Scala analysis: xen14-mclaren-nonoctave-14-3
14th 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: 135.854 cents 135.853929 2: 271.708 cents 271.707857 3: 407.562 cents 407.561786 4: 543.416 cents 543.415715 5: 679.270 cents 679.269643 6: 815.124 cents 815.123572 7: 950.977 cents 950.977500 8: 1086.831 cents 1086.831429 9: 1222.685 cents 1222.685358 10: 1358.539 cents 1358.539286 11: 1494.393 cents 1494.393215 12: 1630.247 cents 1630.247144 13: 1766.101 cents 1766.101072 14: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 135.8539 cents 135.8539 1: 135.8539 cents 135.8539 2: 135.8539 cents 135.8539 3: 135.8539 cents 135.8539 4: 135.8539 cents 135.8539 5: 135.8539 cents 135.8539 6: 135.8539 cents 135.8539 7: 135.8539 cents 135.8539 8: 135.8539 cents 135.8539 9: 135.8539 cents 135.8539 10: 135.8539 cents 135.8539 11: 135.8539 cents 135.8539 12: 135.8539 cents 135.8539 13: 135.8539 cents 135.8539 14: 135.8539 cents 135.8539
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 14 135.85393 cents 2: 14 271.70786 cents 3: 14 407.56179 cents 4: 14 543.41571 cents 5: 14 679.26964 cents 6: 14 815.12357 cents 7: 14 950.97750 cents 8: 14 1086.83143 cents 9: 14 1222.68536 cents 10: 14 1358.53929 cents 11: 14 1494.39322 cents 12: 14 1630.24714 cents 13: 14 1766.10107 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 0.0 : 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 135.9 : 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 271.7 : 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 407.6 : 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 543.4 : 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 679.3 : 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 815.1 : 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 951.0 : 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 1086.8: 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 1222.7: 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 1358.5: 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 1494.4: 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 1630.2: 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 1766.1: 135.9 271.7 407.6 543.4 679.3 815.1 951.0 1086.8 1222.7 1358.5 1494.4 1630.2 1766.1 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 135.8539 .. 135.8539 cents 1/1, 0.0000 cents 135.85393 cents 2: 271.7079 .. 271.7079 cents 1/1, 0.0000 cents 135.85393 cents 3: 407.5618 .. 407.5618 cents 1/1, 0.0000 cents 135.85393 cents 4: 543.4157 .. 543.4157 cents 1/1, 0.0000 cents 135.85393 cents 5: 679.2696 .. 679.2696 cents 1/1, 0.0000 cents 135.85393 cents 6: 815.1236 .. 815.1236 cents 1/1, 0.0000 cents 135.85393 cents 7: 950.9775 .. 950.9775 cents 1/1, 0.0000 cents 135.85393 cents 8: 1086.8314 .. 1086.8314 cents 1/1, 0.0000 cents 135.85393 cents 9: 1222.6854 .. 1222.6854 cents 1/1, 0.0000 cents 135.85393 cents 10: 1358.5393 .. 1358.5393 cents 1/1, 0.0000 cents 135.85393 cents 11: 1494.3932 .. 1494.3932 cents 1/1, 0.0000 cents 135.85393 cents 12: 1630.2471 .. 1630.2471 cents 1/1, 0.0000 cents 135.85393 cents 13: 1766.1011 .. 1766.1011 cents 1/1, 0.0000 cents 135.85393 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 135.85393 cents, class 1 Average step (divided formal octave): 135.8539 cents Largest one step interval : 135.85393 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 135.85393 cents, amount: 14 Most common interval of one step : 135.85393 cents, amount: 14 Least squares average step : 135.85393 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 135.85393 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.071429 redundancy: 0.928571 Efficiency x scale size : 1.000000 Number of different interval sizes : 13 = 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 : 0 Scale contains two identical disjunct pentachords Best fifths form a closed circle Best major 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
14: 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 3 S SD: 11.3427 cents 2 x x x x 3 x x x 4 x x 5 x 6 S SD: 13.6001 cents 3 x x x 4 x x 5 x 6 x 7:8 x 9 S SD: 18.5332 cents 4 x x 5 x 6 x 7 x 8:9 x 10:11:12 S SD: 9.6877 cents 5 x 6 x 7 x 8:9 x 10:11:12:13:14:15 S SD: 9.8744 cents 6 x 7 x 8:9 x 10:11:12:13:14:15:17:18 SD: 10.5239 cents 7 x 8:9 x 10:11:12:13:14:15:17:18:19:21 SD: 9.5153 cents 8 x 9:10:11:12:13:14:15:16:18:19:21:22:24 SD: 8.0808 cents 9:10 x 11:12:13:14:16:17:18:20:21:23:25:27 SD: 9.8221 cents 10:11:12:13:14:15:16:17:19:20:22:24:26:28:30 SD: 7.3167 cents 11:12:13:14:15:16:18:19:21:22:24:26:28:31:33 SD: 5.3555 cents 16:17:19:20:22:24:26:28:30:32:35:38:41:44:48 SD: 4.7224 cents 19:21:22:24:26:28:30:33:36:39:42:45:49:53:57 SD: 4.3478 cents 22:24:26:28:30:33:35:38:41:45:48:52:56:61:66 SD: 3.1367 cents 23:25:27:29:31:34:37:40:43:47:50:55:59:64:69 SD: 2.9084 cents 25:27:29:32:34:37:40:43:47:51:55:59:64:69:75 SD: 2.5188 cents 30:32:35:38:41:44:48:52:56:61:66:71:77:83:90 SD: 2.2905 cents 33:36:39:42:45:49:53:57:62:67:72:78:85:92:99 SD: 2.2641 cents 35:38:41:44:48:52:56:61:66:71:77:83:90:97:105 SD: 1.6637 cents 41:44:48:52:56:61:66:71:77:83:90:97:105:114:123 SD: 1.4892 cents 46:50:54:58:63:68:74:80:86:93:101:109:118:128:138 SD: 1.3122 cents 48:52:56:61:66:71:77:83:90:97:105:114:123:133:144 SD: 1.0541 cents 60:65:70:76:82:89:96:104:112:122:132:142:154:166:180 SD: 1.0148 cents 71:77:83:90:97:105:114:123:133:144:156:168:182:197:213 SD: 0.7123 cents 87:94:102:110:119:129:139:151:163:176:191:206:223:241:261 SD: 0.6470 cents 98:106:115:124:134:145:157:170:184:199:215:232:251:272:294 SD: 0.6426 cents 108:117:126:137:148:160:173:187:202:219:237:256:277:300:324 SD: 0.6216 cents 111:120:130:140:152:164:178:192:208:225:243:263:285:308:333 SD: 0.6082 cents 112:121:131:142:153:166:179:194:210:227:245:266:287:311:336 SD: 0.6008 cents 113:122:132:143:155:167:181:196:212:229:248:268:290:313:339 SD: 0.5784 cents 123:133:144:156:168:182:197:213:230:249:270:292:315:341:369 SD: 0.5665 cents 124:134:145:157:170:184:199:215:232:251:272:294:318:344:372 SD: 0.5362 cents 125:135:146:158:171:185:200:217:234:253:274:296:321:347:375 SD: 0.5357 cents 135:146:158:171:185:200:216:234:253:274:296:320:346:374:405 SD: 0.3639 cents 158:171:185:200:216:234:253:274:296:320:346:375:405:438:474 SD: 0.3261 cents 195:211:228:247:267:289:312:338:365:395:427:462:500:541:585 SD: 0.3085 cents 206:223:241:261:282:305:330:357:386:417:452:488:528:571:618 SD: 0.3059 cents 219:237:256:277:300:324:351:379:410:444:480:519:562:607:657 SD: 0.2962 cents 223:241:261:282:305:330:357:386:418:452:489:529:572:619:669 SD: 0.2552 cents 246:266:288:311:337:364:394:426:461:498:539:583:631:682:738 SD: 0.2519 cents 260:281:304:329:356:385:416:450:487:527:570:616:667:721:780 SD: 0.2210 cents 271:293:317:343:371:401:434:469:508:549:594:642:695:752:813 SD: 0.1923 cents 306:331:358:387:419:453:490:530:573:620:671:725:785:849:918 SD: 0.1574 cents 366:396:428:463:501:542:586:634:686:742:802:868:939:1015:1098 SD: 0.1478 cents 377:408:441:477:516:558:604:653:706:764:826:894:967:1046:1131 SD: 0.1374 cents 418:452:489:529:572:619:669:724:783:847:916:991:1072:1159:1254 SD: 0.1003 cents 429:464:502:543:587:635:687:743:804:869:940:1017:1100:1190:1287 SD: 0.0971 cents 464:502:543:587:635:687:743:804:869:940:1017:1100:1190:1287:1392 SD: 0.0962 cents 489:529:572:619:669:724:783:847:916:991:1072:1159:1254:1356:1467 SD: 0.0924 cents 564:610:660:714:772:835:903:977:1057:1143:1236:1337:1446:1564:1692 SD: 0.0879 cents