Scala analysis: xen18-schulter-didymic-1-4-12
1/4-Didymic temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76.049 cents 76.048999 2: 193.157 cents 193.156857 3: 310.265 cents 310.264715 4: 386.314 cents 386.313714 5: 503.422 cents 503.421572 6: 579.471 cents 579.470571 7: 696.578 cents 696.578428 8: 772.627 cents 772.627428 9: 889.735 cents 889.735285 10: 1006.843 cents 1006.843143 11: 1082.892 cents 1082.892142 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 117.1079 cents 117.1079 1: 76.0490 cents 76.0490 2: 117.1079 cents 117.1079 3: 117.1079 cents 117.1079 4: 76.0490 cents 76.0490 5: 117.1079 cents 117.1079 6: 76.0490 cents 76.0490 7: 117.1079 cents 117.1079 8: 76.0490 cents 76.0490 9: 117.1079 cents 117.1079 10: 117.1079 cents 117.1079 11: 76.0490 cents 76.0490 12: 117.1079 cents 117.1079
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 76.04900 cents 1: 7 117.10786 cents 2: 10 193.15686 cents 2: 2 234.21572 cents 3: 3 269.20586 cents 3: 9 310.26472 cents 4: 8 386.31371 cents 4: 4 427.37257 cents 5: 1 462.36271 cents 5: 11 503.42157 cents 6: 6 579.47057 cents 6: 6 620.52943 cents 7: 11 696.57843 cents 7: 1 737.63729 cents 8: 4 772.62743 cents 8: 8 813.68629 cents 9: 9 889.73528 cents 9: 3 930.79414 cents 10: 2 965.78428 cents 10: 10 1006.84314 cents 11: 7 1082.89214 cents 11: 5 1123.95100 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 76.0 193.2 310.3 386.3 503.4 579.5 696.6 772.6 889.7 1006.8 1082.9 1200.0 76.0 : 117.1 234.2 310.3 427.4 503.4 620.5 696.6 813.7 930.8 1006.8 1124.0 1200.0 193.2 : 117.1 193.2 310.3 386.3 503.4 579.5 696.6 813.7 889.7 1006.8 1082.9 1200.0 310.3 : 76.0 193.2 269.2 386.3 462.4 579.5 696.6 772.6 889.7 965.8 1082.9 1200.0 386.3 : 117.1 193.2 310.3 386.3 503.4 620.5 696.6 813.7 889.7 1006.8 1124.0 1200.0 503.4 : 76.0 193.2 269.2 386.3 503.4 579.5 696.6 772.6 889.7 1006.8 1082.9 1200.0 579.5 : 117.1 193.2 310.3 427.4 503.4 620.5 696.6 813.7 930.8 1006.8 1124.0 1200.0 696.6 : 76.0 193.2 310.3 386.3 503.4 579.5 696.6 813.7 889.7 1006.8 1082.9 1200.0 772.6 : 117.1 234.2 310.3 427.4 503.4 620.5 737.6 813.7 930.8 1006.8 1124.0 1200.0 889.7 : 117.1 193.2 310.3 386.3 503.4 620.5 696.6 813.7 889.7 1006.8 1082.9 1200.0 1006.8: 76.0 193.2 269.2 386.3 503.4 579.5 696.6 772.6 889.7 965.8 1082.9 1200.0 1082.9: 117.1 193.2 310.3 427.4 503.4 620.5 696.6 813.7 889.7 1006.8 1124.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.0490 .. 117.1079 cents 41.05886 cents 76.04900 cents 2: 193.1569 .. 234.2157 cents 41.05886 cents 76.04900 cents 3: 269.2059 .. 310.2647 cents 41.05886 cents 34.99014 cents 4: 386.3137 .. 427.3726 cents 41.05886 cents 76.04900 cents 5: 462.3627 .. 503.4216 cents 41.05886 cents 34.99014 cents 6: 579.4706 .. 620.5294 cents 41.05886 cents 76.04900 cents 7: 696.5784 .. 737.6373 cents 41.05886 cents 76.04900 cents 8: 772.6274 .. 813.6863 cents 41.05886 cents 34.99014 cents 9: 889.7353 .. 930.7941 cents 41.05886 cents 76.04900 cents 10: 965.7843 .. 1006.8431 cents 41.05886 cents 34.99014 cents 11: 1082.8921 .. 1123.9510 cents 41.05886 cents 76.04900 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 76.04900 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 117.10786 cents Average / Smallest step : 1.314942 Largest / Average step : 1.171079 Largest / Smallest step : 1.539900 Median interval of one step : 117.10786 cents, amount: 7 Most common interval of one step : 117.10786 cents, amount: 7 Least squares average step : 99.04196 cents, oct.: 1188.50352 cents Scale is strictly proper Scale has Myhill's property chromas: 41.05886 cents and 34.99014 cents, ratio: 1.173441 generators: 5 of 503.42157 cents and 7 of 696.57843 cents ET pair of linear temperament : 12&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 789-tone equal temperament with octave 1200.000 cents degrees: 50 127 204 254 331 381 458 508 585 662 712 789 generators: 331 and 458 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABABBAB Step pattern size order : SLLSLSLSLLSL Scale is a Constant Structure, by a margin of 34.99014 cents Ratio Whole / Half tone : 1.649393 Scale diversity : 1.218585 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.623627 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 34.99014 cents Most common intervals : 503.42157 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 117.108 696.578 cents Most common triad is 0.0 503.422 696.578 cents, amount: 10 Number of recognisable fifths : 11, average 696.5784 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.5835 c. M:-27.3726 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 7.8493 c. M: 14.7327 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 0.8344 c. M:-1.5661 c. Meantone Chromatic (53/220-comma) 112: 7 11 11 7 11 7 11 7 11 11 7 11 SP M DE SD: 0.6387 c. M: 1.1989 c. Meantone Chromatic (7/27-comma), Meanpop-12 143: 9 14 14 9 14 9 14 9 14 14 9 14 SP M DE SD: 0.3194 c. M: 0.5995 c. Meantone Chromatic (19/75-comma) 174: 11 17 17 11 17 11 17 11 17 17 11 17 SP M DE SD: 0.1138 c. M: 0.2136 c. Meantone Chromatic (1/4-comma), Milliet de Chales-12 205: 13 20 20 13 20 13 20 13 20 20 13 20 SP M DE SD: 0.0296 c. M:-0.0555 c. 584: 37 57 57 37 57 37 57 37 57 57 37 57 SP M DE SD: 0.0132 c. M: 0.0247 c. 789: 50 77 77 50 77 50 77 50 77 77 50 77 SP M DE SD: 0.0021 c. M: 0.0039 c. 1783: 113 174 174 113 174 113 174 113 174 174 113 174 SP M DE SD: 0.0016 c. M:-0.0030 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 2.6883 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.5345 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.5989 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.5782 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2706 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.2680 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.6897 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.1069 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.1972 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.2532 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 8.4297 cents 13:14:15 x 16:17:18:19:20:22:23:24:26 S SD: 9.8610 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.1809 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 5.7483 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 5.1415 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 4.0289 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.3833 cents 25:26:28:30:31:33:35:37:39:42:45:47:50 SD: 3.1611 cents 32:33:36:38:40:43:45:48:50:54:57:60:64 SD: 3.0625 cents 35:37:39:42:44:47:49:52:55:59:63:65:70 SD: 2.9948 cents 36:38:40:43:45:48:50:54:56:60:64:67:72 SD: 2.4501 cents 40:42:45:48:50:54:56:60:63:67:72:75:80 SD: 2.4426 cents 41:43:46:49:51:55:57:61:64:69:73:77:82 SD: 2.0480 cents 45:47:50:54:56:60:63:67:70:75:80:84:90 SD: 1.8789 cents 48:50:54:57:60:64:67:72:75:80:86:90:96 SD: 1.7374 cents 51:53:57:61:64:68:71:76:80:85:91:95:102 SD: 1.6136 cents 60:63:67:72:75:80:84:90:94:100:107:112:120 SD: 1.3322 cents 67:70:75:80:84:90:94:100:105:112:120:125:134 SD: 1.1656 cents 68:71:76:81:85:91:95:102:106:114:122:127:136 SD: 1.0355 cents 83:87:93:99:104:111:116:124:130:139:148:155:166 SD: 1.0172 cents 85:89:95:102:106:114:119:127:133:142:152:159:170 SD: 0.8433 cents 91:95:102:109:114:122:127:136:142:152:163:170:182 SD: 0.7388 cents 113:118:126:135:141:151:158:169:177:189:202:211:226 SD: 0.6674 cents 128:134:143:153:160:171:179:191:200:214:229:239:256 SD: 0.5028 cents 153:160:171:183:191:205:214:229:239:256:274:286:306 SD: 0.4375 cents 204:213:228:244:255:273:285:305:319:341:365:381:408 SD: 0.2302 cents 332:347:371:397:415:444:464:496:519:555:594:621:664 SD: 0.2091 cents 380:397:425:455:475:508:531:568:594:635:680:710:760 SD: 0.2080 cents 397:415:444:475:496:531:555:594:620:664:710:742:794 SD: 0.1761 cents 448:468:501:536:560:599:626:670:700:749:801:837:896 SD: 0.1259 cents 551:576:616:659:689:737:770:824:861:921:986:1030:1102 SD: 0.1091 cents