Scala analysis: majraj3
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: 10/9 182.403712 minor whole tone 3: 6/5 315.641287 minor third 4: 162/125 448.878862 5: 4/3 498.044999 perfect fourth 6: 25/18 568.717426 classic augmented fourth 7: 3/2 701.955001 perfect fifth 8: 125/81 751.121138 9: 5/3 884.358713 major sixth, BP sixth 10: 9/5 1017.596288 just minor seventh, BP seventh 11: 50/27 1066.762425 grave major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 250/243 49.1661 maximal diesis, Porcupine comma 3: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 250/243 49.1661 maximal diesis, Porcupine comma 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 250/243 49.1661 maximal diesis, Porcupine comma 9: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 10: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 11: 250/243 49.1661 maximal diesis, Porcupine comma 12: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 250/243 49.166 cents maximal diesis, Porcupine comma 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 7 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 3125/2916 119.839 cents quasi-equal 10-tone semitone 2: 7 10/9 182.404 cents minor whole tone 2: 1 9/8 203.910 cents major whole tone 2: 3 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 3: 3 125/108 253.076 cents semi-augmented whole tone 3: 9 6/5 315.641 cents minor third 4: 1 15625/13122 302.242 cents 4: 3 100/81 364.807 cents grave major third 4: 3 5/4 386.314 cents major third 4: 5 162/125 448.879 cents 5: 3 625/486 435.480 cents 5: 5 4/3 498.045 cents perfect fourth 5: 2 27/20 519.551 cents acute fourth 5: 2 4374/3125 582.116 cents 6: 6 25/18 568.717 cents classic augmented fourth 6: 6 36/25 631.283 cents classic diminished fifth 7: 2 3125/2187 617.884 cents 7: 2 40/27 680.449 cents grave fifth 7: 5 3/2 701.955 cents perfect fifth 7: 3 972/625 764.520 cents 8: 5 125/81 751.121 cents 8: 3 8/5 813.686 cents minor sixth 8: 3 81/50 835.193 cents acute minor sixth 8: 1 26244/15625 897.758 cents 9: 9 5/3 884.359 cents major sixth, BP sixth 9: 3 216/125 946.924 cents semi-augmented sixth 10: 3 1250/729 933.525 cents 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 7 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 5832/3125 1080.161 cents 11: 7 50/27 1066.762 cents grave major seventh 11: 1 48/25 1129.328 cents classic diminished octave 11: 4 243/125 1150.834 cents octave - maximal diesis Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 133.2 182.4 315.6 448.9 498.0 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 133.2 : 49.2 182.4 315.6 364.8 435.5 568.7 617.9 751.1 884.4 933.5 1066.8 1200.0 182.4 : 133.2 266.5 315.6 386.3 519.6 568.7 702.0 835.2 884.4 1017.6 1150.8 1200.0 315.6 : 133.2 182.4 253.1 386.3 435.5 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 448.9 : 49.2 119.8 253.1 302.2 435.5 568.7 617.9 751.1 884.4 933.5 1066.8 1200.0 498.0 : 70.7 203.9 253.1 386.3 519.6 568.7 702.0 835.2 884.4 1017.6 1150.8 1200.0 568.7 : 133.2 182.4 315.6 448.9 498.0 631.3 764.5 813.7 946.9 1080.2 1129.3 1200.0 702.0 : 49.2 182.4 315.6 364.8 498.0 631.3 680.4 813.7 946.9 996.1 1066.8 1200.0 751.1 : 133.2 266.5 315.6 448.9 582.1 631.3 764.5 897.8 946.9 1017.6 1150.8 1200.0 884.4 : 133.2 182.4 315.6 448.9 498.0 631.3 764.5 813.7 884.4 1017.6 1066.8 1200.0 1017.6: 49.2 182.4 315.6 364.8 498.0 631.3 680.4 751.1 884.4 933.5 1066.8 1200.0 1066.8: 133.2 266.5 315.6 448.9 582.1 631.3 702.0 835.2 884.4 1017.6 1150.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.1661 .. 133.2376 cents 6561/6250, 84.0714 cents 250/243, 49.1661 cents 2: 119.8386 .. 266.4751 cents 2125764/1953125, 146.6366 cents 78125/78732,-13.3990 cents 3: 253.0761 .. 315.6413 cents 648/625, 62.5651 cents 78125/78732,-13.3990 cents 4: 302.2423 .. 448.8789 cents 2125764/1953125, 146.6366 cents 78125/78732,-13.3990 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 .. 897.7577 cents 2125764/1953125, 146.6366 cents 78125/78732,-13.3990 cents 9: 884.3587 .. 946.9239 cents 648/625, 62.5651 cents 78125/78732,-13.3990 cents 10: 933.5249 .. 1080.1614 cents 2125764/1953125, 146.6366 cents 78125/78732,-13.3990 cents 11: 1066.7624 .. 1150.8339 cents 6561/6250, 84.0714 cents 78125/78732,-13.3990 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 250/243, 49.1661 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 27/25, 133.2376 cents Average / Smallest step : 2.033920 Largest / Average step : 1.332376 Largest / Smallest step : 2.709946 Median interval of one step : 27/25, 133.2376 cents, amount: 7 Most common interval of one step : 27/25, 133.2376 cents, amount: 7 Least squares average step : 98.97730 cents, oct.: 1187.72762 cents Scale is not proper Step pattern alph. order: ABAABCABAABA Step pattern size order : LSLLSMLSLLSL Scale is a Constant Structure, by a margin of 13.39901 cents Scale diversity : 1.368656 Lumma stability : 0.081944 Lumma impropriety factor : 0.111658 Rothenberg efficiency : 0.419108 redundancy: 0.580892 Efficiency x scale size : 5.029293 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 2 Lowest interval variety : 2 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 : 5, average 701.9550 cents Scale contains two identical disjunct hexachords Scale contains a complete diamond : 3 5 9 Formal octave complements present : 11 = 91.6667% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 125 Scale harmonicity : 0.015940 Average absolute harmonicity : 0.172708 Specific harmonicity : 0.104012 Fundamental : 1/20250, -14.3056 octaves, 0.0129 Hz. Guide tone : 40500, 15.3056 octaves, 10595835.395 Hz. Exponens Consonantiae : 8.201250E+08, 29.61127 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 366.0, average 30.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.71516, average 1.05960 Sum of Tenney's harmonic distance : 25.34370, average 2.11198 Vogel's harmonic complexity : 28.75000 Wille's k value : 15187 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 14 Triangular lattice diameter : 8 Lattice compactness : 292.36432, average 3.74826 Lattice compactness (without 2's) : 268.81625, average 3.44636 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.41667 9 1 3: -4 .. 4 -0.16667 24 2 5: -3 .. 3 0.16667 16 9 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 40 / 12 = 3.33333 Scale is weakly epimorphic with val: <12 17 26| Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 20 29|
FIT/MODE
12: 1 1 1 2 0 1 1 1 1 1 1 1 N T3 SD: 27.8490 c. M:-51.1211 c. 15: 2 0 2 2 0 1 2 0 2 2 0 2 N SD: 20.6934 c. M:-31.1211 c. 19: 2 1 2 2 1 1 2 1 2 2 1 2 P D3 SD: 5.7147 c. M:-7.2182 c. 27: 3 1 3 3 1 2 3 1 3 3 1 3 P SD: 5.5749 c. M: 9.1561 c. 45: 5 2 5 5 2 2 5 2 5 5 2 5 N D3 SD: 5.3128 c. M: 8.7174 c. 46: 5 2 5 5 2 3 5 2 5 5 2 5 P SD: 3.2413 c. M:-5.4006 c. 53: 6 2 6 6 2 3 6 2 6 6 2 6 N SD: 2.2151 c. M:-3.9513 c. 72: 8 3 8 8 3 4 8 3 8 8 3 8 N SD: 1.2320 c. M: 2.0508 c. 99: 11 4 11 11 4 6 11 4 11 11 4 11 N SD: 0.6302 c. M:-1.0753 c. 171: 19 7 19 19 7 10 19 7 19 19 7 19 N SD: 0.1720 c. M: 0.2964 c. 270: 30 11 30 30 11 16 30 11 30 30 11 30 N SD: 0.1504 c. M:-0.2672 c. 441: 49 18 49 49 18 26 49 18 49 49 18 49 N SD: 0.0764 c. M:-0.1007 c. 730: 81 30 81 81 30 43 81 30 81 81 30 81 N SD: 0.0672 c. M:-0.1117 c. 901: 100 37 100 100 37 53 100 37 100 100 37 100 N SD: 0.0468 c. M:-0.0682 c. 1171: 130 48 130 130 48 69 130 48 130 130 48 130 N SD: 0.0182 c. M: 0.0317 c. 1342: 149 55 149 149 55 79 149 55 149 149 55 149 N SD: 0.0099 c. M:-0.0176 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: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 19.8320 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 12.8136 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.6302 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.0419 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 12.1462 cents 9 x 10:11 x 12 x x 14:15:16:17:18 S SD: 6.6582 cents 10 x 11:12:13 x 14:15 x 17:18:19:20 SD: 6.7325 cents 11:12 x 13:14 x 15 x 17:18:20 x 22 SD: 8.2090 cents 12:13 x 14 x 16:17:18:19:20 x 22:24 S SD: 8.5054 cents 13:14 x 16:17 x 18 x 20:22:23:24:26 S SD: 6.9053 cents 14:15:16:17:18:19 x 21:22:23:25:26:28 SD: 7.0048 cents 15:16:17:18:19:20:21 x 23:25:27:28:30 SD: 5.5394 cents 16:17:18:19:21 x 22:24:25:27:29:30:32 SD: 5.6806 cents 17:18:19:20:22:23:24 x 26:28:31 x 34 SD: 7.1174 cents 18:19:20:22:23:24:25:27:28:30:32:33:36 SD: 5.3597 cents 19 x 21:23 x 25:26 x 29:32:34:35:38 SD: 5.4170 cents 20 x 22:24:26:27:28:30:31:33:36:37:40 SD: 3.3372 cents 21:23 x 25:27:28:29 x 32:35:38:39:42 SD: 4.0681 cents 22:24 x 26 x 29:31:33:34:37:40:41:44 SD: 5.1894 cents 23:25:26:28:30:31:32 x 35:38:41:43:46 SD: 5.3699 cents 24:26:27:29:31:32:33:36:37:40:43:44:48 SD: 3.0518 cents 26:28:29:31:34:35:36:39:40:43:47:48:52 SD: 2.6710 cents 34:37:38:41:44:45:47:51:52:57:61:63:68 SD: 2.5847 cents 36:39:40:43:47:48:50:54:56:60:65:67:72 SD: 1.9509 cents 46:50:51:55:60:61:64:69:71:77:83:85:92 SD: 1.8390 cents 48:52:53:58:62:64:67:72:74:80:86:89:96 SD: 1.8070 cents 51:55:57:61:66:68:71:77:79:85:92:94:102 SD: 1.6973 cents 54:58:60:65:70:72:75:81:83:90:97:100:108 SD: 1.1187 cents 72:78:80:86:93:96:100:108:111:120:130:133:144 SD: 1.1083 cents 74:80:82:89:96:99:103:111:114:123:133:137:148 SD: 0.9469 cents 90:97:100:108:117:120:125:135:139:150:162:167:180 SD: 0.6184 cents 126:136:140:151:163:168:175:189:194:210:227:233:252 SD: 0.5290 cents 136:147:151:163:176:181:189:204:210:227:245:252:272 SD: 0.5013 cents 160:173:178:192:207:213:222:240:247:267:288:296:320 SD: 0.5008 cents 162:175:180:194:210:216:225:243:250:270:292:300:324 SD: 0.3600 cents 190:205:211:228:246:253:264:285:293:317:342:352:380 SD: 0.3500 cents 210:227:233:252:272:280:292:315:324:350:378:389:420 SD: 0.3096 cents 216:233:240:259:280:288:300:324:333:360:389:400:432 SD: 0.2643 cents 250:270:278:300:324:333:347:375:386:417:450:463:500 SD: 0.2481 cents 270:292:300:324:350:360:375:405:417:450:486:500:540 SD: 0.2313 cents 300:324:333:360:389:400:417:450:463:500:540:556:600 SD: 0.2304 cents 324:350:360:389:420:432:450:486:500:540:583:600:648 SD: 0.1006 cents 486:525:540:583:630:648:675:729:750:810:875:900:972 SD: 0.0756 cents