Scala analysis: xen14-mclaren-nonoctave-13-3
Pierce-Bohlen scale, 13th root of 3
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 146.304 cents 146.304231 2: 292.608 cents 292.608462 3: 438.913 cents 438.912693 4: 585.217 cents 585.216923 5: 731.521 cents 731.521154 6: 877.825 cents 877.825385 7: 1024.130 cents 1024.129616 8: 1170.434 cents 1170.433847 9: 1316.738 cents 1316.738078 10: 1463.042 cents 1463.042308 11: 1609.347 cents 1609.346539 12: 1755.651 cents 1755.650770 13: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 146.3042 cents 146.3042 1: 146.3042 cents 146.3042 2: 146.3042 cents 146.3042 3: 146.3042 cents 146.3042 4: 146.3042 cents 146.3042 5: 146.3042 cents 146.3042 6: 146.3042 cents 146.3042 7: 146.3042 cents 146.3042 8: 146.3042 cents 146.3042 9: 146.3042 cents 146.3042 10: 146.3042 cents 146.3042 11: 146.3042 cents 146.3042 12: 146.3042 cents 146.3042 13: 146.3042 cents 146.3042
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 146.30423 cents 2: 13 292.60846 cents 3: 13 438.91269 cents 4: 13 585.21692 cents 5: 13 731.52115 cents 6: 13 877.82538 cents 7: 13 1024.12962 cents 8: 13 1170.43385 cents 9: 13 1316.73808 cents 10: 13 1463.04231 cents 11: 13 1609.34654 cents 12: 13 1755.65077 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 0.0 : 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 146.3 : 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 292.6 : 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 438.9 : 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 585.2 : 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 731.5 : 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 877.8 : 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 1024.1: 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 1170.4: 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 1316.7: 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 1463.0: 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 1609.3: 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 1755.7: 146.3 292.6 438.9 585.2 731.5 877.8 1024.1 1170.4 1316.7 1463.0 1609.3 1755.7 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 146.3042 .. 146.3042 cents 1/1, 0.0000 cents 146.30423 cents 2: 292.6085 .. 292.6085 cents 1/1, 0.0000 cents 146.30423 cents 3: 438.9127 .. 438.9127 cents 1/1, 0.0000 cents 146.30423 cents 4: 585.2169 .. 585.2169 cents 1/1, 0.0000 cents 146.30423 cents 5: 731.5212 .. 731.5212 cents 1/1, 0.0000 cents 146.30423 cents 6: 877.8254 .. 877.8254 cents 1/1, 0.0000 cents 146.30423 cents 7: 1024.1296 .. 1024.1296 cents 1/1, 0.0000 cents 146.30423 cents 8: 1170.4338 .. 1170.4338 cents 1/1, 0.0000 cents 146.30423 cents 9: 1316.7381 .. 1316.7381 cents 1/1, 0.0000 cents 146.30423 cents 10: 1463.0423 .. 1463.0423 cents 1/1, 0.0000 cents 146.30423 cents 11: 1609.3465 .. 1609.3465 cents 1/1, 0.0000 cents 146.30423 cents 12: 1755.6508 .. 1755.6508 cents 1/1, 0.0000 cents 146.30423 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 146.30423 cents, class 1 Average step (divided formal octave): 146.3042 cents Largest one step interval : 146.30423 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 146.30423 cents, amount: 13 Most common interval of one step : 146.30423 cents, amount: 13 Least squares average step : 146.30423 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 146.30423 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.076923 redundancy: 0.923077 Efficiency x scale size : 1.000000 Number of different interval sizes : 12 = 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 tetrachords Best fifths form a closed circle Best major thirds form a closed circle 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
13: 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 2 x x x x 3 S SD: 14.7831 cents 2 x x x x 3 x x 4 x x 5 x 6 S SD: 11.9343 cents 3 x x 4 x x 5 x 6 x 7 x 8:9 S SD: 14.6691 cents 4 x x 5 x 6 x 7:8 x 9:10:11:12 S SD: 13.4742 cents 5 x 6 x 7 x 8:9:10:11:12:13:14:15 S SD: 11.5756 cents 6 x 7:8 x 9:10:11:12:13:14:15:17:18 SD: 9.0228 cents 7 x 8:9:10:11:12:13:14:15:16:18:19:21 SD: 10.5529 cents 8:9 x 10:11:12:13:14:16:17:19:20:22:24 SD: 10.3106 cents 9:10:11:12:13:14:15:16:18:19:21:23:25:27 SD: 9.1694 cents 10:11:12:13:14:15:17:18:20:21:23:25:28:30 SD: 6.5797 cents 11:12:13:14:15:17:18:20:22:24:26:28:30:33 SD: 6.5210 cents 15:16:18:19:21:23:25:27:29:32:35:38:41:45 SD: 4.7912 cents 20:22:24:26:28:31:33:36:39:43:47:51:55:60 SD: 3.9997 cents 21:23:25:27:29:32:35:38:41:45:49:53:58:63 SD: 2.6663 cents 27:29:32:35:38:41:45:49:53:58:63:68:74:81 SD: 2.5649 cents 32:35:38:41:45:49:53:58:63:68:75:81:88:96 SD: 1.8976 cents 38:41:45:49:53:58:63:69:75:81:88:96:105:114 SD: 1.8769 cents 42:46:50:54:59:64:70:76:83:90:98:106:116:126 SD: 1.6205 cents 45:49:53:58:63:69:75:81:88:96:105:114:124:135 SD: 1.5011 cents 53:58:63:68:74:81:88:96:104:113:123:134:146:159 SD: 1.4773 cents 55:60:65:71:77:84:91:99:108:118:128:139:152:165 SD: 1.0727 cents 59:64:70:76:83:90:98:107:116:126:137:149:163:177 SD: 1.0624 cents 65:71:77:84:91:99:108:117:128:139:151:165:179:195 SD: 0.9962 cents 70:76:83:90:98:107:116:126:138:150:163:177:193:210 SD: 0.9322 cents 77:84:91:99:108:117:128:139:151:165:179:195:212:231 SD: 0.9231 cents 80:87:95:103:112:122:133:145:157:171:186:203:221:240 SD: 0.8009 cents 82:89:97:106:115:125:136:148:161:175:191:208:226:246 SD: 0.7451 cents 103:112:122:133:144:157:171:186:203:220:240:261:284:309 SD: 0.6582 cents 112:122:133:144:157:171:186:202:220:240:261:284:309:336 SD: 0.6412 cents 114:124:135:147:160:174:189:206:224:244:265:289:314:342 SD: 0.3797 cents 156:170:185:201:219:238:259:282:307:334:363:395:430:468 SD: 0.3746 cents 180:196:213:232:252:275:299:325:354:385:419:456:496:540 SD: 0.3290 cents 201:219:238:259:282:307:334:363:395:430:468:509:554:603 SD: 0.2747 cents 229:249:271:295:321:349:380:414:450:490:533:580:631:687 SD: 0.2675 cents 238:259:282:307:334:363:395:430:468:509:554:603:656:714 SD: 0.2234 cents 259:282:307:334:363:395:430:468:509:554:603:656:714:777 SD: 0.2206 cents 294:320:348:379:412:449:488:531:578:629:684:745:811:882 SD: 0.2185 cents 295:321:349:380:414:450:490:533:580:631:687:747:813:885 SD: 0.2072 cents 315:343:373:406:442:481:523:569:619:674:733:798:868:945 SD: 0.2066 cents 316:344:374:407:443:482:525:571:621:676:736:801:871:948 SD: 0.1821 cents 353:384:418:455:495:539:586:638:694:755:822:894:973:1059 SD: 0.1427 cents 430:468:509:554:603:656:714:777:845:920:1001:1089:1185:1290 SD: 0.1187 cents 500:544:592:644:701:763:830:903:983:1070:1164:1267:1378:1500 SD: 0.1133 cents 510:555:604:657:715:778:847:921:1003:1091:1187:1292:1406:1530 SD: 0.1096 cents 544:592:644:701:763:830:903:983:1070:1164:1267:1378:1500:1632 SD: 0.1029 cents 554:603:656:714:777:845:920:1001:1089:1185:1290:1404:1527:1662 SD: 0.1026 cents 565:615:669:728:792:862:938:1021:1111:1209:1315:1431:1558:1695 SD: 0.0948 cents