Scala analysis: ragisyn12
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: 243/200 337.147577 acute minor third 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: 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: 250/243 49.1661 maximal diesis, Porcupine comma 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 2187/2000 154.7439 Gorgo limma 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: 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 : 49.2 182.4 337.1 386.3 519.6 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 49.2 : 133.2 288.0 337.1 470.4 519.6 652.8 702.0 835.2 968.4 1017.6 1150.8 1200.0 182.4 : 154.7 203.9 337.1 386.3 519.6 568.7 702.0 835.2 884.4 1017.6 1066.8 1200.0 337.1 : 49.2 182.4 231.6 364.8 414.0 547.2 680.4 729.6 862.9 912.0 1045.3 1200.0 386.3 : 133.2 182.4 315.6 364.8 498.0 631.3 680.4 813.7 862.9 996.1 1150.8 1200.0 519.6 : 49.2 182.4 231.6 364.8 498.0 547.2 680.4 729.6 862.9 1017.6 1066.8 1200.0 568.7 : 133.2 182.4 315.6 448.9 498.0 631.3 680.4 813.7 968.4 1017.6 1150.8 1200.0 702.0 : 49.2 182.4 315.6 364.8 498.0 547.2 680.4 835.2 884.4 1017.6 1066.8 1200.0 751.1 : 133.2 266.5 315.6 448.9 498.0 631.3 786.0 835.2 968.4 1017.6 1150.8 1200.0 884.4 : 133.2 182.4 315.6 364.8 498.0 652.8 702.0 835.2 884.4 1017.6 1066.8 1200.0 1017.6: 49.2 182.4 231.6 364.8 519.6 568.7 702.0 751.1 884.4 933.5 1066.8 1200.0 1066.8: 133.2 182.4 315.6 470.4 519.6 652.8 702.0 835.2 884.4 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 .. 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 : 98.72764 cents, oct.: 1184.73165 cents Scale is not proper Step pattern alph. order: ABCABABABBAB Step pattern size order : SMLSMSMSMMSM 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 : 5 9 Formal octave complements present : 3 = 25.0000% 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: 243 Scale harmonicity : 0.015957 Average absolute harmonicity : 0.160214 Specific harmonicity : 0.098553 Fundamental : 1/48600, -15.5687 octaves, 0.0054 Hz. Guide tone : 60750, 15.8906 octaves, 15893753.092 Hz. Exponens Consonantiae : 2.952450E+09, 31.45927 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 683.5, average 56.95833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.91234, average 1.24269 Sum of Tenney's harmonic distance : 29.15528, average 2.42961 Vogel's harmonic complexity : 29.83333 Wille's k value : 29524 Wilson's harmonic complexity : 55 Rectangular lattice diameter : 15 Triangular lattice diameter : 10 Lattice compactness : 334.47416, average 4.28813 Lattice compactness (without 2's) : 298.88444, average 3.83185 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.41667 13 1 3: -5 .. 5 -0.50000 28 1 5: -2 .. 3 0.75000 17 10 Average exponent except 2's : 3 / 12 = 0.25000 Average absolute exponent except 2's: 45 / 12 = 3.75000 Scale is JI-epimorphic with val: <12 19 28| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 28.6848 c. M:-50.8339 c. Twelve-tone Chromatic (1/11-comma) 14: 1 1 2 1 1 1 1 1 1 2 0 2 N D3 SD: 24.6251 c. M:-42.2577 c. 15: 1 1 2 1 1 1 2 0 2 2 0 2 N D3 SD: 22.5566 c. M: 39.5513 c. 18: 1 2 2 1 2 1 2 0 2 2 1 2 N T3 SD: 18.0508 c. M:-31.3783 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 9.8163 c. M: 21.3581 c. Meantone Chromatic (1/3-comma) 24: 1 3 3 1 2 1 3 1 3 2 1 3 N SD: 13.6497 c. M: 19.5513 c. 25: 1 3 3 1 3 1 3 1 2 3 1 3 N SD: 11.0206 c. M: 20.3587 c. 26: 1 3 3 1 3 1 3 1 3 3 1 3 N M DE SD: 10.0265 c. M: 17.0829 c. Meantone Chromatic (4/9-comma) 27: 1 3 4 1 3 1 3 1 3 3 1 3 N SD: 9.0707 c. M:-18.4080 c. 32: 1 4 4 1 4 1 4 1 4 3 1 4 N SD: 9.2313 c. M: 16.7624 c. 34: 1 4 5 1 4 1 4 1 4 4 1 4 N SD: 8.2192 c. M:-15.7936 c. 38: 2 4 5 1 4 2 4 2 4 4 2 4 N SD: 8.1885 c. M: 14.2881 c. 43: 2 5 5 2 5 1 5 2 5 4 2 5 N SD: 8.0017 c. M: 12.9451 c. 44: 2 5 5 2 5 2 5 2 4 5 2 5 N SD: 7.4269 c. M:-12.5152 c. 46: 2 5 6 2 5 2 5 2 5 5 2 5 N SD: 3.1523 c. M:-5.4006 c. 53: 2 6 7 2 6 2 6 2 6 6 2 6 N SD: 2.2227 c. M: 3.9513 c. 72: 3 8 9 3 8 3 8 3 8 8 3 8 N SD: 1.9262 c. M: 3.8142 c. 99: 4 11 13 4 11 4 11 4 11 11 4 11 N SD: 1.0772 c. M:-2.2464 c. 118: 5 13 15 5 13 5 13 5 13 13 5 13 N SD: 0.9498 c. M:-1.6813 c. 171: 7 19 22 7 19 7 19 7 19 19 7 19 N SD: 0.2052 c. M: 0.3488 c. 441: 18 49 57 18 49 18 49 18 49 49 18 49 N SD: 0.1249 c. M:-0.2674 c. 559: 23 62 72 23 62 23 62 23 62 62 23 62 N SD: 0.1210 c. M:-0.2205 c. 612: 25 68 79 25 68 25 68 25 68 68 25 68 N SD: 0.0827 c. M: 0.1465 c. 783: 32 87 101 32 87 32 87 32 87 87 32 87 N SD: 0.0861 c. M: 0.1633 c. 901: 37 100 116 37 100 37 100 37 100 100 37 100 N SD: 0.0854 c. M: 0.1886 c. 1000: 41 111 129 41 111 41 111 41 111 111 41 111 N SD: 0.0516 c. M:-0.0863 c. 1171: 48 130 151 48 130 48 130 48 130 130 48 130 N SD: 0.0169 c. M:-0.0317 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: 13.5162 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 12.5876 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 14.6543 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 9.2934 cents 9 x 10:11 x 12 x x 14:15:16:17:18 S SD: 6.1185 cents 10 x 11:12 x x 14:15 x 17:18:19:20 SD: 8.0093 cents 11 x 12:13:14:15 x x 17:18:20 x 22 SD: 9.6024 cents 12 x 13 x 15:16:17:18:19:20 x 22:24 SD: 8.4885 cents 13 x 14:16 x x 18 x 20:22:23:24:26 S SD: 8.9275 cents 14 x 16:17:18:19 x 21:22:23:25:26:28 SD: 8.1615 cents 15:16:17:18:19:20:21 x 23:25:27:28:30 SD: 7.6303 cents 16:17:18:19:20 x 22:24:25:27:29:30:32 SD: 7.5950 cents 17:18:19 x 21:23:24 x 26:28:31 x 34 SD: 7.8433 cents 18:19:20:22:23:24:25:27:28:30:32:33:36 SD: 5.8606 cents 19:20:21:23:24:26 x x 29:32:34:35:38 SD: 5.8759 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 4.2207 cents 21:22:23 x 26:28:29 x 32:35:38:39:42 SD: 5.5024 cents 23:24:26:28:29:31:32 x 35:38:41:43:46 SD: 5.0748 cents 24:25:27:29:30:32:33:36:37:40:43:44:48 SD: 3.8652 cents 26:27:29:32:33:35:36:39:40:43:47:48:52 SD: 3.5801 cents 28:29:31:34:35:38:39:42:43:47:50:52:56 SD: 2.2346 cents 36:37:40:44:45:49:50:54:56:60:65:67:72 SD: 2.0463 cents 46:47:51:56:58:62:64:69:71:77:83:85:92 SD: 1.8594 cents 56:58:62:68:70:76:78:84:86:93:101:104:112 SD: 1.7221 cents 60:62:67:73:75:81:83:90:93:100:108:111:120 SD: 1.3094 cents 64:66:71:78:80:86:89:96:99:107:115:119:128 SD: 1.2534 cents 72:74:80:87:90:97:100:108:111:120:130:133:144 SD: 1.0431 cents 80:82:89:97:100:108:111:120:123:133:144:148:160 SD: 0.9300 cents 100:103:111:122:125:135:139:150:154:167:180:185:200 SD: 0.7793 cents 108:111:120:131:135:146:150:162:167:180:194:200:216 SD: 0.5385 cents 136:140:151:165:170:184:189:204:210:227:245:252:272 SD: 0.4914 cents 144:148:160:175:180:194:200:216:222:240:259:267:288 SD: 0.4195 cents 180:185:200:219:225:243:250:270:278:300:324:333:360 SD: 0.3067 cents 208:214:231:253:260:281:289:312:321:347:374:385:416 SD: 0.3031 cents 252:259:280:306:315:340:350:378:389:420:454:467:504 SD: 0.2524 cents 280:288:311:340:350:378:389:420:432:467:504:519:560 SD: 0.2056 cents 340:350:378:413:425:459:472:510:525:567:612:630:680 SD: 0.2045 cents 344:354:382:418:430:464:478:516:531:573:619:637:688 SD: 0.1980 cents 380:391:422:462:475:513:528:570:586:633:684:704:760 SD: 0.1969 cents 414:426:460:503:518:559:575:621:639:690:745:767:828 SD: 0.1636 cents 460:473:511:559:575:621:639:690:710:767:828:852:920 SD: 0.1155 cents 600:617:667:729:750:810:833:900:926:1000:1080:1111:1200 SD: 0.1152 cents