Mohajira - Revision history

FloraC: + infobox

2026-04-08T10:19:16Z

+ infobox

@@ Line 1: / Line 1: @@
-{{interwiki
+{{Interwiki
 | de = Mohajira
 | es =
 | ja =
 }}
 '''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.

Xenllium at 10:43, 15 January 2026

2026-01-15T10:43:07Z

← Older revision		Revision as of 10:43, 15 January 2026
Line 16:		Line 16:
	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"
	\|-		\|-

ArrowHead294: Minus signs instead of hyphen-minuses

2025-11-17T17:49:19Z

Minus signs instead of hyphen-minuses

← Older revision		Revision as of 17:49, 17 November 2025
Line 9:		Line 9:
	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 technical data, see [[Meantone family #Mohajira]].		For technical data, see [[Meantone family #Mohajira]].
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	\| POTE: ~128/105 = 348.4149{{c}}		\| POTE: ~128/105 = 348.4149{{c}}
	\|}		\|}

	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit norm-based tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit norm-based tunings

FloraC: /* Interval chain */

2025-11-17T17:41:46Z

Interval chain

← Older revision		Revision as of 17:41, 17 November 2025
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	\| 4		\| 4
	\| 194.0		\| 194.0
	\| 9/8, 10/9		\| '''9/8''', 10/9
	\|-		\|-
	\| 5		\| 5

FloraC: Text replacement - "prime-optimized" to "norm-based"

2025-09-12T14:06:07Z

Text replacement - "prime-optimized" to "norm-based"

← Older revision		Revision as of 14:06, 12 September 2025
Line 186:		Line 186:
	== Tunings ==		== Tunings ==
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
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	\|}		\|}
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|

FloraC: + tunings

2025-08-24T12:30:33Z

+ tunings

← Older revision		Revision as of 12:30, 24 August 2025
Line 183:		Line 183:

	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.		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 prime-optimized 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 prime-optimized 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 ==

FloraC: Cleanup & + categories

2025-08-24T11:18:12Z

Cleanup & + categories

← Older revision		Revision as of 11:18, 24 August 2025
Line 5:		Line 5:
	\| ja =		\| ja =
	}}		}}
	'''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~~.		'''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 ==
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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.

	== 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]]

FloraC: /* Interval chain */ ratios

2025-08-24T11:14:32Z

Interval chain: ratios

← Older revision		Revision as of 11:14, 24 August 2025
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	\| 3		\| 3
	\| 1045.5		\| 1045.5
	\| 20/11~~, 11/6~~		\| 11/6, 20/11
	\|-		\|-
	\| 4		\| 4
Line 45:		Line 45:
	\| 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
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	\| 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
	\|}		\|}

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	\| -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
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	\| -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>

FloraC: /* Interval chain */ tuning

2025-08-24T11:09:04Z

Interval chain: tuning

Show changes

FloraC: /* Interval chain */ split the table

2025-08-24T11:01:50Z

Interval chain: split the table

Show changes