Scala analysis: archytas12_tuning-math_19356_19356
A distributionally even scale in archytas (64/63 planar) temperament, ababacbababc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 121.030 cents 121.030000 2: 218.090 cents 218.090000 3: 271.350 cents 271.350000 4: 392.380 cents 392.380000 5: 489.440 cents 489.440000 6: 610.470 cents 610.470000 7: 707.530 cents 707.530000 8: 828.560 cents 828.560000 9: 881.820 cents 881.820000 10: 978.880 cents 978.880000 11: 1099.910 cents 1099.910000 12: 1196.970 cents 1196.970000
SHOW/INTERVAL
0: 97.0600 cents 97.0600 1: 121.0300 cents 121.0300 2: 97.0600 cents 97.0600 3: 53.2600 cents 53.2600 4: 121.0300 cents 121.0300 5: 97.0600 cents 97.0600 6: 121.0300 cents 121.0300 7: 97.0600 cents 97.0600 8: 121.0300 cents 121.0300 9: 53.2600 cents 53.2600 10: 97.0600 cents 97.0600 11: 121.0300 cents 121.0300 12: 97.0600 cents 97.0600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 53.26000 cents 1: 5 97.06000 cents 1: 5 121.03000 cents 2: 2 150.32000 cents 2: 2 174.29000 cents 2: 8 218.09000 cents 3: 6 271.35000 cents 3: 3 315.15000 cents 3: 3 339.12000 cents 4: 4 368.41000 cents 4: 4 392.38000 cents 4: 4 436.18000 cents 5: 10 489.44000 cents 5: 1 533.24000 cents 5: 1 557.21000 cents 6: 6 586.50000 cents 6: 6 610.47000 cents 7: 1 639.76000 cents 7: 1 663.73000 cents 7: 10 707.53000 cents 8: 4 760.79000 cents 8: 4 804.59000 cents 8: 4 828.56000 cents 9: 3 857.85000 cents 9: 3 881.82000 cents 9: 6 925.62000 cents 10: 8 978.88000 cents 10: 2 1022.68000 cents 10: 2 1046.65000 cents 11: 5 1075.94000 cents 11: 5 1099.91000 cents 11: 2 1143.71000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.90909 = 32/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 121.0 218.1 271.3 392.4 489.4 610.5 707.5 828.6 881.8 978.9 1099.9 1197.0 121.0 : 97.1 150.3 271.3 368.4 489.4 586.5 707.5 760.8 857.8 978.9 1075.9 1197.0 218.1 : 53.3 174.3 271.4 392.4 489.4 610.5 663.7 760.8 881.8 978.9 1099.9 1197.0 271.3 : 121.0 218.1 339.1 436.2 557.2 610.5 707.5 828.6 925.6 1046.7 1143.7 1197.0 392.4 : 97.1 218.1 315.1 436.2 489.4 586.5 707.5 804.6 925.6 1022.7 1075.9 1197.0 489.4 : 121.0 218.1 339.1 392.4 489.4 610.5 707.5 828.6 925.6 978.9 1099.9 1197.0 610.5 : 97.1 218.1 271.3 368.4 489.4 586.5 707.5 804.6 857.8 978.9 1075.9 1197.0 707.5 : 121.0 174.3 271.4 392.4 489.4 610.5 707.5 760.8 881.8 978.9 1099.9 1197.0 828.6 : 53.3 150.3 271.3 368.4 489.4 586.5 639.8 760.8 857.8 978.9 1075.9 1197.0 881.8 : 97.1 218.1 315.2 436.2 533.2 586.5 707.5 804.6 925.6 1022.7 1143.7 1197.0 978.9 : 121.0 218.1 339.1 436.2 489.4 610.5 707.5 828.6 925.6 1046.7 1099.9 1197.0 1099.9: 97.1 218.1 315.1 368.4 489.4 586.5 707.5 804.6 925.6 978.9 1075.9 1197.0 1197.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.2600 .. 121.0300 cents 67.77000 cents 53.26000 cents 2: 150.3200 .. 218.0900 cents 67.77000 cents 29.29000 cents 3: 271.3500 .. 339.1200 cents 67.77000 cents 53.26000 cents 4: 368.4100 .. 436.1800 cents 67.77000 cents 29.29000 cents 5: 489.4400 .. 557.2100 cents 67.77000 cents 53.26000 cents 6: 586.5000 .. 610.4700 cents 23.97000 cents 29.29000 cents 7: 639.7600 .. 707.5300 cents 67.77000 cents 29.29000 cents 8: 760.7900 .. 828.5600 cents 67.77000 cents 53.26000 cents 9: 857.8500 .. 925.6200 cents 67.77000 cents 29.29000 cents 10: 978.8800 .. 1046.6500 cents 67.77000 cents 53.26000 cents 11: 1075.9400 .. 1143.7100 cents 67.77000 cents 29.29000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 53.26000 cents, class 1 Average step (divided formal octave): 99.7475 cents Largest one step interval : 121.03000 cents Average / Smallest step : 1.872841 Largest / Average step : 1.213364 Largest / Smallest step : 2.272437 Median interval of one step : 97.06000 cents, amount: 5 Least squares average step : 99.72280 cents, oct.: 1196.67360 cents Scale is strictly proper Scale is 3-distributional even Step pattern alph. order: ABCABABACBAB Step pattern size order : LMSLMLMLSMLM Scale is a Constant Structure, by a margin of 29.29000 cents Scale diversity : 1.372118 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.413795 Rothenberg efficiency : 0.514153 redundancy: 0.485847 Efficiency x scale size : 6.169841 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.90909 = 32/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 23.97000 cents Most common intervals : 489.44000 cents & inv., amount: 10 Most common triad is 0.0 489.440 707.530 cents, amount: 8 Number of recognisable fifths : 10, average 707.5300 cents Number of recognisable fourths : 10, average 489.4400 cents Formal octave complements present : 5 = 41.6667% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.0248 c. M: 30.5800 c. Twelve-tone Chromatic (1/11-comma) 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 18.6189 c. M:-33.5100 c. Twelve-tone Chromatic (2/11-comma positive) 22: 2 2 1 2 2 2 2 2 1 2 2 2 SP B ME SD: 8.4031 c. M: 12.4441 c. Jubilee-12 27: 3 2 1 3 2 3 2 3 1 2 3 2 P D3 SD: 7.2687 c. M:-13.7522 c. 39: 4 3 2 4 3 4 3 4 2 3 4 3 SP D3 SD: 4.0909 c. M:-8.2346 c. 49: 5 4 2 5 4 5 4 5 2 4 5 4 SP D3 SD: 1.5434 c. M: 2.6424 c. 88: 9 7 4 9 7 9 7 9 4 7 9 7 SP D3 SD: 1.2883 c. M:-2.3056 c. 110: 11 9 5 11 9 11 9 11 5 9 11 9 SP D3 SD: 0.8056 c. M: 1.5625 c. 137: 14 11 6 14 11 14 11 14 6 11 14 11 SP D3 SD: 0.7892 c. M:-1.4557 c. 159: 16 13 7 16 13 16 13 16 7 13 16 13 SP D3 SD: 0.5650 c. M: 1.0308 c. 198: 20 16 9 20 16 20 16 20 9 16 20 16 SP D3 SD: 0.4296 c. M:-0.7942 c. 247: 25 20 11 25 20 25 20 25 11 20 25 20 SP D3 SD: 0.0966 c. M:-0.1579 c. 653: 66 53 29 66 53 66 53 66 29 53 66 53 SP D3 SD: 0.0671 c. M: 0.1315 c. 851: 86 69 38 86 69 86 69 86 38 69 86 69 SP D3 SD: 0.0662 c. M:-0.1132 c. 900: 91 73 40 91 73 91 73 91 40 73 91 73 SP D3 SD: 0.0262 c. M: 0.0521 c. 1147: 116 93 51 116 93 116 93 116 51 93 116 93 SP D3 SD: 0.0159 c. M:-0.0313 c. 2047: 207 166 91 207 166 207 166 207 91 166 207 166 SP D3 SD: 0.0170 c. M: 0.0290 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 3.0300 cents 2 x x x x x x 3 x x x x 4 S SD: 3.1726 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.1565 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 3.3368 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.3757 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.6535 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 12.0071 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.0593 cents 9 x 10 x 11:12:13:14 x 15:16:17:18 S SD: 9.7246 cents 10:11 x 12 x 13:14:15:16:17:18:19:20 S SD: 9.5717 cents 11:12 x 13:14:15:16:17:18 x 19:21:22 SD: 9.8527 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 4.4803 cents 13:14 x 15:16:17:19:20:21:22:23:25:26 SD: 8.0863 cents 14:15:16 x 18:19:20:21 x 23:25:26:28 SD: 7.4461 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 6.2166 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 4.4442 cents 19:20 x 22:24:25:27:29:31:32:33:36:38 SD: 5.5120 cents 20:21:23 x 25:27:28:30:32:33:35:38:40 SD: 5.9908 cents 21:23:24:25:26:28:30:32:34:35:37:40:42 SD: 5.1578 cents 22:24:25:26:28:29:31:33:36:37:39:42:44 SD: 5.0864 cents 23:25:26:27:29:31:33:35:37:38:40:43:46 SD: 4.5167 cents 24:26:27:28:30:32:34:36:39:40:42:45:48 S SD: 2.7914 cents 28:30:32:33:35:37:40:42:45:47:49:53:56 SD: 2.5213 cents 36:39:41:42:45:48:51:54:58:60:63:68:72 SD: 2.2076 cents 42:45:48:49:53:56:60:63:68:70:74:79:84 SD: 1.9419 cents 51:55:58:60:64:68:73:77:82:85:90:96:102 SD: 1.9193 cents 52:56:59:61:65:69:74:78:84:87:92:98:104 SD: 1.5117 cents 54:58:61:63:68:72:77:81:87:90:95:102:108 SD: 1.3643 cents 59:63:67:69:74:78:84:89:95:98:104:111:118 SD: 1.1533 cents 71:76:81:83:89:94:101:107:115:118:125:134:142 SD: 1.1429 cents 82:88:93:96:103:109:117:123:132:136:144:155:164 SD: 1.0566 cents 83:89:94:97:104:110:118:125:134:138:146:157:166 SD: 0.5680 cents 125:134:142:146:157:166:178:188:202:208:220:236:250 SD: 0.5239 cents 165:177:187:193:207:219:235:248:266:275:290:311:329 SD: 0.5147 cents 166:178:188:194:208:220:236:250:268:276:292:313:331 SD: 0.4784 cents 178:191:202:208:223:236:253:268:287:296:313:336:355 SD: 0.4192 cents 194:208:220:227:243:257:276:292:313:323:341:366:387 SD: 0.4028 cents 196:210:222:229:246:260:279:295:316:326:345:370:391 SD: 0.3715 cents 208:223:236:243:261:276:296:313:336:346:366:393:415 SD: 0.3032 cents 248:266:281:290:311:329:353:373:400:413:437:468:495 SD: 0.2823 cents 260:279:295:304:326:345:370:391:420:433:458:491:519 SD: 0.2725 cents 275:295:312:322:345:365:391:414:444:458:484:519:549 SD: 0.2447 cents 319:342:362:373:400:423:454:480:515:531:562:602:637 SD: 0.2055 cents 358:384:406:419:449:475:509:539:578:596:630:676:715 SD: 0.1939 cents 388:416:440:454:487:515:552:584:626:646:683:732:775 SD: 0.1839 cents 456:489:517:533:572:605:649:686:736:759:803:861:910 SD: 0.1696 cents 471:505:534:551:591:625:670:709:760:784:829:889:940 SD: 0.1232 cents 554:594:628:648:695:735:788:834:894:922:975:1046:1106 SD: 0.1223 cents 566:607:642:662:710:751:805:852:913:942:996:1068:1130 SD: 0.1188 cents 596:639:676:697:748:791:848:897:962:992:1049:1125:1190 SD: 0.1078 cents