Scala analysis: majraj1
Majraj 648/625 6561/6250 scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 125/108 253.076139 semi-augmented whole tone 3: 729/625 266.475150 two (large limma, BP small semitone, Zarlino semitone) 4: 5/4 386.313714 major third 5: 27/20 519.551289 acute fourth 6: 25/18 568.717426 classic augmented fourth 7: 3/2 701.955001 perfect fifth 8: 81/50 835.192576 acute minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 9/5 1017.596288 just minor seventh, BP seventh 11: 243/125 1150.833863 octave - maximal diesis 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 250/243 49.1661 maximal diesis, Porcupine comma 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 3125/2916 119.8386 quasi-equal 10-tone semitone 3: 78732/78125 13.3990 medium semicomma, Sensi comma 4: 3125/2916 119.8386 quasi-equal 10-tone semitone 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 250/243 49.1661 maximal diesis, Porcupine comma 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 9: 250/243 49.1661 maximal diesis, Porcupine comma 10: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 11: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 12: 250/243 49.1661 maximal diesis, Porcupine comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 78732/78125 13.399 cents medium semicomma, Sensi comma 1: 3 250/243 49.166 cents maximal diesis, Porcupine comma 1: 2 3125/2916 119.839 cents quasi-equal 10-tone semitone 1: 6 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 6 10/9 182.404 cents minor whole tone 2: 2 125/108 253.076 cents semi-augmented whole tone 2: 2 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 3: 1 125/108 253.076 cents semi-augmented whole tone 3: 2 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 3: 2 15625/13122 302.242 cents 3: 7 6/5 315.641 cents minor third 4: 2 6/5 315.641 cents minor third 4: 2 100/81 364.807 cents grave major third 4: 2 5/4 386.314 cents major third 4: 2 625/486 435.480 cents 4: 4 162/125 448.879 cents 5: 2 625/486 435.480 cents 5: 2 162/125 448.879 cents 5: 4 4/3 498.045 cents perfect fourth 5: 1 27/20 519.551 cents acute fourth 5: 2 25/18 568.717 cents classic augmented fourth 5: 1 4374/3125 582.116 cents 6: 4 25/18 568.717 cents classic augmented fourth 6: 2 4374/3125 582.116 cents 6: 2 3125/2187 617.884 cents 6: 4 36/25 631.283 cents classic diminished fifth 7: 1 3125/2187 617.884 cents 7: 2 36/25 631.283 cents classic diminished fifth 7: 1 40/27 680.449 cents grave fifth 7: 4 3/2 701.955 cents perfect fifth 7: 2 125/81 751.121 cents 7: 2 972/625 764.520 cents 8: 4 125/81 751.121 cents 8: 2 972/625 764.520 cents 8: 2 8/5 813.686 cents minor sixth 8: 2 81/50 835.193 cents acute minor sixth 8: 2 5/3 884.359 cents major sixth, BP sixth 9: 7 5/3 884.359 cents major sixth, BP sixth 9: 2 26244/15625 897.758 cents 9: 2 1250/729 933.525 cents 9: 1 216/125 946.924 cents semi-augmented sixth 10: 2 1250/729 933.525 cents 10: 2 216/125 946.924 cents semi-augmented sixth 10: 6 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 50/27 1066.762 cents grave major seventh 11: 6 50/27 1066.762 cents grave major seventh 11: 2 5832/3125 1080.161 cents 11: 3 243/125 1150.834 cents octave - maximal diesis 11: 1 78125/39366 1186.601 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.54545 = 50/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 133.2 253.1 266.5 386.3 519.6 568.7 702.0 835.2 884.4 1017.6 1150.8 1200.0 133.2 : 119.8 133.2 253.1 386.3 435.5 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 253.1 : 13.4 133.2 266.5 315.6 448.9 582.1 631.3 764.5 897.8 946.9 1080.2 1200.0 266.5 : 119.8 253.1 302.2 435.5 568.7 617.9 751.1 884.4 933.5 1066.8 1186.6 1200.0 386.3 : 133.2 182.4 315.6 448.9 498.0 631.3 764.5 813.7 946.9 1066.8 1080.2 1200.0 519.6 : 49.2 182.4 315.6 364.8 498.0 631.3 680.4 813.7 933.5 946.9 1066.8 1200.0 568.7 : 133.2 266.5 315.6 448.9 582.1 631.3 764.5 884.4 897.8 1017.6 1150.8 1200.0 702.0 : 133.2 182.4 315.6 448.9 498.0 631.3 751.1 764.5 884.4 1017.6 1066.8 1200.0 835.2 : 49.2 182.4 315.6 364.8 498.0 617.9 631.3 751.1 884.4 933.5 1066.8 1200.0 884.4 : 133.2 266.5 315.6 448.9 568.7 582.1 702.0 835.2 884.4 1017.6 1150.8 1200.0 1017.6: 133.2 182.4 315.6 435.5 448.9 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 1150.8: 49.2 182.4 302.2 315.6 435.5 568.7 617.9 751.1 884.4 933.5 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 13.3990 .. 133.2376 cents 3125/2916, 119.8386 cents 78732/78125, 13.3990 cents 2: 133.2376 .. 266.4751 cents 27/25, 133.2376 cents 1/1, 0.0000 cents 3: 253.0761 .. 315.6413 cents 648/625, 62.5651 cents 78125/78732,-13.3990 cents 4: 315.6413 .. 448.8789 cents 27/25, 133.2376 cents 1/1, 0.0000 cents 5: 435.4799 .. 582.1164 cents 2125764/1953125, 146.6366 cents 78125/78732,-13.3990 cents 6: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 78125/78732,-13.3990 cents 7: 617.8836 .. 764.5201 cents 2125764/1953125, 146.6366 cents 78125/78732,-13.3990 cents 8: 751.1211 .. 884.3587 cents 27/25, 133.2376 cents 78125/78732,-13.3990 cents 9: 884.3587 .. 946.9239 cents 648/625, 62.5651 cents 1/1, 0.0000 cents 10: 933.5249 .. 1066.7624 cents 27/25, 133.2376 cents 78125/78732,-13.3990 cents 11: 1066.7624 .. 1186.6010 cents 3125/2916, 119.8386 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 78732/78125, 13.3990 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 27/25, 133.2376 cents Average / Smallest step : 7.463238 Largest / Average step : 1.332376 Largest / Smallest step : 9.943837 Median interval of one step : 126.53807 cents, amount: 0 Most common interval of one step : 27/25, 133.2376 cents, amount: 6 Least squares average step : 101.20572 cents, oct.: 1214.46869 cents Scale is not proper Step pattern alph. order: ABCBADAADAAD Step pattern size order : DCACDBDDBDDB Scale is not a Constant Structure Scale diversity : 1.317248 Lumma stability : 0.022332 Lumma impropriety factor : 0.066995 Rothenberg efficiency : 0.439743 redundancy: 0.560257 Efficiency x scale size : 5.276912 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.54545 = 50/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 78732/78125, 13.3990 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 9 Most common triad is 0.0 315.641 884.359 cents, amount: 6 Number of recognisable fifths : 4, average 701.9550 cents Formal octave complements present : 1 = 8.3333% Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties -- Prime limit : 5 Odd number limit : 78125 (O: 78125 U: 78125) Highest odd numerator or denominator: 729 Scale harmonicity : 0.013928 Average absolute harmonicity : 0.156542 Specific harmonicity : 0.087984 Fundamental : 1/67500, -16.0426 octaves, 0.0039 Hz. Guide tone : 182250, 17.4756 octaves, 47681259.276 Hz. Exponens Consonantiae : 1.230188E+10, 33.51816 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 1133.5, average 94.45833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 16.34370, average 1.36198 Sum of Tenney's harmonic distance : 31.30334, average 2.60861 Vogel's harmonic complexity : 32.33333 Wille's k value : 45562 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 16 Triangular lattice diameter : 9 Lattice compactness : 338.79737, average 4.34356 Lattice compactness (without 2's) : 314.57614, average 4.03303 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.66667 10 1 3: -3 .. 6 1.50000 30 1 5: -4 .. 3 -0.50000 20 10 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 50 / 12 = 4.16667 Scale is weakly epimorphic with val: <12 17 26| Scale is weakly epimorphic with val: <12 18 25| Scale is weakly epimorphic with val: <12 18 29| Scale is weakly epimorphic with val: <12 18 31| Scale is weakly epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 20 29|
FIT/MODE
12: 1 1 0 1 2 0 2 1 0 2 1 1 N T3 SD: 51.7587 c. M: 86.3137 c. 13: 1 2 0 1 2 0 2 1 1 1 1 1 N D3 SD: 27.0180 c. M: 43.1416 c. 14: 2 1 0 2 1 1 1 2 0 2 1 1 N D3 SD: 24.6589 c. M:-42.2577 c. 15: 2 1 0 2 1 1 2 1 1 2 1 1 N D3 SD: 23.1868 c. M: 39.5513 c. 17: 2 2 0 1 2 1 2 2 1 1 2 1 N SD: 21.4753 c. M: 33.3725 c. 18: 2 2 0 2 2 1 2 2 0 2 2 1 P B D3 SD: 19.2456 c. M:-31.4741 c. 19: 2 2 0 2 2 1 2 2 1 2 2 1 P D3 SD: 9.1108 c. M: 14.2881 c. 27: 3 3 0 3 3 1 3 3 1 3 3 1 P SD: 8.5525 c. M:-13.7820 c. 33: 4 3 0 4 3 2 3 4 1 4 4 1 N SD: 9.9374 c. M:-13.6863 c. 34: 4 3 1 3 4 1 4 4 1 4 4 1 N SD: 8.4471 c. M:-15.8778 c. 42: 5 4 0 5 4 2 5 4 2 5 4 2 N SD: 8.1668 c. M:-13.6863 c. 43: 5 4 1 4 5 1 5 5 2 4 5 2 N SD: 7.9392 c. M: 12.9451 c. 44: 5 4 1 4 5 2 5 5 1 5 5 2 N SD: 6.6952 c. M: 11.6314 c. 46: 5 5 0 5 5 2 5 5 2 5 5 2 P SD: 3.8561 c. M:-7.7934 c. 53: 6 5 1 5 6 2 6 6 2 6 6 2 N SD: 2.6744 c. M:-5.2230 c. 72: 8 7 1 7 8 3 8 8 3 8 8 3 N SD: 1.8441 c. M: 3.0761 c. 99: 11 10 1 10 11 4 11 11 4 11 11 4 N SD: 0.9978 c. M:-1.6608 c. 171: 19 17 2 17 19 7 19 19 7 19 19 7 N SD: 0.2226 c. M: 0.4446 c. 270: 30 27 3 27 30 11 30 30 11 30 30 11 N SD: 0.2562 c. M:-0.4487 c. 441: 49 44 5 44 49 18 49 49 18 49 49 18 N SD: 0.1181 c. M:-0.1915 c. 612: 68 61 7 61 68 25 68 68 25 68 68 25 N SD: 0.0972 c. M:-0.1915 c. 730: 81 73 8 73 81 30 81 81 30 81 81 30 N SD: 0.0909 c. M: 0.1738 c. 901: 100 90 10 90 100 37 100 100 37 100 100 37 N SD: 0.0776 c. M: 0.1284 c. 1000: 111 100 11 100 111 41 111 111 41 111 111 41 N SD: 0.0605 c. M:-0.1239 c. 1171: 130 117 13 117 130 48 130 130 48 130 130 48 N SD: 0.0213 c. M:-0.0409 c. 1342: 149 134 15 134 149 55 149 149 55 149 149 55 N SD: 0.0164 c. M: 0.0282 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: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 7.1688 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 12.1926 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.0817 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 6.3940 cents 7 x 8 x 9 x 10 x 11:12:13 x 14 S SD: 16.4875 cents 8 x 9 x 10 x 11:12:13 x 14 x 16 S SD: 10.2291 cents 9:10 x x 11:12 x 14 x 15:16 x 18 S SD: 13.4165 cents 10:11 x 12 x x 14:15:16:17:18:19:20 S SD: 9.1796 cents 11:12 x 13:14:15 x 17:18 x 20:21:22 SD: 8.8584 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 6.3294 cents 13:14:15 x 16 x 18:20:21:22:23:25:26 SD: 6.8468 cents 14:15:16 x 18:19 x 21:23 x 25:27:28 SD: 7.1154 cents 16:17 x 19:20 x 22:24:26:27:29:31:32 SD: 5.2289 cents 17:18 x 20:21:23:24:26 x 28:31:33:34 SD: 6.8501 cents 18:19 x 21:23:24:25:27:29:30:32:35:36 SD: 5.7746 cents 19:21:22 x 24:26 x 29:31:32:34:37:38 SD: 6.3099 cents 20:22:23 x 25:27:28:30:32:33:36:39:40 SD: 4.1825 cents 21:23:24 x 26:28:29:32:34:35:38:41:42 SD: 4.7991 cents 23:25 x 27:29:31:32:35:37:38:41:45:46 SD: 3.9530 cents 24:26 x 28:30:32:33:36:39:40:43:47:48 SD: 2.9439 cents 25:27:29 x 31:34:35:38:41:42:45:49:50 SD: 3.9944 cents 26:28:30 x 33:35:36:39:42:43:47:51:52 SD: 3.2825 cents 27:29:31 x 34:36:38:41:44:45:49:52:54 SD: 4.5044 cents 28:30:32:33:35:38:39:42:45:47:50:54:56 SD: 3.5586 cents 29:31 x 34:36:39:40:44:47:48:52:56:58 SD: 3.4504 cents 30:32 x 35:38:41:42:45:49:50:54:58:60 SD: 3.9856 cents 31:33:36 x 39:42:43:47:50:52:56:60:62 SD: 3.4577 cents 32:35:37 x 40:43:44:48:52:53:58:62:64 SD: 3.1141 cents 33:36:38 x 41:45:46:50:53:55:59:64:66 SD: 3.5374 cents 34:37:39:40:43:46:47:51:55:57:61:66:68 SD: 2.9756 cents 35:38 x 41:44:47:49:53:57:58:63:68:70 SD: 2.8213 cents 36:39 x 42:45:49:50:54:58:60:65:70:72 SD: 1.6992 cents 37:40 x 43:46:50:51:56:60:62:67:72:74 SD: 2.4869 cents 38:41:44 x 48:51:53:57:62:63:68:74:76 SD: 2.6279 cents 39:42:45 x 49:53:54:59:63:65:70:76:78 SD: 2.1796 cents 40:43:46:47:50:54:56:60:65:67:72:78:80 SD: 2.1596 cents 42:45 x 49:53:57:58:63:68:70:76:82:84 SD: 2.5416 cents 43:46 x 50:54:58:60:65:70:72:77:84:86 SD: 2.7235 cents 44:48:51 x 55:59:61:66:71:73:79:86:88 SD: 2.3555 cents 45:49:52 x 56:61:63:68:73:75:81:87:90 SD: 2.5209 cents 46:50:53:54:58:62:64:69:75:77:83:89:92 SD: 2.3794 cents 48:52 x 56:60:65:67:72:78:80:86:93:96 SD: 1.4610 cents 49:53 x 57:61:66:68:74:79:82:88:95:98 SD: 1.7948 cents 50:54:58 x 63:68:69:75:81:83:90:97:100 SD: 2.1377 cents 51:55:59 x 64:69:71:77:83:85:92:99:102 SD: 1.5601 cents 52:56:60:61:65:70:72:78:84:87:94:101:104 SD: 1.5109 cents 54:58 x 63:68:73:75:81:87:90:97:105:108 SD: 1.7329 cents 55:59 x 64:69:74:76:83:89:92:99:107:110 SD: 1.9492 cents 56:60:65 x 70:76:78:84:91:93:101:109:112 SD: 1.8314 cents 57:62:66 x 71:77:79:86:92:95:103:111:114 SD: 1.8209 cents 59:64:68:69:74:80:82:89:96:98:106:115:118 SD: 1.7561 cents 60:65:69:70:75:81:83:90:97:100:108:117:120 SD: 1.2950 cents 61:66 x 71:76:82:85:92:99:102:110:119:122 SD: 1.6259 cents 62:67:72 x 78:84:86:93:100:103:112:121:124 SD: 1.7610 cents 63:68:73 x 79:85:88:95:102:105:113:122:126 SD: 1.5746 cents 64:69:74:75:80:86:89:96:104:107:115:124:128 SD: 1.3105 cents 67:72 x 78:84:90:93:101:109:112:121:130:134 SD: 1.7849 cents 68:73:79 x 85:92:94:102:110:113:122:132:136 SD: 1.5804 cents 69:75:80 x 86:93:96:104:112:115:124:134:138 SD: 1.4848 cents 71:77:82:83:89:96:99:107:115:118:128:138:142 SD: 1.3317 cents 72:78:83:84:90:97:100:108:117:120:130:140:144 SD: 1.0089 cents 74:80 x 86:93:100:103:111:120:123:133:144:148 SD: 1.2248 cents 75:81:87 x 94:101:104:113:122:125:135:146:150 SD: 1.2108 cents 76:82:88:89:95:103:106:114:123:127:137:148:152 SD: 1.1429 cents 77:83:89:90:96:104:107:116:125:128:139:150:154 SD: 1.1132 cents 80:86 x 93:100:108:111:120:130:133:144:156:160 SD: 1.2090 cents 81:87:94 x 101:109:113:122:131:135:146:157:162 SD: 1.6026 cents 82:89:95:96:103:111:114:123:133:137:148:159:164 SD: 1.3874 cents 83:90:96:97:104:112:115:125:134:138:149:161:166 SD: 1.2718 cents 84:91:97:98:105:113:117:126:136:140:151:163:168 SD: 0.9215 cents 86:93 x 100:108:116:119:129:139:143:155:167:172 SD: 1.2295 cents 87:94:101 x 109:117:121:131:141:145:157:169:174 SD: 1.1475 cents 88:95:102:103:110:119:122:132:143:147:158:171:176 SD: 0.9316 cents 93:100:108 x 116:126:129:140:151:155:167:181:186 SD: 1.3586 cents 94:102:109:110:118:127:131:141:152:157:169:183:188 SD: 1.2741 cents 95:103:110:111:119:128:132:143:154:158:171:185:190 SD: 0.9875 cents 96:104:111:112:120:130:133:144:156:160:173:187:192 SD: 0.9260 cents 99:107:115 x 124:134:138:149:160:165:178:192:198 SD: 1.2356 cents 100:108:116:117:125:135:139:150:162:167:180:194:200 SD: 0.6975 cents 105:113 x 122:131:142:146:158:170:175:189:204:210 SD: 1.0695 cents 108:117:125:126:135:146:150:162:175:180:194:210:216 SD: 0.5730 cents 126:136:146:147:158:170:175:189:204:210:227:245:252 SD: 0.5255 cents 152:164:176:177:190:205:211:228:246:253:274:295:304 SD: 0.5129 cents 160:173:185:187:200:216:222:240:259:267:288:311:320 SD: 0.4462 cents 180:194:208:210:225:243:250:270:292:300:324:350:360 SD: 0.4277 cents 192:207:222:224:240:259:267:288:311:320:346:373:384 SD: 0.4087 cents 200:216:231:233:250:270:278:300:324:333:360:389:400 SD: 0.3999 cents 211:228:244:246:264:285:293:317:342:352:380:410:422 SD: 0.3705 cents 216:233:250:252:270:292:300:324:350:360:389:420:432 SD: 0.2791 cents 240:259:278:280:300:324:333:360:389:400:432:467:480 SD: 0.2676 cents 252:272:292:294:315:340:350:378:408:420:454:490:504 SD: 0.2590 cents 260:281:301:303:325:351:361:390:421:433:468:505:520 SD: 0.2498 cents 288:311:333:336:360:389:400:432:467:480:518:560:576 SD: 0.2444 cents 300:324:347:350:375:405:417:450:486:500:540:583:600 SD: 0.1593 cents 324:350:375:378:405:437:450:486:525:540:583:630:648 SD: 0.1556 cents 360:389:417:420:450:486:500:540:583:600:648:700:720 SD: 0.1531 cents 440:475:509:513:550:594:611:660:713:733:792:855:880 SD: 0.1520 cents 476:514:551:555:595:643:661:714:771:793:857:925:952 SD: 0.1435 cents 500:540:579:583:625:675:694:750:810:833:900:972:1000 SD: 0.1406 cents 540:583:625:630:675:729:750:810:875:900:972:1050:1080 SD: 0.0756 cents