Scala analysis: whelp3
well-temperament with three pure thirds
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92.401 cents 92.401428 2: 193.157 cents 193.156857 3: 293.912 cents 293.912285 4: 386.314 cents 386.313714 5: 501.155 cents 501.155286 6: 591.202 cents 591.201673 7: 698.845 cents 698.844714 8: 793.157 cents 793.156857 9: 887.469 cents 887.469000 10: 995.112 cents 995.112040 11: 1085.158 cents 1085.158428 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 114.8416 cents 114.8416 1: 92.4014 cents 92.4014 2: 100.7554 cents 100.7554 3: 100.7554 cents 100.7554 4: 92.4014 cents 92.4014 5: 114.8416 cents 114.8416 6: 90.0464 cents 90.0464 7: 107.6430 cents 107.6430 8: 94.3121 cents 94.3121 9: 94.3121 cents 94.3121 10: 107.6430 cents 107.6430 11: 90.0464 cents 90.0464 12: 114.8416 cents 114.8416
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 90.04639 cents 1: 2 92.40143 cents 1: 2 94.31214 cents 1: 2 100.75543 cents 1: 2 107.64304 cents 1: 2 114.84157 cents 2: 1 188.62429 cents 2: 2 193.15686 cents 2: 2 197.68943 cents 2: 1 201.51086 cents 2: 2 201.95518 cents 2: 2 204.88796 cents 2: 2 207.24300 cents 3: 2 292.00157 cents 3: 2 293.91228 cents 3: 2 296.26733 cents 3: 2 297.28939 cents 3: 2 307.99843 cents 3: 2 312.53100 cents 4: 3 386.31371 cents 4: 2 398.04482 cents 4: 1 403.91037 cents 4: 2 404.93243 cents 4: 2 406.84314 cents 4: 2 408.75386 cents 5: 2 493.95675 cents 5: 2 498.80025 cents 5: 2 499.24457 cents 5: 4 501.15529 cents 5: 2 505.68786 cents 6: 1 584.00314 cents 6: 2 591.20167 cents 6: 2 593.55672 cents 6: 2 600.00000 cents 6: 2 606.44329 cents 6: 2 608.79833 cents 6: 1 615.99686 cents 7: 2 694.31214 cents 7: 4 698.84471 cents 7: 2 700.75543 cents 7: 2 701.19975 cents 7: 2 706.04325 cents 8: 2 791.24614 cents 8: 2 793.15686 cents 8: 2 795.06757 cents 8: 1 796.08963 cents 8: 2 801.95518 cents 8: 3 813.68629 cents 9: 2 887.46900 cents 9: 2 892.00157 cents 9: 2 902.71061 cents 9: 2 903.73267 cents 9: 2 906.08772 cents 9: 2 907.99843 cents 10: 2 992.75700 cents 10: 2 995.11204 cents 10: 2 998.04482 cents 10: 1 998.48914 cents 10: 2 1002.31057 cents 10: 2 1006.84314 cents 10: 1 1011.37571 cents 11: 2 1085.15843 cents 11: 2 1092.35696 cents 11: 2 1099.24457 cents 11: 2 1105.68786 cents 11: 2 1107.59857 cents 11: 2 1109.95361 cents Highest number of different intervals for one interval class: 7 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 : 92.4 193.2 293.9 386.3 501.2 591.2 698.8 793.2 887.5 995.1 1085.2 1200.0 92.4 : 100.8 201.5 293.9 408.8 498.8 606.4 700.8 795.1 902.7 992.8 1107.6 1200.0 193.2 : 100.8 193.2 308.0 398.0 505.7 600.0 694.3 802.0 892.0 1006.8 1099.2 1200.0 293.9 : 92.4 207.2 297.3 404.9 499.2 593.6 701.2 791.2 906.1 998.5 1099.2 1200.0 386.3 : 114.8 204.9 312.5 406.8 501.2 608.8 698.8 813.7 906.1 1006.8 1107.6 1200.0 501.2 : 90.0 197.7 292.0 386.3 494.0 584.0 698.8 791.2 892.0 992.8 1085.2 1200.0 591.2 : 107.6 202.0 296.3 403.9 494.0 608.8 701.2 802.0 902.7 995.1 1110.0 1200.0 698.8 : 94.3 188.6 296.3 386.3 501.2 593.6 694.3 795.1 887.5 1002.3 1092.4 1200.0 793.2 : 94.3 202.0 292.0 406.8 499.2 600.0 700.8 793.2 908.0 998.0 1105.7 1200.0 887.5 : 107.6 197.7 312.5 404.9 505.7 606.4 698.8 813.7 903.7 1011.4 1105.7 1200.0 995.1 : 90.0 204.9 297.3 398.0 498.8 591.2 706.0 796.1 903.7 998.0 1092.4 1200.0 1085.2: 114.8 207.2 308.0 408.8 501.2 616.0 706.0 813.7 908.0 1002.3 1110.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.0464 .. 114.8416 cents 24.79519 cents 90.04639 cents 2: 188.6243 .. 207.2430 cents 18.61871 cents 73.78271 cents 3: 292.0016 .. 312.5310 cents 20.52943 cents 84.75857 cents 4: 386.3137 .. 408.7539 cents 22.44014 cents 73.78271 cents 5: 493.9568 .. 505.6879 cents 11.73110 cents 85.20290 cents 6: 584.0031 .. 615.9969 cents 31.99372 cents 78.31529 cents 7: 694.3121 .. 706.0432 cents 11.73110 cents 78.31529 cents 8: 791.2461 .. 813.6863 cents 22.44014 cents 85.20290 cents 9: 887.4690 .. 907.9984 cents 20.52943 cents 73.78271 cents 10: 992.7570 .. 1011.3757 cents 18.61871 cents 84.75857 cents 11: 1085.1584 .. 1109.9536 cents 24.79519 cents 73.78271 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 90.04639 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 114.84157 cents Average / Smallest step : 1.110539 Largest / Average step : 1.148416 Largest / Smallest step : 1.275360 Median interval of one step : 97.53379 cents, amount: 0 Least squares average step : 99.18607 cents, oct.: 1190.23284 cents Scale is strictly proper Step pattern alph. order: ABBACDEFFEDC Step pattern size order : BDDBFAECCEAF Scale is a Constant Structure, by a margin of 73.78271 cents Scale diversity : 1.160508 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.809814 Rothenberg efficiency : 0.249074 redundancy: 0.750926 Efficiency x scale size : 2.988889 Number of different interval sizes : 67 = 6.09091 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.09091 = 67/11 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.44433 cents Most common intervals : 501.15529 cents & inv., amount: 4 Most common triad is 0.0 501.155 698.845 cents, amount: 2 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 24.7952 cents: 2 5 7 10 Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 8 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.4510 c. M:-14.8416 c. Twelve-tone Chromatic (1/11-comma) 38: 3 3 3 3 4 3 3 3 3 3 3 4 SP D3 S SD: 7.6142 c. M: 16.1647 c. 40: 3 3 4 3 4 3 3 3 4 3 3 4 SP D3 SD: 8.3977 c. M: 13.1569 c. 41: 3 3 4 3 4 3 4 3 3 4 3 4 SP M ME SD: 6.6243 c. M: 17.5471 c. 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 6.8913 c. M:-13.0645 c. Meantone Chromatic (1/5-comma) 50: 4 4 4 4 5 4 4 4 4 4 4 5 SP D3 S SD: 4.9992 c. M: 11.1120 c. 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 3.7342 c. M:-10.6167 c. Schismic-12 55: 4 5 4 5 5 4 5 4 5 5 4 5 SP M ME SD: 5.8008 c. M: 10.2759 c. 56: 4 5 5 4 5 5 5 4 4 5 5 5 SP D3 S SD: 6.6093 c. M: 9.3978 c. 61: 5 5 5 5 6 4 6 4 5 6 4 6 SP SD: 5.8921 c. M:-10.3201 c. 62: 5 5 5 5 6 5 5 5 5 5 5 6 SP D3 S SD: 4.0100 c. M:-8.7983 c. 63: 5 5 5 5 6 5 6 5 5 5 5 6 SP D3 SD: 5.0886 c. M: 8.1980 c. 65: 5 5 6 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.0795 c. M: 8.5415 c. 74: 6 6 6 6 7 5 7 6 6 6 6 7 SP D3 SD: 3.6133 c. M: 7.4179 c. 77: 6 6 7 6 7 6 7 6 6 7 6 7 SP M ME SD: 3.0199 c. M: 6.1439 c. 81: 6 7 7 6 8 6 7 7 6 7 6 8 SP SD: 2.9333 c. M:-6.8431 c. 83: 6 7 7 7 8 6 7 7 6 8 6 8 SP SD: 3.9745 c. M: 5.6544 c. 86: 7 7 7 7 8 6 8 7 7 7 7 8 SP D3 SD: 3.5048 c. M:-5.5543 c. 89: 7 7 8 7 8 7 8 7 7 8 7 8 SP M ME SD: 3.3453 c. M:-6.9764 c. 93: 7 8 8 7 9 7 8 7 8 8 7 9 SP SD: 2.5221 c. M: 6.0601 c. 94: 7 8 8 7 9 7 9 7 7 9 7 9 SP D3 S SD: 2.9932 c. M: 6.6179 c. 95: 7 8 8 8 9 7 8 8 7 9 7 9 SP SD: 3.3558 c. M:-5.2652 c. 100: 8 8 8 8 10 7 9 8 8 9 7 10 SP S SD: 3.0283 c. M: 5.9123 c. 103: 8 9 8 8 10 8 9 8 8 9 8 10 SP SD: 2.5000 c. M:-4.9014 c. 105: 8 9 9 8 10 8 9 8 9 9 8 10 SP SD: 2.4282 c. M: 4.5854 c. 106: 8 9 9 8 10 8 10 8 8 10 8 10 SP D3 S SD: 2.1430 c. M: 4.4501 c. 118: 9 10 10 9 11 9 11 9 9 11 9 11 SP D3 S SD: 1.7900 c. M:-2.9772 c. 130: 10 11 11 10 12 10 12 10 10 12 10 12 SP D3 S SD: 1.8556 c. M:-4.0723 c. 144: 11 12 12 11 14 11 13 11 11 13 11 14 SP S SD: 2.1232 c. M: 4.1357 c. 146: 11 13 12 11 14 11 13 12 11 13 11 14 SP SD: 1.8802 c. M:-4.1034 c. 156: 12 13 13 12 15 12 14 12 12 14 12 15 SP S SD: 1.5029 c. M: 2.8536 c. 168: 13 14 14 13 16 13 15 13 13 15 13 16 SP S SD: 1.1454 c. M: 2.2549 c. 180: 14 15 15 14 17 14 16 14 14 16 14 17 SP S SD: 1.1063 c. M:-2.1317 c. 218: 17 18 18 17 21 16 20 17 17 20 16 21 SP S SD: 1.1596 c. M: 2.2108 c. 223: 17 19 19 17 21 17 20 17 18 20 17 21 SP SD: 1.1697 c. M: 2.1255 c. 229: 18 19 19 18 22 17 20 18 18 21 17 22 SP SD: 1.3618 c. M:-1.9217 c. 230: 18 19 19 18 22 17 21 18 18 21 17 22 SP S SD: 0.9345 c. M: 1.7384 c. 242: 19 20 20 19 23 18 22 19 19 22 18 23 SP S SD: 0.9152 c. M:-1.8134 c. 280: 22 23 24 21 27 21 25 22 22 25 21 27 SP SD: 0.8703 c. M:-1.8843 c. 285: 22 24 24 22 27 21 26 22 23 25 22 27 SP SD: 0.9960 c. M: 1.7280 c. 292: 22 25 24 23 28 22 26 23 23 26 22 28 SP SD: 0.8839 c. M: 2.1315 c. 297: 23 25 25 23 28 22 27 23 24 26 23 28 SP SD: 1.0803 c. M:-1.7103 c. 299: 23 25 25 23 29 22 27 23 24 27 22 29 SP SD: 1.0537 c. M: 2.5214 c. 304: 23 26 25 24 29 23 27 24 24 27 23 29 SP SD: 0.8114 c. M: 1.8070 c. 307: 24 25 26 24 29 23 28 24 24 28 23 29 SP SD: 1.0392 c. M:-1.6306 c. 310: 24 26 26 24 29 24 28 24 24 28 23 30 SP SD: 0.9839 c. M:-1.8004 c. 311: 24 26 26 24 30 23 28 25 24 28 23 30 SP SD: 0.6921 c. M:-1.6984 c. 316: 24 27 26 25 30 24 28 25 25 28 24 30 SP SD: 0.8704 c. M: 1.5072 c. 323: 25 27 27 25 31 24 29 25 26 29 24 31 SP SD: 0.6396 c. M: 1.8256 c. 324: 25 27 27 25 31 25 29 25 26 29 24 31 SP SD: 0.9879 c. M:-1.4199 c. 327: 25 28 27 25 32 24 29 26 26 29 25 31 SP SD: 0.9453 c. M:-1.5970 c. 333: 26 28 28 25 32 25 30 26 26 30 25 32 SP SD: 0.8435 c. M:-1.5832 c. 335: 26 28 28 26 32 25 30 26 27 30 25 32 SP SD: 0.6349 c. M: 1.5151 c. 347: 27 29 29 27 33 26 31 27 28 31 26 33 SP SD: 0.7536 c. M:-1.2918 c. 364: 28 31 30 28 35 27 33 29 28 33 27 35 SP SD: 0.7318 c. M:-1.3486 c. 375: 29 31 32 29 36 28 33 30 29 34 28 36 SP SD: 0.8027 c. M:-1.2447 c. 376: 29 32 31 29 36 28 34 30 29 34 28 36 SP SD: 0.6984 c. M:-1.5240 c. 388: 30 32 33 30 37 29 35 30 31 35 29 37 SP SD: 0.6594 c. M: 1.4043 c. 392: 30 33 33 30 38 29 35 31 31 35 29 38 SP S SD: 0.6396 c. M: 1.4850 c. 400: 31 33 34 31 38 30 36 31 32 36 30 38 SP SD: 0.6697 c. M: 1.1569 c. 404: 31 34 34 31 39 30 36 32 32 36 30 39 SP S SD: 0.4976 c. M: 1.0000 c. 416: 32 35 35 32 40 31 37 33 33 37 31 40 SP S SD: 0.4719 c. M:-0.9925 c. 457: 35 39 38 35 44 34 41 36 36 41 34 44 SP SD: 0.4714 c. M:-1.1539 c. 469: 36 39 40 36 45 35 42 37 37 42 35 45 SP SD: 0.4381 c. M: 1.2592 c. 481: 37 40 41 37 46 36 43 38 38 43 36 46 SP SD: 0.4364 c. M: 1.0571 c. 493: 38 41 42 38 47 37 44 39 39 44 37 47 SP SD: 0.5230 c. M:-0.9691 c. 498: 38 42 42 38 48 37 45 39 39 45 37 48 SP S SD: 0.5405 c. M: 0.8402 c. 503: 39 42 42 39 48 38 45 39 40 45 38 48 SP SD: 0.4415 c. M: 1.1091 c. 510: 39 43 43 39 49 38 46 40 40 46 38 49 SP S SD: 0.3547 c. M: 0.6367 c. 522: 40 44 44 40 50 39 47 41 41 47 39 50 SP S SD: 0.2233 c. M: 0.4474 c. 534: 41 45 45 41 51 40 48 42 42 48 40 51 SP S SD: 0.2294 c. M:-0.4697 c. 702: 54 59 59 54 67 53 63 55 55 63 53 67 SP S SD: 0.2046 c. M:-0.3117 c. 1013: 78 85 85 78 97 76 91 80 79 91 76 97 SP SD: 0.1781 c. M:-0.5253 c. 1025: 79 86 86 79 98 77 92 80 81 92 77 98 SP SD: 0.1750 c. M: 0.5715 c. 1094: 84 92 92 84 105 82 98 86 86 98 82 105 SP S SD: 0.1680 c. M: 0.3321 c. 1106: 85 93 93 85 106 83 99 87 87 99 83 106 SP S SD: 0.1121 c. M: 0.1772 c. 1336: 103 112 112 103 128 100 120 105 105 120 100 128 SP S SD: 0.1038 c. M: 0.1997 c. 1348: 104 113 113 104 129 101 121 106 106 121 101 129 SP S SD: 0.0877 c. M:-0.1802 c. 1870: 144 157 157 144 179 140 168 147 147 168 140 179 SP S SD: 0.0761 c. M: 0.1856 c. 1882: 145 158 158 145 180 141 169 148 148 169 141 180 SP S SD: 0.0868 c. M:-0.2121 c. 1920: 148 161 161 148 184 144 172 151 151 172 144 184 SP S SD: 0.0918 c. M: 0.1623 c. 1932: 149 162 162 149 185 145 173 152 152 173 145 185 SP S SD: 0.0843 c. M:-0.1452 c. 2026: 156 170 170 156 194 152 182 159 159 182 152 194 SP S SD: 0.0954 c. M: 0.2035 c. 2038: 157 171 171 157 195 153 183 160 160 183 153 195 SP S SD: 0.0612 c. M: 0.1285 c. 2050: 158 172 172 158 196 154 184 161 161 184 154 196 SP S SD: 0.0584 c. M:-0.1099 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: 1.5551 cents 3 x x x x 4 x x x 5 x x 6 S SD: 1.4662 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.6174 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.6802 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.5306 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.8619 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.4965 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.6676 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.8296 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.0211 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.4342 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.3390 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.8844 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.4324 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.3055 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.5424 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.4942 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.4475 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 3.3864 cents 32:34:36:38:40:43:45:48:51:53:57:60:64 SD: 2.3820 cents 36:38:40:43:45:48:51:54:57:60:64:67:72 SD: 1.9980 cents 48:51:54:57:60:64:68:72:76:80:85:90:96 S SD: 1.8699 cents 52:55:58:62:65:69:73:78:82:87:92:97:104 SD: 1.7266 cents 54:57:60:64:68:72:76:81:85:90:96:101:108 SD: 1.6073 cents 59:62:66:70:74:79:83:88:93:99:105:110:118 SD: 1.4431 cents 60:63:67:71:75:80:84:90:95:100:107:112:120 SD: 1.3064 cents 69:73:77:82:86:92:97:103:109:115:123:129:138 SD: 1.1006 cents 76:80:85:90:95:102:107:114:120:127:135:142:152 SD: 0.8754 cents 93:98:104:110:116:124:131:139:147:155:165:174:186 SD: 0.6843 cents 108:114:121:128:135:144:152:162:171:180:192:202:216 SD: 0.6001 cents 125:132:140:148:156:167:176:187:198:209:222:234:250 SD: 0.5469 cents 145:153:162:172:181:194:204:217:229:242:258:271:290 SD: 0.5010 cents 163:172:182:193:204:218:229:244:258:272:290:305:326 SD: 0.4856 cents 167:176:187:198:209:223:235:250:264:279:297:313:334 SD: 0.4134 cents 179:189:200:212:224:239:252:268:283:299:318:335:358 SD: 0.2755 cents 272:287:304:322:340:363:383:407:430:454:483:509:544 SD: 0.2704 cents 287:303:321:340:359:383:404:430:454:479:510:537:574 SD: 0.2676 cents 312:329:349:370:390:417:439:467:493:521:554:584:624 SD: 0.2141 cents 363:383:406:430:454:485:511:544:574:606:645:679:726 SD: 0.2098 cents 364:384:407:431:455:486:512:545:576:608:647:681:728 SD: 0.2091 cents 384:405:429:455:480:513:540:575:607:641:682:719:768 SD: 0.1712 cents 459:484:513:544:574:613:646:687:726:766:816:859:918 SD: 0.1692 cents 475:501:531:563:594:634:668:711:751:793:844:889:950 SD: 0.1564 cents 476:502:532:564:595:636:670:713:753:795:846:891:952 SD: 0.1446 cents 491:518:549:582:614:656:691:735:776:820:872:919:982 SD: 0.1349 cents 492:519:550:583:615:657:692:737:778:821:874:921:984 SD: 0.1332 cents 509:537:569:603:636:680:716:762:805:850:904:953:1018 SD: 0.1298 cents 545:575:609:646:681:728:767:816:862:910:968:1020:1090 SD: 0.1297 cents 551:581:616:653:689:736:775:825:871:920:979:1031:1102 SD: 0.1047 cents