Scala analysis: neidhardt1
Neidhardt I temperament (1724)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 94.135 cents 94.135000 2: 196.090 cents 196.090000 3: 296.090 cents 296.090000 4: 392.180 cents 392.180000 5: 4/3 498.044999 perfect fourth 6: 592.180 cents 592.180000 7: 698.045 cents 698.045000 8: 796.090 cents 796.090000 9: 894.135 cents 894.135000 10: 16/9 996.089998 Pythagorean minor seventh 11: 1092.180 cents 1092.180000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 107.8200 cents 107.8200 1: 94.1350 cents 94.1350 2: 101.9550 cents 101.9550 3: 100.0000 cents 100.0000 4: 96.0900 cents 96.0900 5: 105.8650 cents 105.8650 6: 94.1350 cents 94.1350 7: 105.8650 cents 105.8650 8: 98.0450 cents 98.0450 9: 98.0450 cents 98.0450 10: 101.9550 cents 101.9550 11: 96.0900 cents 96.0900 12: 107.8200 cents 107.8200
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: 2 105.86500 cents 1: 1 107.82000 cents 2: 3 196.09000 cents 2: 1 198.04500 cents 2: 3 200.00000 cents 2: 3 201.95500 cents 2: 2 203.91000 cents 3: 3 296.09000 cents 3: 4 298.04500 cents 3: 2 301.95500 cents 3: 1 303.91000 cents 3: 2 305.86500 cents 4: 1 392.18000 cents 4: 1 394.13500 cents 4: 2 396.09000 cents 4: 2 400.00000 cents 4: 1 401.95500 cents 4: 5 403.91000 cents 5: 4 4/3 498.045 cents perfect fourth 5: 4 500.00000 cents 5: 4 501.95500 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: 4 698.04500 cents 7: 4 700.00000 cents 7: 4 701.95500 cents 8: 5 796.09000 cents 8: 1 798.04500 cents 8: 2 800.00000 cents 8: 2 803.91000 cents 8: 1 805.86500 cents 8: 1 807.82000 cents 9: 2 894.13500 cents 9: 1 896.09000 cents 9: 2 898.04500 cents 9: 4 901.95500 cents 9: 3 903.91000 cents 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 3 998.04500 cents 10: 3 1000.00000 cents 10: 1 1001.95500 cents 10: 3 1003.91000 cents 11: 1 1092.18000 cents 11: 2 1094.13500 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: 5.54545 = 61/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 94.1 196.1 296.1 392.2 498.0 592.2 698.0 796.1 894.1 996.1 1092.2 1200.0 94.1 : 102.0 202.0 298.0 403.9 498.0 603.9 702.0 800.0 902.0 998.0 1105.9 1200.0 196.1 : 100.0 196.1 302.0 396.1 502.0 600.0 698.0 800.0 896.1 1003.9 1098.0 1200.0 296.1 : 96.1 202.0 296.1 402.0 500.0 598.0 700.0 796.1 903.9 998.0 1100.0 1200.0 392.2 : 105.9 200.0 305.9 403.9 502.0 603.9 700.0 807.8 902.0 1003.9 1103.9 1200.0 498.0 : 94.1 200.0 298.0 396.1 498.0 594.1 702.0 796.1 898.0 998.0 1094.1 1200.0 592.2 : 105.9 203.9 302.0 403.9 500.0 607.8 702.0 803.9 903.9 1000.0 1105.9 1200.0 698.0 : 98.0 196.1 298.0 394.1 502.0 596.1 698.0 798.0 894.1 1000.0 1094.1 1200.0 796.1 : 98.0 200.0 296.1 403.9 498.0 600.0 700.0 796.1 902.0 996.1 1102.0 1200.0 894.1 : 102.0 198.0 305.9 400.0 502.0 602.0 698.0 803.9 898.0 1003.9 1102.0 1200.0 996.1 : 96.1 203.9 298.0 400.0 500.0 596.1 702.0 796.1 902.0 1000.0 1098.0 1200.0 1092.2: 107.8 202.0 303.9 403.9 500.0 605.9 700.0 805.9 903.9 1002.0 1103.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 94.1350 .. 107.8200 cents 13.68500 cents 94.13500 cents 2: 196.0900 .. 203.9100 cents 7.82000 cents 88.27000 cents 3: 296.0900 .. 305.8650 cents 9.77500 cents 92.18000 cents 4: 392.1800 .. 403.9100 cents 11.73000 cents 86.31500 cents 5: 498.0450 .. 501.9550 cents 3.91000 cents 94.13500 cents 6: 592.1800 .. 607.8200 cents 15.64000 cents 90.22500 cents 7: 698.0450 .. 701.9550 cents 3.91000 cents 90.22500 cents 8: 796.0900 .. 807.8200 cents 11.73000 cents 94.13500 cents 9: 894.1350 .. 903.9100 cents 9.77500 cents 86.31500 cents 10: 996.0900 .. 1003.9100 cents 7.82000 cents 92.18000 cents 11: 1092.1800 .. 1105.8650 cents 13.68500 cents 88.27000 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 : 107.82000 cents Average / Smallest step : 1.062304 Largest / Average step : 1.078200 Largest / Smallest step : 1.145376 Median interval of one step : 99.02250 cents, amount: 0 Least squares average step : 99.48268 cents, oct.: 1193.79212 cents Scale is strictly proper Step pattern alph. order: ABCDEAEFFBDG Step pattern size order : AEDBFAFCCEBG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 86.31500 cents Scale diversity : 1.075532 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.908767 Rothenberg efficiency : 0.259933 redundancy: 0.740067 Efficiency x scale size : 3.119192 Number of different interval sizes : 61 = 5.54545 / class Number of one step interval sizes : 7 Highest interval variety : 9 Mean interval variety : 5.54545 = 61/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1.95500 cents Most common intervals : 403.91000 cents & inv., amount: 5 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 3 different sizes of fifth 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 15.6400 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 : 3 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.1724 c. M:-7.8200 c. Twelve-tone Chromatic (1/11-comma) 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 5.1689 c. M: 11.1161 c. Schismic-12 63: 5 5 6 5 5 5 6 5 5 5 5 6 SP D3 SD: 5.1219 c. M:-8.6719 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.7113 c. M: 7.9812 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 2.8761 c. M:-6.5074 c. 86: 7 7 7 7 8 6 8 7 7 7 7 8 SP D3 SD: 3.2419 c. M: 6.1335 c. 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 2.4513 c. M:-6.1572 c. 90: 7 8 7 7 8 7 8 8 7 8 7 8 SP D3 SD: 3.6660 c. M: 5.5133 c. 93: 7 8 8 7 9 7 8 8 7 8 8 8 SP D3 SD: 3.3543 c. M:-5.1808 c. 98: 8 8 8 8 9 7 9 8 8 8 8 9 SP D3 SD: 2.5673 c. M: 4.4249 c. 101: 8 9 8 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.2977 c. M:-5.8902 c. 102: 8 9 8 8 9 8 9 9 8 9 8 9 SP D3 SD: 3.1021 c. M: 3.9447 c. 105: 8 9 9 8 10 8 9 9 8 9 9 9 SP D3 SD: 2.9384 c. M:-4.9629 c. 110: 9 9 9 9 10 8 10 9 9 9 9 10 SP D3 SD: 2.1622 c. M:-4.0468 c. 113: 9 10 9 9 10 9 10 9 9 10 9 10 SP M ME SD: 2.3047 c. M:-5.6799 c. 114: 9 10 9 9 10 9 10 10 9 10 9 10 SP D3 SD: 2.7612 c. M:-3.9100 c. 117: 9 10 10 9 11 9 10 10 9 10 9 11 SP SD: 2.6728 c. M: 5.0005 c. 122: 10 10 10 10 11 9 11 10 10 10 10 11 SP D3 SD: 1.9663 c. M:-4.2257 c. 134: 11 11 11 11 12 10 12 11 11 11 11 12 SP D3 SD: 1.9205 c. M:-4.3725 c. 142: 11 12 12 11 13 11 13 11 12 12 11 13 SP D3 SD: 1.8112 c. M: 3.4476 c. 154: 12 13 13 12 14 12 14 12 13 13 12 14 SP D3 SD: 1.5420 c. M:-3.2537 c. 158: 12 14 13 13 14 12 14 13 13 13 13 14 SP D3 S SD: 1.8054 c. M:-3.2208 c. 166: 13 14 14 13 15 13 15 13 14 14 13 15 SP D3 SD: 1.4042 c. M:-3.1598 c. 169: 13 15 14 13 15 13 15 14 14 14 14 15 SP SD: 1.7927 c. M: 2.8309 c. 176: 14 15 14 15 15 14 15 15 14 15 14 16 SP D3 SD: 1.7565 c. M:-3.2745 c. 177: 14 15 15 14 15 14 16 14 15 15 14 16 SP SD: 1.6277 c. M: 3.1297 c. 178: 14 15 15 14 16 14 16 14 15 15 14 16 SP D3 SD: 1.3760 c. M:-3.0786 c. 180: 14 15 15 15 16 14 16 14 15 15 15 16 SP T3 SD: 1.8999 c. M: 2.7567 c. 181: 14 16 15 14 16 14 16 15 15 15 15 16 SP SD: 1.6136 c. M:-2.8050 c. 189: 15 16 16 15 16 15 17 15 16 16 15 17 SP SD: 1.5263 c. M: 2.8069 c. 190: 15 16 16 15 17 15 17 15 16 16 15 17 SP D3 SD: 1.4254 c. M:-3.0076 c. 192: 15 16 16 16 17 15 17 15 16 16 16 17 SP T3 SD: 1.7616 c. M: 2.3400 c. 193: 15 17 16 15 17 15 17 16 16 16 16 17 SP SD: 1.5239 c. M:-2.8737 c. 196: 15 17 16 16 17 16 17 16 16 17 15 18 SP SD: 1.5003 c. M: 2.3841 c. 200: 16 17 16 16 18 16 17 17 16 17 16 18 SP SD: 1.5125 c. M: 2.1800 c. 201: 16 17 17 16 17 16 18 16 17 17 16 18 SP SD: 1.5018 c. M: 2.5226 c. 202: 16 17 17 16 18 16 18 16 17 17 16 18 SP D3 SD: 1.5211 c. M:-2.9451 c. 203: 16 17 17 16 18 16 18 17 16 17 17 18 SP SD: 1.4784 c. M: 2.9865 c. 207: 16 18 17 17 18 16 18 17 17 18 16 19 SP SD: 1.4680 c. M: 2.3928 c. 208: 16 18 17 17 18 17 18 17 17 18 16 19 SP SD: 1.3473 c. M:-2.0508 c. 215: 17 18 18 17 19 17 19 18 17 18 18 19 SP SD: 1.3187 c. M: 2.6016 c. 220: 17 19 18 18 19 18 19 18 18 19 17 20 SP SD: 1.2720 c. M:-2.3655 c. 227: 18 19 19 18 20 18 20 19 18 19 19 20 SP SD: 1.2335 c. M: 2.2574 c. 239: 19 20 20 19 21 19 21 20 19 20 20 21 SP SD: 1.2136 c. M:-2.3807 c. 243: 19 21 20 19 22 19 21 20 20 21 19 22 SP SD: 1.0837 c. M: 2.0565 c. 246: 19 21 21 19 22 19 22 20 20 21 20 22 SP SD: 1.2045 c. M: 1.9361 c. 251: 20 21 21 20 22 20 22 20 21 21 20 23 SP SD: 1.1866 c. M: 2.4645 c. 255: 20 22 21 20 23 20 22 21 21 22 20 23 SP SD: 0.9999 c. M: 1.5918 c. 258: 20 22 22 20 23 20 23 21 21 22 21 23 SP SD: 1.0004 c. M:-1.5844 c. 267: 21 23 22 21 24 21 23 22 22 23 21 24 SP SD: 0.9794 c. M:-1.6628 c. 270: 21 23 23 21 24 21 24 22 22 23 22 24 SP SD: 0.8539 c. M:-1.6878 c. 282: 22 24 24 22 25 22 25 23 23 24 23 25 SP SD: 0.7719 c. M:-1.7823 c. 294: 23 25 25 23 26 23 26 24 24 25 24 26 SP SD: 0.7554 c. M:-1.8692 c. 306: 24 26 26 24 27 24 27 25 25 26 25 27 SP SD: 0.7935 c. M:-1.9492 c. 318: 25 27 26 26 28 25 28 26 26 27 25 29 SP SD: 0.7051 c. M: 1.7504 c. 330: 26 28 27 27 29 26 29 27 27 28 26 30 SP SD: 0.6582 c. M: 1.5445 c. 333: 26 28 28 27 29 26 30 27 27 28 27 30 SP SD: 0.8589 c. M: 1.4954 c. 337: 26 29 28 27 30 26 30 28 27 29 27 30 SP SD: 0.8556 c. M: 1.5534 c. 342: 27 29 28 28 30 27 30 28 28 29 27 31 SP SD: 0.6654 c. M: 1.3532 c. 345: 27 29 29 28 30 27 31 28 28 29 28 31 SP SD: 0.7645 c. M: 1.3074 c. 354: 28 30 29 29 31 28 31 29 29 30 28 32 SP SD: 0.7152 c. M: 1.1747 c. 357: 28 30 30 29 31 28 32 29 29 30 29 32 SP SD: 0.7143 c. M: 1.1320 c. 369: 29 31 31 30 32 29 33 30 30 31 30 33 SP SD: 0.7077 c. M:-1.3159 c. 404: 32 34 34 32 36 31 36 33 33 34 33 36 SP SD: 0.6913 c. M: 1.0909 c. 410: 32 35 34 33 36 32 36 34 33 35 33 37 SP SD: 0.7645 c. M: 1.4596 c. 412: 32 35 35 33 36 32 37 33 34 35 33 37 SP SD: 0.7365 c. M:-1.0239 c. 416: 33 35 35 33 37 32 37 34 34 35 34 37 SP SD: 0.6999 c. M:-1.0892 c. 422: 33 36 35 34 37 33 37 35 34 36 34 38 SP SD: 0.6534 c. M: 1.3625 c. 434: 34 37 36 35 38 34 38 36 35 37 35 39 SP SD: 0.5715 c. M: 1.2708 c. 446: 35 38 37 36 39 35 39 37 36 38 36 40 SP SD: 0.5244 c. M: 1.1840 c. 458: 36 39 38 37 40 36 40 38 37 39 37 41 SP SD: 0.5148 c. M: 1.1018 c. 470: 37 40 39 38 41 37 41 39 38 40 38 42 SP SD: 0.5390 c. M: 1.0237 c. 487: 38 41 41 39 43 38 43 40 40 41 39 44 SP SD: 0.6276 c. M: 1.4288 c. 490: 38 42 41 39 43 39 43 40 40 42 39 44 SP SD: 0.4930 c. M: 1.0738 c. 492: 39 41 41 40 43 39 43 40 41 41 40 44 SP SD: 0.7596 c. M:-0.9870 c. 494: 39 42 41 39 44 39 43 41 40 42 40 44 SP SD: 0.6136 c. M: 1.0869 c. 498: 39 42 42 40 44 39 44 40 41 42 40 45 SP SD: 0.6337 c. M: 0.9093 c. 499: 39 42 42 40 44 39 44 41 41 42 40 45 SP SD: 0.5325 c. M: 1.3004 c. 502: 39 43 42 40 44 40 44 41 41 43 40 45 SP SD: 0.4723 c. M: 0.9079 c. 510: 40 43 43 41 45 40 45 41 42 43 41 46 SP SD: 0.6184 c. M: 0.7959 c. 511: 40 43 43 41 45 40 45 42 42 43 41 46 SP SD: 0.4609 c. M: 1.1781 c. 523: 41 44 44 42 46 41 46 43 43 44 42 47 SP SD: 0.4191 c. M: 1.0613 c. 535: 42 45 45 43 47 42 47 44 44 45 43 48 SP SD: 0.4109 c. M: 0.9498 c. 564: 44 48 47 45 50 44 50 46 46 48 45 51 SP SD: 0.4568 c. M: 0.6906 c. 576: 45 49 48 46 51 45 51 47 47 49 46 52 SP SD: 0.3395 c. M: 0.5133 c. 588: 46 50 49 47 52 46 52 48 48 50 47 53 SP SD: 0.2270 c. M: 0.3433 c. 600: 47 51 50 48 53 47 53 49 49 51 48 54 SP SD: 0.1191 c. M: 0.1800 c. 612: 48 52 51 49 54 48 54 50 50 52 49 55 SP SD: 0.0153 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: 3.2588 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.0402 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.0650 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.8159 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.9143 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.3982 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.0986 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1505 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.1764 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.4282 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.3948 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.8071 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.0883 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.0846 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 5.0294 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.0451 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.6561 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.4250 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.9185 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1996 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.1433 cents 48:51:54:57:60:64:68:72:76:80:85:90:96 S SD: 1.8710 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.7110 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.3298 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.2956 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 1.2611 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 1.0040 cents 75:79:84:89:94:100:106:112:119:126:133:141:150 SD: 0.9283 cents 86:91:96:102:108:115:121:129:136:144:153:162:172 SD: 0.9172 cents 90:95:101:107:113:120:127:135:143:151:160:169:180 SD: 0.8114 cents 91:96:102:108:114:121:128:136:144:153:162:171:182 SD: 0.7306 cents 108:114:121:128:135:144:152:162:171:181:192:203:216 SD: 0.6180 cents 123:130:138:146:154:164:173:184:195:206:219:231:246 SD: 0.5174 cents 149:157:167:177:187:199:210:223:236:250:265:280:298 SD: 0.4996 cents 157:166:176:186:197:209:221:235:249:263:279:295:314 SD: 0.4624 cents 176:186:197:209:221:235:248:263:279:295:313:331:352 SD: 0.4504 cents 177:187:198:210:222:236:249:265:280:297:315:333:354 SD: 0.3933 cents 198:209:222:235:248:264:279:296:314:332:352:372:396 SD: 0.3889 cents 216:228:242:256:271:288:304:323:342:362:384:406:432 SD: 0.2306 cents 284:300:318:337:356:379:400:425:450:476:505:534:568 SD: 0.2079 cents 306:323:343:363:384:408:431:458:485:513:544:575:612 SD: 0.2035 cents 358:378:401:425:449:477:504:536:567:600:636:673:716 SD: 0.1804 cents 449:474:503:533:563:599:632:672:711:753:798:844:898 SD: 0.1631 cents 483:510:541:573:606:644:680:723:765:810:859:908:966 SD: 0.1263 cents 558:589:625:662:700:744:786:835:884:935:992:1049:1116 SD: 0.1253 cents 574:606:643:681:720:765:808:859:909:962:1020:1079:1148 SD: 0.1120 cents