Scala analysis: xen14-mclaren-nonoctave-15-3
15th root of 3 non-octave scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 126.797 cents 126.797000 2: 253.594 cents 253.594000 3: 380.391 cents 380.391000 4: 507.188 cents 507.188000 5: 633.985 cents 633.985000 6: 760.782 cents 760.782000 7: 887.579 cents 887.579000 8: 1014.376 cents 1014.376000 9: 1141.173 cents 1141.173001 10: 1267.970 cents 1267.970001 11: 1394.767 cents 1394.767001 12: 1521.564 cents 1521.564001 13: 1648.361 cents 1648.361001 14: 1775.158 cents 1775.158001 15: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 126.7970 cents 126.7970 1: 126.7970 cents 126.7970 2: 126.7970 cents 126.7970 3: 126.7970 cents 126.7970 4: 126.7970 cents 126.7970 5: 126.7970 cents 126.7970 6: 126.7970 cents 126.7970 7: 126.7970 cents 126.7970 8: 126.7970 cents 126.7970 9: 126.7970 cents 126.7970 10: 126.7970 cents 126.7970 11: 126.7970 cents 126.7970 12: 126.7970 cents 126.7970 13: 126.7970 cents 126.7970 14: 126.7970 cents 126.7970 15: 126.7970 cents 126.7970
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 15 126.79700 cents 2: 15 253.59400 cents 3: 15 380.39100 cents 4: 15 507.18800 cents 5: 15 633.98500 cents 6: 15 760.78200 cents 7: 15 887.57900 cents 8: 15 1014.37600 cents 9: 15 1141.17300 cents 10: 15 1267.97000 cents 11: 15 1394.76700 cents 12: 15 1521.56400 cents 13: 15 1648.36100 cents 14: 15 1775.15800 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 126.8 : 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 253.6 : 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 380.4 : 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 507.2 : 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 634.0 : 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 760.8 : 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 887.6 : 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 1014.4: 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 1141.2: 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 1268.0: 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 1394.8: 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 1521.6: 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 1648.4: 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 1775.2: 126.8 253.6 380.4 507.2 634.0 760.8 887.6 1014.4 1141.2 1268.0 1394.8 1521.6 1648.4 1775.2 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.7970 .. 126.7970 cents 1/1, 0.0000 cents 126.79700 cents 2: 253.5940 .. 253.5940 cents 1/1, 0.0000 cents 126.79700 cents 3: 380.3910 .. 380.3910 cents 1/1, 0.0000 cents 126.79700 cents 4: 507.1880 .. 507.1880 cents 1/1, 0.0000 cents 126.79700 cents 5: 633.9850 .. 633.9850 cents 1/1, 0.0000 cents 126.79700 cents 6: 760.7820 .. 760.7820 cents 1/1, 0.0000 cents 126.79700 cents 7: 887.5790 .. 887.5790 cents 1/1, 0.0000 cents 126.79700 cents 8: 1014.3760 .. 1014.3760 cents 1/1, 0.0000 cents 126.79700 cents 9: 1141.1730 .. 1141.1730 cents 1/1, 0.0000 cents 126.79700 cents 10: 1267.9700 .. 1267.9700 cents 1/1, 0.0000 cents 126.79700 cents 11: 1394.7670 .. 1394.7670 cents 1/1, 0.0000 cents 126.79700 cents 12: 1521.5640 .. 1521.5640 cents 1/1, 0.0000 cents 126.79700 cents 13: 1648.3610 .. 1648.3610 cents 1/1, 0.0000 cents 126.79700 cents 14: 1775.1580 .. 1775.1580 cents 1/1, 0.0000 cents 126.79700 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 126.79700 cents, class 1 Average step (divided formal octave): 126.7970 cents Largest one step interval : 126.79700 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 126.79700 cents, amount: 15 Most common interval of one step : 126.79700 cents, amount: 15 Least squares average step : 126.79700 cents, oct.: 1901.95500 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 126.79700 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.066667 redundancy: 0.933333 Efficiency x scale size : 1.000000 Number of different interval sizes : 14 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 0 Number of recognisable fourths : 15, average 507.1880 cents Scale contains two identical disjunct pentachords Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x 2 x x x x x 3 S SD: 29.4135 cents 2 x x x x x 3 x x 4 x x x 5 x 6 S SD: 25.9460 cents 3 x x x 4 x x 5 x 6 x x 7:8 x 9 S SD: 15.8240 cents 4 x x 5 x x 6 x 7:8 x 9 x 10:11:12 S SD: 14.5414 cents 5 x 6 x x 7:8 x 9:10 x 11:12:13:14:15 S SD: 11.7381 cents 6 x 7 x 8 x 9:10:11:12 x 13:14:16:17:18 S SD: 12.1316 cents 7 x 8:9 x 10:11:12:13:14:15:16:17:18:20:21 S SD: 10.6627 cents 8 x 9:10:11 x 12:13:14:15:17:18:19:21:22:24 SD: 10.3490 cents 9:10 x 11:12:13:14:15:16:17:19:20:22:23:25:27 SD: 6.5222 cents 10:11:12 x 13:14:16:17:18:19:21:22:24:26:28:30 SD: 9.2359 cents 11:12:13:14:15:16:17:18:20:21:23:25:26:29:31:33 SD: 6.5178 cents 12:13:14:15:16:17:19:20:22:23:25:27:29:31:33:36 SD: 4.6101 cents 15:16:17:19:20:22:23:25:27:29:31:34:36:39:42:45 SD: 4.4879 cents 18:19:21:22:24:26:28:30:32:35:37:40:43:47:50:54 SD: 4.1663 cents 20:22:23:25:27:29:31:33:36:39:42:45:48:52:56:60 SD: 3.6594 cents 24:26:28:30:32:35:37:40:43:46:50:54:58:62:67:72 SD: 2.4463 cents 25:27:29:31:34:36:39:42:45:48:52:56:60:65:70:75 SD: 2.3344 cents 29:31:34:36:39:42:45:48:52:56:60:65:70:75:81:87 SD: 2.2113 cents 36:39:42:45:48:52:56:60:65:70:75:81:87:93:100:108 SD: 1.9314 cents 38:41:44:47:51:55:59:63:68:73:79:85:92:98:106:114 SD: 1.7561 cents 45:48:52:56:60:65:70:75:81:87:94:101:108:117:125:135 SD: 1.5738 cents 49:53:57:61:66:71:76:82:88:95:102:110:118:127:137:147 SD: 1.3003 cents 52:56:60:65:70:75:81:87:93:101:108:116:125:135:145:156 SD: 1.2829 cents 56:60:65:70:75:81:87:94:101:108:116:125:135:145:156:168 SD: 1.2730 cents 58:62:67:72:78:84:90:97:104:112:121:130:140:150:162:174 SD: 1.2594 cents 61:66:71:76:82:88:95:102:110:118:127:137:147:158:170:183 SD: 1.2085 cents 63:68:73:78:84:91:98:105:113:122:131:141:152:163:176:189 SD: 1.1726 cents 64:69:74:80:86:92:99:107:115:124:133:143:154:166:178:192 SD: 0.9146 cents 76:82:88:95:102:110:118:127:137:147:158:170:183:197:212:228 SD: 0.7879 cents 88:95:102:110:118:127:137:147:158:170:183:197:212:228:245:264 SD: 0.7133 cents 89:96:103:111:119:128:138:149:160:172:185:199:214:231:248:267 SD: 0.6982 cents 94:101:109:117:126:136:146:157:169:182:196:210:226:244:262:282 SD: 0.6716 cents 102:110:118:127:137:147:158:170:183:197:212:228:246:264:284:306 SD: 0.6108 cents 109:117:126:136:146:157:169:182:196:211:227:244:262:282:304:327 SD: 0.5637 cents 118:127:137:147:158:170:183:197:212:228:245:264:284:306:329:354 SD: 0.4537 cents 134:144:155:167:180:193:208:224:241:259:279:300:323:347:374:402 SD: 0.4448 cents 147:158:170:183:197:212:228:245:264:284:306:329:354:381:410:441 SD: 0.3251 cents 183:197:212:228:245:264:284:306:329:354:381:410:441:474:510:549 SD: 0.3186 cents 196:211:227:244:263:283:304:327:352:379:408:439:472:508:546:588 SD: 0.2916 cents 208:224:241:259:279:300:323:347:374:402:433:466:501:539:580:624 SD: 0.2748 cents 221:238:256:275:296:319:343:369:397:427:460:495:532:573:616:663 SD: 0.2700 cents 223:240:258:278:299:322:346:372:401:431:464:499:537:578:622:669 SD: 0.2494 cents 235:253:272:293:315:339:365:392:422:454:489:526:566:609:655:705 SD: 0.2281 cents 265:285:307:330:355:382:411:442:476:512:551:593:638:687:739:795 SD: 0.2263 cents 285:307:330:355:382:411:442:476:512:551:593:638:686:738:795:855 SD: 0.1937 cents 330:355:382:411:442:476:512:551:593:638:686:739:795:855:920:990 SD: 0.1471 cents 355:382:411:442:476:512:551:593:638:686:738:795:855:920:990:1065 SD: 0.1448 cents 382:411:442:476:512:551:593:638:686:738:795:855:920:990:1065:1146 SD: 0.1432 cents 423:455:490:527:567:610:656:706:760:818:880:947:1019:1096:1179:1269 SD: 0.1398 cents 448:482:519:558:600:646:695:748:805:866:932:1003:1079:1161:1249:1344 SD: 0.1378 cents 461:496:534:574:618:665:715:770:828:891:959:1032:1110:1195:1285:1383 SD: 0.1366 cents 464:499:537:578:622:669:720:775:834:897:965:1039:1117:1202:1294:1392 SD: 0.1319 cents 473:509:548:589:634:682:734:790:850:914:984:1059:1139:1226:1319:1419 SD: 0.1299 cents 475:511:550:592:637:685:737:793:853:918:988:1063:1144:1231:1324:1425 SD: 0.1160 cents 488:525:565:608:654:704:757:815:877:943:1015:1092:1175:1265:1361:1464 SD: 0.1085 cents 500:538:579:623:670:721:776:835:898:967:1040:1119:1204:1296:1394:1500 SD: 0.0934 cents 538:579:623:670:721:776:835:898:967:1040:1119:1204:1296:1394:1500:1614 SD: 0.0931 cents