Scala analysis: TO-523
Possible 5/23-comma temperament ordinaire
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 86.535 cents 86.535080 2: 194.557 cents 194.556800 3: 294.129 cents 294.129200 4: 389.114 cents 389.113610 5: 502.722 cents 502.721600 6: 585.534 cents 585.534490 7: 697.278 cents 697.278400 8: 789.382 cents 789.381840 9: 891.835 cents 891.835210 10: 997.016 cents 997.016210 11: 1086.392 cents 1086.392010 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 113.6080 cents 113.6080 1: 86.5351 cents 86.5351 2: 108.0217 cents 108.0217 3: 99.5724 cents 99.5724 4: 94.9844 cents 94.9844 5: 113.6080 cents 113.6080 6: 82.8129 cents 82.8129 7: 111.7439 cents 111.7439 8: 92.1034 cents 92.1034 9: 102.4534 cents 102.4534 10: 105.1810 cents 105.1810 11: 89.3758 cents 89.3758 12: 113.6080 cents 113.6080
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 82.81289 cents 1: 1 86.53508 cents 1: 1 89.37580 cents 1: 1 92.10344 cents 1: 1 94.98441 cents 1: 1 99.57240 cents 1: 1 102.45337 cents 1: 1 105.18100 cents 1: 1 108.02172 cents 1: 1 111.74391 cents 1: 2 113.60799 cents 2: 5 194.55680 cents 2: 1 196.42088 cents 2: 1 200.14307 cents 2: 1 202.98379 cents 2: 1 203.84735 cents 2: 1 207.59412 cents 2: 1 207.63437 cents 2: 1 208.59240 cents 3: 1 286.66024 cents 3: 1 289.51887 cents 3: 1 291.40529 cents 3: 1 294.12920 cents 3: 1 297.01017 cents 3: 1 299.73781 cents 3: 1 302.57853 cents 3: 1 306.30072 cents 3: 4 308.16480 cents 4: 3 389.11361 cents 4: 1 390.97769 cents 4: 1 394.69987 cents 4: 1 397.54059 cents 4: 1 400.26823 cents 4: 1 403.14920 cents 4: 1 407.73719 cents 4: 1 410.61816 cents 4: 1 411.48172 cents 4: 1 416.18652 cents 5: 1 494.29461 cents 5: 1 495.25264 cents 5: 1 497.11299 cents 5: 1 497.15324 cents 5: 1 498.99941 cents 5: 1 500.85752 cents 5: 6 502.72160 cents 6: 1 583.67041 cents 6: 1 585.53449 cents 6: 1 589.25668 cents 6: 1 592.09740 cents 6: 1 594.82504 cents 6: 1 597.70601 cents 6: 1 602.29399 cents 6: 1 605.17496 cents 6: 1 607.90260 cents 6: 1 610.74332 cents 6: 1 614.46551 cents 6: 1 616.32959 cents 7: 6 697.27840 cents 7: 1 699.14248 cents 7: 1 701.00059 cents 7: 1 702.84676 cents 7: 1 702.88701 cents 7: 1 704.74736 cents 7: 1 705.70539 cents 8: 1 783.81348 cents 8: 1 788.51828 cents 8: 1 789.38184 cents 8: 1 792.26281 cents 8: 1 796.85080 cents 8: 1 799.73177 cents 8: 1 802.45941 cents 8: 1 805.30013 cents 8: 1 809.02231 cents 8: 3 810.88639 cents 9: 4 891.83521 cents 9: 1 893.69928 cents 9: 1 897.42147 cents 9: 1 900.26219 cents 9: 1 902.98983 cents 9: 1 905.87080 cents 9: 1 908.59471 cents 9: 1 910.48113 cents 9: 1 913.33976 cents 10: 1 991.40760 cents 10: 1 992.36563 cents 10: 1 992.40588 cents 10: 1 996.15265 cents 10: 1 997.01621 cents 10: 1 999.85693 cents 10: 1 1003.57912 cents 10: 5 1005.44320 cents 11: 2 1086.39201 cents 11: 1 1088.25609 cents 11: 1 1091.97828 cents 11: 1 1094.81900 cents 11: 1 1097.54663 cents 11: 1 1100.42760 cents 11: 1 1105.01559 cents 11: 1 1107.89656 cents 11: 1 1110.62420 cents 11: 1 1113.46492 cents 11: 1 1117.18711 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 9.27273 = 102/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 86.5 194.6 294.1 389.1 502.7 585.5 697.3 789.4 891.8 997.0 1086.4 1200.0 86.5 : 108.0 207.6 302.6 416.2 499.0 610.7 702.8 805.3 910.5 999.9 1113.5 1200.0 194.6 : 99.6 194.6 308.2 391.0 502.7 594.8 697.3 802.5 891.8 1005.4 1092.0 1200.0 294.1 : 95.0 208.6 291.4 403.1 495.3 597.7 702.9 792.3 905.9 992.4 1100.4 1200.0 389.1 : 113.6 196.4 308.2 400.3 502.7 607.9 697.3 810.9 897.4 1005.4 1105.0 1200.0 502.7 : 82.8 194.6 286.7 389.1 494.3 583.7 697.3 783.8 891.8 991.4 1086.4 1200.0 585.5 : 111.7 203.8 306.3 411.5 500.9 614.5 701.0 809.0 908.6 1003.6 1117.2 1200.0 697.3 : 92.1 194.6 299.7 389.1 502.7 589.3 697.3 796.9 891.8 1005.4 1088.3 1200.0 789.4 : 102.5 207.6 297.0 410.6 497.2 605.2 704.7 799.7 913.3 996.2 1107.9 1200.0 891.8 : 105.2 194.6 308.2 394.7 502.7 602.3 697.3 810.9 893.7 1005.4 1097.5 1200.0 997.0 : 89.4 203.0 289.5 397.5 497.1 592.1 705.7 788.5 900.3 992.4 1094.8 1200.0 1086.4: 113.6 200.1 308.2 407.7 502.7 616.3 699.1 810.9 903.0 1005.4 1110.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.8129 .. 113.6080 cents 30.79510 cents 82.81289 cents 2: 194.5568 .. 208.5924 cents 14.03560 cents 80.94881 cents 3: 286.6602 .. 308.1648 cents 21.50456 cents 78.06784 cents 4: 389.1136 .. 416.1865 cents 27.07291 cents 80.94881 cents 5: 494.2946 .. 502.7216 cents 8.42699 cents 78.10809 cents 6: 583.6704 .. 616.3296 cents 32.65918 cents 80.94881 cents 7: 697.2784 .. 705.7054 cents 8.42699 cents 80.94881 cents 8: 783.8135 .. 810.8864 cents 27.07291 cents 78.10809 cents 9: 891.8352 .. 913.3398 cents 21.50455 cents 80.94882 cents 10: 991.4076 .. 1005.4432 cents 14.03560 cents 78.06784 cents 11: 1086.3920 .. 1117.1871 cents 30.79510 cents 80.94881 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 82.81289 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 113.60799 cents Average / Smallest step : 1.207541 Largest / Average step : 1.136080 Largest / Smallest step : 1.371864 Median interval of one step : 101.01289 cents, amount: 0 Most common interval of one step : 113.60799 cents, amount: 2 Least squares average step : 99.20662 cents, oct.: 1190.47939 cents Scale is strictly proper Step pattern alph. order: ABCDEFGHIJKE Step pattern size order : BIFEKAJDGHCK Scale is a Constant Structure, by a margin of 78.06784 cents Scale diversity : 1.172612 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.803059 Rothenberg efficiency : 0.208829 redundancy: 0.791171 Efficiency x scale size : 2.505952 Number of different interval sizes : 102 = 9.27273 / class Number of one step interval sizes : 11 Highest interval variety : 12 Mean interval variety : 9.27273 = 102/11 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 0.04025 cents Most common intervals : 502.72160 cents & inv., amount: 6 Most common triad is 0.0 502.722 697.278 cents, amount: 5 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 30.7951 cents: 2 3 5 7 10 Limited inverse transpositions with margin 30.7951 cents: 1 4 6 8 9 11 -- 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: 8.9511 c. M:-14.4655 c. Twelve-tone Chromatic (1/11-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 7.5426 c. M:-15.5482 c. Meantone Chromatic (53/220-comma) 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 6.0850 c. M: 13.7864 c. Schismic-12 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 5.0341 c. M:-12.8475 c. Meantone Chromatic (1/5-comma) 47: 3 5 4 3 5 3 4 4 4 4 4 4 SP D3 SD: 7.3593 c. M:-12.2538 c. 49: 4 4 4 4 5 3 4 4 4 5 3 5 SP SD: 7.5111 c. M: 11.5641 c. 50: 3 5 4 4 5 3 5 4 4 4 4 5 SP D3 S SD: 7.1154 c. M: 14.5351 c. 52: 4 4 5 4 5 3 5 4 5 4 4 5 SP D3 SD: 5.8815 c. M: 9.9414 c. 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 4.6481 c. M:-9.2168 c. Schismic-12 55: 4 5 5 4 5 4 5 4 5 5 4 5 SP M ME SD: 4.5315 c. M:-11.3253 c. Meantone Chromatic (3/17-comma) 61: 4 6 5 5 6 4 5 5 5 6 4 6 SP SD: 5.5456 c. M:-8.7538 c. 62: 4 6 5 5 6 4 6 5 5 5 5 6 SP D3 S SD: 4.5779 c. M: 9.9194 c. 64: 5 5 6 5 6 4 6 5 6 5 5 6 SP D3 SD: 4.8578 c. M:-8.1648 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 4.4110 c. M:-8.5201 c. 66: 5 6 5 5 7 4 6 5 6 6 5 6 SP SD: 4.9554 c. M: 7.5637 c. 67: 5 6 6 5 6 5 6 5 6 6 5 6 SP M ME SD: 4.7304 c. M:-10.3484 c. Meantone Chromatic (4/25-comma) 70: 5 6 6 6 6 5 7 5 6 6 5 7 SP D3 S SD: 3.9696 c. M: 6.3920 c. 74: 5 7 6 6 7 5 7 6 6 6 6 7 SP D3 S SD: 3.2439 c. M: 7.8270 c. 78: 6 7 6 6 8 5 7 6 7 7 6 7 SP SD: 4.1191 c. M:-5.9157 c. 81: 6 7 7 6 8 5 8 6 7 7 6 8 SP SD: 3.6697 c. M: 7.7567 c. 82: 6 7 7 7 7 6 8 6 7 7 6 8 SP D3 S SD: 3.2756 c. M:-6.0083 c. 86: 6 8 7 7 8 6 8 7 7 7 7 8 SP D3 S SD: 2.7946 c. M: 6.3185 c. 93: 7 8 8 7 9 6 9 7 8 8 7 9 SP SD: 2.5287 c. M: 4.8893 c. 105: 8 9 9 8 10 7 10 8 9 9 8 10 SP SD: 2.0277 c. M:-4.8935 c. 106: 8 9 9 8 10 8 10 8 9 9 8 10 SP D3 SD: 2.9900 c. M: 4.6084 c. 110: 8 10 9 9 10 8 10 8 10 9 9 10 SP D3 SD: 2.7822 c. M:-4.5171 c. 113: 8 10 10 9 10 8 11 8 10 10 8 11 SP SD: 2.7601 c. M:-3.8067 c. 114: 8 10 10 9 11 8 10 9 10 10 8 11 SP SD: 2.6183 c. M: 5.0831 c. 117: 8 11 10 9 11 8 11 9 10 10 9 11 SP SD: 1.7796 c. M: 4.4838 c. 129: 9 12 11 10 12 9 12 10 11 11 10 12 SP SD: 1.6843 c. M:-3.5452 c. 136: 10 12 11 11 13 9 13 10 12 12 10 13 SP SD: 1.8516 c. M: 4.0877 c. 144: 10 13 12 12 13 10 14 11 12 13 10 14 SP SD: 2.4892 c. M: 3.2017 c. 147: 11 13 12 12 14 10 13 12 12 13 11 14 SP SD: 2.2338 c. M: 3.4008 c. 148: 11 13 12 12 14 10 14 11 13 13 11 14 SP SD: 1.4023 c. M: 2.8954 c. 155: 11 14 13 12 15 11 14 12 13 14 11 15 SP SD: 1.5061 c. M:-2.8526 c. 160: 12 14 13 13 15 11 15 12 14 14 12 15 SP SD: 1.3376 c. M:-3.4649 c. 167: 12 15 14 13 16 11 16 13 14 15 12 16 SP SD: 1.3225 c. M: 3.4986 c. 172: 12 16 14 14 16 12 16 13 15 15 13 16 SP S SD: 1.2793 c. M: 2.8141 c. 179: 13 16 15 14 17 12 17 14 15 16 13 17 SP SD: 1.0387 c. M: 2.2943 c. 191: 14 17 16 15 18 13 18 15 16 17 14 18 SP SD: 1.0911 c. M:-2.2412 c. 222: 16 20 18 18 21 15 21 17 19 19 17 21 SP SD: 1.0799 c. M: 2.4216 c. 232: 17 21 19 18 22 16 22 18 19 21 17 22 SP SD: 1.3315 c. M: 2.1800 c. 234: 17 21 19 19 22 16 22 18 20 20 18 22 SP SD: 0.9441 c. M: 2.1444 c. 246: 18 22 20 20 23 17 23 19 21 21 19 23 SP SD: 1.0221 c. M: 1.8943 c. 253: 18 23 21 20 24 17 24 19 22 22 19 24 SP SD: 0.9610 c. M: 2.1353 c. 260: 19 23 22 20 25 18 24 20 22 23 19 25 SP SD: 0.9310 c. M: 1.7766 c. 261: 19 23 22 21 24 18 25 20 22 23 19 25 SP SD: 1.2089 c. M:-1.6910 c. 262: 19 23 22 21 25 18 24 20 23 23 19 25 SP SD: 1.1600 c. M: 2.1904 c. 265: 19 24 22 21 25 18 25 20 23 23 20 25 SP SD: 0.6654 c. M: 1.4573 c. 277: 20 25 23 22 26 19 26 21 24 24 21 26 SP SD: 0.5837 c. M:-0.9726 c. 377: 27 34 31 30 36 26 35 29 32 33 28 36 SP SD: 0.6276 c. M: 1.2910 c. 389: 28 35 32 31 37 27 36 30 33 34 29 37 SP SD: 0.4685 c. M: 1.0701 c. 401: 29 36 33 32 38 28 37 31 34 35 30 38 SP SD: 0.4565 c. M:-0.9992 c. 420: 30 38 35 33 40 29 39 32 36 37 31 40 SP SD: 0.4502 c. M: 0.8208 c. 432: 31 39 36 34 41 30 40 33 37 38 32 41 SP SD: 0.2991 c. M:-0.5766 c. 444: 32 40 37 35 42 31 41 34 38 39 33 42 SP SD: 0.3242 c. M:-0.9520 c. 611: 44 55 51 48 58 42 57 47 52 54 45 58 SP SD: 0.2903 c. M:-0.6925 c. 623: 45 56 52 49 59 43 58 48 53 55 46 59 SP SD: 0.2908 c. M:-0.7366 c. 654: 47 59 54 52 62 45 61 50 56 57 49 62 SP SD: 0.3046 c. M: 0.6859 c. 666: 48 60 55 53 63 46 62 51 57 58 50 63 SP SD: 0.2302 c. M: 0.6198 c. 678: 49 61 56 54 64 47 63 52 58 59 51 64 SP SD: 0.2572 c. M: 0.5560 c. 709: 51 64 59 56 67 49 66 54 61 62 53 67 SP SD: 0.2491 c. M: 0.6653 c. 721: 52 65 60 57 68 50 67 55 62 63 54 68 SP SD: 0.2836 c. M: 0.4775 c. 740: 53 67 61 59 70 51 69 57 63 65 55 70 SP SD: 0.2833 c. M: 0.6157 c. 833: 60 75 69 66 79 57 78 64 71 73 62 79 SP SD: 0.2271 c. M: 0.6605 c. 845: 61 76 70 67 80 58 79 65 72 74 63 80 SP SD: 0.1540 c. M: 0.4457 c. 857: 62 77 71 68 81 59 80 66 73 75 64 81 SP SD: 0.1697 c. M:-0.3498 c. 1012: 73 91 84 80 96 70 94 78 86 89 75 96 SP SD: 0.1678 c. M:-0.3415 c. 1098: 79 99 91 87 104 76 102 84 94 96 82 104 SP SD: 0.1619 c. M: 0.3108 c. 1110: 80 100 92 88 105 77 103 85 95 97 83 105 SP SD: 0.1586 c. M:-0.4115 c. 1265: 91 114 105 100 120 87 118 97 108 111 94 120 SP SD: 0.1405 c. M: 0.2380 c. 1277: 92 115 106 101 121 88 119 98 109 112 95 121 SP SD: 0.0566 c. M: 0.0999 c. 1289: 93 116 107 102 122 89 120 99 110 113 96 122 SP SD: 0.0341 c. M:-0.0673 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: 2.3383 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.9396 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.1781 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.7101 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.8418 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.4674 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.5715 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.1563 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.7900 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.7919 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 7.0813 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.5754 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.0693 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.4642 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.2273 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.9113 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 4.8447 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.3379 cents 23:24:26:27:29:31:32:34:36:39:41:43:46 SD: 4.1047 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.4296 cents 27:28:30:32:34:36:38:40:43:45:48:51:54 SD: 3.4174 cents 32:34:36:38:40:43:45:48:50:54:57:60:64 SD: 2.7059 cents 33:35:37:39:41:44:46:49:52:55:59:62:66 SD: 2.5228 cents 39:41:44:46:49:52:55:58:62:65:69:73:78 SD: 2.4218 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 2.0779 cents 42:44:47:50:53:56:59:63:66:70:75:79:84 SD: 1.9299 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.9065 cents 53:56:59:63:66:71:74:79:84:89:94:99:106 SD: 1.9000 cents 54:57:60:64:68:72:76:81:85:90:96:101:108 SD: 1.7808 cents 55:58:62:65:69:74:77:82:87:92:98:103:110 SD: 1.7194 cents 57:60:64:68:71:76:80:85:90:95:101:107:114 SD: 1.7065 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.0414 cents 77:81:86:91:96:103:108:115:121:129:137:144:154 SD: 1.0366 cents 92:97:103:109:115:123:129:138:145:154:164:172:184 SD: 0.7648 cents 95:100:106:113:119:127:133:142:150:159:169:178:190 SD: 0.7563 cents 119:125:133:141:149:159:167:178:188:199:212:223:238 SD: 0.4160 cents 178:187:199:211:223:238:250:266:281:298:317:333:356 SD: 0.4102 cents 194:204:217:230:243:259:272:290:306:325:345:363:388 SD: 0.3179 cents 211:222:236:250:264:282:296:316:333:353:375:395:422 SD: 0.2946 cents 234:246:262:277:293:313:328:350:369:392:416:438:468 SD: 0.2871 cents 254:267:284:301:318:340:356:380:401:425:452:476:508 SD: 0.2727 cents 258:271:289:306:323:345:362:386:407:432:459:483:516 SD: 0.2516 cents 270:284:302:320:338:361:379:404:426:452:480:506:540 SD: 0.2037 cents 329:346:368:390:412:440:461:492:519:551:585:616:658 SD: 0.1984 cents 353:371:395:418:442:472:495:528:557:591:628:661:706 SD: 0.1476 cents 448:471:501:531:561:599:628:670:707:750:797:839:896 SD: 0.1290 cents 599:630:670:710:750:801:840:896:945:1003:1065:1122:1198 SD: 0.1244 cents