Scala analysis: whelp1
well-temperament with one pure third
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92.179 cents 92.179265 2: 193.157 cents 193.156857 3: 294.134 cents 294.134449 4: 386.314 cents 386.313714 5: 494.155 cents 494.155249 6: 593.011 cents 593.011258 7: 693.178 cents 693.177657 8: 793.157 cents 793.156857 9: 893.136 cents 893.136057 10: 993.302 cents 993.302456 11: 1092.158 cents 1092.158465 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 107.8415 cents 107.8415 1: 92.1793 cents 92.1793 2: 100.9776 cents 100.9776 3: 100.9776 cents 100.9776 4: 92.1793 cents 92.1793 5: 107.8415 cents 107.8415 6: 98.8560 cents 98.8560 7: 100.1664 cents 100.1664 8: 99.9792 cents 99.9792 9: 99.9792 cents 99.9792 10: 100.1664 cents 100.1664 11: 98.8560 cents 98.8560 12: 107.8415 cents 107.8415
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 92.17926 cents 1: 2 98.85601 cents 1: 2 99.97920 cents 1: 2 100.16640 cents 1: 2 100.97759 cents 1: 2 107.84154 cents 2: 2 193.15686 cents 2: 2 199.02241 cents 2: 1 199.95840 cents 2: 2 200.02080 cents 2: 2 200.14560 cents 2: 1 201.95518 cents 2: 2 206.69754 cents 3: 2 294.13445 cents 3: 2 298.87681 cents 3: 2 299.00161 cents 3: 2 300.12480 cents 3: 2 300.99839 cents 3: 2 306.86394 cents 4: 1 386.31371 cents 4: 2 398.98081 cents 4: 2 399.04321 cents 4: 2 399.85440 cents 4: 1 400.29120 cents 4: 2 401.97598 cents 4: 2 406.84314 cents 5: 2 494.15525 cents 5: 2 499.02241 cents 5: 2 499.14721 cents 5: 2 500.02080 cents 5: 2 500.83199 cents 5: 2 506.82234 cents 6: 2 593.01126 cents 6: 1 598.00322 cents 6: 2 599.00161 cents 6: 2 600.00000 cents 6: 2 600.99839 cents 6: 1 601.99678 cents 6: 2 606.98874 cents 7: 2 693.17766 cents 7: 2 699.16801 cents 7: 2 699.97920 cents 7: 2 700.85279 cents 7: 2 700.97759 cents 7: 2 705.84475 cents 8: 2 793.15686 cents 8: 2 798.02402 cents 8: 1 799.70880 cents 8: 2 800.14560 cents 8: 2 800.95679 cents 8: 2 801.01919 cents 8: 1 813.68629 cents 9: 2 893.13606 cents 9: 2 899.00161 cents 9: 2 899.87520 cents 9: 2 900.99839 cents 9: 2 901.12319 cents 9: 2 905.86555 cents 10: 2 993.30246 cents 10: 1 998.04482 cents 10: 2 999.85440 cents 10: 2 999.97920 cents 10: 1 1000.04160 cents 10: 2 1000.97759 cents 10: 2 1006.84314 cents 11: 2 1092.15846 cents 11: 2 1099.02241 cents 11: 2 1099.83360 cents 11: 2 1100.02080 cents 11: 2 1101.14399 cents 11: 2 1107.82074 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.45455 = 71/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 193.2 294.1 386.3 494.2 593.0 693.2 793.2 893.1 993.3 1092.2 1200.0 92.2 : 101.0 202.0 294.1 402.0 500.8 601.0 701.0 801.0 901.1 1000.0 1107.8 1200.0 193.2 : 101.0 193.2 301.0 399.9 500.0 600.0 700.0 800.1 899.0 1006.8 1099.0 1200.0 294.1 : 92.2 200.0 298.9 399.0 499.0 599.0 699.2 798.0 905.9 998.0 1099.0 1200.0 386.3 : 107.8 206.7 306.9 406.8 506.8 607.0 705.8 813.7 905.9 1006.8 1107.8 1200.0 494.2 : 98.9 199.0 299.0 399.0 499.1 598.0 705.8 798.0 899.0 1000.0 1092.2 1200.0 593.0 : 100.2 200.1 300.1 400.3 499.1 607.0 699.2 800.1 901.1 993.3 1101.1 1200.0 693.2 : 100.0 200.0 300.1 399.0 506.8 599.0 700.0 801.0 893.1 1001.0 1099.8 1200.0 793.2 : 100.0 200.1 299.0 406.8 499.0 600.0 701.0 793.2 901.0 999.9 1100.0 1200.0 893.1 : 100.2 199.0 306.9 399.0 500.0 601.0 693.2 801.0 899.9 1000.0 1100.0 1200.0 993.3 : 98.9 206.7 298.9 399.9 500.8 593.0 700.9 799.7 899.9 999.9 1099.8 1200.0 1092.2: 107.8 200.0 301.0 402.0 494.2 602.0 700.9 801.0 901.0 1001.0 1101.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1793 .. 107.8415 cents 15.66227 cents 92.17926 cents 2: 193.1569 .. 206.6975 cents 13.54069 cents 85.31532 cents 3: 294.1344 .. 306.8639 cents 12.72949 cents 87.43691 cents 4: 386.3137 .. 406.8431 cents 20.52943 cents 79.44977 cents 5: 494.1552 .. 506.8223 cents 12.66709 cents 87.31211 cents 6: 593.0113 .. 606.9887 cents 13.97748 cents 86.18891 cents 7: 693.1777 .. 705.8448 cents 12.66709 cents 86.18891 cents 8: 793.1569 .. 813.6863 cents 20.52943 cents 87.31211 cents 9: 893.1361 .. 905.8656 cents 12.72949 cents 79.44977 cents 10: 993.3025 .. 1006.8431 cents 13.54069 cents 87.43691 cents 11: 1092.1585 .. 1107.8207 cents 15.66227 cents 85.31532 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 92.17926 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 107.84154 cents Average / Smallest step : 1.084843 Largest / Average step : 1.078415 Largest / Smallest step : 1.169911 Median interval of one step : 100.07280 cents, amount: 0 Least squares average step : 99.25767 cents, oct.: 1191.09204 cents Scale is strictly proper Step pattern alph. order: ABBACDEFFEDC Step pattern size order : AEEAFBDCCDBF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 79.44977 cents Scale diversity : 1.113324 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.863137 Rothenberg efficiency : 0.243687 redundancy: 0.756313 Efficiency x scale size : 2.924242 Number of different interval sizes : 71 = 6.45455 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.45455 = 71/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 0.06240 cents Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 20.5294 cents: 1 2 3 5 6 7 9 10 11 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: 7.4137 c. M:-13.6863 c. Twelve-tone Chromatic (1/11-comma) 41: 3 4 3 3 4 3 4 3 4 3 3 4 SP M ME SD: 7.3400 c. M:-14.1810 c. 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 7.5136 c. M:-12.8423 c. Meantone Chromatic (1/5-comma) 44: 3 4 4 3 4 4 3 4 4 3 4 4 SP B ME S SD: 6.7147 c. M: 11.4843 c. 50: 4 4 4 4 5 4 4 4 4 4 5 4 SP B ME SD: 6.2391 c. M:-11.8415 c. 52: 4 4 5 4 4 5 4 4 5 4 4 5 SP B ME S SD: 6.2040 c. M: 9.5399 c. Demolished-12 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 5.5364 c. M:-10.6167 c. Schismic-12 54: 4 5 4 4 5 5 4 5 4 5 4 5 SP D3 SD: 5.5784 c. M: 8.5359 c. 56: 4 5 5 4 5 5 4 5 5 4 5 5 SP B ME S SD: 4.9003 c. M: 7.5882 c. Bidia-12 64: 5 5 6 5 5 6 5 5 6 5 5 6 SP B ME S SD: 5.1531 c. M:-7.4363 c. 65: 5 5 6 5 6 5 6 5 5 6 5 6 SP M ME SD: 4.4797 c. M: 8.5415 c. 66: 5 6 5 5 6 6 5 6 5 6 5 6 SP D3 SD: 4.4888 c. M:-6.9887 c. 68: 5 6 6 5 6 6 5 6 6 5 6 6 SP B ME S SD: 4.1372 c. M:-6.9887 c. Bidia-12 75: 6 6 6 6 7 6 6 7 6 6 6 7 SP D3 SD: 3.6988 c. M:-6.8431 c. 81: 6 7 7 6 7 7 7 7 6 7 7 7 SP D3 SD: 3.3816 c. M:-6.8431 c. 83: 6 7 7 7 7 7 7 7 7 7 7 7 SP M ME SD: 3.8971 c. M:-6.6367 c. 87: 7 7 7 7 8 7 7 8 7 7 7 8 SP D3 SD: 3.1906 c. M:-6.8431 c. 89: 7 7 8 7 8 7 7 8 7 8 7 8 SP M ME SD: 3.4318 c. M: 5.5372 c. 93: 7 8 8 7 8 8 8 7 8 8 8 8 SP D3 SD: 2.9595 c. M: 6.0601 c. 99: 8 8 8 8 9 8 8 8 9 8 8 9 SP D3 SD: 2.8116 c. M: 5.2781 c. 102: 8 8 9 8 9 8 9 8 9 8 9 9 SP D3 SD: 3.0286 c. M: 5.0672 c. 105: 8 9 9 8 9 9 9 8 9 9 9 9 SP D3 SD: 2.7465 c. M:-4.9844 c. 106: 8 9 9 8 10 8 9 9 9 9 8 10 SP D3 S SD: 2.6718 c. M: 5.3660 c. 109: 8 10 9 8 10 9 9 9 9 9 9 10 SP D3 SD: 2.4143 c. M:-5.0083 c. 112: 9 9 9 9 10 9 10 9 9 10 9 10 SP D3 S SD: 2.7887 c. M: 4.8487 c. 114: 9 9 10 9 10 9 10 9 10 9 10 10 SP D3 SD: 2.6327 c. M: 3.8288 c. 118: 9 10 10 9 11 9 10 10 10 10 9 11 SP D3 S SD: 2.2624 c. M:-4.1498 c. 121: 9 10 11 9 11 10 10 10 10 10 10 11 SP D3 SD: 2.1428 c. M: 4.7271 c. 132: 10 11 11 10 12 11 11 11 11 11 11 12 SP T3 S SD: 2.4947 c. M: 4.4955 c. 133: 10 11 12 10 12 11 11 11 11 11 11 12 SP D3 SD: 1.9922 c. M: 3.6832 c. 144: 11 12 12 11 13 12 12 12 12 12 12 13 SP T3 S SD: 1.7087 c. M: 2.9804 c. 156: 12 13 13 12 14 13 13 13 13 13 13 14 SP T3 S SD: 1.0818 c. M: 1.8476 c. 168: 13 14 14 13 15 14 14 14 14 14 14 15 SP T3 S SD: 0.6586 c. M: 1.2981 c. 180: 14 15 15 14 16 15 15 15 15 15 15 16 SP T3 S SD: 0.6044 c. M:-1.1749 c. 348: 27 29 29 27 31 29 29 29 29 29 29 31 SP T3 S SD: 0.5765 c. M: 1.0518 c. 442: 34 37 37 34 40 36 37 37 37 37 36 40 SP S SD: 0.6201 c. M: 1.1561 c. 454: 35 38 38 35 41 37 38 38 38 38 37 41 SP S SD: 0.4902 c. M: 0.9408 c. 457: 35 39 38 35 41 38 38 38 38 38 38 41 SP SD: 0.4726 c. M:-1.1539 c. 466: 36 39 39 36 42 38 39 39 39 39 38 42 SP S SD: 0.4280 c. M: 0.7366 c. 478: 37 40 40 37 43 39 40 40 40 40 39 43 SP S SD: 0.4479 c. M:-0.8398 c. 534: 41 45 45 41 48 44 44 45 44 45 44 48 SP SD: 0.4407 c. M: 1.0428 c. 546: 42 46 46 42 49 45 45 46 45 46 45 49 SP SD: 0.4362 c. M: 0.8700 c. 547: 42 46 46 42 49 45 46 46 45 46 45 49 SP SD: 0.4357 c. M:-0.9931 c. 559: 43 47 47 43 50 46 47 46 47 47 46 50 SP SD: 0.4305 c. M: 1.0281 c. 575: 44 49 48 44 52 47 48 48 48 48 47 52 SP SD: 0.4028 c. M:-0.9301 c. 587: 45 49 50 45 53 48 49 49 49 49 48 53 SP SD: 0.3885 c. M: 0.9933 c. 599: 46 50 51 46 54 49 50 50 50 50 49 54 SP SD: 0.3849 c. M: 0.8363 c. 634: 49 53 53 49 57 52 53 53 53 53 52 57 SP S SD: 0.3776 c. M: 0.7591 c. 646: 50 54 54 50 58 53 54 54 54 54 53 58 SP S SD: 0.3632 c. M:-0.7000 c. 672: 52 56 57 51 61 55 56 56 56 56 56 60 SP SD: 0.4459 c. M:-0.6987 c. 677: 52 57 57 52 61 56 56 56 57 56 56 61 SP SD: 0.4183 c. M: 0.8378 c. 678: 52 57 57 52 61 56 57 56 57 56 56 61 SP SD: 0.3650 c. M:-0.6693 c. 690: 53 58 58 53 62 57 58 57 58 57 57 62 SP SD: 0.3413 c. M:-0.7770 c. 714: 55 60 60 55 64 59 59 60 59 60 59 64 SP SD: 0.3343 c. M: 0.7407 c. 726: 56 61 61 56 65 60 60 61 60 61 60 65 SP SD: 0.3535 c. M: 0.6157 c. 743: 57 62 63 57 67 61 62 62 62 62 61 67 SP SD: 0.3433 c. M: 0.9630 c. 755: 58 64 63 58 68 62 63 63 63 63 62 68 SP SD: 0.2490 c. M:-0.7504 c. 767: 59 64 65 59 69 63 64 64 64 64 63 69 SP SD: 0.2434 c. M: 0.7188 c. 779: 60 65 66 60 70 64 65 65 65 65 64 70 SP SD: 0.2677 c. M: 0.6023 c. 791: 61 66 67 61 71 65 66 66 66 66 65 71 SP SD: 0.3296 c. M:-0.5384 c. 808: 62 68 68 62 73 66 68 67 67 68 66 73 SP S SD: 0.3260 c. M: 0.5743 c. 820: 63 69 69 63 74 67 69 68 68 69 67 74 SP S SD: 0.3035 c. M:-0.4809 c. 864: 66 73 73 66 78 71 72 72 72 72 71 78 SP S SD: 0.2630 c. M: 0.5126 c. 876: 67 74 74 67 79 72 73 73 73 73 72 79 SP S SD: 0.2287 c. M: 0.3984 c. 888: 68 75 75 68 80 73 74 74 74 74 73 80 SP S SD: 0.2374 c. M:-0.4601 c. 900: 69 76 76 69 81 74 75 75 75 75 74 81 SP S SD: 0.2824 c. M:-0.5322 c. 923: 71 78 77 71 83 76 77 77 77 77 76 83 SP SD: 0.2161 c. M:-0.5593 c. 935: 72 79 78 72 84 77 78 78 78 78 77 84 SP SD: 0.2158 c. M:-0.6399 c. 947: 73 79 80 73 85 78 79 79 79 79 78 85 SP SD: 0.2148 c. M: 0.5486 c. 1032: 79 87 87 79 93 85 86 86 86 86 85 93 SP S SD: 0.1861 c. M: 0.3188 c. 1044: 80 88 88 80 94 86 87 87 87 87 86 94 SP S SD: 0.1251 c. M: 0.2252 c. 1056: 81 89 89 81 95 87 88 88 88 88 87 95 SP S SD: 0.1082 c. M:-0.1837 c. 1212: 93 102 102 93 109 100 101 101 101 101 100 109 SP S SD: 0.1122 c. M: 0.2331 c. 1224: 94 103 103 94 110 101 102 102 102 102 101 110 SP S SD: 0.0641 c. M: 0.1652 c. 1404: 108 118 118 108 126 116 117 117 117 117 116 126 SP S SD: 0.0980 c. M:-0.1511 c. 1690: 130 142 142 130 152 139 141 141 141 141 139 152 SP S SD: 0.0978 c. M: 0.1700 c. 1979: 152 167 166 152 178 163 165 165 165 165 163 178 SP SD: 0.0952 c. M:-0.2742 c. 1991: 153 167 168 153 179 164 166 166 166 166 164 179 SP SD: 0.0945 c. M: 0.2890 c. 2212: 170 186 186 170 199 182 185 184 184 185 182 199 SP S SD: 0.0870 c. M: 0.1885 c. 2224: 171 187 187 171 200 183 186 185 185 186 183 200 SP S SD: 0.0813 c. M:-0.1677 c. 2280: 175 192 192 175 205 188 190 190 190 190 188 205 SP S SD: 0.0710 c. M:-0.1466 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: 4.3887 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.2002 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.5007 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.9610 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.7305 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.5658 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.6505 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.4596 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1151 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.0933 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.3873 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.0508 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.3236 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.3882 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.8268 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.6926 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.3505 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.6092 cents 27:28:30:32:34:36:38:40:43:45:48:51:54 SD: 3.3660 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.9570 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.7397 cents 33:35:37:39:41:44:46:49:52:55:59:62:66 SD: 2.5558 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.1420 cents 43:45:48:51:54:57:61:64:68:72:76:81:86 SD: 1.9355 cents 49:52:55:58:61:65:69:73:77:82:87:92:98 SD: 1.6018 cents 52:55:58:62:65:69:73:78:82:87:92:98:104 SD: 1.5813 cents 59:62:66:70:74:78:83:88:93:99:105:111:118 SD: 1.3538 cents 67:71:75:79:84:89:94:100:106:112:119:126:134 SD: 1.3125 cents 69:73:77:82:86:92:97:103:109:116:122:130:138 SD: 1.2313 cents 75:79:84:89:94:100:106:112:119:126:133:141:150 SD: 1.0406 cents 76:80:85:90:95:101:107:113:120:127:135:143:152 SD: 0.7899 cents 93:98:104:110:116:124:131:139:147:156:165:175:186 SD: 0.6556 cents 108:114:121:128:135:144:152:161:171:181:192:203:216 SD: 0.5904 cents 124:131:139:147:155:165:175:185:196:208:220:233:248 SD: 0.5748 cents 145:153:162:172:181:193:204:216:229:243:257:272:290 SD: 0.5605 cents 151:159:169:179:189:201:213:225:239:253:268:284:302 SD: 0.5070 cents 160:169:179:190:200:213:225:239:253:268:284:301:320 SD: 0.4882 cents 167:176:187:198:209:222:235:249:264:280:296:314:334 SD: 0.4546 cents 169:178:189:200:211:225:238:252:267:283:300:318:338 SD: 0.4408 cents 179:189:200:212:224:238:252:267:283:300:318:336:358 SD: 0.3703 cents 203:214:227:241:254:270:286:303:321:340:360:381:406 SD: 0.3699 cents 221:233:247:262:276:294:311:330:349:370:392:415:442 SD: 0.3251 cents 237:250:265:281:296:315:334:354:375:397:421:445:474 SD: 0.3113 cents 255:269:285:302:319:339:359:381:403:427:453:479:510 SD: 0.3107 cents 272:287:304:322:340:362:383:406:430:456:483:511:544 SD: 0.2442 cents 296:312:331:351:370:394:417:442:468:496:525:556:592 SD: 0.2113 cents 363:383:406:430:454:483:511:542:574:608:644:682:726 SD: 0.1894 cents 372:392:416:441:465:495:524:555:588:623:660:699:744 SD: 0.1690 cents 475:501:531:563:594:632:669:709:751:796:843:893:950 SD: 0.1101 cents