Scala analysis: xen18-erlich-dominant-12
5L 7s MOS for Dominant, L=114.53, s=88.94
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88.940 cents 88.940000 2: 203.470 cents 203.470000 3: 292.410 cents 292.410000 4: 406.940 cents 406.940000 5: 495.880 cents 495.880000 6: 610.410 cents 610.410000 7: 699.350 cents 699.350000 8: 788.290 cents 788.290000 9: 902.820 cents 902.820000 10: 991.760 cents 991.760000 11: 1106.290 cents 1106.290000 12: 1195.230 cents 1195.230000
SHOW/INTERVAL
0: 88.9400 cents 88.9400 1: 88.9400 cents 88.9400 2: 114.5300 cents 114.5300 3: 88.9400 cents 88.9400 4: 114.5300 cents 114.5300 5: 88.9400 cents 88.9400 6: 114.5300 cents 114.5300 7: 88.9400 cents 88.9400 8: 88.9400 cents 88.9400 9: 114.5300 cents 114.5300 10: 88.9400 cents 88.9400 11: 114.5300 cents 114.5300 12: 88.9400 cents 88.9400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 88.94000 cents 1: 5 114.53000 cents 2: 2 177.88000 cents 2: 10 203.47000 cents 3: 9 292.41000 cents 3: 3 318.00000 cents 4: 4 381.35000 cents 4: 8 406.94000 cents 5: 11 495.88000 cents 5: 1 521.47000 cents 6: 6 584.82000 cents 6: 6 610.41000 cents 7: 1 673.76000 cents 7: 11 699.35000 cents 8: 8 788.29000 cents 8: 4 813.88000 cents 9: 3 877.23000 cents 9: 9 902.82000 cents 10: 10 991.76000 cents 10: 2 1017.35000 cents 11: 5 1080.70000 cents 11: 7 1106.29000 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 : 88.9 203.5 292.4 406.9 495.9 610.4 699.4 788.3 902.8 991.8 1106.3 1195.2 88.9 : 114.5 203.5 318.0 406.9 521.5 610.4 699.3 813.9 902.8 1017.3 1106.3 1195.2 203.5 : 88.9 203.5 292.4 406.9 495.9 584.8 699.3 788.3 902.8 991.8 1080.7 1195.2 292.4 : 114.5 203.5 318.0 406.9 495.9 610.4 699.3 813.9 902.8 991.8 1106.3 1195.2 406.9 : 88.9 203.5 292.4 381.3 495.9 584.8 699.4 788.3 877.2 991.8 1080.7 1195.2 495.9 : 114.5 203.5 292.4 406.9 495.9 610.4 699.4 788.3 902.8 991.8 1106.3 1195.2 610.4 : 88.9 177.9 292.4 381.3 495.9 584.8 673.8 788.3 877.2 991.8 1080.7 1195.2 699.4 : 88.9 203.5 292.4 406.9 495.9 584.8 699.4 788.3 902.8 991.8 1106.3 1195.2 788.3 : 114.5 203.5 318.0 406.9 495.9 610.4 699.4 813.9 902.8 1017.4 1106.3 1195.2 902.8 : 88.9 203.5 292.4 381.3 495.9 584.8 699.4 788.3 902.8 991.8 1080.7 1195.2 991.8 : 114.5 203.5 292.4 406.9 495.9 610.4 699.4 813.9 902.8 991.8 1106.3 1195.2 1106.3: 88.9 177.9 292.4 381.3 495.9 584.8 699.4 788.3 877.2 991.8 1080.7 1195.2 1195.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.9400 .. 114.5300 cents 25.59000 cents 88.94000 cents 2: 177.8800 .. 203.4700 cents 25.59000 cents 63.35000 cents 3: 292.4100 .. 318.0000 cents 25.59000 cents 88.94000 cents 4: 381.3500 .. 406.9400 cents 25.59000 cents 63.35000 cents 5: 495.8800 .. 521.4700 cents 25.59000 cents 88.94000 cents 6: 584.8200 .. 610.4100 cents 25.59000 cents 63.35000 cents 7: 673.7600 .. 699.3500 cents 25.59000 cents 63.35000 cents 8: 788.2900 .. 813.8800 cents 25.59000 cents 88.94000 cents 9: 877.2300 .. 902.8200 cents 25.59000 cents 63.35000 cents 10: 991.7600 .. 1017.3500 cents 25.59000 cents 88.94000 cents 11: 1080.7000 .. 1106.2900 cents 25.59000 cents 63.35000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 88.94000 cents, class 1 Average step (divided formal octave): 99.6025 cents Largest one step interval : 114.53000 cents Average / Smallest step : 1.119884 Largest / Average step : 1.149871 Largest / Smallest step : 1.287722 Median interval of one step : 88.94000 cents, amount: 7 Most common interval of one step : 88.94000 cents, amount: 7 Least squares average step : 99.84528 cents, oct.: 1198.14332 cents Scale is strictly proper Scale has Myhill's property chromas: 25.59000 cents and 63.35000 cents, ratio: 2.475576 generators: 5 of 495.88000 cents and 7 of 699.35000 cents ET pair of linear temperament : 12&41 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 981-tone equal temperament with octave 1195.230 cents degrees: 73 167 240 334 407 501 574 647 741 814 908 981 generators: 407 and 574 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABAABABA Step pattern size order : SLSLSLSSLSLS Scale is a Constant Structure, by a margin of 63.35000 cents Scale diversity : 1.170556 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.764489 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 : 25.59000 cents Most common intervals : 495.88000 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 88.940 699.350 cents Most common triad is 0.0 495.880 699.350 cents, amount: 10 Number of recognisable fifths : 11, average 699.3500 cents Number of recognisable fourths : 11, average 495.8800 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.4383 c. M: 12.7950 c. Twelve-tone Chromatic (1/11-comma) 29: 2 3 2 3 2 3 2 2 3 2 3 2 SP M ME SD: 4.5417 c. M:-7.8124 c. 41: 3 4 3 4 3 4 3 3 4 3 4 3 SP M ME SD: 1.0354 c. M:-1.7810 c. 53: 4 5 4 5 4 5 4 4 5 4 5 4 SP M ME SD: 0.8832 c. M: 1.5192 c. 94: 7 9 7 9 7 9 7 7 9 7 9 7 SP M DE SD: 0.0464 c. M: 0.0798 c. 511: 38 49 38 49 38 49 38 38 49 38 49 38 SP M DE SD: 0.0404 c. M:-0.0695 c. 605: 45 58 45 58 45 58 45 45 58 45 58 45 SP M DE SD: 0.0269 c. M:-0.0463 c. 699: 52 67 52 67 52 67 52 52 67 52 67 52 SP M DE SD: 0.0171 c. M:-0.0294 c. 793: 59 76 59 76 59 76 59 59 76 59 76 59 SP M DE SD: 0.0095 c. M:-0.0164 c. 887: 66 85 66 85 66 85 66 66 85 66 85 66 SP M DE SD: 0.0036 c. M:-0.0062 c. 981: 73 94 73 94 73 94 73 73 94 73 94 73 SP M DE SD: 0.0012 c. M: 0.0020 c. 1868: 139 179 139 179 139 179 139 139 179 139 179 139 SP M DE SD: 0.0011 c. M:-0.0019 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 4.7700 cents 2 x x x x x x 3 x x x x 4 S SD: 2.7175 cents 3 x x x x 4 x x x 5 x x 6 S SD: 6.3967 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.8301 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 10.3019 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 10.8883 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 8.7843 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 10.5387 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.9476 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.8423 cents 11 x 12:13:14:15:16 x 17:19:20:21:22 SD: 10.5890 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.3967 cents 13:14:15 x 16:17 x 19:21:22:23:25:26 SD: 10.5241 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 7.2649 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 6.2794 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.4034 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.3596 cents 26:27:29:31:33:35:37:39:41:44:46:49:52 SD: 3.2161 cents 31:33:35:37:39:41:44:46:49:52:55:59:62 SD: 2.9747 cents 33:35:37:39:42:44:47:49:52:56:59:63:66 SD: 2.7760 cents 34:36:38:40:43:45:48:51:54:57:60:64:68 SD: 2.7509 cents 37:39:42:44:47:49:53:55:58:62:66:70:74 SD: 2.7466 cents 38:40:43:45:48:51:54:57:60:64:67:72:76 SD: 1.7467 cents 54:57:61:64:68:72:77:81:85:91:96:102:108 SD: 1.3112 cents 75:79:84:89:95:100:107:112:118:126:133:142:150 SD: 1.1409 cents 76:80:85:90:96:101:108:114:120:128:135:144:152 SD: 1.0595 cents 88:93:99:104:111:117:125:132:139:148:156:167:176 SD: 1.0248 cents 94:99:106:111:119:125:134:141:148:158:167:178:187 SD: 0.9118 cents 97:102:109:115:123:129:138:145:153:163:172:184:193 SD: 0.7712 cents 113:119:127:134:143:150:161:169:178:190:200:214:225 SD: 0.7711 cents 114:120:128:135:144:152:162:171:180:192:202:216:227 SD: 0.5704 cents 135:142:152:160:171:180:192:202:213:227:239:256:269 SD: 0.5678 cents 151:159:170:179:191:201:215:226:238:254:268:286:301 SD: 0.3831 cents 208:219:234:246:263:277:296:312:328:350:369:394:415 SD: 0.3345 cents 241:254:271:285:305:321:343:361:380:406:427:457:481 SD: 0.3302 cents 265:279:298:314:335:353:377:397:418:446:470:502:529 SD: 0.2493 cents 305:321:343:361:386:406:434:457:481:514:541:578:608 SD: 0.1690 cents 418:440:470:495:529:557:595:626:659:704:741:792:834 SD: 0.1639 cents 456:480:513:540:577:607:649:683:719:768:809:864:909 SD: 0.1442 cents 494:520:556:585:625:658:703:740:779:832:876:936:985 SD: 0.1319 cents 570:600:641:675:721:759:811:854:899:960:1011:1080:1137 SD: 0.0875 cents