Scala analysis: ragisyn2
Ragisyn 6561/6250 81/80 scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 250/243 49.166137 maximal diesis, Porcupine comma 2: 10/9 182.403712 minor whole tone 3: 6/5 315.641287 minor third 4: 100/81 364.807424 grave major third 5: 4/3 498.044999 perfect fourth 6: 1000/729 547.211136 7: 40/27 680.448711 grave fifth 8: 10000/6561 729.614849 two (grave major third) 9: 400/243 862.852423 grave major sixth 10: 16/9 996.089998 Pythagorean minor seventh 11: 4000/2187 1045.256136 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 2187/2000 154.7439 Gorgo limma 1: 250/243 49.1661 maximal diesis, Porcupine comma 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 4: 250/243 49.1661 maximal diesis, Porcupine comma 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: 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: 2187/2000 154.7439 Gorgo limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 250/243 49.166 cents maximal diesis, Porcupine comma 1: 6 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 2187/2000 154.744 cents Gorgo limma 2: 8 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 2 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 3: 2 2500/2187 231.570 cents 3: 1 125/108 253.076 cents semi-augmented whole tone 3: 7 6/5 315.641 cents minor third 3: 2 243/200 337.148 cents acute minor third 4: 6 100/81 364.807 cents grave major third 4: 2 5/4 386.314 cents major third 4: 2 162/125 448.879 cents 4: 2 6561/5000 470.385 cents 5: 1 25000/19683 413.974 cents 5: 6 4/3 498.045 cents perfect fourth 5: 5 27/20 519.551 cents acute fourth 6: 4 1000/729 547.211 cents 6: 2 25/18 568.717 cents classic augmented fourth 6: 2 36/25 631.283 cents classic diminished fifth 6: 4 729/500 652.789 cents 7: 5 40/27 680.449 cents grave fifth 7: 6 3/2 701.955 cents perfect fifth 7: 1 19683/12500 786.026 cents 8: 2 10000/6561 729.615 cents two (grave major third) 8: 2 125/81 751.121 cents 8: 2 8/5 813.686 cents minor sixth 8: 6 81/50 835.193 cents acute minor sixth 9: 2 400/243 862.852 cents grave major sixth 9: 7 5/3 884.359 cents major sixth, BP sixth 9: 1 216/125 946.924 cents semi-augmented sixth 9: 2 2187/1250 968.430 cents 10: 2 1250/729 933.525 cents 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 8 9/5 1017.596 cents just minor seventh, BP seventh 11: 1 4000/2187 1045.256 cents 11: 6 50/27 1066.762 cents grave major seventh 11: 5 243/125 1150.834 cents octave - maximal diesis Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 49.2 182.4 315.6 364.8 498.0 547.2 680.4 729.6 862.9 996.1 1045.3 1200.0 49.2 : 133.2 266.5 315.6 448.9 498.0 631.3 680.4 813.7 946.9 996.1 1150.8 1200.0 182.4 : 133.2 182.4 315.6 364.8 498.0 547.2 680.4 813.7 862.9 1017.6 1066.8 1200.0 315.6 : 49.2 182.4 231.6 364.8 414.0 547.2 680.4 729.6 884.4 933.5 1066.8 1200.0 364.8 : 133.2 182.4 315.6 364.8 498.0 631.3 680.4 835.2 884.4 1017.6 1150.8 1200.0 498.0 : 49.2 182.4 231.6 364.8 498.0 547.2 702.0 751.1 884.4 1017.6 1066.8 1200.0 547.2 : 133.2 182.4 315.6 448.9 498.0 652.8 702.0 835.2 968.4 1017.6 1150.8 1200.0 680.4 : 49.2 182.4 315.6 364.8 519.6 568.7 702.0 835.2 884.4 1017.6 1066.8 1200.0 729.6 : 133.2 266.5 315.6 470.4 519.6 652.8 786.0 835.2 968.4 1017.6 1150.8 1200.0 862.9 : 133.2 182.4 337.1 386.3 519.6 652.8 702.0 835.2 884.4 1017.6 1066.8 1200.0 996.1 : 49.2 203.9 253.1 386.3 519.6 568.7 702.0 751.1 884.4 933.5 1066.8 1200.0 1045.3: 154.7 203.9 337.1 470.4 519.6 652.8 702.0 835.2 884.4 1017.6 1150.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.1661 .. 154.7439 cents 531441/500000, 105.5777 cents 250/243, 49.1661 cents 2: 182.4037 .. 266.4751 cents 6561/6250, 84.0714 cents 20000/19683, 27.6598 cents 3: 231.5698 .. 337.1476 cents 531441/500000, 105.5777 cents 1562500/1594323,-34.9053 cents 4: 364.8074 .. 470.3852 cents 531441/500000, 105.5777 cents 20000/19683, 27.6598 cents 5: 413.9736 .. 519.5513 cents 531441/500000, 105.5777 cents 125000000/129140163,-56.4116 cents 6: 547.2111 .. 652.7889 cents 531441/500000, 105.5777 cents 20000/19683, 27.6598 cents 7: 680.4487 .. 786.0264 cents 531441/500000, 105.5777 cents 20000/19683, 27.6598 cents 8: 729.6148 .. 835.1926 cents 531441/500000, 105.5777 cents 125000000/129140163,-56.4116 cents 9: 862.8524 .. 968.4302 cents 531441/500000, 105.5777 cents 20000/19683, 27.6598 cents 10: 933.5249 .. 1017.5963 cents 6561/6250, 84.0714 cents 1562500/1594323,-34.9053 cents 11: 1045.2561 .. 1150.8339 cents 531441/500000, 105.5777 cents 20000/19683, 27.6598 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 : 2187/2000, 154.7439 cents Average / Smallest step : 2.033920 Largest / Average step : 1.547439 Largest / Smallest step : 3.147367 Median interval of one step : 27/25, 133.2376 cents, amount: 6 Most common interval of one step : 27/25, 133.2376 cents, amount: 6 Least squares average step : 96.64318 cents, oct.: 1159.71818 cents Scale is not proper Step pattern alph. order: ABBABABABBAC Step pattern size order : SMMSMSMSMMSL Scale is a Constant Structure, by a margin of 13.39901 cents Scale diversity : 1.376389 Lumma stability : 0.220243 Lumma impropriety factor : 0.152195 Rothenberg efficiency : 0.367989 redundancy: 0.632011 Efficiency x scale size : 4.415873 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 78732/78125, 13.3990 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 8 Most common triad is 0.0 182.404 1017.596 cents, amount: 6 Number of recognisable fifths : 6, average 701.9550 cents Formal octave complements present : 1 = 8.3333% Scale is differentially coherent in interval classes 2 and 3 combined Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 5 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 6561 Scale harmonicity : 0.016393 Average absolute harmonicity : 0.144015 Specific harmonicity : 0.096015 Fundamental : 1/32805, -15.0016 octaves, 0.0080 Hz. Guide tone : 60000, 15.8727 octaves, 15697533.918 Hz. Exponens Consonantiae : 1.968300E+09, 30.87430 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 12963.0, average 1080.25000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 21.21518, average 1.76793 Sum of Tenney's harmonic distance : 44.30467, average 3.69206 Vogel's harmonic complexity : 28.58333 Wille's k value : 16402 Wilson's harmonic complexity : 52 Rectangular lattice diameter : 14 Triangular lattice diameter : 9 Lattice compactness : 353.43183, average 4.53118 Lattice compactness (without 2's) : 305.83868, average 3.92101 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 5 2.58333 31 1 3: -8 .. 1 -3.50000 44 2 5: -1 .. 4 1.50000 20 9 Average exponent except 2's :-24 / 12 =-2.00000 Average absolute exponent except 2's: 64 / 12 = 5.33333 Scale is JI-epimorphic with val: <12 19 28| = patent
FIT/MODE
12: 0 2 1 1 1 0 2 0 2 1 0 2 N T3 SD: 30.4760 c. M: 49.1661 c. 13: 0 2 1 1 1 1 1 1 1 2 0 2 N D3 SD: 27.1814 c. M: 49.1661 c. 14: 1 1 2 0 2 0 2 1 1 2 0 2 N D3 SD: 24.4416 c. M:-41.8137 c. 15: 1 1 2 1 1 1 2 0 2 2 0 2 N D3 SD: 24.3342 c. M:-43.9100 c. 16: 1 1 2 1 2 0 2 1 2 1 1 2 P D3 SD: 21.5606 c. M:-37.1476 c. 17: 1 2 1 1 2 1 2 0 2 2 1 2 N SD: 19.5719 c. M: 33.2883 c. 18: 1 2 2 0 2 1 2 1 2 2 1 2 N T3 SD: 17.7687 c. M: 31.4741 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 16.8926 c. M:-28.4281 c. Meantone Chromatic (1/3-comma) 22: 1 2 3 1 2 1 2 1 3 2 1 3 N SD: 13.9412 c. M: 25.9033 c. 24: 1 3 2 1 3 1 3 1 2 3 1 3 P D3 SD: 12.2018 c. M:-20.3852 c. 25: 1 3 3 1 2 1 3 1 3 3 1 3 N SD: 12.8886 c. M:-20.3587 c. 26: 1 3 3 1 3 1 3 1 3 3 1 3 N M DE SD: 10.3287 c. M:-19.2946 c. Meantone Chromatic (4/9-comma) 30: 1 4 3 1 3 2 3 1 4 3 1 4 N SD: 10.6244 c. M: 18.0450 c. 31: 1 4 3 1 4 1 4 1 3 4 1 4 N D3 SD: 9.6957 c. M: 16.4203 c. 33: 1 4 4 1 4 1 4 1 4 3 2 4 N SD: 8.7958 c. M: 14.2718 c. 39: 2 4 4 2 4 2 4 2 4 4 2 5 N SD: 6.7240 c. M:-12.3723 c. 46: 2 5 5 2 5 2 5 2 5 5 2 6 N SD: 2.1902 c. M: 4.7857 c. 72: 3 8 8 3 8 3 8 3 8 8 3 9 N SD: 2.7712 c. M:-4.7439 c. 99: 4 11 11 4 11 4 11 4 11 11 4 13 N SD: 1.6481 c. M: 2.8319 c. 118: 5 13 13 5 13 5 13 5 13 13 5 15 N SD: 1.4132 c. M:-2.5885 c. 125: 5 14 14 5 14 5 14 5 14 14 5 16 N SD: 1.0537 c. M:-2.3100 c. 164: 7 18 18 7 18 7 18 7 18 18 7 21 N SD: 1.1586 c. M:-2.0925 c. 171: 7 19 19 7 19 7 19 7 19 19 7 22 N SD: 0.2223 c. M:-0.4012 c. 388: 16 43 43 16 43 16 43 16 43 43 16 50 N SD: 0.1714 c. M:-0.3184 c. 559: 23 62 62 23 62 23 62 23 62 62 23 72 N SD: 0.1373 c. M:-0.2599 c. 612: 25 68 68 25 68 25 68 25 68 68 25 79 N SD: 0.1083 c. M: 0.2031 c. 783: 32 87 87 32 87 32 87 32 87 87 32 101 N SD: 0.0671 c. M: 0.1240 c. 954: 39 106 106 39 106 39 106 39 106 106 39 123 N SD: 0.0665 c. M:-0.1364 c. 1000: 41 111 111 41 111 41 111 41 111 111 41 129 N SD: 0.0425 c. M: 0.0900 c. 1171: 48 130 130 48 130 48 130 48 130 130 48 151 N SD: 0.0121 c. M:-0.0226 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: 10.7531 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: 10.2114 cents 5 x x 6 x x 7 x x 8:9 x 10 S SD: 12.8468 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.6039 cents 7 x 8 x x 9 x 10:11 x 12:13:14 S SD: 19.0414 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.3817 cents 9 x 10 x 11:12 x 13:14:15:16 x 18 S SD: 7.8388 cents 10 x 11:12 x 13:14:15 x 16:18 x 20 S SD: 10.3172 cents 11 x 12:13:14 x 15:16:17:18 x 20:22 S SD: 8.8799 cents 12 x 13:14:15:16 x 18 x 20:21:22:24 S SD: 8.9218 cents 13 x 14 x 16:17:18:19:20:21:23:24:26 SD: 8.0953 cents 14 x 16:17 x x 19:21 x 23:25:26:28 SD: 8.2674 cents 15:16:17:18:19:20:21:22:23:25:27 x 30 SD: 8.9287 cents 16:17:18:19:20:21:22:24 x 26:28:29:32 SD: 7.6474 cents 17:18:19:20:21 x 23:25:26:28:30:31:34 SD: 6.2450 cents 18:19:20 x 22:24:25:27 x 30:32:33:36 SD: 6.0678 cents 19:20:21:23 x 25:26:28:29:31:34:35:38 SD: 5.0064 cents 20:21:22:24:25:27 x 30 x 33:36:37:40 SD: 6.1700 cents 21:22:23:25:26:28:29:31:32:35:37:38:42 SD: 4.5938 cents 23:24:26 x 28:31:32:34:35:38:41:42:46 SD: 5.0809 cents 24:25:27:29:30:32:33:36:37:40:43:44:48 SD: 4.6116 cents 25:26:28:30:31:33:34:37:38:41:44:46:50 SD: 3.3339 cents 27:28:30:32:33:36:37:40:41:44:48:49:54 SD: 3.2101 cents 29:30:32:35:36:39:40:43:44:48:52:53:58 SD: 2.7796 cents 34:35:38:41:42:45:47:50:52:56:60:62:68 SD: 2.5109 cents 35:36:39:42:43:47:48:52:53:58:62:64:70 SD: 1.9918 cents 46:47:51:55:57:61:63:68:70:76:82:84:92 SD: 1.7192 cents 54:56:60:65:67:72:74:80:82:89:96:99:108 SD: 1.5790 cents 60:62:67:72:74:80:82:89:91:99:107:110:120 SD: 1.4834 cents 63:65:70:76:78:84:86:93:96:104:112:115:126 SD: 1.3890 cents 64:66:71:77:79:85:88:95:98:105:114:117:128 SD: 1.2598 cents 65:67:72:78:80:87:89:96:99:107:116:119:130 SD: 1.1756 cents 71:73:79:85:88:95:97:105:108:117:126:130:142 SD: 1.1604 cents 81:83:90:97:100:108:111:120:123:133:144:148:162 SD: 0.9385 cents 99:102:110:119:122:132:136:147:151:163:176:181:198 SD: 0.5813 cents 135:139:150:162:167:180:185:200:206:222:240:247:270 SD: 0.4106 cents 170:175:189:204:210:227:233:252:259:280:302:311:340 SD: 0.3340 cents 210:216:233:252:259:280:288:311:320:346:373:384:420 SD: 0.3239 cents 234:241:260:281:289:312:321:347:357:385:416:428:468 SD: 0.2855 cents 280:288:311:336:346:373:384:415:427:461:498:512:560 SD: 0.2366 cents 315:324:350:378:389:420:432:467:480:519:560:576:630 SD: 0.1860 cents 345:355:383:414:426:460:473:511:526:568:613:631:690 SD: 0.1808 cents 414:426:460:497:511:552:568:613:631:681:736:757:828 SD: 0.1538 cents 486:500:540:583:600:648:667:720:741:800:864:889:972 SD: 0.1026 cents