Scala analysis: butterfly1
"Butterfly I" well-temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 94.922 cents 94.921880 2: 195.703 cents 195.703130 3: 296.484 cents 296.484380 4: 392.578 cents 392.578130 5: 498.047 cents 498.046880 6: 592.969 cents 592.968750 7: 698.438 cents 698.437500 8: 794.531 cents 794.531250 9: 895.312 cents 895.312500 10: 996.094 cents 996.093750 11: 1091.016 cents 1091.015600 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 108.9844 cents 108.9844 1: 94.9219 cents 94.9219 2: 100.7812 cents 100.7812 3: 100.7813 cents 100.7813 4: 96.0937 cents 96.0937 5: 105.4688 cents 105.4688 6: 94.9219 cents 94.9219 7: 105.4688 cents 105.4688 8: 96.0937 cents 96.0937 9: 100.7813 cents 100.7813 10: 100.7813 cents 100.7813 11: 94.9218 cents 94.9218 12: 108.9844 cents 108.9844
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 94.92188 cents 1: 2 96.09375 cents 1: 4 100.78125 cents 1: 2 105.46875 cents 1: 1 108.98440 cents 2: 2 195.70313 cents 2: 2 196.87500 cents 2: 2 200.39062 cents 2: 4 201.56250 cents 2: 2 203.90625 cents 3: 4 296.48438 cents 3: 2 297.65625 cents 3: 1 298.82813 cents 3: 2 302.34375 cents 3: 2 304.68750 cents 3: 1 305.85937 cents 4: 2 392.57813 cents 4: 2 397.26562 cents 4: 2 399.60938 cents 4: 2 401.95312 cents 4: 2 403.12500 cents 4: 2 405.46875 cents 5: 5 498.04688 cents 5: 3 500.39063 cents 5: 2 501.56250 cents 5: 2 502.73437 cents 6: 2 592.96875 cents 6: 2 596.48438 cents 6: 2 598.82812 cents 6: 2 601.17188 cents 6: 2 603.51562 cents 6: 2 607.03125 cents 7: 2 697.26563 cents 7: 2 698.43750 cents 7: 3 699.60937 cents 7: 5 701.95312 cents 8: 2 794.53125 cents 8: 2 796.87500 cents 8: 2 798.04688 cents 8: 2 800.39062 cents 8: 2 802.73438 cents 8: 2 807.42187 cents 9: 1 894.14063 cents 9: 2 895.31250 cents 9: 2 897.65625 cents 9: 1 901.17187 cents 9: 2 902.34375 cents 9: 4 903.51562 cents 10: 2 996.09375 cents 10: 4 998.43750 cents 10: 2 999.60938 cents 10: 2 1003.12500 cents 10: 2 1004.29687 cents 11: 1 1091.01560 cents 11: 2 1094.53125 cents 11: 4 1099.21875 cents 11: 2 1103.90625 cents 11: 3 1105.07812 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.27273 = 58/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 94.9 195.7 296.5 392.6 498.0 593.0 698.4 794.5 895.3 996.1 1091.0 1200.0 94.9 : 100.8 201.6 297.7 403.1 498.0 603.5 699.6 800.4 901.2 996.1 1105.1 1200.0 195.7 : 100.8 196.9 302.3 397.3 502.7 598.8 699.6 800.4 895.3 1004.3 1099.2 1200.0 296.5 : 96.1 201.6 296.5 402.0 498.0 598.8 699.6 794.5 903.5 998.4 1099.2 1200.0 392.6 : 105.5 200.4 305.9 402.0 502.7 603.5 698.4 807.4 902.3 1003.1 1103.9 1200.0 498.0 : 94.9 200.4 296.5 397.3 498.0 593.0 702.0 796.9 897.7 998.4 1094.5 1200.0 593.0 : 105.5 201.6 302.3 403.1 498.0 607.0 702.0 802.7 903.5 999.6 1105.1 1200.0 698.4 : 96.1 196.9 297.7 392.6 501.6 596.5 697.3 798.0 894.1 999.6 1094.5 1200.0 794.5 : 100.8 201.6 296.5 405.5 500.4 601.2 702.0 798.0 903.5 998.4 1103.9 1200.0 895.3 : 100.8 195.7 304.7 399.6 500.4 601.2 697.3 802.7 897.7 1003.1 1099.2 1200.0 996.1 : 94.9 203.9 298.8 399.6 500.4 596.5 702.0 796.9 902.3 998.4 1099.2 1200.0 1091.0: 109.0 203.9 304.7 405.5 501.6 607.0 702.0 807.4 903.5 1004.3 1105.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 94.9219 .. 108.9844 cents 14.06252 cents 94.92188 cents 2: 195.7031 .. 203.9062 cents 8.20312 cents 86.71873 cents 3: 296.4844 .. 305.8594 cents 9.37499 cents 92.57813 cents 4: 392.5781 .. 405.4688 cents 12.89062 cents 86.71876 cents 5: 498.0469 .. 502.7344 cents 4.68749 cents 92.57813 cents 6: 592.9687 .. 607.0313 cents 14.06250 cents 90.23438 cents 7: 697.2656 .. 701.9531 cents 4.68749 cents 90.23438 cents 8: 794.5312 .. 807.4219 cents 12.89062 cents 92.57813 cents 9: 894.1406 .. 903.5156 cents 9.37499 cents 86.71876 cents 10: 996.0938 .. 1004.2969 cents 8.20312 cents 92.57813 cents 11: 1091.0156 .. 1105.0781 cents 14.06252 cents 86.71873 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 94.92185 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 108.98440 cents Average / Smallest step : 1.053498 Largest / Average step : 1.089844 Largest / Smallest step : 1.148149 Median interval of one step : 100.78125 cents, amount: 4 Most common interval of one step : 100.78125 cents, amount: 4 Least squares average step : 99.47596 cents, oct.: 1193.71153 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 81 167 253 335 425 506 596 678 764 850 931 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 601 of 704.297 cents and inv. generated superset size: 422 = 410 more = 3516.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBCDADCBBAE Step pattern size order : ACCBDADBCCAE Scale is a Constant Structure, by a margin of 86.71873 cents Scale diversity : 1.077392 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.906250 Rothenberg efficiency : 0.265025 redundancy: 0.734975 Efficiency x scale size : 3.180303 Number of different interval sizes : 58 = 5.27273 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.27273 = 58/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.17187 cents Most common intervals : 498.04688 cents & inv., amount: 5 Most common triad is 0.0 498.047 701.953 cents, amount: 2 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 4 different sizes of fifth Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 14.0626 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.1255 c. M:-8.9844 c. Twelve-tone Chromatic (1/11-comma) 55: 4 5 5 4 5 4 5 4 5 5 4 5 SP M ME SD: 5.0714 c. M: 9.0767 c. Meantone Chromatic (3/17-comma) 63: 5 5 6 5 5 5 6 5 5 5 5 6 SP D3 SD: 4.9556 c. M:-8.2775 c. 64: 5 5 6 5 6 5 5 5 6 5 5 6 SP D3 SD: 5.0856 c. M: 8.2031 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.9701 c. M: 9.1587 c. 66: 5 6 5 6 5 6 5 6 5 6 5 6 SP B ME SD: 5.3414 c. M: 7.5284 c. 67: 5 6 6 5 6 5 6 5 6 6 5 6 SP M ME SD: 4.1217 c. M:-7.9932 c. Meantone Chromatic (4/25-comma) 75: 6 6 7 6 6 6 7 6 6 6 6 7 SP D3 SD: 4.2695 c. M:-7.5156 c. 76: 6 6 7 6 7 6 6 6 7 6 6 7 SP D3 SD: 4.3093 c. M:-7.2163 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 3.1423 c. M: 7.0008 c. 86: 7 7 7 7 8 6 8 7 7 7 7 8 SP D3 SD: 3.3171 c. M: 6.9222 c. 88: 7 7 8 7 8 6 8 7 8 7 7 8 SP D3 SD: 3.8097 c. M: 6.6051 c. 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 2.7074 c. M:-6.5441 c. 90: 7 8 7 7 8 7 8 8 7 8 7 8 SP D3 SD: 4.1664 c. M: 6.3021 c. 91: 7 8 8 7 8 7 8 7 8 8 7 8 SP M ME SD: 3.4027 c. M:-6.8123 c. Meantone Chromatic (1/7-comma), Romieu-12 92: 7 8 8 7 8 7 9 7 8 7 8 8 SP D3 SD: 3.7810 c. M: 6.0122 c. 97: 8 8 8 8 8 8 8 8 8 8 8 9 SP M ME SD: 3.5439 c. M: 6.4030 c. 98: 8 8 8 8 9 7 9 8 8 8 8 9 SP D3 SD: 2.6390 c. M: 5.2136 c. 101: 8 8 9 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.3917 c. M: 5.6041 c. 107: 8 9 9 9 9 9 9 9 9 9 8 10 SP D3 SD: 3.2913 c. M: 5.2023 c. 109: 9 9 9 9 9 9 9 9 9 9 9 10 SP M ME SD: 3.1110 c. M: 5.2681 c. 110: 9 9 9 9 10 8 10 9 9 9 9 10 SP D3 SD: 2.2260 c. M: 3.8778 c. 113: 9 9 10 9 10 9 10 9 9 10 9 10 SP M ME SD: 2.2157 c. M: 4.5527 c. 122: 10 10 10 10 11 9 11 10 10 10 10 11 SP D3 SD: 2.0177 c. M:-3.5925 c. 129: 10 11 11 10 11 11 11 10 11 11 10 12 SP D3 SD: 2.3743 c. M: 5.0236 c. 130: 10 11 11 10 12 10 12 10 11 11 10 12 SP D3 SD: 2.1279 c. M: 4.8858 c. 131: 10 11 11 11 11 11 11 11 11 11 10 12 SP D3 SD: 2.5140 c. M: 3.3904 c. 134: 11 11 11 11 12 10 12 11 11 11 11 12 SP D3 SD: 1.9574 c. M:-3.5856 c. 142: 11 12 12 11 13 11 13 11 12 12 11 13 SP D3 SD: 1.6899 c. M: 3.8457 c. 143: 11 12 12 12 12 12 12 12 12 12 11 13 SP D3 SD: 2.3406 c. M: 2.9420 c. 146: 12 12 12 12 13 11 13 12 12 12 12 13 SP D3 SD: 1.9918 c. M:-3.7083 c. 150: 12 12 13 12 13 12 13 12 13 12 12 14 SP D3 SD: 2.2220 c. M: 4.0937 c. 152: 12 13 13 12 13 12 13 13 12 13 12 14 SP D3 SD: 2.1848 c. M: 3.7007 c. 153: 12 13 13 12 14 12 13 12 13 13 12 14 SP SD: 1.7385 c. M:-3.9139 c. 154: 12 13 13 12 14 12 14 12 13 13 12 14 SP D3 SD: 1.3959 c. M: 2.9677 c. 166: 13 14 14 13 15 13 15 13 14 14 13 15 SP D3 SD: 1.2405 c. M:-2.7673 c. 178: 14 15 15 14 16 14 16 14 15 15 14 16 SP D3 SD: 1.2070 c. M:-2.6861 c. 186: 15 15 16 15 16 15 16 15 16 15 15 17 SP D3 SD: 1.4108 c. M: 2.5454 c. 189: 15 16 16 15 16 15 17 15 16 16 15 17 SP SD: 1.3768 c. M: 2.8088 c. 190: 15 16 16 15 17 15 17 15 16 16 15 17 SP D3 SD: 1.2619 c. M:-2.6151 c. 198: 16 16 17 16 17 16 17 16 17 16 16 18 SP D3 SD: 1.3354 c. M: 2.1544 c. 202: 16 17 17 16 18 16 18 16 17 17 16 18 SP D3 SD: 1.3681 c. M:-2.5526 c. 210: 17 17 18 17 18 17 18 17 18 17 17 19 SP D3 SD: 1.3344 c. M:-2.2210 c. 214: 17 18 18 17 19 17 19 17 18 18 17 19 SP D3 SD: 1.4984 c. M:-2.4971 c. 219: 17 19 18 18 19 17 19 18 18 19 17 20 SP SD: 1.4238 c. M: 2.5471 c. 220: 17 19 18 18 19 18 19 18 18 19 17 20 SP SD: 1.3765 c. M: 2.1946 c. 227: 18 19 19 18 20 18 20 18 19 19 18 21 SP SD: 1.2943 c. M: 2.2612 c. 229: 18 19 20 18 20 18 20 19 19 19 18 21 SP SD: 1.2075 c. M:-2.2056 c. 239: 19 20 20 19 21 19 21 19 20 20 19 22 SP SD: 1.0285 c. M: 1.9515 c. 251: 20 21 21 20 22 20 22 20 21 21 20 23 SP SD: 0.8172 c. M: 1.6714 c. 263: 21 22 22 21 23 21 23 21 22 22 21 24 SP SD: 0.6727 c. M: 1.4169 c. 275: 22 23 23 22 24 22 24 22 23 23 22 25 SP SD: 0.6095 c. M: 1.1847 c. 375: 30 31 32 30 33 29 33 30 32 31 30 34 SP SD: 0.8586 c. M:-1.1531 c. 376: 30 31 32 30 33 30 33 30 32 31 30 34 SP SD: 0.6541 c. M:-1.4960 c. 393: 31 33 33 31 35 31 35 31 33 33 31 36 SP SD: 0.7389 c. M: 1.7384 c. 397: 31 34 33 32 35 31 35 32 33 34 31 36 SP SD: 0.6821 c. M:-1.3874 c. 405: 32 34 34 32 36 32 36 32 34 34 32 37 SP SD: 0.5967 c. M: 1.4670 c. 417: 33 35 35 33 37 33 37 33 35 35 33 38 SP SD: 0.4798 c. M: 1.2112 c. 429: 34 36 36 34 38 34 38 34 36 36 34 39 SP SD: 0.3985 c. M: 0.9697 c. 441: 35 37 37 35 39 35 39 35 37 37 35 40 SP SD: 0.3656 c. M:-0.8822 c. 453: 36 38 38 36 40 36 40 36 38 38 36 41 SP SD: 0.3844 c. M:-0.9002 c. 465: 37 39 39 37 41 37 41 37 39 39 37 42 SP SD: 0.4419 c. M:-0.9173 c. 547: 43 46 46 44 48 43 48 44 46 46 43 50 SP SD: 0.4541 c. M: 0.8141 c. 559: 44 47 47 45 49 44 49 45 47 47 44 51 SP SD: 0.3676 c. M: 0.7631 c. 571: 45 48 48 46 50 45 50 46 48 48 45 52 SP SD: 0.3050 c. M: 0.7142 c. 583: 46 49 49 47 51 46 51 47 49 49 46 53 SP SD: 0.2766 c. M: 0.6673 c. 649: 51 55 54 52 57 52 57 52 54 55 51 59 SP SD: 0.4961 c. M: 0.6663 c. 651: 51 55 55 52 57 52 57 52 55 54 52 59 SP SD: 0.4424 c. M: 0.9127 c. 660: 52 56 55 53 58 52 58 53 55 56 52 60 SP SD: 0.3451 c. M: 0.7670 c. 672: 53 57 56 54 59 53 59 54 56 57 53 61 SP SD: 0.3356 c. M:-0.7254 c. 704: 56 59 59 56 62 56 62 56 59 59 56 64 SP SD: 0.3716 c. M: 0.6392 c. 706: 56 59 59 57 62 56 62 56 60 59 56 64 SP SD: 0.3607 c. M: 0.7635 c. 713: 56 60 60 57 63 56 63 57 60 60 56 65 SP SD: 0.3544 c. M: 0.6722 c. 716: 57 60 60 57 63 57 63 57 60 60 57 65 SP SD: 0.3582 c. M:-0.6088 c. 725: 57 61 61 58 64 57 64 58 61 61 57 66 SP SD: 0.2905 c. M: 0.5771 c. 737: 58 62 62 59 65 58 65 59 62 62 58 67 SP SD: 0.2444 c. M: 0.4850 c. 749: 59 63 63 60 66 59 66 60 63 63 59 68 SP SD: 0.2238 c. M:-0.4350 c. 761: 60 64 64 61 67 60 67 61 64 64 60 69 SP SD: 0.2325 c. M:-0.4897 c. 773: 61 65 65 62 68 61 68 62 65 65 61 70 SP SD: 0.2654 c. M:-0.5427 c. 846: 67 71 71 68 74 67 74 68 71 71 67 77 SP SD: 0.2540 c. M: 0.5652 c. 858: 68 72 72 69 75 68 75 69 72 72 68 78 SP SD: 0.2400 c. M: 0.5354 c. 976: 77 82 82 78 86 77 86 78 82 82 77 89 SP SD: 0.2521 c. M: 0.4418 c. 988: 78 83 83 79 87 78 87 79 83 83 78 90 SP SD: 0.1868 c. M: 0.3273 c. 1000: 79 84 84 80 88 79 88 80 84 84 79 91 SP SD: 0.1230 c. M: 0.2156 c. 1012: 80 85 85 81 89 80 89 81 85 85 80 92 SP SD: 0.0608 c. M: 0.1065 c. 1024: 81 86 86 82 90 81 90 82 86 86 81 93 SP SD: 0.0000 c. M:-0.0000 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: 1.7588 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.6513 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.0496 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.2266 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.7309 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.7040 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.5882 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.0278 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1647 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.1868 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.4574 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.4347 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.7522 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.1288 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.9671 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.0537 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.7217 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.4594 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.8475 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1941 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.1670 cents 48:51:54:57:60:64:68:72:76:81:85:90:96 SD: 1.8395 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.6885 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.3633 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.2942 cents 66:70:74:78:83:88:93:99:104:111:117:124:132 SD: 1.2838 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 1.2779 cents 69:73:77:82:87:92:97:103:109:116:123:130:138 SD: 1.2774 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 1.0019 cents 75:79:84:89:94:100:106:112:119:126:133:141:150 SD: 0.9606 cents 86:91:96:102:108:115:121:129:136:144:153:162:172 SD: 0.9160 cents 90:95:101:107:113:120:127:135:142:151:160:169:180 SD: 0.7322 cents 91:96:102:108:114:121:128:136:144:153:162:171:182 SD: 0.7236 cents 108:114:121:128:135:144:152:162:171:181:192:203:216 SD: 0.6820 cents 117:124:131:139:147:156:165:175:185:196:208:220:234 SD: 0.6446 cents 123:130:138:146:154:164:173:184:195:206:219:231:246 SD: 0.6254 cents 125:132:140:148:157:167:176:187:198:210:222:235:250 SD: 0.6039 cents 139:147:156:165:174:185:196:208:220:233:247:261:278 SD: 0.5917 cents 141:149:158:167:177:188:199:211:223:236:251:265:282 SD: 0.5852 cents 149:157:167:177:187:199:210:223:236:250:265:280:298 SD: 0.5273 cents 161:170:180:191:202:215:227:241:255:270:286:302:322 SD: 0.4301 cents 177:187:198:210:222:236:249:265:280:297:315:332:354 SD: 0.3339 cents 235:248:263:279:295:313:331:352:372:394:418:441:470 SD: 0.3008 cents 252:266:282:299:316:336:355:377:399:423:448:473:504 SD: 0.2426 cents 318:336:356:377:399:424:448:476:503:533:565:597:636 SD: 0.2222 cents 342:361:383:406:429:456:482:512:541:574:608:642:684 SD: 0.1951 cents 369:390:413:438:463:492:520:552:584:619:656:693:738 SD: 0.1625 cents 428:452:479:508:537:571:603:641:677:718:761:804:856 SD: 0.1610 cents 443:468:496:526:556:591:624:663:701:743:788:832:886 SD: 0.1525 cents 477:504:534:566:598:636:672:714:755:800:848:896:954 SD: 0.1263 cents 551:582:617:654:691:735:776:825:872:924:980:1035:1102 SD: 0.1222 cents 567:599:635:673:711:756:799:849:897:951:1008:1065:1134 SD: 0.1184 cents 585:618:655:694:734:780:824:876:926:981:1040:1099:1170 SD: 0.1066 cents