Scala analysis: sonic15
A distributionally even scale in sonic temperament, abababababababc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96.020 cents 96.020000 2: 164.120 cents 164.120000 3: 215.600 cents 215.600000 4: 311.620 cents 311.620000 5: 379.720 cents 379.720000 6: 475.740 cents 475.740000 7: 543.840 cents 543.840000 8: 639.860 cents 639.860000 9: 707.960 cents 707.960000 10: 803.980 cents 803.980000 11: 872.080 cents 872.080000 12: 968.100 cents 968.100000 13: 1036.200 cents 1036.200000 14: 1132.220 cents 1132.220000 15: 1200.320 cents 1200.320000
SHOW/INTERVAL
0: 68.1000 cents 68.1000 1: 96.0200 cents 96.0200 2: 68.1000 cents 68.1000 3: 51.4800 cents 51.4800 4: 96.0200 cents 96.0200 5: 68.1000 cents 68.1000 6: 96.0200 cents 96.0200 7: 68.1000 cents 68.1000 8: 96.0200 cents 96.0200 9: 68.1000 cents 68.1000 10: 96.0200 cents 96.0200 11: 68.1000 cents 68.1000 12: 96.0200 cents 96.0200 13: 68.1000 cents 68.1000 14: 96.0200 cents 96.0200 15: 68.1000 cents 68.1000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 51.48000 cents 1: 7 68.10000 cents 1: 7 96.02000 cents 2: 1 119.58000 cents 2: 1 147.50000 cents 2: 13 164.12000 cents 3: 3 215.60000 cents 3: 6 232.22000 cents 3: 6 260.14000 cents 4: 2 283.70000 cents 4: 2 311.62000 cents 4: 11 328.24000 cents 5: 5 379.72000 cents 5: 5 396.34000 cents 5: 5 424.26000 cents 6: 3 447.82000 cents 6: 3 475.74000 cents 6: 9 492.36000 cents 7: 7 543.84000 cents 7: 4 560.46000 cents 7: 4 588.38000 cents 8: 4 611.94000 cents 8: 4 639.86000 cents 8: 7 656.48000 cents 9: 9 707.96000 cents 9: 3 724.58000 cents 9: 3 752.50000 cents 10: 5 776.06000 cents 10: 5 803.98000 cents 10: 5 820.60000 cents 11: 11 872.08000 cents 11: 2 888.70000 cents 11: 2 916.62000 cents 12: 6 940.18000 cents 12: 6 968.10000 cents 12: 3 984.72000 cents 13: 13 1036.20000 cents 13: 1 1052.82000 cents 13: 1 1080.74000 cents 14: 7 1104.30000 cents 14: 7 1132.22000 cents 14: 1 1148.84000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 96.0 164.1 215.6 311.6 379.7 475.7 543.8 639.9 708.0 804.0 872.1 968.1 1036.2 1132.2 1200.3 96.0 : 68.1 119.6 215.6 283.7 379.7 447.8 543.8 611.9 708.0 776.1 872.1 940.2 1036.2 1104.3 1200.3 164.1 : 51.5 147.5 215.6 311.6 379.7 475.7 543.8 639.9 708.0 804.0 872.1 968.1 1036.2 1132.2 1200.3 215.6 : 96.0 164.1 260.1 328.2 424.3 492.4 588.4 656.5 752.5 820.6 916.6 984.7 1080.7 1148.8 1200.3 311.6 : 68.1 164.1 232.2 328.2 396.3 492.4 560.5 656.5 724.6 820.6 888.7 984.7 1052.8 1104.3 1200.3 379.7 : 96.0 164.1 260.1 328.2 424.3 492.4 588.4 656.5 752.5 820.6 916.6 984.7 1036.2 1132.2 1200.3 475.7 : 68.1 164.1 232.2 328.2 396.3 492.4 560.5 656.5 724.6 820.6 888.7 940.2 1036.2 1104.3 1200.3 543.8 : 96.0 164.1 260.1 328.2 424.3 492.4 588.4 656.5 752.5 820.6 872.1 968.1 1036.2 1132.2 1200.3 639.9 : 68.1 164.1 232.2 328.2 396.3 492.4 560.5 656.5 724.6 776.1 872.1 940.2 1036.2 1104.3 1200.3 708.0 : 96.0 164.1 260.1 328.2 424.3 492.4 588.4 656.5 708.0 804.0 872.1 968.1 1036.2 1132.2 1200.3 804.0 : 68.1 164.1 232.2 328.2 396.3 492.4 560.5 611.9 708.0 776.1 872.1 940.2 1036.2 1104.3 1200.3 872.1 : 96.0 164.1 260.1 328.2 424.3 492.4 543.8 639.9 708.0 804.0 872.1 968.1 1036.2 1132.2 1200.3 968.1 : 68.1 164.1 232.2 328.2 396.3 447.8 543.8 611.9 708.0 776.1 872.1 940.2 1036.2 1104.3 1200.3 1036.2: 96.0 164.1 260.1 328.2 379.7 475.7 543.8 639.9 708.0 804.0 872.1 968.1 1036.2 1132.2 1200.3 1132.2: 68.1 164.1 232.2 283.7 379.7 447.8 543.8 611.9 708.0 776.1 872.1 940.2 1036.2 1104.3 1200.3 1200.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.4800 .. 96.0200 cents 44.54000 cents 51.48000 cents 2: 119.5800 .. 164.1200 cents 44.54000 cents 23.56000 cents 3: 215.6000 .. 260.1400 cents 44.54000 cents 51.48000 cents 4: 283.7000 .. 328.2400 cents 44.54000 cents 23.56000 cents 5: 379.7200 .. 424.2600 cents 44.54000 cents 51.48000 cents 6: 447.8200 .. 492.3600 cents 44.54000 cents 23.56000 cents 7: 543.8400 .. 588.3800 cents 44.54000 cents 51.48000 cents 8: 611.9400 .. 656.4800 cents 44.54000 cents 23.56000 cents 9: 707.9600 .. 752.5000 cents 44.54000 cents 51.48000 cents 10: 776.0600 .. 820.6000 cents 44.54000 cents 23.56000 cents 11: 872.0800 .. 916.6200 cents 44.54000 cents 51.48000 cents 12: 940.1800 .. 984.7200 cents 44.54000 cents 23.56000 cents 13: 1036.2000 .. 1080.7400 cents 44.54000 cents 51.48000 cents 14: 1104.3000 .. 1148.8400 cents 44.54000 cents 23.56000 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 51.48000 cents, class 1 Average step (divided formal octave): 80.0213 cents Largest one step interval : 96.02000 cents Average / Smallest step : 1.554416 Largest / Average step : 1.199930 Largest / Smallest step : 1.865190 Median interval of one step : 68.10000 cents, amount: 7 Least squares average step : 79.79382 cents, oct.: 1196.90734 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABABABABABAB Step pattern size order : LMSLMLMLMLMLMLM Scale is a Constant Structure, by a margin of 23.56000 cents Scale diversity : 1.324399 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.480505 Number of different interval sizes : 42 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 16.62000 cents Most common intervals : 164.12000 cents & inv., amount: 13 Scale is a chain of 7 triads 0.0 96.020 164.120 cents Most common triad is 0.0 164.120 1036.200 cents, amount: 11 Number of recognisable fifths : 9, average 707.9600 cents Number of recognisable fourths : 9, average 492.3600 cents Best minor thirds form a closed circle Formal octave complements present : 3 = 20.0000% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.8160 c. M:-24.4640 c. 22: 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 P M ME S SD: 9.9290 c. M:-15.7400 c. 34: 3 2 1 3 2 2 2 3 2 3 2 2 2 3 2 P T3 SD: 9.8084 c. M: 16.7941 c. 35: 3 2 1 3 2 3 2 3 2 2 2 3 2 3 2 P D3 SD: 8.5888 c. M: 15.1983 c. 36: 3 2 1 3 2 3 2 3 2 3 2 3 2 3 2 P T3 SD: 7.7674 c. M: 15.5467 c. 37: 3 2 2 3 2 3 2 3 2 3 2 3 2 3 2 SP M ME S SD: 7.2457 c. M:-12.7908 c. 45: 4 2 2 4 2 4 2 4 3 3 3 3 3 3 3 P SD: 7.4117 c. M:-12.2320 c. 50: 4 3 2 4 3 4 3 4 2 4 3 4 3 4 3 P SD: 6.4470 c. M: 11.7744 c. 51: 4 3 2 4 3 4 3 4 3 4 3 4 3 4 3 SP T3 SD: 3.1296 c. M: 5.6561 c. 66: 5 4 3 5 4 5 4 5 4 5 4 5 4 5 4 SP T3 SD: 2.8583 c. M: 5.0867 c. 73: 6 4 3 6 4 6 4 6 4 6 4 6 4 6 4 SP T3 SD: 1.4585 c. M:-2.6364 c. 88: 7 5 4 7 5 7 5 7 5 7 5 7 5 7 5 SP T3 SD: 1.3538 c. M:-2.6400 c. 124: 10 7 5 10 7 10 7 10 7 10 7 10 7 10 7 SP T3 SD: 1.2980 c. M: 2.6400 c. 139: 11 8 6 11 8 11 8 11 8 11 8 11 8 11 8 SP T3 SD: 0.6214 c. M: 1.0306 c. 212: 17 12 9 17 12 17 12 17 12 17 12 17 12 17 12 SP T3 SD: 0.2114 c. M: 0.4483 c. 351: 28 20 15 28 20 28 20 28 20 28 20 28 20 28 20 SP T3 SD: 0.2484 c. M: 0.4259 c. 439: 35 25 19 35 25 35 25 35 25 35 25 35 25 35 25 SP T3 SD: 0.2072 c. M:-0.4029 c. 512: 41 29 22 41 29 41 29 41 29 41 29 41 29 41 29 SP T3 SD: 0.1036 c. M:-0.1819 c. 651: 52 37 28 52 37 52 37 52 37 52 37 52 37 52 37 SP T3 SD: 0.0802 c. M: 0.1419 c. 724: 58 41 31 58 41 58 41 58 41 58 41 58 41 58 41 SP T3 SD: 0.0776 c. M:-0.1382 c. 863: 69 49 37 69 49 69 49 69 49 69 49 69 49 69 49 SP T3 SD: 0.0401 c. M: 0.0653 c. 1375: 110 78 59 110 78 110 78 110 78 110 78 110 78 110 78 SP T3 SD: 0.0149 c. M:-0.0267 c. 2238: 179 127 96 179 127 179 127 179 127 179 127 179 127 179 127 SP T3 SD: 0.0090 c. M: 0.0159 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 0.3200 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 3.0068 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 8.4878 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 2.2384 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 8.8366 cents 6 x x x 7 x 8 x x 9 x 10 x 11 x 12 S SD: 8.9135 cents 7 x x 8 x x 9 x 10 x 11 x 12:13 x 14 S SD: 10.4404 cents 8 x x 9 x 10 x 11 x 12 x 13:14 x 15:16 S SD: 7.0711 cents 9 x 10 x x 11:12 x 13 x 14:15:16 x 17:18 S SD: 8.1032 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 7.1149 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 6.6479 cents 12 x 13 x 14:15:16 x 17:18:19:20:21:22:23:24 S SD: 5.9051 cents 13:14 x 15 x 16:17:18:19:20:21:22:23:24:25:26 S SD: 6.8501 cents 14:15 x 16:17 x 18:19:20:21:22:23:24:25:27:28 SD: 6.3097 cents 15:16 x 17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 5.3540 cents 16:17 x 18:19:20:21:22:23:24:25:26:28:29:31:32 SD: 3.8446 cents 17:18 x 19:20:21:22:23:25:26:27:28:30:31:33:34 SD: 5.0765 cents 18:19:20 x x 22:24:25:26:27:29:30:31:33:35:36 SD: 5.1202 cents 20:21:22:23:24:25:26:27:29:30:32:33:35:36:38:40 SD: 3.5893 cents 26:27:29 x 31:32:34:36:38:39:41:43:45:47:50:52 SD: 4.2661 cents 27:29:30:31:32:34:36:37:39:41:43:45:47:49:52:54 SD: 3.8478 cents 28:30:31:32:34:35:37:38:41:42:45:46:49:51:54:56 SD: 3.5268 cents 29:31:32:33:35:36:38:40:42:44:46:48:51:53:56:58 SD: 2.4476 cents 32:34:35:36:38:40:42:44:46:48:51:53:56:58:62:64 SD: 2.1185 cents 40:42:44:45:48:50:53:55:58:60:64:66:70:73:77:80 SD: 1.7848 cents 49:52:54:56:59:61:64:67:71:74:78:81:86:89:94:98 SD: 1.7536 cents 51:54:56:58:61:64:67:70:74:77:81:84:89:93:98:102 SD: 1.3909 cents 52:55:57:59:62:65:68:71:75:78:83:86:91:95:100:104 SD: 1.3885 cents 60:63:66:68:72:75:79:82:87:90:95:99:105:109:115:120 SD: 1.3197 cents 67:71:74:76:80:83:88:92:97:101:107:111:117:122:129:134 SD: 1.1510 cents 69:73:76:78:83:86:91:94:100:104:110:114:121:126:133:138 SD: 1.1220 cents 70:74:77:79:84:87:92:96:101:105:111:116:122:127:135:140 SD: 1.0996 cents 73:77:80:83:87:91:96:100:106:110:116:121:128:133:140:146 SD: 1.0636 cents 76:80:84:86:91:95:100:104:110:114:121:126:133:138:146:152 SD: 1.0473 cents 81:86:89:92:97:101:107:111:117:122:129:134:142:147:156:162 SD: 0.9068 cents 89:94:98:101:107:111:117:122:129:134:142:147:156:162:171:178 SD: 0.8106 cents 101:107:111:114:121:126:133:138:146:152:161:167:177:184:194:202 SD: 0.7050 cents 105:111:115:119:126:131:138:144:152:158:167:174:184:191:202:210 SD: 0.6810 cents 121:128:133:137:145:151:159:166:175:182:193:200:212:220:233:242 SD: 0.5958 cents 127:134:140:144:152:158:167:174:184:191:202:210:222:231:244:254 SD: 0.4958 cents 143:151:157:162:171:178:188:196:207:215:228:237:250:260:275:286 SD: 0.4645 cents 159:168:175:180:190:198:209:218:230:239:253:263:278:289:306:318 SD: 0.4186 cents 188:199:207:213:225:234:247:257:272:283:299:311:329:342:362:376 SD: 0.4048 cents 192:203:211:217:230:239:253:263:278:289:305:318:336:349:369:384 SD: 0.3968 cents 203:215:223:230:243:253:267:278:294:306:323:336:355:369:390:406 SD: 0.3813 cents 208:220:229:236:249:259:274:285:301:313:331:344:364:378:400:416 SD: 0.3425 cents 211:223:232:239:253:263:278:289:305:318:336:349:369:384:406:422 SD: 0.3411 cents 212:224:233:240:254:264:279:290:307:319:337:351:371:386:408:424 SD: 0.2472 cents 293:310:322:332:351:365:386:401:424:441:466:485:513:533:564:586 SD: 0.2454 cents 301:318:331:341:360:375:396:412:436:453:479:498:527:548:579:602 SD: 0.2357 cents 315:333:346:357:377:392:415:431:456:474:501:521:551:573:606:630 SD: 0.2249 cents 331:350:364:375:396:412:436:453:479:498:527:548:579:602:637:662 SD: 0.2019 cents 354:374:389:401:424:441:466:485:512:533:563:586:619:644:681:708 SD: 0.1774 cents 420:444:462:476:503:523:553:575:608:632:668:695:735:764:808:840 SD: 0.1441 cents 452:478:497:512:541:563:595:619:654:680:719:748:791:822:869:904 SD: 0.1349 cents 521:551:573:590:624:649:686:713:754:784:829:862:911:948:1002:1042 SD: 0.1317 cents 542:573:596:614:649:675:713:742:784:816:862:897:948:986:1042:1084 SD: 0.1209 cents 543:574:597:615:650:676:715:743:786:817:864:899:950:988:1044:1086 SD: 0.1207 cents 582:615:640:659:697:725:766:797:842:876:926:963:1018:1059:1119:1164 SD: 0.0999 cents