Scala analysis: whelp2
well-temperament with two pure thirds
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 91.657 cents 91.656592 2: 192.721 cents 192.721296 3: 293.612 cents 293.611776 4: 386.314 cents 386.313714 5: 493.767 cents 493.766642 6: 591.637 cents 591.637234 7: 699.090 cents 699.090162 8: 791.792 cents 791.792100 9: 892.683 cents 892.682580 10: 993.747 cents 993.747284 11: 1085.404 cents 1085.403876 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 114.5961 cents 114.5961 1: 91.6566 cents 91.6566 2: 101.0647 cents 101.0647 3: 100.8905 cents 100.8905 4: 92.7019 cents 92.7019 5: 107.4529 cents 107.4529 6: 97.8706 cents 97.8706 7: 107.4529 cents 107.4529 8: 92.7019 cents 92.7019 9: 100.8905 cents 100.8905 10: 101.0647 cents 101.0647 11: 91.6566 cents 91.6566 12: 114.5961 cents 114.5961
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 91.65659 cents 1: 2 92.70194 cents 1: 1 97.87059 cents 1: 2 100.89048 cents 1: 2 101.06470 cents 1: 2 107.45293 cents 1: 1 114.59612 cents 2: 2 192.72130 cents 2: 2 193.59242 cents 2: 2 200.15487 cents 2: 2 201.95518 cents 2: 2 205.32352 cents 2: 2 206.25272 cents 3: 2 293.61178 cents 3: 2 294.65712 cents 3: 1 297.90931 cents 3: 2 298.02546 cents 3: 2 301.04535 cents 3: 2 307.31742 cents 3: 1 312.77645 cents 4: 2 386.31371 cents 4: 2 398.91594 cents 4: 2 398.97401 cents 4: 2 402.11005 cents 4: 2 405.47839 cents 4: 2 408.20790 cents 5: 2 493.76664 cents 5: 1 498.18032 cents 5: 2 499.86449 cents 5: 2 499.98064 cents 5: 1 500.03872 cents 5: 2 500.90984 cents 5: 2 506.36887 cents 6: 2 591.63723 cents 6: 2 592.56643 cents 6: 2 599.07080 cents 6: 2 600.92920 cents 6: 2 607.43357 cents 6: 2 608.36277 cents 7: 2 693.63113 cents 7: 2 699.09016 cents 7: 1 699.96128 cents 7: 2 700.01936 cents 7: 2 700.13551 cents 7: 1 701.81968 cents 7: 2 706.23336 cents 8: 2 791.79210 cents 8: 2 794.52161 cents 8: 2 797.88995 cents 8: 2 801.02599 cents 8: 2 801.08406 cents 8: 2 813.68629 cents 9: 1 887.22355 cents 9: 2 892.68258 cents 9: 2 898.95465 cents 9: 2 901.97454 cents 9: 1 902.09069 cents 9: 2 905.34288 cents 9: 2 906.38822 cents 10: 2 993.74728 cents 10: 2 994.67648 cents 10: 2 998.04482 cents 10: 2 999.84513 cents 10: 2 1006.40758 cents 10: 2 1007.27870 cents 11: 1 1085.40388 cents 11: 2 1092.54707 cents 11: 2 1098.93530 cents 11: 2 1099.10952 cents 11: 1 1102.12941 cents 11: 2 1107.29806 cents 11: 2 1108.34341 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.54545 = 72/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 91.7 192.7 293.6 386.3 493.8 591.6 699.1 791.8 892.7 993.7 1085.4 1200.0 91.7 : 101.1 202.0 294.7 402.1 500.0 607.4 700.1 801.0 902.1 993.7 1108.3 1200.0 192.7 : 100.9 193.6 301.0 398.9 506.4 599.1 700.0 801.0 892.7 1007.3 1098.9 1200.0 293.6 : 92.7 200.2 298.0 405.5 498.2 599.1 700.1 791.8 906.4 998.0 1099.1 1200.0 386.3 : 107.5 205.3 312.8 405.5 506.4 607.4 699.1 813.7 905.3 1006.4 1107.3 1200.0 493.8 : 97.9 205.3 298.0 398.9 500.0 591.6 706.2 797.9 899.0 999.8 1092.5 1200.0 591.6 : 107.5 200.2 301.0 402.1 493.8 608.4 700.0 801.1 902.0 994.7 1102.1 1200.0 699.1 : 92.7 193.6 294.7 386.3 500.9 592.6 693.6 794.5 887.2 994.7 1092.5 1200.0 791.8 : 100.9 202.0 293.6 408.2 499.9 600.9 701.8 794.5 902.0 999.8 1107.3 1200.0 892.7 : 101.1 192.7 307.3 399.0 500.0 600.9 693.6 801.1 899.0 1006.4 1099.1 1200.0 993.7 : 91.7 206.3 297.9 399.0 499.9 592.6 700.0 797.9 905.3 998.0 1098.9 1200.0 1085.4: 114.6 206.3 307.3 408.2 500.9 608.4 706.2 813.7 906.4 1007.3 1108.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 91.6566 .. 114.5961 cents 22.93953 cents 91.65659 cents 2: 192.7213 .. 206.2527 cents 13.53142 cents 78.12517 cents 3: 293.6118 .. 312.7764 cents 19.16467 cents 87.35906 cents 4: 386.3137 .. 408.2079 cents 21.89419 cents 73.53727 cents 5: 493.7666 .. 506.3689 cents 12.60222 cents 85.55874 cents 6: 591.6372 .. 608.3628 cents 16.72553 cents 85.26837 cents 7: 693.6311 .. 706.2334 cents 12.60222 cents 85.26837 cents 8: 791.7921 .. 813.6863 cents 21.89419 cents 85.55874 cents 9: 887.2236 .. 906.3882 cents 19.16467 cents 73.53727 cents 10: 993.7473 .. 1007.2787 cents 13.53142 cents 87.35906 cents 11: 1085.4039 .. 1108.3434 cents 22.93953 cents 78.12517 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 91.65659 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 114.59612 cents Average / Smallest step : 1.091029 Largest / Average step : 1.145961 Largest / Smallest step : 1.250277 Median interval of one step : 100.89048 cents, amount: 2 Least squares average step : 99.17057 cents, oct.: 1190.04688 cents Scale is strictly proper Step pattern alph. order: ABCDEFEDCBAG Step pattern size order : AEDBFCFBDEAG Scale is a Constant Structure, by a margin of 73.53727 cents Scale diversity : 1.136903 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.835842 Rothenberg efficiency : 0.242424 redundancy: 0.757576 Efficiency x scale size : 2.909091 Number of different interval sizes : 72 = 6.54545 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.54545 = 72/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 0.05807 cents Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 22.9395 cents: 2 5 7 9 10 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: 8.3336 c. M:-14.5961 c. Twelve-tone Chromatic (1/11-comma) 39: 3 3 4 3 3 3 4 3 3 3 3 4 SP D3 SD: 8.1648 c. M:-14.0805 c. 40: 3 3 4 3 3 4 3 3 4 3 3 4 SP B ME S SD: 8.1491 c. M: 13.7666 c. Diminished-12, Demolished-12 41: 3 3 4 3 4 3 4 3 3 4 3 4 SP M ME SD: 7.2569 c. M: 17.1115 c. 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 7.1306 c. M:-13.3650 c. Meantone Chromatic (1/5-comma) 44: 3 4 4 3 4 4 4 3 4 3 4 4 SP D3 SD: 6.8687 c. M: 11.9291 c. 49: 4 4 4 4 4 4 5 3 4 5 3 5 SP D3 SD: 7.0199 c. M:-11.1139 c. 50: 4 4 4 4 5 4 4 4 4 4 4 5 SP D3 S SD: 5.6761 c. M:-10.2334 c. 52: 4 4 5 4 4 5 4 4 5 4 4 5 SP B ME S SD: 6.1257 c. M: 9.1513 c. Demolished-12 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 4.6834 c. M:-11.0523 c. Schismic-12 56: 4 5 5 4 5 5 5 4 5 4 5 5 SP D3 SD: 5.6779 c. M:-8.3628 c. 61: 5 5 5 5 5 5 6 4 5 6 4 6 SP D3 SD: 5.6636 c. M:-9.5314 c. 62: 5 5 5 5 6 5 5 5 5 5 5 6 SP D3 S SD: 4.6396 c. M:-9.4592 c. 63: 5 5 5 5 6 5 6 5 5 5 5 6 SP D3 SD: 4.3719 c. M:-8.2079 c. 65: 5 5 6 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.7808 c. M: 8.1059 c. 71: 5 6 6 6 6 6 6 6 6 6 5 7 SP D3 SD: 4.4288 c. M: 7.1495 c. 74: 6 6 6 6 6 6 7 6 6 6 6 7 SP D3 S SD: 4.0298 c. M: 7.8535 c. 75: 6 6 6 6 7 6 7 5 7 6 6 7 SP D3 SD: 3.7302 c. M: 7.7921 c. 77: 6 6 7 6 7 6 7 6 6 7 6 7 SP M ME SD: 3.5881 c. M: 5.7083 c. 81: 6 7 7 6 7 7 7 6 7 7 6 8 SP D3 SD: 3.2072 c. M: 6.6069 c. 83: 6 7 7 7 7 7 7 7 7 7 6 8 SP D3 SD: 3.6110 c. M: 5.1143 c. 86: 7 7 7 7 7 7 8 7 7 7 7 8 SP D3 S SD: 3.6047 c. M:-6.0178 c. 87: 7 7 7 7 8 7 8 6 8 7 7 8 SP D3 SD: 3.3333 c. M: 5.5852 c. 93: 7 8 8 7 8 8 8 7 8 8 7 9 SP D3 SD: 2.3087 c. M: 4.6953 c. 94: 7 8 8 7 9 7 9 7 8 8 7 9 SP D3 SD: 2.3878 c. M: 4.4032 c. 105: 8 9 9 8 9 9 9 8 9 9 8 10 SP D3 SD: 2.0139 c. M:-3.5311 c. 106: 8 9 9 8 10 8 10 8 9 9 8 10 SP D3 SD: 2.0513 c. M:-4.3466 c. 118: 9 10 10 9 11 9 11 9 10 10 9 11 SP D3 SD: 2.1469 c. M:-4.5384 c. 130: 10 11 11 10 12 10 12 10 11 11 10 12 SP D3 SD: 2.4456 c. M:-4.6949 c. 132: 10 11 11 10 12 11 12 10 11 11 10 13 SP SD: 2.3402 c. M: 4.4955 c. 134: 10 11 12 10 12 11 12 10 12 11 10 13 SP SD: 2.2162 c. M: 4.6616 c. 136: 10 12 11 11 12 11 12 11 11 12 10 13 SP SD: 1.9663 c. M: 3.4213 c. 144: 11 12 12 11 13 12 13 11 12 12 11 14 SP SD: 1.5460 c. M: 2.9804 c. 156: 12 13 13 12 14 13 14 12 13 13 12 15 SP SD: 0.9868 c. M: 1.6983 c. 168: 13 14 14 13 15 14 15 13 14 14 13 16 SP SD: 0.7950 c. M:-1.2199 c. 274: 21 23 23 21 25 22 25 21 23 23 21 26 SP SD: 0.7724 c. M:-1.6398 c. 286: 22 24 24 22 26 23 26 22 24 24 22 27 SP SD: 0.8971 c. M:-1.6091 c. 292: 22 25 24 23 26 24 26 23 24 25 22 28 SP SD: 0.8747 c. M: 1.8310 c. 304: 23 26 25 24 27 25 27 24 25 26 23 29 SP SD: 0.8304 c. M:-1.6290 c. 314: 24 26 27 24 28 26 28 24 27 26 24 30 SP SD: 0.7877 c. M: 1.6385 c. 324: 25 27 27 25 29 27 29 25 27 27 25 31 SP SD: 0.8344 c. M: 1.1740 c. 326: 25 27 28 25 29 27 29 25 28 27 25 31 SP SD: 0.7966 c. M:-1.7959 c. 335: 26 28 28 26 30 27 30 26 28 28 26 32 SP SD: 0.7564 c. M: 1.5085 c. 343: 26 29 29 26 31 28 31 26 29 29 26 33 SP SD: 0.7007 c. M: 1.4741 c. 355: 27 30 30 27 32 29 32 27 30 30 27 34 SP SD: 0.4665 c. M: 0.9616 c. 367: 28 31 31 28 33 30 33 28 31 31 28 35 SP SD: 0.3561 c. M:-0.6662 c. 535: 41 45 45 41 48 44 48 41 45 45 41 51 SP SD: 0.3386 c. M:-0.7229 c. 547: 42 46 46 42 49 45 49 42 46 46 42 52 SP SD: 0.3947 c. M:-0.7270 c. 617: 47 52 52 48 55 50 55 48 52 52 47 59 SP SD: 0.3726 c. M: 0.8730 c. 618: 47 52 52 48 55 51 55 48 52 52 47 59 SP SD: 0.3973 c. M:-0.5958 c. 641: 49 54 54 49 58 52 57 50 54 54 49 61 SP SD: 0.3853 c. M: 0.8062 c. 659: 50 56 55 51 59 54 59 51 55 56 50 63 SP SD: 0.3411 c. M: 0.6096 c. 671: 51 57 56 52 60 55 60 52 56 57 51 64 SP SD: 0.3288 c. M:-0.5895 c. 743: 57 62 63 57 67 60 67 57 63 62 57 71 SP SD: 0.3847 c. M: 0.5275 c. 746: 57 63 63 57 67 61 67 57 63 63 57 71 SP SD: 0.3735 c. M:-0.7582 c. 749: 57 63 63 58 67 61 67 58 63 63 57 72 SP SD: 0.4189 c. M: 0.7577 c. 752: 57 64 63 58 67 62 67 58 63 64 57 72 SP SD: 0.4140 c. M: 0.6991 c. 755: 58 63 64 58 68 61 68 58 64 63 58 72 SP SD: 0.3740 c. M:-0.5625 c. 761: 58 64 64 59 68 62 68 59 64 64 58 73 SP SD: 0.3052 c. M: 0.5356 c. 773: 59 65 65 60 69 63 69 60 65 65 59 74 SP SD: 0.2220 c. M: 0.5132 c. 785: 60 66 66 61 70 64 70 61 66 66 60 75 SP SD: 0.2012 c. M: 0.4914 c. 929: 71 78 78 72 83 76 83 72 78 78 71 89 SP SD: 0.2489 c. M: 0.4211 c. 941: 72 79 79 73 84 77 84 73 79 79 72 90 SP SD: 0.1933 c. M: 0.3360 c. 953: 73 80 80 74 85 78 85 74 80 80 73 91 SP SD: 0.1898 c. M:-0.2637 c. 1035: 79 87 87 80 93 84 93 80 87 87 79 99 SP SD: 0.1818 c. M: 0.3329 c. 1047: 80 88 88 81 94 85 94 81 88 88 80 100 SP SD: 0.1415 c. M: 0.2332 c. 1059: 81 89 89 82 95 86 95 82 89 89 81 101 SP SD: 0.1594 c. M:-0.2843 c. 1128: 86 95 95 87 101 92 101 87 95 95 86 108 SP SD: 0.1729 c. M: 0.3027 c. 1140: 87 96 96 88 102 93 102 88 96 96 87 109 SP SD: 0.1007 c. M: 0.2132 c. 1152: 88 97 97 89 103 94 103 89 97 97 88 110 SP SD: 0.0793 c. M:-0.1446 c. 2187: 167 184 184 169 196 178 196 169 184 184 167 209 SP SD: 0.0711 c. M: 0.1420 c. 2199: 168 185 185 170 197 179 197 170 185 185 168 210 SP SD: 0.0573 c. M: 0.0956 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 1.4324 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.1197 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.2714 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.0416 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.6555 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.4603 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.6272 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.6202 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.2779 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.4428 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.4765 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.0987 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.2549 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.6087 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.8351 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.2022 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.5139 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 3.1551 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.7460 cents 33:35:37:39:41:44:46:49:52:55:59:62:66 SD: 2.7035 cents 34:36:38:40:43:45:48:51:54:57:60:64:68 SD: 2.6496 cents 36:38:40:43:45:48:51:54:57:60:64:67:72 SD: 2.1260 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 1.9663 cents 49:52:55:58:61:65:69:73:77:82:87:92:98 SD: 1.7656 cents 52:55:58:62:65:69:73:78:82:87:92:97:104 SD: 1.4231 cents 69:73:77:82:86:92:97:103:109:116:123:129:138 SD: 1.3086 cents 71:75:79:84:89:94:100:106:112:119:126:133:142 SD: 1.1978 cents 76:80:85:90:95:101:107:114:120:127:135:142:152 SD: 0.5724 cents 145:153:162:172:181:193:204:217:229:243:257:271:290 SD: 0.4788 cents 169:178:189:200:211:225:238:253:267:283:300:316:338 SD: 0.3796 cents 179:189:200:212:224:238:252:268:283:300:318:335:358 SD: 0.3339 cents 221:233:247:262:276:294:311:331:349:370:392:414:442 SD: 0.2470 cents 255:269:285:302:319:339:359:382:403:427:453:477:510 SD: 0.2280 cents 297:313:332:352:371:395:418:445:469:497:527:556:594 SD: 0.2140 cents 348:367:389:412:435:463:490:521:550:583:618:651:696 SD: 0.1923 cents 388:409:434:460:485:516:546:581:613:650:689:726:776 SD: 0.1660 cents 400:422:447:474:500:532:563:599:632:670:710:749:800 SD: 0.1136 cents 476:502:532:564:595:633:670:713:752:797:845:891:952 SD: 0.0677 cents