Scala analysis: limx15
Linear 5-limit temperament with minor third as generator
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 67.970 cents 67.970000 2: 181.052 cents 181.052500 3: 249.023 cents 249.022500 4: 316.993 cents 316.992500 5: 384.962 cents 384.962500 6: 4/3 498.044999 perfect fourth 7: 566.015 cents 566.015000 8: 633.985 cents 633.985000 9: 3/2 701.955001 perfect fifth 10: 815.038 cents 815.037500 11: 883.007 cents 883.007500 12: 950.977 cents 950.977500 13: 1018.947 cents 1018.947500 14: 1132.030 cents 1132.030000 15: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 67.9700 cents 67.9700 1: 67.9700 cents 67.9700 2: 113.0825 cents 113.0825 3: 67.9700 cents 67.9700 4: 67.9700 cents 67.9700 5: 67.9700 cents 67.9700 6: 113.0825 cents 113.0825 7: 67.9700 cents 67.9700 8: 67.9700 cents 67.9700 9: 67.9700 cents 67.9700 10: 113.0825 cents 113.0825 11: 67.9700 cents 67.9700 12: 67.9700 cents 67.9700 13: 67.9700 cents 67.9700 14: 113.0825 cents 113.0825 15: 67.9700 cents 67.9700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 67.97000 cents 1: 4 113.08250 cents 2: 7 135.94000 cents 2: 8 181.05250 cents 3: 3 203.91000 cents 3: 12 249.02250 cents 4: 14 316.99250 cents 4: 1 362.10500 cents 5: 10 384.96250 cents 5: 5 430.07500 cents 6: 6 452.93250 cents 6: 9 4/3 498.045 cents perfect fourth 7: 2 520.90250 cents 7: 13 566.01500 cents 8: 13 633.98500 cents 8: 2 679.09750 cents 9: 9 3/2 701.955 cents perfect fifth 9: 6 747.06750 cents 10: 5 769.92500 cents 10: 10 815.03750 cents 11: 1 837.89500 cents 11: 14 883.00750 cents 12: 12 950.97750 cents 12: 3 996.09000 cents 13: 8 1018.94750 cents 13: 7 1064.06000 cents 14: 4 1086.91750 cents 14: 11 1132.03000 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 13 14 15 0.0 : 68.0 181.1 249.0 317.0 385.0 498.0 566.0 634.0 702.0 815.0 883.0 951.0 1018.9 1132.0 1200.0 68.0 : 113.1 181.1 249.0 317.0 430.1 498.0 566.0 634.0 747.1 815.0 883.0 951.0 1064.1 1132.0 1200.0 181.1 : 68.0 135.9 203.9 317.0 385.0 452.9 520.9 634.0 702.0 769.9 837.9 951.0 1018.9 1086.9 1200.0 249.0 : 68.0 135.9 249.0 317.0 385.0 452.9 566.0 634.0 702.0 769.9 883.0 951.0 1018.9 1132.0 1200.0 317.0 : 68.0 181.1 249.0 317.0 385.0 498.0 566.0 634.0 702.0 815.0 883.0 951.0 1064.1 1132.0 1200.0 385.0 : 113.1 181.1 249.0 317.0 430.1 498.0 566.0 634.0 747.1 815.0 883.0 996.1 1064.1 1132.0 1200.0 498.0 : 68.0 135.9 203.9 317.0 385.0 452.9 520.9 634.0 702.0 769.9 883.0 951.0 1018.9 1086.9 1200.0 566.0 : 68.0 135.9 249.0 317.0 385.0 452.9 566.0 634.0 702.0 815.0 883.0 951.0 1018.9 1132.0 1200.0 634.0 : 68.0 181.1 249.0 317.0 385.0 498.0 566.0 634.0 747.1 815.0 883.0 951.0 1064.1 1132.0 1200.0 702.0 : 113.1 181.1 249.0 317.0 430.1 498.0 566.0 679.1 747.1 815.0 883.0 996.1 1064.1 1132.0 1200.0 815.0 : 68.0 135.9 203.9 317.0 385.0 452.9 566.0 634.0 702.0 769.9 883.0 951.0 1018.9 1086.9 1200.0 883.0 : 68.0 135.9 249.0 317.0 385.0 498.0 566.0 634.0 702.0 815.0 883.0 951.0 1018.9 1132.0 1200.0 951.0 : 68.0 181.1 249.0 317.0 430.1 498.0 566.0 634.0 747.1 815.0 883.0 951.0 1064.1 1132.0 1200.0 1018.9: 113.1 181.1 249.0 362.1 430.1 498.0 566.0 679.1 747.1 815.0 883.0 996.1 1064.1 1132.0 1200.0 1132.0: 68.0 135.9 249.0 317.0 385.0 452.9 566.0 634.0 702.0 769.9 883.0 951.0 1018.9 1086.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9700 .. 113.0825 cents 45.11250 cents 67.97000 cents 2: 135.9400 .. 181.0525 cents 45.11250 cents 22.85750 cents 3: 203.9100 .. 249.0225 cents 45.11250 cents 22.85750 cents 4: 316.9925 .. 362.1050 cents 45.11250 cents 67.97000 cents 5: 384.9625 .. 430.0750 cents 45.11250 cents 22.85750 cents 6: 452.9325 .. 498.0450 cents 45.11250 cents 22.85750 cents 7: 520.9025 .. 566.0150 cents 45.11250 cents 22.85750 cents 8: 633.9850 .. 679.0975 cents 45.11250 cents 67.97000 cents 9: 701.9550 .. 747.0675 cents 45.11250 cents 22.85750 cents 10: 769.9250 .. 815.0375 cents 45.11250 cents 22.85750 cents 11: 837.8950 .. 883.0075 cents 45.11250 cents 22.85750 cents 12: 950.9775 .. 996.0900 cents 45.11250 cents 67.97000 cents 13: 1018.9475 .. 1064.0600 cents 45.11250 cents 22.85750 cents 14: 1086.9175 .. 1132.0300 cents 45.11250 cents 22.85750 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 67.97000 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 113.08250 cents Average / Smallest step : 1.176990 Largest / Average step : 1.413531 Largest / Smallest step : 1.663712 Median interval of one step : 67.97000 cents, amount: 11 Most common interval of one step : 67.97000 cents, amount: 11 Least squares average step : 79.90298 cents, oct.: 1198.54476 cents Scale is strictly proper Scale has Myhill's property chromas: 45.11250 cents and 22.85750 cents, ratio: 1.973641 generators: 4 of 316.99250 cents and 11 of 883.00750 cents ET pair of linear temperament : 15&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1889-tone equal temperament with octave 2/1 degrees: 107 285 392 499 606 784 891 998 1105 1283 1390 1497 1604 1782 1889 generators: 499 and 1390 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAAABAAABA Step pattern size order : SLSSSLSSSLSSSLS Scale is a Constant Structure, by a margin of 22.85750 cents Scale diversity : 1.193692 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.473688 Rothenberg efficiency : 0.711111 redundancy: 0.288889 Efficiency x scale size : 10.666667 Number of different interval sizes : 28 = 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 : 22.85750 cents Most common intervals : 316.99250 cents & inv., amount: 14 Scale is a chain of 7 triads 0.0 316.992 633.985 cents Most common triad is 0.0 316.993 883.007 cents, amount: 13 Number of recognisable fifths : 9, average 701.9550 cents Scale contains two identical disjunct heptachords Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 Formal octave complements present : 15 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 7-8 -- 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: 12.9939 c. M:-21.0525 c. 19: 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 P M ME I SD: 5.1977 c. M:-8.4212 c. 34: 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2 SP M ME I SD: 2.8280 c. M:-4.5819 c. 53: 3 5 3 3 3 5 3 3 3 5 3 3 3 5 3 SP M DE I SD: 0.0491 c. M:-0.0796 c. 1041: 59 98 59 59 59 98 59 59 59 98 59 59 59 98 59 SP M DE I SD: 0.0449 c. M:-0.0727 c. 1094: 62 103 62 62 62 103 62 62 62 103 62 62 62 103 62 SP M DE I SD: 0.0403 c. M:-0.0653 c. 1147: 65 108 65 65 65 108 65 65 65 108 65 65 65 108 65 SP M DE I SD: 0.0362 c. M:-0.0586 c. 1200: 68 113 68 68 68 113 68 68 68 113 68 68 68 113 68 SP M DE I SD: 0.0324 c. M:-0.0525 c. 1253: 71 118 71 71 71 118 71 71 71 118 71 71 71 118 71 SP M DE I SD: 0.0290 c. M:-0.0469 c. 1306: 74 123 74 74 74 123 74 74 74 123 74 74 74 123 74 SP M DE I SD: 0.0258 c. M:-0.0418 c. 1359: 77 128 77 77 77 128 77 77 77 128 77 77 77 128 77 SP M DE I SD: 0.0229 c. M:-0.0370 c. 1412: 80 133 80 80 80 133 80 80 80 133 80 80 80 133 80 SP M DE I SD: 0.0202 c. M:-0.0327 c. 1465: 83 138 83 83 83 138 83 83 83 138 83 83 83 138 83 SP M DE I SD: 0.0177 c. M:-0.0286 c. 1518: 86 143 86 86 86 143 86 86 86 143 86 86 86 143 86 SP M DE I SD: 0.0153 c. M:-0.0248 c. 1571: 89 148 89 89 89 148 89 89 89 148 89 89 89 148 89 SP M DE I SD: 0.0132 c. M:-0.0213 c. 1624: 92 153 92 92 92 153 92 92 92 153 92 92 92 153 92 SP M DE I SD: 0.0111 c. M:-0.0180 c. 1677: 95 158 95 95 95 158 95 95 95 158 95 95 95 158 95 SP M DE I SD: 0.0092 c. M:-0.0149 c. 1730: 98 163 98 98 98 163 98 98 98 163 98 98 98 163 98 SP M DE I SD: 0.0074 c. M:-0.0120 c. 1783: 101 168 101 101 101 168 101 101 101 168 101 101 101 168 101 SP M DE I SD: 0.0057 c. M:-0.0093 c. 1836: 104 173 104 104 104 173 104 104 104 173 104 104 104 173 104 SP M DE I SD: 0.0042 c. M:-0.0067 c. 1889: 107 178 107 107 107 178 107 107 107 178 107 107 107 178 107 SP M DE I SD: 0.0027 c. M:-0.0043 c. 1942: 110 183 110 110 110 183 110 110 110 183 110 110 110 183 110 SP M DE I SD: 0.0013 c. M:-0.0020 c. 1995: 113 188 113 113 113 188 113 113 113 188 113 113 113 188 113 SP M DE I SD: 0.0001 c. M:-0.0001 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 0.0000 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 0.4504 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 4.4749 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 3.3325 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 5.8819 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 12.1753 cents 8 x 9 x x 10 x 11 x 12:13 x 14 x 15:16 S SD: 7.5246 cents 9 x 10 x 11 x 12 x 13 x 14:15 x 16:17:18 S SD: 7.8018 cents 10 x 11 x 12 x 13:14 x 15:16 x 17:18:19:20 S SD: 6.2736 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 8.0553 cents 12 x 13:14 x 15:16 x 17:18:19:20:21:22:23:24 S SD: 5.7388 cents 13 x 14:15 x 16:17:18:19:20:21:22 x 23:25:26 SD: 7.9050 cents 14:15 x 16:17 x 19 x 20:21:22:23:24:25:27:28 SD: 6.8377 cents 15:16 x 17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 5.6288 cents 16:17:18 x 19:20:21:22:23:24:26:27:28:29:31:32 SD: 5.0692 cents 17:18:19:20 x 21:23:24:25:26:27:28:29:31:33:34 SD: 6.5232 cents 18:19:20:21:22 x 24:25:26:27:29:30:31:32:35:36 SD: 3.9252 cents 20:21:22:23:24:25:27:28:29:30:32:33:35:36:38:40 SD: 3.2780 cents 24:25:27:28:29:30:32:33:35:36:38:40:42:43:46:48 SD: 3.2444 cents 25:26:28:29:30:31:33:35:36:38:40:42:43:45:48:50 SD: 2.9410 cents 30:31:33:35:36:37:40:42:43:45:48:50:52:54:58:60 SD: 2.7188 cents 36:37:40:42:43:45:48:50:52:54:58:60:62:65:69:72 SD: 2.2177 cents 44:46:49:51:53:55:59:61:63:66:70:73:76:79:85:88 SD: 1.7912 cents 45:47:50:52:54:56:60:62:65:68:72:75:78:81:87:90 SD: 1.4729 cents 52:54:58:60:62:65:69:72:75:78:83:87:90:94:100:104 SD: 1.3971 cents 56:58:62:65:67:70:75:78:81:84:90:93:97:101:108:112 SD: 1.3936 cents 60:62:67:69:72:75:80:83:87:90:96:100:104:108:115:120 SD: 1.3703 cents 64:67:71:74:77:80:85:89:92:96:102:107:111:115:123:128 SD: 1.3111 cents 65:68:72:75:78:81:87:90:94:98:104:108:113:117:125:130 SD: 1.2472 cents 70:73:78:81:84:87:93:97:101:105:112:117:121:126:135:140 SD: 1.0975 cents 72:75:80:83:86:90:96:100:104:108:115:120:125:130:138:144 SD: 0.9599 cents 80:83:89:92:96:100:107:111:115:120:128:133:139:144:154:160 SD: 0.9235 cents 90:94:100:104:108:112:120:125:130:135:144:150:156:162:173:180 SD: 0.7335 cents 108:112:120:125:130:135:144:150:156:162:173:180:187:195:208:216 SD: 0.6688 cents 116:121:129:134:139:145:155:161:167:174:186:193:201:209:223:232 SD: 0.6187 cents 120:125:133:139:144:150:160:166:173:180:192:200:208:216:231:240 SD: 0.5896 cents 129:134:143:149:155:161:172:179:186:194:207:215:223:232:248:258 SD: 0.5614 cents 144:150:160:166:173:180:192:200:208:216:231:240:249:259:277:288 SD: 0.5230 cents 153:159:170:177:184:191:204:212:221:230:245:255:265:276:294:306 SD: 0.4864 cents 156:162:173:180:187:195:208:216:225:234:250:260:270:281:300:312 SD: 0.4056 cents 180:187:200:208:216:225:240:250:260:270:288:300:312:324:346:360 SD: 0.3809 cents 200:208:222:231:240:250:267:277:288:300:320:333:346:360:385:400 SD: 0.3763 cents 201:209:223:232:241:251:268:279:290:302:322:335:348:362:387:402 SD: 0.3603 cents 220:229:244:254:264:275:293:305:317:330:352:366:381:396:423:440 SD: 0.3176 cents 228:237:253:263:274:285:304:316:329:342:365:380:395:411:438:456 SD: 0.2704 cents 246:256:273:284:295:307:328:341:355:369:394:410:426:443:473:492 SD: 0.2512 cents 298:310:331:344:358:372:397:413:430:447:477:496:516:537:573:596 SD: 0.1899 cents 354:368:393:409:425:442:472:491:511:531:567:590:613:638:681:708 SD: 0.1893 cents 373:388:414:431:448:466:497:517:538:560:597:621:646:672:717:746 SD: 0.1860 cents 374:389:415:432:449:467:499:519:539:561:599:623:648:674:719:748 SD: 0.1853 cents 398:414:442:460:478:497:531:552:574:597:637:663:689:717:765:796 SD: 0.1721 cents 418:435:464:483:502:522:557:580:603:627:669:696:724:753:804:836 SD: 0.1633 cents 452:470:502:522:543:565:603:627:652:678:724:753:783:814:869:904 SD: 0.1506 cents 454:472:504:524:545:567:605:630:655:681:727:756:786:818:873:908 SD: 0.1489 cents 478:497:531:552:574:597:637:663:689:717:765:796:828:861:919:956 SD: 0.1370 cents 498:518:553:575:598:622:664:691:718:747:797:829:863:897:958:996 SD: 0.1362 cents 518:539:575:598:622:647:691:718:747:777:829:863:897:933:996:1036 SD: 0.1321 cents 522:543:580:603:627:652:696:724:753:783:836:869:904:940:1004:1044 SD: 0.1297 cents 574:597:637:663:689:717:765:796:828:861:919:956:994:1034:1104:1148 SD: 0.1065 cents 582:605:646:672:699:727:776:807:839:873:932:969:1008:1048:1119:1164 SD: 0.1042 cents