Scala analysis: Dent_523WT
Tom Dent's 5/32-comma proportional-beating well-temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96.145 cents 96.145150 2: 197.181 cents 197.180980 3: 298.167 cents 298.167430 4: 394.362 cents 394.361960 5: 499.389 cents 499.389140 6: 595.553 cents 595.553080 7: 698.590 cents 698.590490 8: 796.892 cents 796.892410 9: 895.771 cents 895.771470 10: 998.778 cents 998.778280 11: 1094.959 cents 1094.958680 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 105.0413 cents 105.0413 1: 96.1451 cents 96.1451 2: 101.0358 cents 101.0358 3: 100.9865 cents 100.9865 4: 96.1945 cents 96.1945 5: 105.0272 cents 105.0272 6: 96.1639 cents 96.1639 7: 103.0374 cents 103.0374 8: 98.3019 cents 98.3019 9: 98.8791 cents 98.8791 10: 103.0068 cents 103.0068 11: 96.1804 cents 96.1804 12: 105.0413 cents 105.0413
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 96.14515 cents 1: 1 96.16394 cents 1: 1 96.18040 cents 1: 1 96.19453 cents 1: 1 98.30192 cents 1: 1 98.87906 cents 1: 1 100.98645 cents 1: 1 101.03583 cents 1: 1 103.00681 cents 1: 1 103.03741 cents 1: 1 105.02718 cents 1: 1 105.04132 cents 2: 3 197.18098 cents 2: 1 199.18721 cents 2: 1 199.20135 cents 2: 1 201.18647 cents 2: 1 201.19112 cents 2: 2 201.22171 cents 2: 1 201.33933 cents 2: 1 201.88587 cents 2: 1 202.02228 cents 3: 1 297.36687 cents 3: 1 297.38565 cents 3: 1 297.50327 cents 3: 1 298.06627 cents 3: 1 298.16743 cents 3: 1 298.21681 cents 3: 1 300.18779 cents 3: 1 300.21839 cents 3: 1 302.20816 cents 3: 1 302.22230 cents 3: 2 304.22853 cents 4: 1 394.36196 cents 4: 1 396.36819 cents 4: 1 396.38233 cents 4: 1 398.37210 cents 4: 1 398.40270 cents 4: 1 400.37368 cents 4: 1 400.42306 cents 4: 1 402.53045 cents 4: 1 403.10759 cents 4: 1 403.20875 cents 4: 1 403.22520 cents 4: 1 403.24399 cents 5: 1 498.72498 cents 5: 1 499.25274 cents 5: 3 499.38914 cents 5: 1 499.40328 cents 5: 1 499.40560 cents 5: 1 499.40793 cents 5: 4 501.40951 cents 6: 1 595.55308 cents 6: 1 595.56954 cents 6: 1 595.58368 cents 6: 1 597.55466 cents 6: 1 597.60404 cents 6: 1 599.71143 cents 6: 1 600.28857 cents 6: 1 602.39596 cents 6: 1 602.44534 cents 6: 1 604.41632 cents 6: 1 604.43046 cents 6: 1 604.44692 cents 7: 4 698.59049 cents 7: 1 700.59207 cents 7: 1 700.59440 cents 7: 1 700.59672 cents 7: 3 700.61085 cents 7: 1 700.74726 cents 7: 1 701.27502 cents 8: 1 796.75601 cents 8: 1 796.77480 cents 8: 1 796.79125 cents 8: 1 796.89241 cents 8: 1 797.46955 cents 8: 1 799.57694 cents 8: 1 799.62632 cents 8: 1 801.59730 cents 8: 1 801.62790 cents 8: 1 803.61767 cents 8: 1 803.63181 cents 8: 1 805.63804 cents 9: 2 895.77147 cents 9: 1 897.77770 cents 9: 1 897.79184 cents 9: 1 899.78161 cents 9: 1 899.81221 cents 9: 1 901.78319 cents 9: 1 901.83257 cents 9: 1 901.93373 cents 9: 1 902.49673 cents 9: 1 902.61435 cents 9: 1 902.63313 cents 10: 1 997.97772 cents 10: 1 998.11413 cents 10: 1 998.66067 cents 10: 2 998.77828 cents 10: 1 998.80888 cents 10: 1 998.81353 cents 10: 1 1000.79865 cents 10: 1 1000.81279 cents 10: 3 1002.81902 cents 11: 1 1094.95868 cents 11: 1 1094.97282 cents 11: 1 1096.96259 cents 11: 1 1096.99319 cents 11: 1 1098.96417 cents 11: 1 1099.01355 cents 11: 1 1101.12094 cents 11: 1 1101.69808 cents 11: 1 1103.80547 cents 11: 1 1103.81960 cents 11: 1 1103.83606 cents 11: 1 1103.85485 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 10.36364 = 114/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 96.1 197.2 298.2 394.4 499.4 595.6 698.6 796.9 895.8 998.8 1095.0 1200.0 96.1 : 101.0 202.0 298.2 403.2 499.4 602.4 700.7 799.6 902.6 998.8 1103.9 1200.0 197.2 : 101.0 197.2 302.2 398.4 501.4 599.7 698.6 801.6 897.8 1002.8 1099.0 1200.0 298.2 : 96.2 201.2 297.4 400.4 498.7 597.6 700.6 796.8 901.8 998.0 1099.0 1200.0 394.4 : 105.0 201.2 304.2 402.5 501.4 604.4 700.6 805.6 901.8 1002.8 1103.8 1200.0 499.4 : 96.2 199.2 297.5 396.4 499.4 595.6 700.6 796.8 897.8 998.8 1095.0 1200.0 595.6 : 103.0 201.3 300.2 403.2 499.4 604.4 700.6 801.6 902.6 998.8 1103.8 1200.0 698.6 : 98.3 197.2 300.2 396.4 501.4 597.6 698.6 799.6 895.8 1000.8 1097.0 1200.0 796.9 : 98.9 201.9 298.1 403.1 499.3 600.3 701.3 797.5 902.5 998.7 1101.7 1200.0 895.8 : 103.0 199.2 304.2 400.4 501.4 602.4 698.6 803.6 899.8 1002.8 1101.1 1200.0 998.8 : 96.2 201.2 297.4 398.4 499.4 595.6 700.6 796.8 899.8 998.1 1097.0 1200.0 1095.0: 105.0 201.2 302.2 403.2 499.4 604.4 700.6 803.6 901.9 1000.8 1103.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 96.1451 .. 105.0413 cents 8.89617 cents 96.14515 cents 2: 197.1810 .. 202.0223 cents 4.84130 cents 92.13966 cents 3: 297.3669 .. 304.2285 cents 6.86166 cents 95.34459 cents 4: 394.3620 .. 403.2440 cents 8.88203 cents 90.13343 cents 5: 498.7250 .. 501.4095 cents 2.68453 cents 95.48099 cents 6: 595.5531 .. 604.4469 cents 8.89384 cents 94.14357 cents 7: 698.5905 .. 701.2750 cents 2.68453 cents 94.14357 cents 8: 796.7560 .. 805.6380 cents 8.88203 cents 95.48099 cents 9: 895.7715 .. 902.6331 cents 6.86166 cents 90.13343 cents 10: 997.9777 .. 1002.8190 cents 4.84130 cents 95.34459 cents 11: 1094.9587 .. 1103.8548 cents 8.89617 cents 92.13966 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 96.14515 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 105.04132 cents Average / Smallest step : 1.040094 Largest / Average step : 1.050413 Largest / Smallest step : 1.092529 Median interval of one step : 99.93276 cents, amount: 0 Least squares average step : 99.68041 cents, oct.: 1196.16490 cents Scale is strictly proper Step pattern alph. order: ABCDEFGHIJKL Step pattern size order : AHGDKBJEFICL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.13343 cents Scale diversity : 1.049961 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.938979 Rothenberg efficiency : 0.188089 redundancy: 0.811911 Efficiency x scale size : 2.257071 Number of different interval sizes : 114 = 10.36364 / class Number of one step interval sizes : 12 Highest interval variety : 12 Mean interval variety : 10.36364 = 114/11 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 0.00232 cents Most common intervals : 501.40951 cents & inv., amount: 4 Most common triad is 0.0 501.410 698.590 cents, amount: 3 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 7 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 8.8962 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions with margin 8.8820 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: 3.3483 c. M:-5.6380 c. Twelve-tone Chromatic (1/11-comma) 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 2.8850 c. M: 5.8838 c. 91: 7 8 8 7 8 7 8 7 8 8 7 8 SP M ME SD: 2.8235 c. M: 5.6836 c. Meantone Chromatic (1/7-comma), Romieu-12 98: 8 8 8 8 9 8 8 8 8 9 7 9 SP D3 SD: 3.1116 c. M:-5.3034 c. 101: 8 8 9 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.7807 c. M: 7.0820 c. 103: 8 9 9 8 9 8 9 8 9 9 8 9 SP M ME SD: 2.4680 c. M:-4.7452 c. Meantone Chromatic (3/22-comma) 113: 9 10 9 9 10 9 10 9 9 10 9 10 SP M ME SD: 1.9578 c. M:-4.5889 c. 115: 9 10 10 9 10 9 10 9 10 10 9 10 SP M ME SD: 2.2417 c. M:-4.4413 c. Meantone Chromatic (3/23-comma), Preston-12 121: 10 10 10 10 10 10 10 10 10 11 9 11 SP D3 SD: 2.8201 c. M: 4.3756 c. 122: 10 10 10 10 11 10 10 10 10 11 9 11 SP D3 SD: 2.4340 c. M:-4.5004 c. 125: 10 11 10 10 11 10 11 10 10 11 10 11 SP M ME SD: 1.7026 c. M:-4.4190 c. 127: 10 11 11 10 11 10 11 10 11 11 10 11 SP M ME SD: 2.1058 c. M:-4.1948 c. Meantone Chromatic (1/8-comma) 133: 11 11 11 11 11 11 11 11 11 12 10 12 SP D3 SD: 2.5163 c. M: 3.8536 c. 134: 11 11 11 11 12 11 11 11 11 12 10 12 SP D3 SD: 2.2464 c. M:-4.4469 c. 137: 11 12 11 11 12 11 12 11 11 12 11 12 SP M ME SD: 1.5463 c. M:-4.2789 c. 141: 11 12 12 11 13 11 12 12 11 12 12 12 SP D3 SD: 2.1763 c. M:-3.1076 c. 146: 12 12 12 12 13 11 13 12 12 13 11 13 SP D3 S SD: 2.0137 c. M:-3.9614 c. 149: 12 12 13 12 13 12 13 12 12 13 12 13 SP M ME SD: 1.4026 c. M: 3.8924 c. 161: 13 13 14 13 14 13 14 13 13 14 13 14 SP M ME SD: 1.2872 c. M: 3.3922 c. 173: 14 14 15 14 15 14 15 14 14 15 14 15 SP M ME SD: 1.2323 c. M: 2.9613 c. 185: 15 15 16 15 16 15 16 15 15 16 15 16 SP M ME SD: 1.2228 c. M: 2.5864 c. 197: 16 16 17 16 17 16 17 16 16 17 16 17 SP M ME SD: 1.2448 c. M: 2.2571 c. 209: 17 17 18 17 18 17 18 17 17 18 17 18 SP M ME SD: 1.2867 c. M: 1.9657 c. 214: 17 18 18 17 19 17 18 18 18 18 17 19 SP D3 S SD: 1.3856 c. M: 3.2634 c. 220: 18 18 19 17 20 17 19 18 18 19 18 19 SP SD: 1.3553 c. M:-2.4290 c. 221: 18 18 19 18 19 18 19 18 18 19 18 19 SP M ME SD: 1.3403 c. M:-2.0181 c. 225: 18 19 19 18 20 18 19 18 19 19 18 20 SP SD: 1.1929 c. M: 2.2257 c. 226: 18 19 19 18 20 18 19 19 19 19 18 20 SP D3 S SD: 1.2181 c. M: 3.0153 c. 237: 19 20 20 19 21 19 20 19 20 20 19 21 SP SD: 1.1304 c. M: 1.9557 c. 238: 19 20 20 19 21 19 20 20 20 20 19 21 SP D3 S SD: 1.0865 c. M: 2.7922 c. 250: 20 21 21 20 22 20 22 20 21 21 20 22 SP D3 SD: 0.9091 c. M:-2.2095 c. 252: 20 21 22 20 22 20 22 20 21 22 20 22 SP T3 SD: 1.1465 c. M: 1.9429 c. 261: 21 22 22 21 23 21 22 21 22 22 21 23 SP SD: 1.0898 c. M:-2.1481 c. 262: 21 22 22 21 23 21 23 21 22 22 21 23 SP D3 SD: 0.8753 c. M:-2.1729 c. 264: 21 22 23 21 23 21 23 21 22 23 21 23 SP T3 SD: 1.0911 c. M:-1.8326 c. 274: 22 23 23 22 24 22 24 22 23 23 22 24 SP D3 SD: 0.8694 c. M:-2.1394 c. 286: 23 24 24 23 25 23 24 24 23 25 23 25 SP D3 SD: 0.8680 c. M: 2.0870 c. 297: 24 25 25 24 26 23 26 24 25 25 24 26 SP SD: 1.0361 c. M:-1.6210 c. 298: 24 25 25 24 26 24 25 25 24 26 24 26 SP D3 SD: 0.8131 c. M: 1.9462 c. 310: 25 26 26 25 27 25 26 26 25 27 25 27 SP D3 SD: 0.7837 c. M: 1.8163 c. 322: 26 27 27 26 28 26 27 27 26 28 26 28 SP D3 SD: 0.7768 c. M: 1.6961 c. 334: 27 28 28 27 29 27 28 28 27 29 27 29 SP D3 SD: 0.7884 c. M: 1.5845 c. 339: 27 29 28 27 30 27 29 28 28 29 27 30 SP SD: 0.8370 c. M: 1.4416 c. 342: 27 29 29 27 30 28 29 28 28 30 27 30 SP SD: 0.8873 c. M: 1.4083 c. 346: 28 29 29 28 30 28 29 29 28 30 28 30 SP D3 SD: 0.8140 c. M: 1.4807 c. 351: 28 30 29 28 31 28 30 29 29 30 28 31 SP SD: 0.7337 c. M: 1.1996 c. 363: 29 31 30 29 32 29 31 30 30 31 29 32 SP SD: 0.6483 c. M:-1.1661 c. 375: 30 32 31 30 33 30 32 31 31 32 30 33 SP SD: 0.5822 c. M:-1.2190 c. 387: 31 33 32 31 34 31 33 32 32 33 31 34 SP SD: 0.5369 c. M:-1.2686 c. 399: 32 34 33 32 35 32 34 33 33 34 32 35 SP SD: 0.5131 c. M:-1.3153 c. 407: 33 34 34 33 35 33 35 33 34 35 32 36 SP SD: 0.7135 c. M:-1.1521 c. 411: 33 35 34 33 36 33 35 34 34 35 33 36 SP SD: 0.5096 c. M:-1.3592 c. 423: 34 36 35 34 37 34 36 35 35 36 34 37 SP SD: 0.5237 c. M:-1.4006 c. 434: 35 36 37 35 38 34 38 35 36 37 35 38 SP SD: 0.7281 c. M: 1.0830 c. 435: 35 36 37 35 38 35 37 36 36 37 35 38 SP SD: 0.5254 c. M: 1.3189 c. 471: 38 39 40 38 41 38 40 39 39 40 38 41 SP SD: 0.5876 c. M:-1.0438 c. 476: 38 40 40 38 42 38 41 39 39 41 38 42 SP S SD: 0.5909 c. M: 1.0846 c. 482: 39 40 41 38 43 38 42 39 40 41 39 42 SP SD: 0.6791 c. M:-1.0258 c. 483: 39 40 41 39 42 39 41 40 40 41 39 42 SP SD: 0.6251 c. M:-1.1229 c. 488: 39 41 41 39 43 39 42 40 40 42 39 43 SP S SD: 0.4992 c. M: 0.9193 c. 500: 40 42 42 40 44 40 43 41 41 43 40 44 SP S SD: 0.4139 c. M: 0.7620 c. 512: 41 43 43 41 45 41 44 42 42 44 41 45 SP S SD: 0.3357 c. M: 0.6120 c. 524: 42 44 44 42 46 42 45 43 43 45 42 46 SP S SD: 0.2663 c. M: 0.4688 c. 536: 43 45 45 43 47 43 46 44 44 46 43 47 SP S SD: 0.2098 c. M: 0.4062 c. 548: 44 46 46 44 48 44 47 45 45 47 44 48 SP S SD: 0.1735 c. M: 0.3572 c. 560: 45 47 47 45 49 45 48 46 46 48 45 49 SP S SD: 0.1662 c. M: 0.3103 c. 1084: 87 91 91 87 95 87 93 89 89 93 87 95 SP S SD: 0.1885 c. M: 0.3815 c. 1108: 89 93 93 89 97 89 95 91 91 95 89 97 SP S SD: 0.1659 c. M: 0.3335 c. 1151: 92 97 97 92 101 92 99 94 95 99 92 101 SP SD: 0.1938 c. M: 0.3676 c. 1163: 93 98 98 93 102 93 100 95 96 100 93 102 SP SD: 0.1602 c. M: 0.3318 c. 1175: 94 99 99 94 103 94 101 96 97 101 94 103 SP SD: 0.1287 c. M: 0.2967 c. 1187: 95 100 100 95 104 95 102 97 98 102 95 104 SP SD: 0.1006 c. M: 0.2622 c. 1199: 96 101 101 96 105 96 103 98 99 103 96 105 SP SD: 0.0786 c. M: 0.2285 c. 1211: 97 102 102 97 106 97 104 99 100 104 97 106 SP SD: 0.0678 c. M: 0.1955 c. 1223: 98 103 103 98 107 98 105 100 101 105 98 107 SP SD: 0.0723 c. M: 0.1631 c. 1235: 99 104 104 99 108 99 106 101 102 106 99 108 SP SD: 0.0892 c. M:-0.1322 c. 1723: 138 145 145 138 151 138 148 141 142 148 138 151 SP SD: 0.0937 c. M: 0.1658 c. 1735: 139 146 146 139 152 139 149 142 143 149 139 152 SP SD: 0.0717 c. M: 0.1256 c. 1747: 140 147 147 140 153 140 150 143 144 150 140 153 SP SD: 0.0516 c. M: 0.0979 c. 1759: 141 148 148 141 154 141 151 144 145 151 141 154 SP SD: 0.0359 c. M: 0.0760 c. 1771: 142 149 149 142 155 142 152 145 146 152 142 155 SP SD: 0.0313 c. M:-0.0717 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: 1.6823 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.8305 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.7992 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.6680 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.4308 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.5355 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.7715 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.0952 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0610 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.1048 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.3802 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.6923 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.5652 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.9715 cents 20:21:22:24:25:27:28:30:32:34:36:38:40 SD: 4.9670 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.1231 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.7157 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.3483 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.8148 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.0790 cents 48:51:54:57:60:64:68:72:76:81:85:90:96 SD: 1.8534 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.7153 cents 51:54:57:61:64:68:72:76:81:86:91:96:102 SD: 1.5493 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.3562 cents 66:70:74:78:83:88:93:99:105:111:118:124:132 SD: 1.3517 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 1.0978 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 1.0064 cents 75:79:84:89:94:100:106:112:119:126:134:141:150 SD: 0.9766 cents 86:91:96:102:108:115:121:129:136:144:153:162:172 SD: 0.9420 cents 90:95:101:107:113:120:127:135:143:151:160:169:180 SD: 0.7200 cents 117:124:131:139:147:156:165:175:185:196:208:220:234 SD: 0.6324 cents 137:145:154:163:172:183:193:205:217:230:244:258:274 SD: 0.6010 cents 149:158:167:177:187:199:210:223:236:250:265:280:298 SD: 0.5743 cents 155:164:174:184:195:207:219:232:246:260:276:292:310 SD: 0.5453 cents 156:165:175:185:196:208:220:234:247:262:278:294:312 SD: 0.5209 cents 159:168:178:189:200:212:224:238:252:267:283:299:318 SD: 0.4183 cents 192:203:215:228:241:256:271:287:304:322:342:361:384 SD: 0.3649 cents 207:219:232:246:260:276:292:310:328:347:369:390:414 SD: 0.3058 cents 246:260:276:292:309:328:347:368:390:413:438:463:492 SD: 0.2907 cents 266:281:298:316:334:355:375:398:421:446:474:501:532 SD: 0.2885 cents 281:297:315:334:353:375:396:421:445:471:500:529:562 SD: 0.2762 cents 282:298:316:335:354:376:398:422:447:473:502:531:564 SD: 0.1898 cents 332:351:372:394:417:443:468:497:526:557:591:625:664 SD: 0.1844 cents 356:376:399:423:447:475:502:533:564:597:634:670:712 SD: 0.1618 cents 457:483:512:543:574:610:645:684:724:767:814:860:914 SD: 0.1452 cents 505:534:566:600:634:674:712:756:800:847:899:951:1010 SD: 0.1379 cents 563:595:631:669:707:751:794:843:892:945:1002:1060:1126 SD: 0.1337 cents 575:608:644:683:722:767:811:861:911:965:1024:1082:1150 SD: 0.1320 cents 580:613:650:689:728:774:818:868:919:973:1033:1092:1160 SD: 0.1145 cents