3L 10s

From Xenharmonic Wiki
Jump to: navigation, search

"3L 10s" is a MOS scale pattern with 3 large steps and 10 small steps. Some notable temperaments that form a MOS with this pattern are magic and würschmidt.

Of course, magic[13] is still slightly improper and würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13 tone per octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13 tone circles favor multiple times over.

1\3 400
13\40 390
12\37 389.189
11\34 388.235
32\99 387.879 Whirrschmidt
21\65 387.692 Worschmidt
31\96 387.5 Würschimdt
10\31 387.097 Würschimdt
19\59 386.441 Sulis
9\28 385.714
8\25 384 Marveltri
7\22 381.818 Sorcery
20\63 380.952
33\104 380.769 Optimal patent val for 11-limit magic
13\41 380.488 Optimal patent val for 13-limit magic
19\60 380 Optimal patent val for 5-limit magic
379.408
6\19 378.947
377.967
17\54 377.778
45\143 377.622
118\375 377.6
191\607 377.595
73\232 377.586
28\89 377.528
11\35 377.143
5\16 375 Boundary of propriety

(Smaller generators are proper)

373.6775
14\45 373.333
37\119 373.109
97\312 373.077
254\817 373.072
157\505 373.069
60/193 373.057
23\74 372.973
372.812
9\29 372.414
13\42 371.429
17\55 370.909
21\68 370.588
25\81 370.37
29\94 370.213
33\107 370.0935
37\120 370
4\13 369.231