Mohajira/Scales - Revision history

VectorGraphics: Switched to the correct mode names

2025-06-30T00:17:16Z

Switched to the correct mode names

← Older revision		Revision as of 00:17, 30 June 2025
Line 7:		Line 7:
	== MOS Neutral Diatonic scale ==		== MOS Neutral Diatonic scale ==
	1 2 v3 ^4 5 6 v7 1 or C D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C		1 2 v3 ^4 5 6 v7 1 or C D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C

	~~For the modes of the Mohajira[7] MOS, names with "Ice" have been proposed, referring to Hidekazu Wakabayashi's [[Iceface tuning]].~~
	{\| class="wikitable"		{\| class="wikitable"
	!~~Iced Major~~		!Dril
	\|C D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C		\|C D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C
	\|M2 N3 S4 P5 M6 N7		\|M2 N3 S4 P5 M6 N7
			\|LsLsLss
	\|-		\|-
	!~~Iced Locrian~~		!Fish
	\|D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C D		\|D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C D
	\|N2 N3 P4 P5 N6 m7		\|N2 N3 P4 P5 N6 m7
			\|sLsLssL
	\|-		\|-
	!~~Iced Phrygian (Iced Minor)~~		!Gil
	\|E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C D E{{demiflat2}}		\|E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C D E{{demiflat2}}
	\|M2 N3 S4 P5 N6 N7		\|M2 N3 S4 P5 N6 N7
			\|LsLssLs
	\|-		\|-
	!~~Iced Lydian~~		!Jwl
	\|F{{demisharp2}} G A B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}}		\|F{{demisharp2}} G A B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}}
	\|N2 N3 P4 s5 N6 m7		\|N2 N3 P4 s5 N6 m7
			\|sLssLsL
	\|-		\|-
	!~~Iced Mixolydian~~		!Kleeth
	\|G A B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}} G		\|G A B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}} G
	\|M2 N3 P4 P5 N6 N7		\|M2 N3 P4 P5 N6 N7
			\|LssLsLs
	\|-		\|-
	!~~Iced Dark Lydian (Iced Coffee)~~		!Led
	\|A B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}} G A		\|A B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}} G A
	\|N2 m3 P4 s5 N6 m7		\|N2 m3 P4 s5 N6 m7
			\|ssLsLsL
	\|-		\|-
	!~~Iced Blizzard (Neutral Scale)~~		!Bish
	\|B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}}		\|B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}}
	\|N2 N3 P4 P5 N6 N7		\|N2 N3 P4 P5 N6 N7
			\|sLsLsLs
	\|}		\|}
	~~Strangely, the mode names do not match the typical order of western mode names due to the odd intervalic nature of Mohajira temperament.~~

	== MODMOS with 1 alteration ==		== MODMOS with 1 alteration ==
	Rast - 1 2 v3 4 5 6 v7 1		Rast - 1 2 v3 4 5 6 v7 1

Sintel: {{breadcrumb}}

2025-06-22T19:02:23Z

← Older revision		Revision as of 19:02, 22 June 2025
Line 1:		Line 1:
			{{breadcrumb}}
	There are many possible Mohajira MOS and MODMOS, this page contains an overview of mostly 7 note scales that are adjacent the [[diatonic]] scale in [[meantone]].		There are many possible Mohajira MOS and MODMOS, this page contains an overview of mostly 7 note scales that are adjacent the [[diatonic]] scale in [[meantone]].
	The scales are organized based on evoking slightly different colors and categorized by different levels of alteration from a diatonic scale. A MOS of Mohajira[10] can be used in order to improvise on all the common MODMOS of Mohajira.		The scales are organized based on evoking slightly different colors and categorized by different levels of alteration from a diatonic scale. A MOS of Mohajira[10] can be used in order to improvise on all the common MODMOS of Mohajira.

Sintel: intro

2025-06-22T18:59:59Z

intro

← Older revision		Revision as of 18:59, 22 June 2025
Line 1:		Line 1:
			There are many possible Mohajira MOS and MODMOS, this page contains an overview of mostly 7 note scales that are adjacent the [[diatonic]] scale in [[meantone]].
			The scales are organized based on evoking slightly different colors and categorized by different levels of alteration from a diatonic scale. A MOS of Mohajira[10] can be used in order to improvise on all the common MODMOS of Mohajira.

			In what follows, 1 2 3 4 5 6 7 refer to the major mode of the diatonic scale.
	~~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.~~

	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.

	== MOS Neutral Diatonic scale ==		== MOS Neutral Diatonic scale ==

Sintel: section titles

2025-06-22T18:55:46Z

section titles

← Older revision		Revision as of 18:55, 22 June 2025
Line 7:		Line 7:
	Here are the scales with 1 2 3 4 5 6 7 being the major scale.		Here are the scales with 1 2 3 4 5 6 7 being the major scale.

	== ~~Level 0 - Mohajira~~ MOS ~~- The~~ Neutral Diatonic scale ==		== MOS Neutral Diatonic scale ==
	1 2 v3 ^4 5 6 v7 1 or C D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C		1 2 v3 ^4 5 6 v7 1 or C D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C

Line 42:		Line 42:
	Strangely, the mode names do not match the typical order of western mode names due to the odd intervalic nature of Mohajira temperament.		Strangely, the mode names do not match the typical order of western mode names due to the odd intervalic nature of Mohajira temperament.

	== ~~Level 1 - Mohajira~~ MODMOS by 1 alteration ==		== MODMOS with 1 alteration ==
	Rast - 1 2 v3 4 5 6 v7 1		Rast - 1 2 v3 4 5 6 v7 1
	{\| class="wikitable"		{\| class="wikitable"
Line 90:		Line 90:
	\|}		\|}

	== ~~Level 2 - Mohajira~~ MODMOS by 2 alterations ==		== MODMOS with 2 alterations ==
	Altered Neapolitan Major - 1 b2 b3 4 5 6 v7 1 or C Db Eb F G A Bd C		Altered Neapolitan Major - 1 b2 b3 4 5 6 v7 1 or C Db Eb F G A Bd C

Line 152:		Line 152:
	Altered Phrygian - 1 v2 b3 4 5 b6 b7 1 or C Dd Eb F G Ab Bb		Altered Phrygian - 1 v2 b3 4 5 b6 b7 1 or C Dd Eb F G Ab Bb

	== ~~Level 3 - Meantone by 3 alterations~~ ==		== Relation to meantone ==
			The ordinary meantone diatonic can be reached by three alternations.
	[[File:Altered_mohajira_levels.PNG\|altered mohajira levels.PNG]]		[[File:Altered_mohajira_levels.PNG\|altered mohajira levels.PNG]]

VectorGraphics: Split out into its own page for now, also reverted "Fridgian" to "Phrygian" as part of my general opposition of non-serious names

2025-06-22T09:47:14Z

Split out into its own page for now, also reverted "Fridgian" to "Phrygian" as part of my general opposition of non-serious names

New page

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.

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.

== Level 0 - Mohajira MOS - The Neutral Diatonic scale ==
1 2 v3 ^4 5 6 v7 1 or C D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C

For the modes of the Mohajira[7] MOS, names with "Ice" have been proposed, referring to Hidekazu Wakabayashi's [[Iceface tuning]].
{| class="wikitable"
!Iced Major
|C D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C
|M2 N3 S4 P5 M6 N7
|-
!Iced Locrian
|D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C D
|N2 N3 P4 P5 N6 m7
|-
!Iced Phrygian (Iced Minor)
|E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}} C D E{{demiflat2}}
|M2 N3 S4 P5 N6 N7
|-
!Iced Lydian
|F{{demisharp2}} G A B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}}
|N2 N3 P4 s5 N6 m7
|-
!Iced Mixolydian
|G A B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}} G
|M2 N3 P4 P5 N6 N7
|-
!Iced Dark Lydian (Iced Coffee)
|A B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}} G A
|N2 m3 P4 s5 N6 m7
|-
!Iced Blizzard (Neutral Scale)
|B{{demiflat2}} C D E{{demiflat2}} F{{demisharp2}} G A B{{demiflat2}}
|N2 N3 P4 P5 N6 N7
|}
Strangely, the mode names do not match the typical order of western mode names due to the odd intervalic nature of Mohajira temperament.

== Level 1 - Mohajira MODMOS by 1 alteration ==
Rast - 1 2 v3 4 5 6 v7 1
{| class="wikitable"
!Mode 1
|C D E{{demiflat2}} F G A B{{demiflat2}} C
|-
!Mode 2
|D E{{demiflat2}} F G A B{{demiflat2}} C D
|-
!Mode 3
|E{{demiflat2}} F G A B{{demiflat2}} C D Ed
|-
!Mode 4
|F G A B{{demiflat2}} C D E{{demiflat2}} F
|-
!Mode 5
|G A B{{demiflat2}} C D E{{demiflat2}} F G
|-
!Mode 6
|A B{{demiflat2}} C D E{{demiflat2}} F G A
|-
!Mode 7
|B{{demiflat2}} C D E{{demiflat2}} F G A B{{demiflat2}}
|}
Turkish Major - 1 2 3 4 5 v6 v7 1
{| class="wikitable"
!Mode 1
|C D E F G A{{demiflat2}} B{{demiflat2}} C
|-
!Mode 2
|D E F G A{{demiflat2}} B{{demiflat2}} C D
|-
!Mode 3
|E F G A{{demiflat2}} B{{demiflat2}} C D E
|-
!Mode 4
|F G A{{demiflat2}} B{{demiflat2}} C D E F
|-
!Mode 5
|G A{{demiflat2}} B{{demiflat2}} C D E F G
|-
!Mode 6
|A{{demiflat2}} B{{demiflat2}} C D E F G A{{demiflat2}}
|-
!Mode 7
|B{{demiflat2}} C D E F G A{{demiflat2}} B{{demiflat2}}
|}

== Level 2 - Mohajira MODMOS by 2 alterations ==
Altered Neapolitan Major - 1 b2 b3 4 5 6 v7 1 or C Db Eb F G A Bd C

Altered Melodic Minor (Altered Dorian) - 1 2 b3 4 5 6 v7 1
{| class="wikitable"
!Mode 1
|C D E♭ F G A B{{demiflat2}} C
|-
!Mode 2
|D E♭ F G A B{{demiflat2}} C D
|-
!Mode 3
|E♭ F G A B{{demiflat2}} C D E
|-
!Mode 4
|F G A B{{demiflat2}} C D E♭ F
|-
!Mode 5
|G A B{{demiflat2}} C D E♭ F G
|-
!Mode 6
|A B{{demiflat2}} C D E♭ F G A
|-
!Mode 7
|B{{demiflat2}} C D E♭ F G A B{{demiflat2}}
|}
Turkish Minor - 1 2 b3 4 5 v6 b7 1 or C D Eb F G Ad Bb C

Altered Major - 1 2 3 4 5 6 v7 1 and 1 v2 3 4 5 6 7 1
{| class="wikitable"
!Mode 1
|C D E F G A B{{demiflat2}} C
|C D{{demiflat2}} E F G A B C
|-
!Mode 2
|D E F G A B{{demiflat2}} C D
|D{{demiflat2}} E F G A B C D{{demiflat2}}
|-
!Mode 3
|E F G A B{{demiflat2}} C D E
|E F G A B C D{{demiflat2}} E
|-
!Mode 4
|F G A B C D{{demiflat2}} E F
|F G A B{{demiflat2}} C D E F
|-
!Mode 5
|G A B{{demiflat2}} C D E F G
|G A B C D{{demiflat2}} E F G
|-
!Mode 6
|A B C D{{demiflat2}} E F G A
|A B C D{{demiflat2}} E F G A
|-
!Mode 7
|B{{demiflat2}} C D E F G A B{{demiflat2}}
|B C D{{demiflat2}} E F G A B
|}
[[Bayati]] or [[trachytonic]] - 1 v2 b3 4 5 b6 b7 1 or C Dd Eb F G Ab Bb

Altered Phrygian - 1 v2 b3 4 5 b6 b7 1 or C Dd Eb F G Ab Bb

== Level 3 - Meantone by 3 alterations ==
[[File:Altered_mohajira_levels.PNG|altered mohajira levels.PNG]]

== Tuning the Turkish Major scale ==
'''Turkish Major''' is a tempered max-variety 3 scale that is equivalent to a [[4L 3s|smitonic]] scale with one of its small steps diminished. This makes a Neapolitan Major scale which does not temper out 36/35. Not tempering 36/35 is actually quite useful, because it's the difference between 4:5:6 and 6:7:9 triads. This is important in a neutral third tone system because the smoothest neutral chord with a perfect fifth is 6:7:9:11. As a result, results of tempering out [[81/80]] or [[64/63]] are not as bad, because the scale must detemper one if it tempers out the other. Strangely, the detempering of 36/35 is not evident due to the odd intervalic nature of the Turkish Major scale. Smitonic in a sense does the opposite of what Neapolitan Major does in common practice, exaggerating 36/35 to the point that 4:5:6 and 6:7:9 triads no longer have a recognizable 3/2, and the small step of Turkish Major becomes equal to the medium steps.
{| class="wikitable"
|+Common '''Turkish Major''' Tunings
! rowspan="2" |Tuning
! rowspan="2" |L:m:s
! rowspan="2" |Good Just Approximations
! rowspan="2" |Other comments
! colspan="6" |Degrees
|-
!D
!E
!F
!G
!Ad
!Bd
|-
|
|
|
|
|(~)9/8
|5/4
''81/64''
|(~)4/3
|(~)3/2
|~175/108
''~44/27''
|~175/96
''~11/6''
|-
|“Just”
|1.649:1.256:1
''2.26:1.63:1''
|Just 5/4
''Just 9/8 and 4/3''
|
|193.157
''203.91''
|386.314
''407.82''
|503.422
''498.045''
|696.578
''701.955''
|843.646
''849.0225''
|1036.803
''1052.9325''
|-
|17edo
|3:2:1
|25/24
|
|211.765
|423.529
|494.118
|705.882
|847.059
|1058.8235
|-
|21edo
|4:2:1
|
|
|228.571
|457.143
|514.286
|742.857
|857.143
|1085.714
|-
|23edo
|4:3:1
|[[Neogothic]] thirds
|Mavila
|208.696
|417.381
|469.565
|678.261
|834.783
|1043.478
|-
|24edo
|4:3:2
|4/3
|Mohajira
|200
|400
|500
|700
|850
|1050
|-
|25edo
|5:2:1
|36/35
|Mavila
|240
|480
|528
|768
|864
|1104
|-
|27edo
|5:3:1
|27/25
|
|222.222
|444.444
|488.889
|711.111
|844.444
|1066.667
|-
|28edo
|5:3:2
|
|Antikythera
|214.286
|428.571
|514.286
|728.571
|857.143
|1071.429
|-
|29edo
|5:4:1
6:2:1
|Neogothic thirds
|Score
|206.897
248.276
|413.793
496.552
|455.172
537.931
|662.069
786.206
|827.586
868.9655
|1034.483
1117.241
|-
|30edo
|5:4:2
|13/8
|Mavila
|200
|400
|480
|680
|840
|1040
|-
|31edo
|5:4:3
6:3:1
|5/4
8/7
|Mohajira
|193.548
232.258
|387.097
464.516
|503.226
|696.774
735.484
|851.613
|1045.161
1083.871
|-
|32edo
|6:3:2
|
|Mavila
|225
|450
|525
|750
|862.5
|1087.5
|-
|33edo
|6:4:1
7:2:1
|9/7
|
|218.182
254.5455
|436.364
509.091
|472.727
545.4545
|690.909
763.636
|836.364
|1054.5455
1090.909
|-
|35edo
|6:4:3
6:5:1

7:3:1
|Neogothic thirds
|Has both “perfect“ fifths of 35edo
|205.714
240
|411.429
480
|514.286
445.714
|720
651.429

754.286
|925.714
822.857

857.143
|1131.429
1028.571

1097.143
|-
|36edo
|6:5:2
7:3:2
|
|Mavila
|200
233.333
|400
466.667
|466.667
533.333
|666.667
766.667
|833.333
866.667
|1033.333
1100
|-
|37edo
|6:5:3
7:4:1

8:2:1
|13/10
|Has 5/4 and both “perfect” fifths of 37edo
|194.595
227.027

259.4595
|389.189
454.054

518.919
|486.4865
551.352
|681.081
713.5135

810.811
|843.243
875.676
|1037.838
1065.866

1135.135
|-
|38edo
|6:5:4
7:4:2
|6/5
14/13
|
|189.474
221.052
|378.947
442.105
|505.263
|694.737
726.316
|852.632
|1042.105
1073.684
|-
|39edo
|7:4:3
7:5:1

8:3:1
|
|Misses 39edo perfect fifth
|215.385
246.154
|430.769
492.308
|523.077
461.5385
|738.4615
676.923

769.231
|861.5385
830.769
|1076.923
1046.154

1107.692
|-
|40edo
|7:5:2
8:3:2
|13/8
|Has both “perfect“ fifths of 40edo
|210
240
|420
480
|480
540
|690
780
|840
870
|1050
1110
|-
|41edo
|7:5:3
7:6:1

8:4:1
|
|
|204.878
234.146
|409.756
468.296
|497.561
439.024
|702.439
643.902

731.707
|848.7805
819.512

848.7805
|1053.6585
1024.39

1082.927
|-
|42edo
|7:5:4
7:6:2
|
|Has both “perfect“ fifths of 42edo
|200
|400
|514.286
457.143
|714.286
657.143
|857.143
828.571
|1057.143
1028.571
|-
|43edo
|7:6:3
8:4:3

8:5:1
|16/15
|
|195.349
223.256
|390.698
446.512
|502.326
530.233

474.419
|697.767
753.488
|865.116
837.209
|1060.465
1088.372
|-
|44edo
|7:6:4
8:5:2
|
|Has both “perfect“ fifths of 44edo
|190.909
218.182
|381.818
436.364
|490.909
|681.818
709.091
|845.4545
|1036.364
1063.636
|-
|45edo
|7:6:5
8:5:3

8:6:1
|27/25
|Golden
Has both “perfect“ fifths of 45edo
|186.667
213.333
|373.333
426.667
|506.667
453.333
|693.333
720

666.667
|853.333
826.667
|1040
1066.666
|-
|46edo
|8:5:4
|
|Misses fifth of 46edo
|208.696
|417.381
|521.739
|730.435
|860.87
|1069.566
|-
|47edo
|8:6:3
8:7:1
|9/8
|Has both “perfect“ fifths of 47edo, all sizes of 47edo major third
|204.255
|408.511
|485.106
434.043
|689.362
638.297
|842.553
817.021
|1046.8085
1021.277
|-
|48edo
|8:7:2
|
|
|200
|400
|450
|650
|825
|1025
|-
|49edo
|8:6:5
8:7:3
|
|Has both “perfect“ fifths of 49edo
|195.918
|391.837
|514.286
465.306
|710.204
661.2245
|857.143
832.653
|1053.061
1028.571
|-
|50edo
|8:7:4
|
|Mavila, only has one 50edo interval
|192
|384
|480
|672
|840
|1032
|-
|51edo
|8:7:5
|
|
|188.235
|376.471
|494.118
|682.353
|847.059
|1035.294
|-
|52edo
|8:7:6
|
|
|184.615
|369.231
|507.692
|692.308
|853.846
|1038.4615
|}

== Harmonization of Mohajira ==
While the structure of mohajira[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 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.

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:

=== Mohajira[10] - The Neutral Superdiatonic Scale ===
{| class="wikitable"
!Mode 1
|3 6 7 10 13 14 17 20 23
|4 8 9 13 17 18 22 26 30
|-
!Mode 2
|3 4 7 10 11 14 17 20 21
|4 5 9 13 14 18 22 26 27
|-
!Mode 3
|1 4 7 8 11 14 17 18 21
|1 5 9 10 14 18 22 23 27
|-
!Mode 4
|3 6 7 10 13 16 17 20 23
|4 8 9 13 17 21 22 26 30
|-
!Mode 5
|3 4 7 10 13 14 17 20 21
|4 5 9 13 17 18 22 26 27
|-
!Mode 6
|1 4 7 10 11 14 17 18 21
|1 5 9 13 14 18 22 23 27
|-
!Mode 7
|3 6 9 10 13 16 17 20 23
|4 8 12 13 17 21 22 26 30
|-
!Mode 8
|3 6 7 10 13 14 17 20 21
|4 8 9 13 17 18 22 26 27
|-
!Mode 9
|3 4 7 10 11 14 17 18 21
|4 5 9 13 14 18 22 23 27
|-
!Mode 10
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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 contexts 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.