Scala analysis: secor_WT2-11
George Secor's 2/11-comma well-temperament, proportional beating
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92.139 cents 92.138840 2: 196.087 cents 196.087210 3: 296.016 cents 296.015620 4: 392.174 cents 392.174420 5: 499.926 cents 499.925620 6: 590.208 cents 590.208350 7: 698.044 cents 698.043610 8: 794.061 cents 794.060620 9: 894.131 cents 894.130820 10: 997.971 cents 997.970620 11: 1090.218 cents 1090.218030 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 109.7820 cents 109.7820 1: 92.1388 cents 92.1388 2: 103.9484 cents 103.9484 3: 99.9284 cents 99.9284 4: 96.1588 cents 96.1588 5: 107.7512 cents 107.7512 6: 90.2827 cents 90.2827 7: 107.8353 cents 107.8353 8: 96.0170 cents 96.0170 9: 100.0702 cents 100.0702 10: 103.8398 cents 103.8398 11: 92.2474 cents 92.2474 12: 109.7820 cents 109.7820
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 90.28273 cents 1: 1 92.13884 cents 1: 1 92.24741 cents 1: 1 96.01701 cents 1: 1 96.15880 cents 1: 1 99.92841 cents 1: 1 100.07020 cents 1: 1 103.83980 cents 1: 1 103.94837 cents 1: 1 107.75120 cents 1: 1 107.83526 cents 1: 1 109.78197 cents 2: 4 196.08721 cents 2: 1 198.03393 cents 2: 1 198.11799 cents 2: 1 201.92081 cents 2: 1 202.02938 cents 2: 1 203.85227 cents 2: 1 203.87678 cents 2: 2 203.91000 cents 3: 1 294.13500 cents 3: 1 294.16822 cents 3: 1 294.19273 cents 3: 1 296.01562 cents 3: 1 296.15741 cents 3: 1 299.92701 cents 3: 1 300.03558 cents 3: 1 303.83841 cents 3: 1 303.92247 cents 3: 3 305.86919 cents 4: 2 392.17442 cents 4: 1 394.12114 cents 4: 1 394.20520 cents 4: 1 398.00802 cents 4: 1 398.11659 cents 4: 1 401.88620 cents 4: 1 402.02799 cents 4: 1 405.79759 cents 4: 1 405.93938 cents 4: 1 407.76227 cents 4: 1 407.78678 cents 5: 3 498.04500 cents 5: 1 498.06951 cents 5: 1 498.07822 cents 5: 1 499.92562 cents 5: 1 500.00968 cents 5: 5 501.95640 cents 6: 1 590.20835 cents 6: 1 590.29241 cents 6: 1 594.09523 cents 6: 1 594.20380 cents 6: 1 597.97341 cents 6: 1 598.11520 cents 6: 1 601.88480 cents 6: 1 602.02659 cents 6: 1 605.79620 cents 6: 1 605.90477 cents 6: 1 609.70759 cents 6: 1 609.79165 cents 7: 5 698.04361 cents 7: 1 699.99032 cents 7: 1 700.07438 cents 7: 1 701.92178 cents 7: 1 701.93049 cents 7: 3 701.95500 cents 8: 1 792.21322 cents 8: 1 792.23773 cents 8: 1 794.06062 cents 8: 1 794.20241 cents 8: 1 797.97201 cents 8: 1 798.11380 cents 8: 1 801.88341 cents 8: 1 801.99198 cents 8: 1 805.79480 cents 8: 1 805.87886 cents 8: 2 807.82558 cents 9: 3 894.13082 cents 9: 1 896.07753 cents 9: 1 896.16159 cents 9: 1 899.96442 cents 9: 1 900.07299 cents 9: 1 903.84259 cents 9: 1 903.98438 cents 9: 1 905.80727 cents 9: 1 905.83178 cents 9: 1 905.86500 cents 10: 2 996.09000 cents 10: 1 996.12322 cents 10: 1 996.14773 cents 10: 1 997.97062 cents 10: 1 998.07919 cents 10: 1 1001.88201 cents 10: 1 1001.96607 cents 10: 4 1003.91279 cents 11: 1 1090.21803 cents 11: 1 1092.16474 cents 11: 1 1092.24880 cents 11: 1 1096.05163 cents 11: 1 1096.16020 cents 11: 1 1099.92980 cents 11: 1 1100.07159 cents 11: 1 1103.84120 cents 11: 1 1103.98299 cents 11: 1 1107.75259 cents 11: 1 1107.86116 cents 11: 1 1109.71727 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 9.63636 = 106/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.1 196.1 296.0 392.2 499.9 590.2 698.0 794.1 894.1 998.0 1090.2 1200.0 92.1 : 103.9 203.9 300.0 407.8 498.1 605.9 701.9 802.0 905.8 998.1 1107.9 1200.0 196.1 : 99.9 196.1 303.8 394.1 502.0 598.0 698.0 801.9 894.1 1003.9 1096.1 1200.0 296.0 : 96.2 203.9 294.2 402.0 498.0 598.1 702.0 794.2 904.0 996.1 1100.1 1200.0 392.2 : 107.8 198.0 305.9 401.9 502.0 605.8 698.0 807.8 900.0 1003.9 1103.8 1200.0 499.9 : 90.3 198.1 294.1 394.2 498.0 590.3 700.1 792.2 896.2 996.1 1092.2 1200.0 590.2 : 107.8 203.9 303.9 407.8 500.0 609.8 701.9 805.9 905.8 1002.0 1109.7 1200.0 698.0 : 96.0 196.1 299.9 392.2 502.0 594.1 698.0 798.0 894.1 1001.9 1092.2 1200.0 794.1 : 100.1 203.9 296.2 405.9 498.1 602.0 702.0 798.1 905.9 996.1 1104.0 1200.0 894.1 : 103.8 196.1 305.9 398.0 502.0 601.9 698.0 805.8 896.1 1003.9 1099.9 1200.0 998.0 : 92.2 202.0 294.2 398.1 498.0 594.2 702.0 792.2 900.1 996.1 1096.2 1200.0 1090.2: 109.8 201.9 305.9 405.8 502.0 609.7 700.0 807.8 903.8 1003.9 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2827 .. 109.7820 cents 19.49924 cents 90.28273 cents 2: 196.0872 .. 203.9100 cents 7.82279 cents 86.30524 cents 3: 294.1350 .. 305.8692 cents 11.73419 cents 90.22500 cents 4: 392.1744 .. 407.7868 cents 15.61236 cents 86.30523 cents 5: 498.0450 .. 501.9564 cents 3.91140 cents 90.25822 cents 6: 590.2084 .. 609.7917 cents 19.58330 cents 88.25195 cents 7: 698.0436 .. 701.9550 cents 3.91139 cents 88.25196 cents 8: 792.2132 .. 807.8256 cents 15.61236 cents 90.25822 cents 9: 894.1308 .. 905.8650 cents 11.73418 cents 86.30524 cents 10: 996.0900 .. 1003.9128 cents 7.82279 cents 90.22500 cents 11: 1090.2180 .. 1109.7173 cents 19.49924 cents 86.30524 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 90.28273 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 109.78197 cents Average / Smallest step : 1.107632 Largest / Average step : 1.097820 Largest / Smallest step : 1.215980 Median interval of one step : 99.99930 cents, amount: 0 Least squares average step : 99.44617 cents, oct.: 1193.35400 cents Scale is strictly proper Step pattern alph. order: ABCDEFGHIJKL Step pattern size order : BIFEJAKDGHCL Scale is a Constant Structure, by a margin of 86.30523 cents Scale diversity : 1.095384 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.886047 Rothenberg efficiency : 0.199200 redundancy: 0.800800 Efficiency x scale size : 2.390404 Number of different interval sizes : 106 = 9.63636 / class Number of one step interval sizes : 12 Highest interval variety : 12 Mean interval variety : 9.63636 = 106/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 0.00871 cents Most common intervals : 501.95640 cents & inv., amount: 5 Most common triad is 0.0 501.956 698.044 cents, amount: 4 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 6 different sizes of fifth Scale is a temperament ordinaire Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 19.5833 cents: 2 3 4 5 7 8 9 10 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: 5.9404 c. M:-9.7916 c. Twelve-tone Chromatic (1/11-comma) 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 4.8169 c. M: 11.1120 c. Schismic-12 55: 4 5 5 4 5 4 5 4 5 5 4 5 SP M ME SD: 4.3284 c. M:-9.4389 c. Meantone Chromatic (3/17-comma) 63: 5 5 6 5 5 5 6 5 5 5 5 6 SP D3 SD: 5.4693 c. M:-8.7463 c. 64: 5 5 6 5 6 4 6 5 6 5 5 6 SP D3 SD: 5.2920 c. M: 8.9584 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.5331 c. M: 7.9770 c. 76: 6 6 7 6 7 5 7 6 7 6 6 7 SP D3 SD: 4.2311 c. M: 6.6135 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 2.9175 c. M:-6.5102 c. 79: 6 7 7 6 7 6 7 6 7 7 6 7 SP M ME SD: 3.3259 c. M:-7.7818 c. Meantone Chromatic (3/20-comma) 86: 7 7 7 7 8 6 8 7 7 8 6 8 SP D3 S SD: 3.1153 c. M:-6.6805 c. 87: 7 7 7 7 8 7 8 7 7 7 7 8 SP D3 SD: 4.2677 c. M: 6.3604 c. 88: 7 7 8 7 8 6 8 7 8 7 7 8 SP D3 SD: 3.6338 c. M:-5.8692 c. 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 2.7143 c. M:-6.1600 c. 94: 7 8 8 8 8 7 9 7 8 8 7 9 SP D3 S SD: 3.0964 c. M: 5.1116 c. 98: 8 8 8 8 9 7 9 8 8 9 7 9 SP D3 S SD: 2.7406 c. M:-6.1110 c. 101: 8 9 8 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.7369 c. M:-5.8930 c. 110: 8 10 9 9 10 8 10 9 9 9 9 10 SP D3 S SD: 2.3187 c. M: 5.2433 c. 116: 9 10 10 9 10 9 10 10 9 10 9 11 SP D3 SD: 3.1622 c. M: 4.9402 c. 117: 9 10 10 9 11 8 11 9 10 10 9 11 SP SD: 2.7209 c. M: 5.5930 c. 118: 9 10 10 10 10 9 11 9 10 10 9 11 SP D3 S SD: 2.1034 c. M:-4.4357 c. 120: 9 11 10 9 11 9 11 9 10 11 9 11 SP D3 SD: 2.6154 c. M: 4.1308 c. 122: 9 11 10 10 11 9 11 10 10 10 10 11 SP D3 S SD: 2.0409 c. M: 4.5280 c. 129: 10 11 11 10 12 9 12 10 11 11 10 12 SP SD: 2.0875 c. M: 4.1618 c. 130: 10 11 11 10 12 10 12 10 11 11 10 12 SP D3 SD: 1.9127 c. M: 4.4821 c. 131: 10 11 11 11 12 9 12 11 11 11 10 12 SP SD: 2.5984 c. M: 3.9488 c. 132: 10 12 11 10 12 10 12 10 11 12 10 12 SP D3 SD: 2.3009 c. M:-3.9844 c. 134: 10 12 11 11 12 10 12 11 11 11 11 12 SP D3 S SD: 1.9617 c. M: 3.9408 c. 141: 11 12 12 11 13 10 13 11 12 12 11 13 SP SD: 1.6459 c. M: 2.9743 c. 153: 12 13 13 12 14 11 14 12 13 13 12 14 SP SD: 1.3920 c. M:-2.0352 c. 165: 13 14 14 13 15 12 15 13 14 14 13 15 SP SD: 1.3142 c. M:-2.4066 c. 177: 14 15 15 14 16 13 16 14 15 15 14 16 SP SD: 1.3705 c. M:-2.7764 c. 183: 14 16 15 15 16 14 16 15 15 16 14 17 SP SD: 1.4273 c. M: 2.9616 c. 189: 15 16 16 15 17 14 17 15 16 16 15 17 SP SD: 1.5043 c. M:-3.0993 c. 195: 15 17 16 16 17 15 17 16 16 17 15 18 SP SD: 1.2547 c. M: 2.6590 c. 204: 16 17 17 17 18 15 19 16 17 18 15 19 SP SD: 1.6060 c. M:-2.0294 c. 207: 16 18 17 17 18 16 18 17 17 18 16 19 SP SD: 1.1996 c. M: 2.3914 c. 208: 16 18 17 17 19 15 19 17 17 18 16 19 SP SD: 1.1071 c. M:-2.0932 c. 220: 17 19 18 18 20 16 20 18 18 19 17 20 SP SD: 1.0699 c. M:-2.3030 c. 232: 18 20 19 19 21 17 21 19 19 20 18 21 SP SD: 1.1235 c. M:-2.4911 c. 244: 19 21 20 20 22 18 22 20 20 21 19 22 SP SD: 1.2339 c. M:-2.6607 c. 248: 19 21 21 20 22 19 22 20 21 21 19 23 SP SD: 1.1653 c. M: 2.5388 c. 251: 19 22 21 20 23 18 23 20 21 22 19 23 SP SD: 1.0235 c. M: 2.1605 c. 252: 19 22 21 20 23 19 23 20 21 22 19 23 SP SD: 1.2137 c. M:-2.0294 c. 255: 20 22 21 20 23 19 23 21 21 22 20 23 SP SD: 1.3125 c. M:-1.9788 c. 259: 20 22 22 21 23 19 24 20 22 22 20 24 SP SD: 1.2880 c. M: 1.8316 c. 260: 20 22 22 21 23 20 23 21 22 22 20 24 SP SD: 1.0356 c. M: 2.2411 c. 263: 20 23 22 21 24 19 24 21 22 23 20 24 SP SD: 0.8854 c. M:-1.9755 c. 273: 21 24 22 22 25 20 25 22 22 24 21 25 SP SD: 1.1356 c. M: 1.8231 c. 274: 21 24 23 22 24 21 24 22 23 24 21 25 SP SD: 1.1289 c. M:-1.9862 c. 275: 21 24 23 22 25 20 25 22 23 24 21 25 SP SD: 0.8342 c. M:-1.8926 c. 284: 22 24 24 23 25 22 25 23 24 24 22 26 SP SD: 1.0018 c. M: 1.7210 c. 287: 22 25 24 23 26 21 26 23 24 25 22 26 SP SD: 0.8618 c. M:-1.8165 c. 295: 23 25 25 23 27 22 27 23 25 25 23 27 SP SD: 1.0191 c. M: 1.6659 c. 299: 23 26 25 24 27 22 27 24 25 26 23 27 SP SD: 0.9454 c. M:-1.7466 c. 301: 23 26 25 24 27 23 27 24 25 26 23 28 SP SD: 1.0571 c. M: 1.8459 c. 305: 23 27 25 25 27 23 27 25 25 27 23 28 SP SD: 0.9971 c. M: 1.6502 c. 307: 24 26 26 24 28 23 28 24 26 26 24 28 SP SD: 0.9890 c. M:-1.6722 c. 313: 24 27 26 25 28 24 28 25 26 27 24 29 SP SD: 0.8615 c. M: 1.5231 c. 317: 24 28 26 26 28 24 28 26 26 28 24 29 SP SD: 0.9517 c. M:-1.5164 c. 325: 25 28 27 26 29 25 29 26 27 28 25 30 SP SD: 0.7172 c. M: 1.4641 c. 337: 26 29 28 27 30 26 30 27 28 29 26 31 SP SD: 0.6373 c. M: 1.4093 c. 349: 27 30 29 28 31 27 31 28 29 30 27 32 SP SD: 0.6282 c. M: 1.3583 c. 382: 29 33 32 31 34 29 34 31 32 33 29 35 SP SD: 0.7749 c. M: 1.3228 c. 385: 30 33 32 31 34 29 35 31 32 33 30 35 SP SD: 0.7390 c. M:-1.3677 c. 392: 30 34 33 31 35 30 35 31 33 34 30 36 SP SD: 0.5808 c. M: 1.2035 c. 404: 31 35 34 32 36 31 36 32 34 35 31 37 SP SD: 0.5525 c. M:-1.0141 c. 429: 33 37 36 34 39 32 39 34 36 37 33 39 SP SD: 0.6317 c. M:-1.2571 c. 435: 33 38 36 35 39 33 39 35 36 38 33 40 SP SD: 0.5497 c. M: 1.1044 c. 447: 34 39 37 36 40 34 40 36 37 39 34 41 SP SD: 0.4782 c. M: 0.8637 c. 459: 35 40 38 37 41 35 41 37 38 40 35 42 SP SD: 0.4589 c. M:-0.7222 c. 533: 41 46 44 43 48 40 48 43 44 46 41 49 SP SD: 0.4820 c. M: 1.0813 c. 535: 41 46 45 43 48 40 48 43 45 46 41 49 SP SD: 0.4239 c. M: 0.9470 c. 545: 42 47 45 44 49 41 49 44 45 47 42 50 SP SD: 0.4306 c. M: 0.9697 c. 547: 42 47 46 44 49 41 49 44 46 47 42 50 SP SD: 0.4250 c. M:-0.9332 c. 557: 43 48 46 45 50 42 50 45 46 48 43 51 SP SD: 0.4184 c. M:-0.9125 c. 576: 44 50 48 46 52 43 52 46 48 50 44 53 SP SD: 0.3695 c. M: 0.6347 c. 588: 45 51 49 47 53 44 53 47 49 51 45 54 SP SD: 0.2419 c. M: 0.4221 c. 600: 46 52 50 48 54 45 54 48 50 52 46 55 SP SD: 0.1216 c. M: 0.2180 c. 612: 47 53 51 49 55 46 55 49 51 53 47 56 SP SD: 0.0398 c. M:-0.0744 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: 1.9557 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.3171 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.4961 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.9706 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.5519 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.8928 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.5108 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.1758 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.2984 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.0213 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.7253 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.4885 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.7850 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.0904 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 5.0584 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 5.0148 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.0687 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.5592 cents 27:28:30:32:34:36:38:40:43:45:48:51:54 SD: 3.4918 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 3.1010 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2370 cents 42:44:47:50:53:56:59:63:66:70:75:79:84 SD: 2.0065 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.6183 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.5042 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.0740 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 0.7716 cents 108:114:121:128:135:144:152:162:171:181:192:203:216 SD: 0.7100 cents 123:130:138:146:154:164:173:184:195:206:219:231:246 SD: 0.6148 cents 141:149:158:167:177:188:198:211:223:236:251:265:282 SD: 0.5547 cents 149:157:167:177:187:199:210:223:236:250:265:280:298 SD: 0.5197 cents 161:170:180:191:202:215:226:241:255:270:287:302:322 SD: 0.5152 cents 165:174:185:196:207:220:232:247:261:277:294:310:330 SD: 0.4282 cents 177:187:198:210:222:236:249:265:280:297:315:332:354 SD: 0.3978 cents 182:192:204:216:228:243:256:272:288:305:324:342:364 SD: 0.3463 cents 236:249:264:280:296:315:332:353:373:396:420:443:472 SD: 0.2898 cents 251:265:281:298:315:335:353:376:397:421:447:471:502 SD: 0.2879 cents 268:283:300:318:336:358:377:401:424:449:477:503:536 SD: 0.2464 cents 290:306:325:344:364:387:408:434:459:486:516:544:580 SD: 0.2206 cents 349:368:391:414:438:466:491:522:552:585:621:655:698 SD: 0.1711 cents 401:423:449:476:503:535:564:600:634:672:714:753:802 SD: 0.1667 cents 433:457:485:514:543:578:609:648:685:726:771:813:866 SD: 0.1638 cents 441:465:494:523:553:589:620:660:698:739:785:828:882 SD: 0.1568 cents 457:482:512:542:573:610:643:684:723:766:813:858:914 SD: 0.1379 cents 531:560:595:630:666:709:747:795:840:890:945:997:1062 SD: 0.1249 cents 586:618:656:695:735:782:824:877:927:982:1043:1100:1172 SD: 0.0962 cents