5L 2s/MODMOSes

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The 5L 2s MOS has multiple well-known MODMOSes, 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

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.

Scale degrees of the modes of 5L 2s (LsLLLLs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m2md
3|3 M6md 		1 LsLLLLs Perf. Maj. Min. Perf. Perf. Maj. Maj. Perf.
3|3 m1md
1|5 M5md 		2 sLLLLsL Perf. Min. Min. Perf. Perf. Maj. Min. Perf.
6|0 A4md 3 LLLLsLs Perf. Maj. Maj. Aug. Aug. Maj. Maj. Perf.
6|0 m6md
4|2 A3md 		4 LLLsLsL Perf. Maj. Maj. Aug. Perf. Maj. Min. Perf.
4|2 m5md
2|4 M2md 		5 LLsLsLL Perf. Maj. Maj. Perf. Perf. Min. Min. Perf.
2|4 d4md
0|6 M1md 		6 LsLsLLL Perf. Maj. Min. Perf. Dim. Min. Min. Perf.
0|6 d3md 7 sLsLLLL Perf. Min. Min. Dim. Dim. Min. Min. Perf.

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 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.

Scale degrees of the modes of 5L 2s (LsLLsAs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
2|4 M6md 1 LsLLsAs Perf. Maj. Min. Perf. Perf. Min. Maj. Perf.
0|6 M5md 2 sLLsAsL Perf. Min. Min. Perf. Dim. Maj. Min. Perf.
5|1 A4md 3 LLsAsLs Perf. Maj. Maj. Perf. Aug. Maj. Maj. Perf.
3|3 A3md 4 LsAsLsL Perf. Maj. Min. Aug. Perf. Maj. Min. Perf.
1|5 M2md 5 sAsLsLL Perf. Min. Maj. Perf. Perf. Min. Min. Perf.
6|0 A1md 6 AsLsLLs Perf. Aug. Maj. Aug. Perf. Maj. Maj. Perf.
0|6 d3md d6md 7 sLsLLsA Perf. Min. Min. Dim. Dim. Min. Dim. Perf.
Common harmonic minor tunings
Tuning A:L:s Good just approximations Other comments 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
Chroma equals L 		184.615 276.923 461.5385 646.154 738.4615 1107.692
14edo 5:2:1 Chroma equals 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
7:2:1 		Chroma equals 2L+s 225
150 		300
225 		525
375 		750
525 		825
600 		1125
17edo 5:3:1
8:2:1 		25/24 Gentle fifth
Chroma equals 3L 		211.765
141.1765 		282.353
211.765 		494.118
352.941 		705.882
494.118 		776.412
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
7:3:1 		6/5 and 14/13
28/27 		Chroma equals L+s 189.474 315.7895
252.632 		505.263
442.105 		694.737
631.579 		821.053
694.737 		1073.684
1136.842
20edo 5:3:2
5:4:1
8:3:1 		13/8 and 15/14 180
240 		300
240 		480
420
540 		720
660
780 		840
720 		1080
1140
21edo 6:3:2
6:4:1 		171.429
228.571 		285.714 457.143
514.286 		628.571
742.857 		742.857
800 		1085.714
1142.857
22edo 7:3:2
7:4:1 		9/7 (and 11/10) 163.636
218.182 		272.727 436.364
490.909 		600
709.091 		709.091
763.636 		1090.909
1145.4545
23edo 8:3:2
8:4:1 		14/11 156.522
208.696 		260.87 417.391
469.565 		573.813
678.261 		678.261
730.435 		1095.652
1147.826
24edo 6:5:1 7 out of 4L 3m 3s 250 300 550 800 850 1150
25edo 7:4:2
7:5:1 		13/11 192
240 		288 480
528 		672
768 		864
816 		1004
1148
26edo 8:5:1 8/7 230.769 276.923 507.692 738.4615 784.615 1153.846
27edo 6:4:3
6:5:2 		27/25 and 7/6 177.778
222.222 		311.111 488.889
533.333 		666.667
755.556 		800
844.444 		1066.667
1111.111
28edo 7:4:3
7:5:2
7:6:1 		14/13
5/4 		171.429
214.286
257.143 		300 471.429
514.286
557.143 		642.857
728.571
814.286 		771.429
814.286
857.143 		1071.429
1111.286
1157.143
29edo 8:4:3
8:5:2
8:6:1 		(11/10 and) 13/11 Gentle fifth 165.517
206.897
248.276 		289.655 455.172
496.552
537.931 		620.69
703.448
786.207 		744.828
786.207
827.586 		1075.862
1117.241
1158.621
30edo 6:5:3 13/8 and 15/14 200
280 		320 520
600 		720
880 		840
920 		1080
1160
31edo 7:5:3
7:6:2 		5/4 193.548
232.258 		309.667 503.226
541.9355 		696.774
774.194 		812.903
851.613 		1083.871
1122.582
32edo 8:5:3
8:7:1 		16/15 Golden
7 out of 5L 5m 2s 		162.5
262.5 		300 412.5
562.5 		675
825 		787.5
862.5 		1087.5
1162.5
33edo 6:5:4 181.818 327.273 509.091 690.909 836.364 1054.5455
34edo 7:5:4
7:6:3 		176.471
211.765 		317.647 494.118
529.412 		670.588
741.1765 		811.765 1058.8235
1094.118
35edo 8:5:4
8:6:3
8:7:2 		171.429
205.714
240 		308.571 480
514.286
548.571 		651.429
720
788.571 		788.571
822.857
857.143 		1062.857
1097.143
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
8:7:4 		4/3
9/8 		175.61
204.878 		321.951 497.561
526.829 		673.171
731.707 		819.512
848.7805 		1053.6585
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

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.

Scale degrees of the modes of 5L 2s (LLsLsAs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m5md 1 LLsLsAs Perf. Maj. Maj. Perf. Perf. Min. Maj. Perf.
3|3 d4md 2 LsLsAsL Perf. Maj. Min. Perf. Dim. Maj. Min. Perf.
1|5 d3md 3 sLsAsLL Perf. Min. Min. Dim. Perf. Min. Min. Perf.
6|0 m2md 4 LsAsLLs Perf. Maj. Min. Aug. Perf. Maj. Maj. Perf.
4|2 m1md 5 sAsLLsL Perf. Min. Maj. Perf. Perf. Maj. Min. Perf.
6|0 A1md A4md 6 AsLLsLs Perf. Aug. Maj. Aug. Aug. Maj. Maj. Perf.
0|6 d6md 7 sLLsLsA Perf. Min. Min. Perf. Dim. Min. Dim. Perf.
Common harmonic major tunings
Tuning A:L:s Good just approximations Other comments 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
Chroma equals L 		184.615 369.308 461.5385 646.154 738.4615 1107.692
14edo 5:2:1 Chroma equals 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
7:2:1 		Chroma equals 2L+s 225
150 		450
300 		525
375 		750
525 		825
600 		1125
17edo 5:3:1
8:2:1 		25/24 Gentle fifth
Chroma equals 3L 		211.765
141.1765 		423.529
282.353 		494.118
352.941 		705.882
494.118 		776.412
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
7:3:1 		14/13
28/27 		Chroma equals L+s 189.474 378.947 505.263
442.105 		694.737
631.579 		821.053
694.737 		1073.684
1136.842
20edo 5:3:2
5:4:1
8:3:1 		13/8 and 15/14 180
240 		360
480 		480
420
540 		720
660
780 		840
720 		1080
1140
21edo 6:3:2
6:4:1 		171.429
228.571 		342.857
457.143 		457.143
514.286 		628.571
742.857 		742.857
800 		1085.714
1142.857
22edo 7:3:2
7:4:1 		9/7 (and 11/10) 163.636
218.182 		327.273
436.364 		436.364
490.909 		600
709.091 		709.091
763.636 		1090.909
1145.4545
23edo 8:3:2
8:4:1 		14/11 156.522
208.696 		313.0435
417.391 		417.391
469.565 		573.813
678.261 		678.261
730.435 		1095.652
1147.826
24edo 6:5:1 7 out of 4L 3m 3s 250 500 550 800 850 1150
25edo 7:4:2
7:5:1 		13/11 192
240 		384
480 		480
528 		672
768 		864
816 		1004
1148
26edo 8:5:1 8/7 230.769 461.5385 507.692 738.4615 784.615 1153.846
27edo 6:4:3
6:5:2 		27/25 and 7/6 177.778
222.222 		355.556
444.444 		488.889
533.333 		666.667
755.556 		800
844.444 		1066.667
1111.111
28edo 7:4:3
7:5:2
7:6:1 		14/13
5/4 		171.429
214.286
257.143 		342.857
428.571
514.286 		471.429
514.286
557.143 		642.857
728.571
814.286 		771.429
814.286
857.143 		1071.429
1111.286
1157.143
29edo 8:4:3
8:5:2
8:6:1 		(11/10 and) 13/11 Gentle fifth 165.517
206.897
248.276 		331.0345
413.793
496.552 		455.172
496.552
537.931 		620.69
703.448
786.207 		744.828
786.207
827.586 		1075.862
1117.241
1158.621
30edo 6:5:3 13/8 and 15/14 200
280 		400
560 		520
600 		720
880 		840
920 		1080
1160
31edo 7:5:3
7:6:2 		5/4 193.548
232.258 		387.097
464.516 		503.226
541.9355 		696.774
774.194 		812.903
851.613 		1083.871
1122.582
32edo 8:5:3
8:7:1 		16/15 Golden
7 out of 5L 5m 2s 		162.5
262.5 		325
525 		412.5
562.5 		675
825 		787.5
862.5 		1087.5
1162.5
33edo 6:5:4 181.818 363.636 509.091 690.909 836.364 1054.5455
34edo 7:5:4
7:6:3 		176.471
211.765 		352.941
423.529 		494.118
529.412 		670.588
741.1765 		811.765 1058.8235
1094.118
35edo 8:5:4
8:6:3
8:7:2 		171.429
205.714
240 		342.857
411.429
480 		480
514.286
548.571 		651.429
720
788.571 		788.571
822.857
857.143 		1062.857
1097.143
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
8:7:4 		4/3
9/8 		175.61
204.878 		351.22
409.756 		497.561
526.829 		673.171
731.707 		819.512
848.7805 		1053.6585
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

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.

Scale degrees of the modes of 5L 2s (sLLLLLs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (diadegree)
0 1 2 3 4 5 6 7
5|1 m1md m2md
1|5 M5md M6md 		1 sLLLLLs Perf. Min. Min. Perf. Perf. Maj. Maj. Perf.
6|0 A4md A5md 2 LLLLLss Perf. Maj. Maj. Aug. Aug. Aug. Maj. Perf.
6|0 A4md m6md
4|2 A3md A4md 		3 LLLLssL Perf. Maj. Maj. Aug. Aug. Maj. Min. Perf.
6|0 m5md m6md
2|4 M2md A3md 		4 LLLssLL Perf. Maj. Maj. Aug. Perf. Min. Min. Perf.
4|2 d4md m5md
0|6 M1md M2md 		5 LLssLLL Perf. Maj. Maj. Perf. Dim. Min. Min. Perf.
2|4 d3md d4md
0|6 M1md d3md 		6 LssLLLL Perf. Maj. Min. Dim. Dim. Min. Min. Perf.
0|6 d2md d3md 7 ssLLLLL Perf. Min. Dim. Dim. Dim. Min. Min. Perf.
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