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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