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The 5L 2s MOS has multiple well-known [[MODMOS]]es, with at least five of these having names of their own. For the sake of ease, "A"- meaning "augmented"- refers to a step that is larger than the MOS's normal "L" step by a single chroma.
The [[5L 2s]] MOS has multiple well-known [[MODMOS]]es, with at least five of these having names of their own. For the sake of ease, "A"- meaning "augmented"- refers to a step that is larger than the MOS's normal "L" step by a single chroma.


== LsLLLLs ==
== LsLLLLs ==
The '''LsLLLLs''' MODMOS is referred to here as the '''Melodic Scale'''. While it is perhaps better known by other names such as "'''melodic minor'''" and "'''jazz minor'''" after this scale's default mode, there is another mode of this scale that can be called "melodic major" and "jazz major", so the scale is referred to here as the "melodic scale" in an attempt to remain neutral concerning the major and minor distinction. The [[3-limit]] version of this MODMOS only differs from 3-limit Dorian by means of having [[243/128]] as a major seventh. Because of it being well known, this MODMOS has multiple [[MODmuddles]] derived from it.
The '''LsLLLLs''' MODMOS is referred to here as the '''Melodic Scale'''. While it is perhaps better known by other names such as "'''melodic minor'''" and "'''jazz minor'''" after this scale's default mode, there is another mode of this scale that can be called "melodic major" and "jazz major", so the scale is referred to here as the "melodic scale" in an attempt to remain neutral concerning the major and minor distinction. The [[3-limit]] version of this MODMOS only differs from 3-limit Dorian by means of having [[243/128]] as a major seventh. Because of it being well known, this MODMOS has multiple [[MODmuddles]] derived from it.
{{MOS mode degrees|MODMOS Step Pattern=LsLLLLs}}


== LsLLsAs ==
== LsLLsAs ==
The '''LsLLsAs''' MODMOS is known as the '''Harmonic Minor Scale'''. The 3-limit version of this MODMOS differs from 3-limit Aeolian by means of having [[256/243]] as a major seventh, and thus, having [[19683/16384]] as the augmented second step. Because of it being well known, this MODMOS has multiple MODmuddles derived from it.
The '''LsLLsAs''' MODMOS is known as the '''Harmonic Minor Scale'''. The 3-limit version of this MODMOS differs from 3-limit Aeolian by means of having [[243/128]] as a major seventh, and thus, having [[19683/16384]] as the augmented second step. Because of it being well known, this MODMOS has multiple MODmuddles derived from it.
{{MOS mode degrees|MODMOS Step Pattern=LsLLsAs}}
 
{| class="wikitable"
|+ style="font-size: 105%;" | Common harmonic minor tunings
|-
! rowspan="2" | '''Tuning'''
! rowspan="2" | A:L:s
! rowspan="2" | Good just approximations
! rowspan="2" | Other comments
! colspan="6" | Degrees
|-
! B
! C
! D
! E
! F
! G#
|-
|
|
|
|
| ~9/8
| ~6/5
| ~4/3
| ~3/2
| 8/5
| ~15/8
|-
| “Just”
| 2.299:1.649:1
| Just 5/4
|
| 193.157
| 310.265
| 503.422
| 696.578
| 813.686
| 1082.892
|-
| 12edo
| 3:2:1
|
|
| 200
| 300
| 500
| 700
| 800
| 1100
|-
| 13edo
| 4:2:1
|
| Wolf fourth and fifth<br />Chroma equals L
| 184.615
| 276.923
| 461.5385
| 646.154
| 738.4615
| 1107.692
|-
| 14edo
| 5:2:1
|
| Chroma equals {{nowrap|L + s}}
| 171.429
| 257.143
| 428.571
| 600
| 685.714
| 1114.286
|-
| 15edo
| 6:2:1
|
| Chroma equals 2L
| 160
| 240
| 400
| 560
| 640
| 1120
|-
| 16edo
| 4:3:1<br />7:2:1
|
| Chroma equals {{nowrap|2L + s}}
| 225<br />150
| 300<br />225
| 525<br />375
| 750<br />525
| 825<br />600
| 1125
|-
| 17edo
| 5:3:1<br />8:2:1
| 25/24
| Gentle fifth<br />Chroma equals 3L
| 211.765<br />141.1765
| 282.353<br />211.765
| 494.118<br />352.941
| 705.882<br />494.118
| 776.412<br />564.706
| 1129.412
|-
| 18edo
| 6:3:1
| 26/25 and 7/6
|
| 200
| 266.667
| 466.667
| 666.667
| 733.333
| 1133.333
|-
| 19edo
| 4:3:2<br />7:3:1
| 6/5 and 14/13<br />28/27
| Chroma equals {{nowrap|L + s}}
| 189.474
| 315.7895<br />252.632
| 505.263<br />442.105
| 694.737<br />631.579
| 821.053<br />694.737
| 1073.684<br />1136.842
|-
| 20edo
| 5:3:2<br />5:4:1<br />8:3:1
| 13/8 and 15/14
|
| 180<br />240
| 300<br />240
| 480<br />420<br />540
| 720<br />660<br />780
| 840<br />720
| 1080<br />1140
|-
| 21edo
| 6:3:2<br />6:4:1
|
|
| 171.429<br />228.571
| 285.714
| 457.143<br />514.286
| 628.571<br />742.857
| 742.857<br />800
| 1085.714<br />1142.857
|-
| 22edo
| 7:3:2<br />7:4:1
| 9/7 (and 11/10)
|
| 163.636<br />218.182
| 272.727
| 436.364<br />490.909
| 600<br />709.091
| 709.091<br />763.636
| 1090.909<br />1145.4545
|-
| 23edo
| 8:3:2<br />8:4:1
| 14/11
|
| 156.522<br />208.696
| 260.87
| 417.391<br />469.565
| 573.813<br />678.261
| 678.261<br />730.435
| 1095.652<br />1147.826
|-
| 24edo
| 6:5:1
|
| 7 out of 4L&nbsp;3m&nbsp;3s
| 250
| 300
| 550
| 800
| 850
| 1150
|-
| 25edo
| 7:4:2<br />7:5:1
| 13/11
|
| 192<br />240
| 288
| 480<br />528
| 672<br />768
| 864<br />816
| 1004<br />1148
|-
| 26edo
| 8:5:1
| 8/7
|
| 230.769
| 276.923
| 507.692
| 738.4615
| 784.615
| 1153.846
|-
| 27edo
| 6:4:3<br />6:5:2
| 27/25 and 7/6
|
| 177.778<br />222.222
| 311.111
| 488.889<br />533.333
| 666.667<br />755.556
| 800<br />844.444
| 1066.667<br />1111.111
|-
| 28edo
| 7:4:3<br />7:5:2<br />7:6:1
| 14/13<br />5/4
|
| 171.429<br />214.286<br />257.143
| 300
| 471.429<br />514.286<br />557.143
| 642.857<br />728.571<br />814.286
| 771.429<br />814.286<br />857.143
| 1071.429<br />1111.286<br />1157.143
|-
| 29edo
| 8:4:3<br />8:5:2<br />8:6:1
| (11/10 and) 13/11
| Gentle fifth
| 165.517<br />206.897<br />248.276
| 289.655
| 455.172<br />496.552<br />537.931
| 620.69<br />703.448<br />786.207
| 744.828<br />786.207<br />827.586
| 1075.862<br />1117.241<br />1158.621
|-
| 30edo
| 6:5:3
| 13/8 and 15/14
|
| 200<br />280
| 320
| 520<br />600
| 720<br />880
| 840<br />920
| 1080<br />1160
|-
| 31edo
| 7:5:3<br />7:6:2
| 5/4
|
| 193.548<br />232.258
| 309.667
| 503.226<br />541.9355
| 696.774<br />774.194
| 812.903<br />851.613
| 1083.871<br />1122.582
|-
| 32edo
| 8:5:3<br />8:7:1
| 16/15
| Golden<br />7 out of 5L&nbsp;5m&nbsp;2s
| 162.5<br />262.5
| 300
| 412.5<br />562.5
| 675<br />825
| 787.5<br />862.5
| 1087.5<br />1162.5
|-
| 33edo
| 6:5:4
|
|
| 181.818
| 327.273
| 509.091
| 690.909
| 836.364
| 1054.5455
|-
| 34edo
| 7:5:4<br />7:6:3
|
|
| 176.471<br />211.765
| 317.647
| 494.118<br />529.412
| 670.588<br />741.1765
| 811.765
| 1058.8235<br />1094.118
|-
| 35edo
| 8:5:4<br />8:6:3<br />8:7:2
|
|
| 171.429<br />205.714<br />240
| 308.571
| 480<br />514.286<br />548.571
| 651.429<br />720<br />788.571
| 788.571<br />822.857<br />857.143
| 1062.857<br />1097.143<br />1131.429
|-
| 37edo
| 7:6:4
|
|
| 194.595
| 324.324
| 518.919
| 713.5135
| 843.243
| 1070.27
|-
| 38edo
| 8:7:3
| 6/5
|
| 221.053
| 315.7895
| 536.842
| 757.895
| 852.632
| 1105.263
|-
| 40edo
| 7:6:5
| 13/8
|
| 180
| 330
| 510
| 690
| 840
| 1050
|-
| 41edo
| 8:6:5<br />8:7:4
| 4/3<br />9/8
|
| 175.61<br />204.878
| 321.951
| 497.561<br />526.829
| 673.171<br />731.707
| 819.512<br />848.7805
| 1053.6585<br />1082.927
|-
| 44edo
| 8:7:5
|
|
| 190.909
| 327.273
| 518.182
| 709.091
| 845.4545
| 1063.636
|-
| 47edo
| 8:7:6
|
|
| 178.723
| 331.915
| 510.638
| 689.372
| 842.553
| 1046.8085
|}


== LLsLsAs ==
== LLsLsAs ==
The '''LLsLsAs''' MODMOS is known as the '''Harmonic Major Scale'''. The 3-limit version of this MODMOS differs from 3-limit Ionian by means of having [[128/81]] as a minor sixth, and thus, having 19683/16384 as the augmented second step. Because of it being at least somewhat well known, this MODMOS has multiple MODmuddles derived from it.
The '''LLsLsAs''' MODMOS is known as the '''Harmonic Major Scale'''. The 3-limit version of this MODMOS differs from 3-limit Ionian by means of having [[128/81]] as a minor sixth, and thus, having 19683/16384 as the augmented second step. Because of it being at least somewhat well known, this MODMOS has multiple MODmuddles derived from it.
{{MOS mode degrees|MODMOS Step Pattern=LLsLsAs}}
 
{| class="wikitable"
|+ style="font-size: 105%;" | Common harmonic major tunings
|-
! rowspan="2" | '''Tuning'''
! rowspan="2" | A:L:s
! rowspan="2" | Good just approximations
! rowspan="2" | Other comments
! colspan="6" | Degrees
|-
! D
! E
! F
! G
! Ab
! B
|-
|
|
|
|
| ~9/8
| 5/4
| ~4/3
| ~3/2
| 8/5
| ~15/8
|-
| “Just”
| 2.299:1.649:1
| Just 5/4
|
| 193.157
| 386.314
| 503.422
| 696.578
| 813.686
| 1082.892
|-
| 12edo
| 3:2:1
|
|
| 200
| 400
| 500
| 700
| 800
| 1100
|-
| 13edo
| 4:2:1
|
| Wolf fourth and fifth<br />Chroma equals L
| 184.615
| 369.308
| 461.5385
| 646.154
| 738.4615
| 1107.692
|-
| 14edo
| 5:2:1
|
| Chroma equals {{nowrap|L + s}}
| 171.429
| 342.857
| 428.571
| 600
| 685.714
| 1114.286
|-
| 15edo
| 6:2:1
|
| Chroma equals 2L
| 160
| 320
| 400
| 560
| 640
| 1120
|-
| 16edo
| 4:3:1<br />7:2:1
|
| Chroma equals {{nowrap|2L + s}}
| 225<br />150
| 450<br />300
| 525<br />375
| 750<br />525
| 825<br />600
| 1125
|-
| 17edo
| 5:3:1<br />8:2:1
| 25/24
| Gentle fifth<br />Chroma equals 3L
| 211.765<br />141.1765
| 423.529<br />282.353
| 494.118<br />352.941
| 705.882<br />494.118
| 776.412<br />564.706
| 1129.412
|-
| 18edo
| 6:3:1
| 26/25 and 7/6
|
| 200
| 400
| 466.667
| 666.667
| 733.333
| 1133.333
|-
| 19edo
| 4:3:2<br />7:3:1
| 14/13<br />28/27
| Chroma equals {{nowrap|L + s}}
| 189.474
| 378.947
| 505.263<br />442.105
| 694.737<br />631.579
| 821.053<br />694.737
| 1073.684<br />1136.842
|-
| 20edo
| 5:3:2<br />5:4:1<br />8:3:1
| 13/8 and 15/14
|
| 180<br />240
| 360<br />480
| 480<br />420<br />540
| 720<br />660<br />780
| 840<br />720
| 1080<br />1140
|-
| 21edo
| 6:3:2<br />6:4:1
|
|
| 171.429<br />228.571
| 342.857<br />457.143
| 457.143<br />514.286
| 628.571<br />742.857
| 742.857<br />800
| 1085.714<br />1142.857
|-
| 22edo
| 7:3:2<br />7:4:1
| 9/7 (and 11/10)
|
| 163.636<br />218.182
| 327.273<br />436.364
| 436.364<br />490.909
| 600<br />709.091
| 709.091<br />763.636
| 1090.909<br />1145.4545
|-
| 23edo
| 8:3:2<br />8:4:1
| 14/11
|
| 156.522<br />208.696
| 313.0435<br />417.391
| 417.391<br />469.565
| 573.813<br />678.261
| 678.261<br />730.435
| 1095.652<br />1147.826
|-
| 24edo
| 6:5:1
|
| 7 out of 4L&nbsp;3m&nbsp;3s
| 250
| 500
| 550
| 800
| 850
| 1150
|-
| 25edo
| 7:4:2<br />7:5:1
| 13/11
|
| 192<br />240
| 384<br />480
| 480<br />528
| 672<br />768
| 864<br />816
| 1004<br />1148
|-
| 26edo
| 8:5:1
| 8/7
|
| 230.769
| 461.5385
| 507.692
| 738.4615
| 784.615
| 1153.846
|-
| 27edo
| 6:4:3<br />6:5:2
| 27/25 and 7/6
|
| 177.778<br />222.222
| 355.556<br />444.444
| 488.889<br />533.333
| 666.667<br />755.556
| 800<br />844.444
| 1066.667<br />1111.111
|-
| 28edo
| 7:4:3<br />7:5:2<br />7:6:1
| 14/13<br />5/4
|
| 171.429<br />214.286<br />257.143
| 342.857<br />428.571<br />514.286
| 471.429<br />514.286<br />557.143
| 642.857<br />728.571<br />814.286
| 771.429<br />814.286<br />857.143
| 1071.429<br />1111.286<br />1157.143
|-
| 29edo
| 8:4:3<br />8:5:2<br />8:6:1
| (11/10 and) 13/11
| Gentle fifth
| 165.517<br />206.897<br />248.276
| 331.0345<br />413.793<br />496.552
| 455.172<br />496.552<br />537.931
| 620.69<br />703.448<br />786.207
| 744.828<br />786.207<br />827.586
| 1075.862<br />1117.241<br />1158.621
|-
| 30edo
| 6:5:3
| 13/8 and 15/14
|
| 200<br />280
| 400<br />560
| 520<br />600
| 720<br />880
| 840<br />920
| 1080<br />1160
|-
| 31edo
| 7:5:3<br />7:6:2
| 5/4
|
| 193.548<br />232.258
| 387.097<br />464.516
| 503.226<br />541.9355
| 696.774<br />774.194
| 812.903<br />851.613
| 1083.871<br />1122.582
|-
| 32edo
| 8:5:3<br />8:7:1
| 16/15
| Golden<br />7 out of 5L&nbsp;5m&nbsp;2s
| 162.5<br />262.5
| 325<br />525
| 412.5<br />562.5
| 675<br />825
| 787.5<br />862.5
| 1087.5<br />1162.5
|-
| 33edo
| 6:5:4
|
|
| 181.818
| 363.636
| 509.091
| 690.909
| 836.364
| 1054.5455
|-
| 34edo
| 7:5:4<br />7:6:3
|
|
| 176.471<br />211.765
| 352.941<br />423.529
| 494.118<br />529.412
| 670.588<br />741.1765
| 811.765
| 1058.8235<br />1094.118
|-
| 35edo
| 8:5:4<br />8:6:3<br />8:7:2
|
|
| 171.429<br />205.714<br />240
| 342.857<br />411.429<br />480
| 480<br />514.286<br />548.571
| 651.429<br />720<br />788.571
| 788.571<br />822.857<br />857.143
| 1062.857<br />1097.143<br />1131.429
|-
| 37edo
| 7:6:4
|
|
| 194.595
| 389.189
| 518.919
| 713.5135
| 843.243
| 1070.27
|-
| 38edo
| 8:7:3
| 6/5
|
| 221.053
| 442.106
| 536.842
| 757.895
| 852.632
| 1105.263
|-
| 40edo
| 7:6:5
| 13/8
|
| 180
| 360
| 510
| 690
| 840
| 1050
|-
| 41edo
| 8:6:5<br />8:7:4
| 4/3<br />9/8
|
| 175.61<br />204.878
| 351.22<br />409.756
| 497.561<br />526.829
| 673.171<br />731.707
| 819.512<br />848.7805
| 1053.6585<br />1082.927
|-
| 44edo
| 8:7:5
|
|
| 190.909
| 381.818
| 518.182
| 709.091
| 845.4545
| 1063.636
|-
| 47edo
| 8:7:6
|
|
| 178.723
| 357.446
| 510.638
| 689.372
| 842.553
| 1046.8085
|}


== sLLLLLs ==
== sLLLLLs ==
The '''sLLLLLs''' MODMOS is referred to here as the '''Greater Neapolitan Scale'''.  While it is perhaps better known as "'''Neapolitan major'''", this terminology can be considered confusing on account of the scale's third degree technically being a minor third.  The 3-limit version of this MODMOS differs from the 3-limit Melodic Scale by means of having [[256/243]] as a minor second.  Because of it being at least somewhat well known, this MODMOS has multiple MODmuddles derived from it.
The '''sLLLLLs''' MODMOS is referred to here as the '''Greater Neapolitan Scale'''.  While it is perhaps better known as "'''Neapolitan major'''", this terminology can be considered confusing on account of the scale's third degree technically being a minor third.  The 3-limit version of this MODMOS differs from the 3-limit Melodic Scale by means of having [[256/243]] as a minor second.  Because of it being at least somewhat well known, this MODMOS has multiple MODmuddles derived from it.
{{MOS mode degrees|MODMOS Step Pattern=sLLLLLs}}
[[Category:Diatonic]]
[[Category:MODMOS]]
[[Category:Tables]]
Retrieved from "https://en.xen.wiki/w/5L_2s/MODMOSes"