized by different levels of alteration from a meantone scale. A Mos of Mohajira[10] can be used in order to improvise on all the common Modmos of mohajira.&lt;br /&gt;
&lt;br /&gt;
Here are the scales with 1 2 3 4 5 6 7 being the major scale.&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Modes and MOS-Level 0 - Mohajira MOS - The Neutral Diatonic scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Level 0 - Mohajira MOS - The Neutral Diatonic scale&lt;/h2&gt;
1 2 v3 ^4 5 6 v7 1 or C D Ed Ft G A Bd C&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Modes and MOS-Level 1 - Mohajira ModMOS by 1 alteration"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Level 1 - Mohajira ModMOS by 1 alteration&lt;/h2&gt;
Rast - 1 2 v3 4 5 6 v7 1 or C D Ed F G A Bd C&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Modes and MOS-Level 2 - Mohajira ModMOS by 2 alteration"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Level 2 - Mohajira ModMOS by 2 alteration&lt;/h2&gt;
Altered Melodic Minor - 1 2 b3 4 5 6 v7 1 or C D Eb F G A Bd C&lt;br /&gt;
Turkish Minor - 1 2 b3 4 5 b6 7 1 or C D Ed F G A Bd C&lt;br /&gt;
Bayati - 1 d2 b3 4 5 b6 b7 1&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Modes and MOS-Level 3 - Meantone by 3 alterations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Level 3 - Meantone by 3 alterations&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:12:&amp;lt;img src=&amp;quot;/file/view/altered%20mohajira%20levels.PNG/519036492/altered%20mohajira%20levels.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/altered%20mohajira%20levels.PNG/519036492/altered%20mohajira%20levels.PNG" alt="altered mohajira levels.PNG" title="altered mohajira levels.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:12 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Harmonization of Mohajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Harmonization of Mohajira&lt;/h1&gt;
While the structure of mohajra[7] may seem similar to the shape of meantone, because of there being only one size of thirds, it's better to harmonize the scale&lt;br /&gt;
with a combination of various voicings of 1-5-7-4 and 1-5-7-3 as well as other combinations of chords such as quartal tetrads. The Rast scales generally have more variety as they contain major and minor thirds as well as neutral thirds. &lt;br /&gt;
&lt;br /&gt;
To introduce more interest into harmony involving mohajira, a 10 note Mos can be used to incorporate various synthetic versions of traditional turkish and middle eastern scales. &lt;br /&gt;
&lt;br /&gt;
The intervals of Mohajira and Neutral harmony work in an almost reverse manner from meantone. The most consonant is 3/2 and 4/3 followed by 11/6, 11/9 and 11/8. In context of a chord with a perfect fifth, 11/9's tend to produce a rather rough chord that sounds good in many context but is quite rough as a tonic chord. It can be good to think of the neutral seventh 11/6 and 3/2 as the base intervals of a chord with 11/8 and 4/3 acting almost in an analogous way to the major and minor third in meantone. This is why 11/8 can be called the major fourth in 24 ET.&lt;br /&gt;
&lt;br /&gt;
See also &lt;a class="wiki_link" href="/Meantone%20family#Mohajira"&gt;Meantone family&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 19:02, 22 June 2025

Mohajira[note 1] 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.

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.

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
1 348.7 11/9, 27/22 -1 851.3 44/27, 18/11
2 697.4 3/2 -2 502.6 4/3
3 1046.1 20/11, 11/6 -3 153.9 11/10, 12/11
4 194.8 9/8, 10/9 -4 1005.2 9/5, 16/9
5 543.5 11/8 -5 656.5 16/11
6 892.2 5/3 -6 307.8 6/5
7 40.9 33/32 -7 1159.1 64/33
8 389.6 5/4 -8 810.4 8/5
9 738.3 32/21 -9 461.7 21/16
10 1087 15/8 -10 113 16/15
11 235.7 8/7 -11 964.3 7/4
12 584.4 45/32 -12 615.6 64/45
13 933.1 12/7 -13 266.9 7/6
14 81.8 25/24 -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

Main article: 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.

Notes

  1. ↑ (/mʊˈhɑːdʒɪɹə, -hæ-/ muu-HA(H)-jirr-ə or /məˈhɑːdʒɪɹə, -hæ-/ mə-HA(H)-jirr-ə, named by Jacques Dudon from Arabic مهاجرة Muhājirah)
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