Scala analysis: lehman-bach
Brad Lehman's Bach keyboard temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 98.045 cents 98.045000 2: 196.090 cents 196.090000 3: 298.045 cents 298.045000 4: 392.180 cents 392.180000 5: 501.955 cents 501.955000 6: 596.090 cents 596.090000 7: 698.045 cents 698.045000 8: 798.045 cents 798.045000 9: 894.135 cents 894.135000 10: 998.045 cents 998.045000 11: 1094.135 cents 1094.135000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 105.8650 cents 105.8650 1: 98.0450 cents 98.0450 2: 98.0450 cents 98.0450 3: 101.9550 cents 101.9550 4: 94.1350 cents 94.1350 5: 109.7750 cents 109.7750 6: 94.1350 cents 94.1350 7: 101.9550 cents 101.9550 8: 100.0000 cents 100.0000 9: 96.0900 cents 96.0900 10: 103.9100 cents 103.9100 11: 96.0900 cents 96.0900 12: 105.8650 cents 105.8650
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 94.13500 cents 1: 2 96.09000 cents 1: 2 98.04500 cents 1: 1 100.00000 cents 1: 2 101.95500 cents 1: 1 103.91000 cents 1: 1 105.86500 cents 1: 1 109.77500 cents 2: 4 196.09000 cents 2: 3 200.00000 cents 2: 2 201.95500 cents 2: 3 203.91000 cents 3: 1 294.13500 cents 3: 2 296.09000 cents 3: 3 298.04500 cents 3: 2 300.00000 cents 3: 1 301.95500 cents 3: 3 305.86500 cents 4: 2 392.18000 cents 4: 1 396.09000 cents 4: 1 398.04500 cents 4: 2 400.00000 cents 4: 2 401.95500 cents 4: 3 403.91000 cents 4: 1 405.86500 cents 5: 1 496.09000 cents 5: 3 498.04500 cents 5: 3 500.00000 cents 5: 5 501.95500 cents 6: 1 592.18000 cents 6: 1 594.13500 cents 6: 2 596.09000 cents 6: 1 598.04500 cents 6: 2 600.00000 cents 6: 1 601.95500 cents 6: 2 603.91000 cents 6: 1 605.86500 cents 6: 1 607.82000 cents 7: 5 698.04500 cents 7: 3 700.00000 cents 7: 3 701.95500 cents 7: 1 703.91000 cents 8: 1 794.13500 cents 8: 3 796.09000 cents 8: 2 798.04500 cents 8: 2 800.00000 cents 8: 1 801.95500 cents 8: 1 803.91000 cents 8: 2 807.82000 cents 9: 3 894.13500 cents 9: 1 898.04500 cents 9: 2 900.00000 cents 9: 3 901.95500 cents 9: 2 903.91000 cents 9: 1 905.86500 cents 10: 3 996.09000 cents 10: 2 998.04500 cents 10: 3 1000.00000 cents 10: 4 1003.91000 cents 11: 1 1090.22500 cents 11: 1 1094.13500 cents 11: 1 1096.09000 cents 11: 2 1098.04500 cents 11: 1 1100.00000 cents 11: 2 1101.95500 cents 11: 2 1103.91000 cents 11: 2 1105.86500 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 6.09091 = 67/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 98.0 196.1 298.0 392.2 502.0 596.1 698.0 798.0 894.1 998.0 1094.1 1200.0 98.0 : 98.0 200.0 294.1 403.9 498.0 600.0 700.0 796.1 900.0 996.1 1102.0 1200.0 196.1 : 102.0 196.1 305.9 400.0 502.0 602.0 698.0 802.0 898.0 1003.9 1102.0 1200.0 298.0 : 94.1 203.9 298.0 400.0 500.0 596.1 700.0 796.1 902.0 1000.0 1098.0 1200.0 392.2 : 109.8 203.9 305.9 405.9 502.0 605.9 702.0 807.8 905.9 1003.9 1105.9 1200.0 502.0 : 94.1 196.1 296.1 392.2 496.1 592.2 698.0 796.1 894.1 996.1 1090.2 1200.0 596.1 : 102.0 202.0 298.0 402.0 498.0 603.9 702.0 800.0 902.0 996.1 1105.9 1200.0 698.0 : 100.0 196.1 300.0 396.1 502.0 600.0 698.0 800.0 894.1 1003.9 1098.0 1200.0 798.0 : 96.1 200.0 296.1 402.0 500.0 598.0 700.0 794.1 903.9 998.0 1100.0 1200.0 894.1 : 103.9 200.0 305.9 403.9 502.0 603.9 698.0 807.8 902.0 1003.9 1103.9 1200.0 998.0 : 96.1 202.0 300.0 398.0 500.0 594.1 703.9 798.0 900.0 1000.0 1096.1 1200.0 1094.1: 105.9 203.9 302.0 403.9 498.0 607.8 702.0 803.9 903.9 1000.0 1103.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 94.1350 .. 109.7750 cents 15.64000 cents 94.13500 cents 2: 196.0900 .. 203.9100 cents 7.82000 cents 86.31500 cents 3: 294.1350 .. 305.8650 cents 11.73000 cents 90.22500 cents 4: 392.1800 .. 405.8650 cents 13.68500 cents 86.31500 cents 5: 496.0900 .. 501.9550 cents 5.86500 cents 90.22500 cents 6: 592.1800 .. 607.8200 cents 15.64000 cents 90.22500 cents 7: 698.0450 .. 703.9100 cents 5.86500 cents 90.22500 cents 8: 794.1350 .. 807.8200 cents 13.68500 cents 90.22500 cents 9: 894.1350 .. 905.8650 cents 11.73000 cents 86.31500 cents 10: 996.0900 .. 1003.9100 cents 7.82000 cents 90.22500 cents 11: 1090.2250 .. 1105.8650 cents 15.64000 cents 86.31500 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 94.13500 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 109.77500 cents Average / Smallest step : 1.062304 Largest / Average step : 1.097750 Largest / Smallest step : 1.166144 Median interval of one step : 99.02250 cents, amount: 0 Least squares average step : 99.65111 cents, oct.: 1195.81329 cents Scale is strictly proper Step pattern alph. order: AABCDCBEFGFH Step pattern size order : CCEAHAEDBFBG Scale is a Constant Structure, by a margin of 86.31500 cents Scale diversity : 1.086988 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.895733 Rothenberg efficiency : 0.245918 redundancy: 0.754082 Efficiency x scale size : 2.951010 Number of different interval sizes : 67 = 6.09091 / class Number of one step interval sizes : 8 Highest interval variety : 9 Mean interval variety : 6.09091 = 67/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.95500 cents Most common intervals : 501.95500 cents & inv., amount: 5 Most common triad is 0.0 501.955 698.045 cents, amount: 4 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 13.6850 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions with margin 13.6850 cents: 1 2 3 4 5 6 7 8 9 10 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: 3.9100 c. M:-7.8200 c. Twelve-tone Chromatic (1/11-comma) 59: 5 5 5 4 6 4 5 5 5 5 5 5 SP D3 SD: 5.1367 c. M:-7.2998 c. 64: 5 5 6 5 6 5 5 6 5 5 5 6 SP D3 SD: 5.1226 c. M: 8.5900 c. 67: 6 5 6 5 6 5 6 6 5 6 5 6 SP M ME SD: 4.5819 c. M:-9.4177 c. 71: 6 6 6 5 7 5 6 6 6 6 6 6 SP D3 SD: 4.2412 c. M:-6.7269 c. 77: 6 6 7 6 7 6 7 6 6 7 6 7 SP M ME SD: 4.1315 c. M: 9.0770 c. 79: 7 6 7 6 7 6 7 7 6 7 6 7 SP M ME SD: 4.0786 c. M:-8.2841 c. 83: 7 7 7 6 8 6 7 7 7 7 7 7 SP D3 SD: 3.6920 c. M:-6.3196 c. 86: 7 7 7 7 8 7 7 7 7 7 7 8 SP D3 S SD: 3.4079 c. M: 7.3473 c. 89: 7 7 8 7 8 7 8 7 7 8 7 8 SP M ME SD: 3.2404 c. M: 7.3260 c. 90: 7 8 7 7 9 7 7 8 7 8 7 8 SP D3 SD: 3.6366 c. M: 5.5133 c. 93: 7 8 8 7 9 7 8 8 7 8 8 8 SP D3 SD: 3.5211 c. M: 7.7224 c. 95: 8 8 8 7 9 7 8 8 8 8 8 8 SP D3 SD: 3.3542 c. M:-6.0153 c. 98: 8 8 8 8 9 8 8 8 8 8 8 9 SP D3 S SD: 2.8105 c. M: 6.2083 c. 101: 8 8 9 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.6111 c. M: 5.9910 c. 102: 8 9 8 8 10 8 8 9 8 9 8 9 SP D3 SD: 3.1021 c. M: 3.9447 c. 105: 9 8 9 8 10 8 9 9 8 9 9 9 SP D3 SD: 2.5732 c. M:-4.8121 c. 110: 9 9 9 9 10 9 9 9 9 9 9 10 SP D3 S SD: 2.4091 c. M: 5.3177 c. 113: 9 9 10 9 10 9 10 9 9 10 9 10 SP M ME SD: 2.1735 c. M: 4.9396 c. 114: 9 10 9 9 11 9 9 10 9 10 9 10 SP D3 SD: 2.7393 c. M:-3.9100 c. 117: 10 9 10 9 11 9 10 10 9 10 10 10 SP D3 SD: 2.2092 c. M:-4.5191 c. 122: 10 10 10 10 11 10 10 10 10 10 10 11 SP D3 S SD: 2.1530 c. M: 4.6024 c. 125: 10 10 11 10 11 10 11 10 10 11 10 11 SP M ME SD: 1.8847 c. M: 4.0900 c. 137: 11 11 12 11 12 11 12 11 11 12 11 12 SP M ME SD: 1.7131 c. M: 3.3893 c. 149: 12 12 13 12 13 12 13 12 12 13 12 13 SP M ME SD: 1.6311 c. M: 2.8014 c. 160: 13 13 14 12 15 12 14 13 13 14 13 14 SP SD: 1.7448 c. M: 3.5900 c. 161: 13 13 14 13 14 13 14 13 13 14 13 14 SP M ME SD: 1.6132 c. M:-2.8511 c. 165: 13 14 14 13 15 13 14 14 13 14 13 15 SP SD: 1.5805 c. M: 3.4995 c. 172: 14 14 15 13 16 13 15 14 14 15 14 15 SP SD: 1.4861 c. M: 3.0667 c. 177: 14 15 15 14 16 14 15 15 14 15 14 16 SP SD: 1.4411 c. M: 3.1297 c. 180: 15 14 16 14 16 14 16 15 14 16 14 16 SP T3 SD: 1.8427 c. M: 2.7567 c. 181: 15 15 15 14 17 14 15 15 15 16 14 16 SP SD: 1.7057 c. M:-3.0600 c. 184: 15 15 16 14 17 14 16 15 15 16 15 16 SP SD: 1.2991 c. M: 2.6117 c. 192: 16 15 17 15 17 15 17 16 15 17 15 17 SP T3 SD: 1.7475 c. M: 2.3400 c. 193: 16 16 16 15 18 15 16 16 16 17 15 17 SP SD: 1.6369 c. M:-2.9913 c. 196: 16 16 17 15 18 15 17 16 16 17 16 17 SP SD: 1.1784 c. M: 2.2124 c. 204: 17 16 18 16 18 16 18 17 16 18 16 18 SP T3 SD: 1.6948 c. M: 1.9724 c. 205: 17 17 17 16 19 16 17 17 17 18 16 18 SP SD: 1.6083 c. M:-2.9344 c. 206: 17 17 17 16 19 16 18 17 16 18 17 18 SP SD: 1.5255 c. M: 2.8729 c. 208: 17 17 18 16 19 16 18 17 17 18 17 18 SP SD: 1.1167 c. M:-2.0188 c. 220: 18 18 19 17 20 17 19 18 18 19 18 19 SP SD: 1.1038 c. M:-2.2286 c. 227: 19 18 19 18 21 18 19 19 18 20 18 20 SP SD: 1.0990 c. M:-2.3955 c. 232: 19 19 20 18 21 18 20 19 19 20 19 20 SP SD: 1.1271 c. M:-2.4167 c. 239: 20 19 20 19 22 19 20 20 19 21 19 21 SP SD: 1.0394 c. M:-2.3734 c. 251: 21 20 21 20 23 20 21 21 20 22 20 22 SP SD: 1.0203 c. M:-2.3534 c. 256: 21 21 22 20 23 20 22 21 21 22 20 23 SP SD: 1.1057 c. M:-1.9550 c. 258: 21 21 22 20 24 20 22 21 21 22 21 23 SP SD: 1.3183 c. M: 2.6962 c. 260: 21 21 23 20 24 20 22 22 21 22 21 23 SP SD: 1.1628 c. M: 2.2438 c. 263: 22 21 22 21 24 21 22 22 21 23 21 23 SP SD: 1.0333 c. M:-2.3352 c. 270: 22 22 23 21 25 21 23 22 22 23 22 24 SP SD: 1.1431 c. M: 2.4894 c. 272: 22 22 24 21 25 21 23 23 22 23 22 24 SP SD: 1.0962 c. M: 1.9724 c. 273: 22 23 23 21 25 22 23 23 21 24 22 24 SP SD: 1.2303 c. M:-1.9550 c. 274: 22 23 23 22 25 21 23 23 22 24 22 24 SP SD: 1.1560 c. M:-1.9806 c. 275: 23 22 23 22 25 22 23 23 22 24 22 24 SP SD: 1.0697 c. M:-2.3186 c. 282: 23 23 24 22 26 22 24 24 22 25 22 25 SP SD: 0.8668 c. M:-1.9550 c. 290: 24 23 25 23 26 23 25 24 23 25 23 26 SP SD: 1.0149 c. M: 1.7212 c. 294: 24 24 25 23 27 23 25 25 23 26 23 26 SP SD: 0.8156 c. M:-1.9550 c. 298: 24 25 25 23 28 23 25 25 24 26 24 26 SP SD: 1.0078 c. M: 1.5760 c. 302: 25 24 26 24 27 24 26 25 24 26 24 27 SP SD: 0.9697 c. M: 1.4198 c. 306: 25 25 26 24 28 24 26 26 24 27 24 27 SP SD: 0.7982 c. M:-1.9550 c. 310: 25 26 26 24 29 24 26 26 25 27 25 27 SP SD: 0.9460 c. M:-1.3489 c. 318: 26 26 27 25 29 25 27 26 26 27 26 28 SP SD: 0.7543 c. M: 1.8186 c. 330: 27 27 28 26 30 26 28 27 27 28 27 29 SP SD: 0.7368 c. M: 1.6814 c. 349: 28 29 30 27 32 27 30 29 28 30 28 31 SP SD: 0.7873 c. M: 1.7699 c. 354: 29 29 30 28 32 28 30 29 29 30 29 31 SP SD: 0.7762 c. M: 1.4348 c. 361: 29 30 31 28 33 28 31 30 29 31 29 32 SP SD: 0.7146 c. M: 1.6461 c. 366: 30 30 31 29 33 29 31 30 30 31 30 32 SP SD: 0.8210 c. M: 1.3237 c. 368: 30 30 31 29 34 29 31 31 29 32 29 33 SP SD: 0.7907 c. M: 1.7437 c. 373: 30 31 32 29 34 29 32 31 30 32 30 33 SP SD: 0.6676 c. M: 1.5303 c. 385: 31 32 33 30 35 30 33 32 31 33 31 34 SP SD: 0.6461 c. M: 1.4216 c. 388: 32 31 33 31 35 31 33 32 31 34 31 34 SP SD: 0.8119 c. M: 1.2446 c. 392: 32 32 33 31 36 31 33 33 31 34 31 35 SP SD: 0.6254 c. M: 1.2779 c. 400: 33 32 34 32 36 32 34 33 32 35 32 35 SP SD: 0.8265 c. M: 1.0900 c. 404: 33 33 34 32 37 32 34 34 32 35 32 36 SP SD: 0.5775 c. M: 1.0657 c. 416: 34 34 35 33 38 33 35 35 33 36 33 37 SP SD: 0.5542 c. M:-1.0254 c. 428: 35 35 36 34 39 34 36 36 34 37 34 38 SP SD: 0.5543 c. M:-1.1063 c. 440: 36 36 37 35 40 35 37 37 35 38 35 39 SP SD: 0.5741 c. M:-1.1827 c. 463: 38 38 39 36 43 36 39 39 37 40 37 41 SP SD: 0.5293 c. M:-0.8862 c. 475: 39 39 40 37 44 37 40 40 38 41 38 42 SP SD: 0.4955 c. M:-0.9626 c. 487: 40 40 41 38 45 38 41 41 39 42 39 43 SP SD: 0.4822 c. M:-1.0353 c. 499: 41 41 42 39 46 39 42 42 40 43 40 44 SP SD: 0.4881 c. M:-1.1044 c. 510: 42 41 44 40 46 40 44 42 41 44 41 45 SP SD: 0.6183 c. M: 0.7959 c. 511: 42 42 43 40 47 40 43 43 41 44 41 45 SP SD: 0.5098 c. M:-1.1703 c. 523: 43 43 44 41 48 41 44 44 42 45 42 46 SP SD: 0.5436 c. M:-1.2331 c. 540: 44 44 46 42 50 42 46 45 43 47 43 48 SP SD: 0.5344 c. M: 1.0689 c. 552: 45 45 47 43 51 43 47 46 44 48 44 49 SP SD: 0.4378 c. M: 0.8757 c. 553: 45 45 47 44 50 44 47 46 44 48 44 49 SP SD: 0.5467 c. M: 0.7916 c. 557: 45 46 47 44 51 44 47 46 45 48 45 49 SP SD: 0.5373 c. M: 1.0971 c. 564: 46 46 48 44 52 44 48 47 45 49 45 50 SP SD: 0.3453 c. M: 0.6906 c. 576: 47 47 49 45 53 45 49 48 46 50 46 51 SP SD: 0.2567 c. M: 0.5133 c. 588: 48 48 50 46 54 46 50 49 47 51 47 52 SP SD: 0.1716 c. M: 0.3433 c. 600: 49 49 51 47 55 47 51 50 48 52 48 53 SP SD: 0.0900 c. M: 0.1800 c. 612: 50 50 52 48 56 48 52 51 49 53 49 54 SP SD: 0.0116 c. M: 0.0231 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: 1.9550 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.5097 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.5144 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.6959 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2834 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.8752 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.6678 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.9305 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.2619 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.0235 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.2446 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.6081 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.5227 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.9606 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.9357 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.3834 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.7885 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.1829 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.8794 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 1.9318 cents 48:51:54:57:60:64:68:72:76:80:85:90:96 S SD: 1.7367 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.7012 cents 51:54:57:61:64:68:72:76:81:85:91:96:102 SD: 1.5633 cents 58:61:65:69:73:78:82:87:92:97:103:109:116 SD: 1.5360 cents 59:62:66:70:74:79:83:88:94:99:105:111:118 SD: 1.4498 cents 65:69:73:77:82:87:92:97:103:109:116:122:130 SD: 1.3870 cents 66:70:74:78:83:88:93:99:105:111:117:124:132 SD: 1.3818 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 0.8430 cents 90:95:101:107:113:120:127:135:143:151:160:169:180 SD: 0.8286 cents 101:107:113:120:127:135:143:151:160:169:180:190:202 SD: 0.7484 cents 102:108:114:121:128:136:144:153:162:171:182:192:204 SD: 0.7427 cents 107:113:120:127:134:143:151:160:170:179:190:201:214 SD: 0.7248 cents 117:124:131:139:147:156:165:175:186:196:208:220:234 SD: 0.6390 cents 133:141:149:158:167:178:188:199:211:223:237:250:266 SD: 0.5132 cents 149:158:167:177:187:199:210:223:236:250:265:280:298 SD: 0.4750 cents 169:179:189:201:212:226:238:253:268:283:301:318:338 SD: 0.4579 cents 176:186:197:209:221:235:248:263:279:295:313:331:352 SD: 0.4404 cents 185:196:207:220:232:247:261:277:293:310:329:348:370 SD: 0.3662 cents 209:221:234:248:262:279:295:313:331:350:372:393:418 SD: 0.3606 cents 217:230:243:258:272:290:306:325:344:364:386:408:434 SD: 0.3505 cents 224:237:251:266:281:299:316:335:355:375:399:421:448 SD: 0.3447 cents 241:255:270:286:302:322:340:361:382:404:429:453:482 SD: 0.2777 cents 244:258:273:290:306:326:344:365:387:409:434:459:488 SD: 0.2668 cents 256:271:287:304:321:342:361:383:406:429:456:482:512 SD: 0.2614 cents 292:309:327:347:366:390:412:437:463:489:520:549:584 SD: 0.2242 cents 326:345:365:387:409:436:460:488:517:546:580:613:652 SD: 0.2163 cents 362:383:405:430:454:484:511:542:574:607:644:681:724 SD: 0.2077 cents 374:396:419:444:469:500:528:560:593:627:666:704:748 SD: 0.2074 cents 377:399:422:448:473:504:532:564:598:632:671:709:754 SD: 0.1551 cents 499:528:559:593:626:667:704:747:791:836:888:939:998 SD: 0.1300 cents 550:582:616:653:690:735:776:823:872:922:979:1035:1100 SD: 0.0977 cents