Scala analysis: ragisyn11
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: 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: 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: 2187/2000 154.7439 Gorgo limma 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: 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: 9 10/9 182.404 cents minor whole tone 2: 1 9/8 203.910 cents major whole tone 2: 1 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 2: 1 59049/50000 287.981 cents 3: 3 2500/2187 231.570 cents 3: 6 6/5 315.641 cents minor third 3: 3 243/200 337.148 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: 3 1000/729 547.211 cents 6: 3 25/18 568.717 cents classic augmented fourth 6: 3 36/25 631.283 cents classic diminished fifth 6: 3 729/500 652.789 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: 3 400/243 862.852 cents grave major sixth 9: 6 5/3 884.359 cents major sixth, BP sixth 9: 3 2187/1250 968.430 cents 10: 1 100000/59049 912.019 cents 10: 1 1250/729 933.525 cents 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 9 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 : 49.2 182.4 315.6 364.8 498.0 547.2 680.4 729.6 884.4 1017.6 1066.8 1200.0 49.2 : 133.2 266.5 315.6 448.9 498.0 631.3 680.4 835.2 968.4 1017.6 1150.8 1200.0 182.4 : 133.2 182.4 315.6 364.8 498.0 547.2 702.0 835.2 884.4 1017.6 1066.8 1200.0 315.6 : 49.2 182.4 231.6 364.8 414.0 568.7 702.0 751.1 884.4 933.5 1066.8 1200.0 364.8 : 133.2 182.4 315.6 364.8 519.6 652.8 702.0 835.2 884.4 1017.6 1150.8 1200.0 498.0 : 49.2 182.4 231.6 386.3 519.6 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 547.2 : 133.2 182.4 337.1 470.4 519.6 652.8 702.0 835.2 968.4 1017.6 1150.8 1200.0 680.4 : 49.2 203.9 337.1 386.3 519.6 568.7 702.0 835.2 884.4 1017.6 1066.8 1200.0 729.6 : 154.7 288.0 337.1 470.4 519.6 652.8 786.0 835.2 968.4 1017.6 1150.8 1200.0 884.4 : 133.2 182.4 315.6 364.8 498.0 631.3 680.4 813.7 862.9 996.1 1045.3 1200.0 1017.6: 49.2 182.4 231.6 364.8 498.0 547.2 680.4 729.6 862.9 912.0 1066.8 1200.0 1066.8: 133.2 182.4 315.6 448.9 498.0 631.3 680.4 813.7 862.9 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 .. 287.9814 cents 531441/500000, 105.5777 cents 20000/19683, 27.6598 cents 3: 231.5698 .. 337.1476 cents 531441/500000, 105.5777 cents 125000000/129140163,-56.4116 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: 912.0186 .. 1017.5963 cents 531441/500000, 105.5777 cents 125000000/129140163,-56.4116 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 : 97.63578 cents, oct.: 1171.62935 cents Scale is not proper Step pattern alph. order: ABBABABACBAB Step pattern size order : SMMSMSMSLMSM Scale is a Constant Structure, by a margin of 27.65985 cents Scale diversity : 1.387010 Lumma stability : 0.220243 Lumma impropriety factor : 0.188039 Rothenberg efficiency : 0.406680 redundancy: 0.593320 Efficiency x scale size : 4.880159 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 : 81/80, 21.5063 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 9 Most common triad is 0.0 182.404 1017.596 cents, amount: 6 Number of recognisable fifths : 6, average 701.9550 cents Scale contains a complete diamond : 3 5 Formal octave complements present : 5 = 41.6667% Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 5 Odd number limit : 59049 (O: 59049 U: 59049) Highest odd numerator or denominator: 6561 Scale harmonicity : 0.015957 Average absolute harmonicity : 0.150493 Specific harmonicity : 0.096963 Fundamental : 1/32805, -15.0016 octaves, 0.0080 Hz. Guide tone : 90000, 16.4576 octaves, 23546300.877 Hz. Exponens Consonantiae : 2.952450E+09, 31.45927 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 9585.0, average 798.75000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.62006, average 1.46834 Sum of Tenney's harmonic distance : 36.17637, average 3.01470 Vogel's harmonic complexity : 29.33333 Wille's k value : 29524 Wilson's harmonic complexity : 55 Rectangular lattice diameter : 15 Triangular lattice diameter : 10 Lattice compactness : 337.03223, average 4.32093 Lattice compactness (without 2's) : 306.20967, average 3.92577 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 1.58333 19 1 3: -8 .. 2 -2.50000 36 1 5: -1 .. 4 1.25000 19 10 Average exponent except 2's :-15 / 12 =-1.25000 Average absolute exponent except 2's: 55 / 12 = 4.58333 Scale is JI-epimorphic with val: <12 19 28| = patent
FIT/MODE
12: 0 2 1 1 1 0 2 0 2 1 1 1 N T3 SD: 27.9302 c. M: 49.1661 c. 13: 1 1 1 1 1 1 1 1 2 1 1 1 P M ME SD: 27.6814 c. M:-43.1416 c. 15: 1 1 2 1 1 1 2 0 2 2 0 2 N D3 SD: 22.5338 c. M:-39.5513 c. 18: 1 2 2 0 2 1 2 1 2 2 1 2 N T3 SD: 18.0812 c. M: 31.4741 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 13.0687 c. M:-28.2799 c. Meantone Chromatic (1/3-comma) 20: 1 2 2 1 2 1 2 1 3 2 1 2 N T3 SD: 11.9191 c. M: 20.4487 c. 24: 1 3 2 1 3 1 3 1 3 2 1 3 P T3 SD: 14.1977 c. M:-20.3852 c. 26: 1 3 3 1 3 1 3 1 3 3 1 3 N M DE SD: 6.6601 c. M:-11.8590 c. Meantone Chromatic (4/9-comma) 44: 2 5 5 1 5 2 5 2 5 5 2 5 N SD: 7.4202 c. M:-11.6314 c. 46: 2 5 5 2 5 2 5 2 6 5 2 5 N SD: 1.8756 c. M:-3.0078 c. 72: 3 8 8 3 8 3 8 3 9 8 3 8 N SD: 1.8650 c. M:-3.7185 c. 99: 4 11 11 4 11 4 11 4 13 11 4 11 N SD: 1.1364 c. M: 2.3421 c. 125: 5 14 14 5 14 5 14 5 16 14 5 14 N SD: 0.8194 c. M: 1.1661 c. 171: 7 19 19 7 19 7 19 7 22 19 7 19 N SD: 0.1427 c. M:-0.2530 c. 441: 18 49 49 18 49 18 49 18 57 49 18 49 N SD: 0.1678 c. M: 0.3631 c. 559: 23 62 62 23 62 23 62 23 72 62 23 62 N SD: 0.1321 c. M:-0.2599 c. 612: 25 68 68 25 68 25 68 25 79 68 25 68 N SD: 0.0991 c. M: 0.2031 c. 783: 32 87 87 32 87 32 87 32 101 87 32 87 N SD: 0.0707 c. M: 0.1240 c. 829: 34 92 92 34 92 34 92 34 107 92 34 92 N SD: 0.0635 c. M: 0.1110 c. 954: 39 106 106 39 106 39 106 39 123 106 39 106 N SD: 0.0633 c. M: 0.1095 c. 1000: 41 111 111 41 111 41 111 41 129 111 41 111 N SD: 0.0300 c. M: 0.0487 c. 1171: 48 130 130 48 130 48 130 48 151 130 48 130 N SD: 0.0127 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: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 14.3692 cents 5 x x 6 x x 7 x x 8:9 x 10 S SD: 15.7997 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.3450 cents 7 x 8 x x 9 x 10:11:12 x 13:14 S SD: 17.7888 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 9.8160 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 7.9411 cents 10 x 11:12 x 13:14:15 x 17:18:19:20 SD: 9.3509 cents 11 x 12:13:14 x 15:16:17:18:20 x 22 S SD: 9.6151 cents 12 x 13:14:15:16 x 18 x 20 x 22:24 S SD: 9.2934 cents 13 x 14 x 16:17:18:19:20:22:23:24:26 S SD: 8.2326 cents 14 x 16:17 x x 19:21 x 23:25:26:28 SD: 8.3284 cents 15:16:17:18:19:20:21:22:23:25:27:28:30 SD: 7.8667 cents 16:17:18:19:20:21:22:24 x 27:29:30:32 SD: 7.4175 cents 17:18:19:20:21 x 23:25:26:28:31 x 34 SD: 7.3846 cents 18:19:20 x 22:24:25:27 x 30:32:33:36 SD: 6.2990 cents 19:20:21:23 x 25:26:28:29:32:34:35:38 SD: 5.0050 cents 20:21:22:24:25:27 x 30 x 33:36:37:40 SD: 5.6940 cents 21:22:23:25:26:28:29:31:32:35:38:39:42 SD: 3.8188 cents 23:24:26 x 28:31:32:34:35:38:41:43:46 SD: 5.6306 cents 24:25:27:29:30:32:33:36:37:40:43:44:48 SD: 4.3849 cents 25:26:28:30:31:33:34:37:38:42:45:46:50 SD: 3.1869 cents 27:28:30:32:33:36:37:40:41:45:49:50:54 SD: 2.8881 cents 29:30:32:35:36:39:40:43:44:48:52:54:58 SD: 2.7357 cents 30:31:33:36:37:40:41:44:46:50:54:56:60 SD: 2.6427 cents 34:35:38:41:42:45:47:50:52:57:61:63:68 SD: 2.4339 cents 35:36:39:42:43:47:48:52:53:58:63:65:70 SD: 1.9028 cents 46:47:51:55:57:61:63:68:70:77:83:85:92 SD: 1.7545 cents 54:56:60:65:67:72:74:80:82:90:97:100:108 SD: 1.5595 cents 60:62:67:72:74:80:82:89:91:100:108:111:120 SD: 1.3358 cents 65:67:72:78:80:87:89:96:99:108:117:120:130 SD: 1.2046 cents 69:71:77:83:85:92:95:102:105:115:124:128:138 SD: 1.0786 cents 75:77:83:90:93:100:103:111:114:125:135:139:150 SD: 1.0214 cents 81:83:90:97:100:108:111:120:123:135:146:150:162 SD: 0.8767 cents 99:102:110:119:122:132:136:147:151:165:178:183:198 SD: 0.6549 cents 129:133:143:155:159:172:177:191:197:215:232:239:258 SD: 0.6366 cents 135:139:150:162:167:180:185:200:206:225:243:250:270 SD: 0.3811 cents 170:175:189:204:210:227:233:252:259:283:306:315:340 SD: 0.3579 cents 204:210:227:245:252:272:280:302:311:340:367:378:408 SD: 0.3258 cents 210:216:233:252:259:280:288:311:320:350:378:389:420 SD: 0.2664 cents 285:293:317:342:352:380:391:422:434:475:513:528:570 SD: 0.2522 cents 315:324:350:378:389:420:432:467:480:525:567:583:630 SD: 0.1496 cents 414:426:460:497:511:552:568:613:631:690:745:767:828 SD: 0.1311 cents 486:500:540:583:600:648:667:720:741:810:875:900:972 SD: 0.1062 cents