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3L 4s - "mosh"


MOS scales of this form are built from a generator that falls between 1\3 (one degree of 3edo - 400 cents) and 2\7 (two degrees of 7edo - 343 cents.

It has the form s L s L s L s and its various "modes" (with Modal UDP Notation and nicknames coined by Andrew Heathwaite) are:

Mode
UDP
Nickname
s L s L s L s
3|3
bish
L s L s L s s
6|0
dril
s L s L s s L
2|4
fish
L s L s s L s
5|1
gil
s L s s L s L
1|5
jwl
L s s L s L s
4|2
kleeth
s s L s L s L
0|6
led
The two notable harmonic entropy minima with this pattern are neutral third scales ("dicot" / "hemififth" / "mohajira") where two generators make a 3/2, and magic, where the generator is a 5/4 but five of them make a 3/1.



g
2g
3g
4g (-1200)
comments
1\3


400.000
800.000
1200.000
400.000


15\46

391.304
782.609
1173.913
365.217


14\43

390.698
781.395
1172.093
362.791


13\40

390.000
780.000
1170.000
360.000


12\37

389.189
778.378
1167.568
356.757


11\34

388.235
776.471
1164.706
352.941


10\31

387.097
774.194
1161.290
348.387
Würschmidt is around here


19\59
386.441
772.881
1159.322
345.763


9\28

385.714
771.429
1157.143
342.857


8\25

384.000
768.000
1152.000
336.000



23\72
383.333
766.667
1150.000
333.333



15\47
382.988
765.957
1148.936
331.915


7\22

381.818
763.636
1145.455
327.273



13\41
380.488
760.976
1141.463
321.951
Magic is around here


19\60
380.000
760.000
1140.000
320.000



25\79
379.747
759.494
1139.2405
318.987


6\19

378.947
757.895
1136.842
315.789



11\35
377.143
754.286
1131.429
308.571



16\51
376.471
752.941
1129.412
305.882


5\16

375.000
750.000
1125.000
300.000
L/s = 4


24\77
374.026
748.052
1122.078
296.104



19\61
373.7705
747.541
1121.3115
295.082



14\45
373.333
746.667
1120.000
293.333



9\29
372.414
744.828
1117.241
289.655



13\42
371.429
742.857
1114.286
285.714



17\55
370.909
741.818
1112.727
283.636




370.204
740.409
1110.613
280.817
L/s = pi

4\13

369.231
738.462
1107.692
276.923
L/s = 3


23\75
368.000
736.000
1104.000
272.000




19\62
367.742
735.484
1103.226
270.968



15\49
367.347
734.694
1102.041
269.388




367.091
734.183
1101.274
268.365
L/s = e


11\36
366.667
733.333
1100.000
266.667




366.256
732.513
1198.77
265.026



7\23
365.217
730.435
1095.652
260.870
Modi Sephiratorum (Kosmorsky)


17\56
364.286
728.571
1092.857
257.143



10\33
363.636
727.272
1090.909
254.545



13\43
362.791
725.581
1088.372
251.163



16\53
362.264
724.528
1086.7925
249.057



19\63
361.905
723.8095
1085.714
247.619


3\10

360.000
720.000
1080.000
240.000
Boundary of propriety(generators smaller than this are proper)


38\127
359.055
718.110
1077.165
236.2205



35\117
358.974
717.949
1076.923
235.898



32\107
358.8785
717.757
1076.6355
235.514



29\97
358.763
717.526
1076.289
235.0515



26\87
358.621
717.241
1075.862
234.483



23\77
358.442
716.883
1075.325
233.767



20\67
358.209
716.418
1074.627
232.836



17\57
357.895
715.7895
1073.684
231.579



14\47
357.447
714.894
1072.340
229.787



11\37
356.757
713.514
1070.270
227.027




356.5035
713.007
1069.511
226.014



8\27
355.556
711.111
1066.667
222.222
Beatles is around here



354.930
709.859
1064.789
219.718
Golden neutral thirds scale


21\71
354.783
709.565
1064.348
219.13



13\44
354.5455
709.091
1063.636
218.182




354.088
708.177
1062.266
216.354


5\17

352.941
705.882
1058.824
211.765
Optimum rank range (L/s=3/2)


12\41
351.220
702.439
1053.659
204.878
2.3.11 neutral thirds scale is around here

7\24

350.000
700.000
1050.000
200.000



16\55
349.091
698.182
1047.273
196.364


9\31

348.387
696.774
1045.161
193.548
Mohajira/dicot is around here

11\38

347.368
694.737
1042.105
189.474

2\7


342.857
685.714
1028.571
171.429


3\10 on this chart represents a dividing line between "neutral third scales" on the bottom (eg. 17edo neutral scale), and something else I don't have a name for yet on the top, with 10edo standing in between. (What do you call this region, dear reader?) Of course, magic is in the top half, but it's a pretty specific scale and doesn't describe the whole range. MOS-wise, the neutral third scales, after three more generations, make MOS 7L 3s ("unfair mosh"); the other scales make MOS 3L 7s ("fair mosh").

In "neutral third scale territory," the generators are all "neutral thirds," and two of them make an approximation of the "perfect fifth." Additionally, the L of the scale is somewhere around a "whole tone" and the s of the scale is somewhere around a "neutral tone".

In the as-yet unnamed northern territory, the generators are major thirds (including some very flat ones), and two generators are definitely sharp of a perfect fifth. L ranges from a "supermajor second" to a "major third" and s is a "semitone" or smaller.