Mohajira - Revision history

Inthar at 03:28, 22 March 2026

2026-03-22T03:28:53Z

← Older revision		Revision as of 03:28, 22 March 2026
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	'''Mohajira''' (stressed on the "ha"), 24 & 7, is an extension to [[~~Rastmic~~]] (Neutral) that is a [[Meantone\|Meantone]] temperament. In other words, the generator is a neutral third representing [[11/9]], which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: [[5/4]]). Thus, [[243/242]] and [[81/80]] are both tempered out. Mohajira, due to its neutral third generator, is a [[Equiheptatonic\|7 cluster temperament]], and its main MOS scale is 3L 4s ("mosh", LsLsLss), with the notable MODMOS ssLLssL (which is associated with the maqam ''Rast'' and (perhaps not coincidentally) the result of applying Mohajira tempering to the just equiheptatonic). Mohajira equates 11/10 with 12/11 and 9/8 with 10/9, and by this distinguishes itself from other temperaments of the just equiheptatonic such as [[Flattone]] and [[Porcupine]].		'''Mohajira''' (stressed on the "ha"), 24 & 7, is an extension to [[Rastmatic]] (Neutral) that is a [[Meantone\|Meantone]] temperament. In other words, the generator is a neutral third representing [[11/9]], which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: [[5/4]]). Thus, [[243/242]] and [[81/80]] are both tempered out. Mohajira, due to its neutral third generator, is a [[Equiheptatonic\|7 cluster temperament]], and its main MOS scale is 3L 4s ("mosh", LsLsLss), with the notable MODMOS ssLLssL (which is associated with the maqam ''Rast'' and (perhaps not coincidentally) the result of applying Mohajira tempering to the just equiheptatonic). Mohajira equates 11/10 with 12/11 and 9/8 with 10/9, and by this distinguishes itself from other temperaments of the just equiheptatonic such as [[Flattone]] and [[Porcupine]].

	As a tuning generated by the [[Tuning stability\|unstable]] interval 11/9, it is perhaps viable to directly map 11/9 to edos and determine the tuning of 11 from there, instead of vice versa.		As a tuning generated by the [[Tuning stability\|unstable]] interval 11/9, it is perhaps viable to directly map 11/9 to edos and determine the tuning of 11 from there, instead of vice versa.

Inthar: /* 2.3.5.11/9 "patent" vals */

2026-03-14T23:42:52Z

2.3.5.11/9 "patent" vals

← Older revision		Revision as of 23:42, 14 March 2026
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	<nowiki>*</nowiki>45e and 52e do not support septimal Mohajira.		<nowiki>*</nowiki>45e and 52e do not support septimal Mohajira.

			{{Navbox regtemp}}
			{{Cat\|Temperaments}}

Inthar at 23:41, 14 March 2026

2026-03-14T23:41:59Z

← Older revision		Revision as of 23:41, 14 March 2026
Line 1:		Line 1:
	'''Mohajira''' (stressed on the "ha"), 24 & 7, is an extension to [[Rastmic]] (Neutral) that is a [[Meantone\|Meantone]] temperament. In other words, the generator is a neutral third representing [[11/9]], which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: [[5/4]]). Thus, [[243/242]] and [[81/80]] are both tempered out. Mohajira, due to its neutral third generator, is a [[Equiheptatonic\|7 cluster temperament]], and its main MOS scale is 3L 4s ("mosh", LsLsLss), with the notable MODMOS ssLLssL (which is associated with the maqam ''~~rast~~'' and (perhaps not coincidentally) the result of applying Mohajira tempering to the just equiheptatonic). Mohajira equates 11/10 with 12/11 and 9/8 with 10/9, and by this distinguishes itself from other temperaments of the just equiheptatonic such as [[Flattone]] and [[Porcupine]].		'''Mohajira''' (stressed on the "ha"), 24 & 7, is an extension to [[Rastmic]] (Neutral) that is a [[Meantone\|Meantone]] temperament. In other words, the generator is a neutral third representing [[11/9]], which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: [[5/4]]). Thus, [[243/242]] and [[81/80]] are both tempered out. Mohajira, due to its neutral third generator, is a [[Equiheptatonic\|7 cluster temperament]], and its main MOS scale is 3L 4s ("mosh", LsLsLss), with the notable MODMOS ssLLssL (which is associated with the maqam ''Rast'' and (perhaps not coincidentally) the result of applying Mohajira tempering to the just equiheptatonic). Mohajira equates 11/10 with 12/11 and 9/8 with 10/9, and by this distinguishes itself from other temperaments of the just equiheptatonic such as [[Flattone]] and [[Porcupine]].

	As a tuning generated by the [[Tuning stability\|unstable]] interval 11/9, it is perhaps viable to directly map 11/9 to edos and determine the tuning of 11 from there, instead of vice versa.		As a tuning generated by the [[Tuning stability\|unstable]] interval 11/9, it is perhaps viable to directly map 11/9 to edos and determine the tuning of 11 from there, instead of vice versa.

Inthar at 23:40, 14 March 2026

2026-03-14T23:40:57Z

← Older revision		Revision as of 23:40, 14 March 2026
Line 1:		Line 1:
	'''Mohajira''' (stressed on the "ha"), 24 & 7, is an extension to [[~~rastmic~~]] (~~neutral~~) that is a [[Meantone'\|~~meantone~~]] temperament. In other words, the generator is a neutral third representing [[11/9]], which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: [[5/4]]). Thus, [[243/242]] and [[81/80]] are both tempered out. Mohajira, due to its neutral third generator, is a [[Equiheptatonic\|7 cluster temperament]], and its main MOS scale is 3L 4s ("mosh", LsLsLss), with the notable MODMOS ssLLssL (which is associated with the maqam ''rast'' and (perhaps not coincidentally) the result of applying ~~mohajira~~ tempering to the just equiheptatonic). Mohajira equates 11/10 with 12/11 and 9/8 with 10/9, and by this distinguishes itself from other temperaments of the just equiheptatonic such as [[~~flattone~~]] and [[~~porcupine~~]].		'''Mohajira''' (stressed on the "ha"), 24 & 7, is an extension to [[Rastmic]] (Neutral) that is a [[Meantone\|Meantone]] temperament. In other words, the generator is a neutral third representing [[11/9]], which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: [[5/4]]). Thus, [[243/242]] and [[81/80]] are both tempered out. Mohajira, due to its neutral third generator, is a [[Equiheptatonic\|7 cluster temperament]], and its main MOS scale is 3L 4s ("mosh", LsLsLss), with the notable MODMOS ssLLssL (which is associated with the maqam ''rast'' and (perhaps not coincidentally) the result of applying Mohajira tempering to the just equiheptatonic). Mohajira equates 11/10 with 12/11 and 9/8 with 10/9, and by this distinguishes itself from other temperaments of the just equiheptatonic such as [[Flattone]] and [[Porcupine]].

	As a tuning generated by the [[Tuning stability\|unstable]] interval 11/9, it is perhaps viable to directly map 11/9 to edos and determine the tuning of 11 from there, instead of vice versa.		As a tuning generated by the [[Tuning stability\|unstable]] interval 11/9, it is perhaps viable to directly map 11/9 to edos and determine the tuning of 11 from there, instead of vice versa.

	Generally, ~~mohajira~~ is also extended to include prime 7 as the semidiminished seventh, though an alternate mapping also available in 31edo shares septimal ~~meantone~~'s mapping of 7 (and contributes much to 31edo's 7-limit structure).		Generally, Mohajira is also extended to include prime 7 as the semidiminished seventh, though an alternate mapping also available in 31edo shares septimal Meantone's mapping of 7 (and contributes much to 31edo's 7-limit structure).

	== Interval table ==		== Interval table ==
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	== Patent vals ==		== Patent vals ==
	Mohajira patent vals are tunings of ~~meantone~~ for which 11 is mapped to the semiaugmented fourth. As such, they are a subset of possible ~~meantone~~ tunings. In fact, the space is rather limited due to how necessarily flat 11/8 is (most ~~meantone~~ tunings have an 11/9 sharp of neutral). Unless otherwise stated, these also support the 7-limit version of the temperament.		Mohajira patent vals are tunings of Meantone for which 11 is mapped to the semiaugmented fourth. As such, they are a subset of possible Meantone tunings. In fact, the space is rather limited due to how necessarily flat 11/8 is (most Meantone tunings have an 11/9 sharp of neutral). Unless otherwise stated, these also support the 7-limit version of the temperament.
	{\| class="wikitable"		{\| class="wikitable"
	!EDO		!EDO
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	<nowiki>**</nowiki>The 11/8 tuning is not the best 11/8.		<nowiki>**</nowiki>The 11/8 tuning is not the best 11/8.

	<nowiki>*</nowiki>45e and 52e do not support septimal ~~mohajira~~.		<nowiki>*</nowiki>45e and 52e do not support septimal Mohajira.

Inthar at 23:39, 14 March 2026

2026-03-14T23:39:16Z

← Older revision		Revision as of 23:39, 14 March 2026
Line 1:		Line 1:
	'''Mohajira''' (24 & 7) is an extension to [[rastmic]] (neutral) that is a [[Meantone'\|meantone]] temperament. In other words, the generator is a neutral third representing [[11/9]], which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: [[5/4]]). Thus, [[243/242]] and [[81/80]] are both tempered out. Mohajira, due to its neutral third generator, is a [[Equiheptatonic\|7 cluster temperament]], and its main MOS scale is 3L 4s ("mosh", LsLsLss), with the notable MODMOS ssLLssL (which is associated with the maqam ''rast'' and (perhaps not coincidentally) the result of applying mohajira tempering to the just equiheptatonic). Mohajira equates 11/10 with 12/11 and 9/8 with 10/9, and by this distinguishes itself from other temperaments of the just equiheptatonic such as [[flattone]] and [[porcupine]].		'''Mohajira''' (stressed on the "ha"), 24 & 7, is an extension to [[rastmic]] (neutral) that is a [[Meantone'\|meantone]] temperament. In other words, the generator is a neutral third representing [[11/9]], which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: [[5/4]]). Thus, [[243/242]] and [[81/80]] are both tempered out. Mohajira, due to its neutral third generator, is a [[Equiheptatonic\|7 cluster temperament]], and its main MOS scale is 3L 4s ("mosh", LsLsLss), with the notable MODMOS ssLLssL (which is associated with the maqam ''rast'' and (perhaps not coincidentally) the result of applying mohajira tempering to the just equiheptatonic). Mohajira equates 11/10 with 12/11 and 9/8 with 10/9, and by this distinguishes itself from other temperaments of the just equiheptatonic such as [[flattone]] and [[porcupine]].

	As a tuning generated by the [[Tuning stability\|unstable]] interval 11/9, it is perhaps viable to directly map 11/9 to edos and determine the tuning of 11 from there, instead of vice versa.		As a tuning generated by the [[Tuning stability\|unstable]] interval 11/9, it is perhaps viable to directly map 11/9 to edos and determine the tuning of 11 from there, instead of vice versa.

Vector: Created page with "'''Mohajira''' (24 & 7) is an extension to rastmic (neutral) that is a meantone temperament. In other words, the generator is a neutral third representing 11/9, which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: 5/4). Thus, 243/242 and 81/80 are both tempered out. Mohajira, due to its neutral third generator, is a 7 cluster temperament, and its main MOS scale is 3L 4s ("mosh", Ls..."

2026-03-14T23:25:04Z

Created page with "'''Mohajira''' (24 & 7) is an extension to rastmic (neutral) that is a meantone temperament. In other words, the generator is a neutral third representing 11/9, which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: 5/4). Thus, 243/242 and 81/80 are both tempered out. Mohajira, due to its neutral third generator, is a 7 cluster temperament, and its main MOS scale is 3L 4s ("mosh", Ls..."

New page

'''Mohajira''' (24 & 7) is an extension to [[rastmic]] (neutral) that is a [[Meantone'|meantone]] temperament. In other words, the generator is a neutral third representing [[11/9]], which stacks twice to a perfect fifth and eight times to the interval 5/1 (octave-reduced: [[5/4]]). Thus, [[243/242]] and [[81/80]] are both tempered out. Mohajira, due to its neutral third generator, is a [[Equiheptatonic|7 cluster temperament]], and its main MOS scale is 3L 4s ("mosh", LsLsLss), with the notable MODMOS ssLLssL (which is associated with the maqam ''rast'' and (perhaps not coincidentally) the result of applying mohajira tempering to the just equiheptatonic). Mohajira equates 11/10 with 12/11 and 9/8 with 10/9, and by this distinguishes itself from other temperaments of the just equiheptatonic such as [[flattone]] and [[porcupine]].

As a tuning generated by the [[Tuning stability|unstable]] interval 11/9, it is perhaps viable to directly map 11/9 to edos and determine the tuning of 11 from there, instead of vice versa.

Generally, mohajira is also extended to include prime 7 as the semidiminished seventh, though an alternate mapping also available in 31edo shares septimal meantone's mapping of 7 (and contributes much to 31edo's 7-limit structure).

== Interval table ==
Generator step table:
{| class="wikitable"
|+
!# up
!Cents
!Just interval
!Neutral diatonic notation
!# down
!Cents
!Just interval
!Neutral diatonic notation
|-
|0
|0
|1/1
|P1
|0
|1200
|2/1
|P8
|-
|1
|348
|11/9, 27/22
|n3
| -1
|852
|18/11, 44/27
|n6
|-
|2
|696
|3/2
|P5
| -2
|504
|4/3
|P4
|-
|3
|1044
|11/6, 20/11
|n7
| -3
|156
|11/10, 12/11
|n2
|-
|4
|192
|10/9, 9/8
|M2
| -4
|1008
|9/5, 16/9
|m7
|-
|5
|540
|11/8, 15/11
|sA4
| -5
|660
|16/11, 22/15
|sd5
|-
|6
|888
|5/3
|M6
| -6
|312
|6/5
|m3
|-
|7
|36
|33/32
|sA1
| -7
|1164
|64/33
|sd8
|-
|8
|384
|5/4
|M3
| -8
|816
|8/5
|m6
|}

== Patent vals ==
Mohajira patent vals are tunings of meantone for which 11 is mapped to the semiaugmented fourth. As such, they are a subset of possible meantone tunings. In fact, the space is rather limited due to how necessarily flat 11/8 is (most meantone tunings have an 11/9 sharp of neutral). Unless otherwise stated, these also support the 7-limit version of the temperament.
{| class="wikitable"
!EDO
!Generator tuning
!Fifth tuning
|-
|24
|350c
|700c
|-
|55
|349.1c
|698.2c
|-
|31
|348.4c
|696.8c
|-
|38
|347.4c
|694.7c
|-
|7
|342.9c
|685.7c
|}

=== 2.3.5.11/9 "patent" vals ===
It may also be desirable to optimize equal temperament mappings for 11/9 instead of 11 itself. Mohajira tunings that do this and are not mentioned above are the following, and usually utilize the second-best 11/8:
{| class="wikitable"
!EDO
!Fifth tuning
!Generator tuning
!11/8 tuning*
|-
|134
|698.51
|349.25
|546.27
|-
|86
|697.67
|348.84
|544.19
|-
|117
|697.44
|348.72
|543.59
|-
|100
|696.00
|348.00
|540.00
|-
|69
|695.65
|347.83
|539.13
|-
|45*
|693.33
|346.67
|533.33
|-
|52*
|692.31
|346.15
|530.77
|}
<nowiki>**</nowiki>The 11/8 tuning is not the best 11/8.

<nowiki>*</nowiki>45e and 52e do not support septimal mohajira.