5L 2s MODMOSes
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.
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.
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. |
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.
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. |
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.
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. |