Scala analysis: ragisyn6
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: 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: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 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: 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: 5 100/81 364.807 cents grave major third 4: 3 5/4 386.314 cents major third 4: 3 162/125 448.879 cents 4: 1 6561/5000 470.385 cents 5: 1 625/486 435.480 cents 5: 7 4/3 498.045 cents perfect fourth 5: 4 27/20 519.551 cents acute fourth 6: 2 1000/729 547.211 cents 6: 4 25/18 568.717 cents classic augmented fourth 6: 4 36/25 631.283 cents classic diminished fifth 6: 2 729/500 652.789 cents 7: 4 40/27 680.449 cents grave fifth 7: 7 3/2 701.955 cents perfect fifth 7: 1 972/625 764.520 cents 8: 1 10000/6561 729.615 cents two (grave major third) 8: 3 125/81 751.121 cents 8: 3 8/5 813.686 cents minor sixth 8: 5 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: 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: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 49.2 182.4 315.6 386.3 519.6 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 49.2 : 133.2 266.5 337.1 470.4 519.6 652.8 702.0 835.2 968.4 1017.6 1150.8 1200.0 182.4 : 133.2 203.9 337.1 386.3 519.6 568.7 702.0 835.2 884.4 1017.6 1066.8 1200.0 315.6 : 70.7 203.9 253.1 386.3 435.5 568.7 702.0 751.1 884.4 933.5 1066.8 1200.0 386.3 : 133.2 182.4 315.6 364.8 498.0 631.3 680.4 813.7 862.9 996.1 1129.3 1200.0 519.6 : 49.2 182.4 231.6 364.8 498.0 547.2 680.4 729.6 862.9 996.1 1066.8 1200.0 568.7 : 133.2 182.4 315.6 448.9 498.0 631.3 680.4 813.7 946.9 1017.6 1150.8 1200.0 702.0 : 49.2 182.4 315.6 364.8 498.0 547.2 680.4 813.7 884.4 1017.6 1066.8 1200.0 751.1 : 133.2 266.5 315.6 448.9 498.0 631.3 764.5 835.2 968.4 1017.6 1150.8 1200.0 884.4 : 133.2 182.4 315.6 364.8 498.0 631.3 702.0 835.2 884.4 1017.6 1066.8 1200.0 1017.6: 49.2 182.4 231.6 364.8 498.0 568.7 702.0 751.1 884.4 933.5 1066.8 1200.0 1066.8: 133.2 182.4 315.6 448.9 519.6 652.8 702.0 835.2 884.4 1017.6 1150.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.1661 .. 133.2376 cents 6561/6250, 84.0714 cents 250/243, 49.1661 cents 2: 182.4037 .. 266.4751 cents 6561/6250, 84.0714 cents 250/243, 49.1661 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: 435.4799 .. 519.5513 cents 6561/6250, 84.0714 cents 1562500/1594323,-34.9053 cents 6: 547.2111 .. 652.7889 cents 531441/500000, 105.5777 cents 20000/19683, 27.6598 cents 7: 680.4487 .. 764.5201 cents 6561/6250, 84.0714 cents 20000/19683, 27.6598 cents 8: 729.6148 .. 835.1926 cents 531441/500000, 105.5777 cents 1562500/1594323,-34.9053 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: 1066.7624 .. 1150.8339 cents 6561/6250, 84.0714 cents 250/243, 49.1661 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 : 98.62838 cents, oct.: 1183.54053 cents Scale is not proper Step pattern alph. order: ABBCBABABBAB Step pattern size order : SLLMLSLSLLSL Scale is a Constant Structure, by a margin of 13.39901 cents Scale diversity : 1.391857 Lumma stability : 0.256087 Lumma impropriety factor : 0.116351 Rothenberg efficiency : 0.377447 redundancy: 0.622553 Efficiency x scale size : 4.529365 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: 5 Number of recognisable fifths : 7, average 701.9550 cents Best fifths form a closed circle 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 : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 243 Scale harmonicity : 0.020027 Average absolute harmonicity : 0.165631 Specific harmonicity : 0.112217 Fundamental : 1/4860, -12.2467 octaves, 0.0538 Hz. Guide tone : 6750, 12.7207 octaves, 1765972.566 Hz. Exponens Consonantiae : 3.280500E+07, 24.96741 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 467.5, average 38.95833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.22570, average 1.10214 Sum of Tenney's harmonic distance : 25.94576, average 2.16215 Vogel's harmonic complexity : 23.58333 Wille's k value : 3280 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 12 Triangular lattice diameter : 8 Lattice compactness : 291.45614, average 3.73662 Lattice compactness (without 2's) : 257.96154, average 3.30720 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.08333 11 1 3: -5 .. 3 -0.83333 24 1 5: -1 .. 3 0.83333 16 10 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 40 / 12 = 3.33333 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: 26.9853 c. M:-50.8339 c. Twelve-tone Chromatic (1/11-comma) 15: 1 1 2 1 1 1 2 0 2 2 0 2 N D3 SD: 22.0427 c. M: 39.5513 c. 16: 1 1 2 1 2 1 1 1 2 2 0 2 N D3 SD: 21.2167 c. M: 32.4037 c. 18: 1 2 2 1 2 1 2 0 2 2 1 2 N T3 SD: 18.7270 c. M:-31.3783 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 7.6386 c. M: 14.2881 c. Meantone Chromatic (1/3-comma) 27: 1 3 3 2 3 1 3 1 3 3 1 3 N SD: 7.4666 c. M:-13.7820 c. 34: 1 4 4 2 4 1 4 1 4 4 1 4 N SD: 6.8632 c. M: 13.8720 c. 41: 2 4 5 2 5 1 5 2 4 5 1 5 N SD: 8.0363 c. M: 13.1039 c. 44: 2 5 5 2 5 2 5 2 4 5 2 5 N SD: 7.6359 c. M:-12.5152 c. 45: 2 5 5 2 5 2 5 2 5 5 2 5 N M DE SD: 7.0498 c. M: 12.9804 c. Meantone Chromatic (2/5-comma) 46: 2 5 5 3 5 2 5 2 5 5 2 5 N SD: 3.1893 c. M:-5.4006 c. 53: 2 6 6 3 6 2 6 2 6 6 2 6 N SD: 2.1399 c. M: 3.9513 c. 72: 3 8 8 4 8 3 8 3 8 8 3 8 N SD: 1.6079 c. M: 2.9804 c. 99: 4 11 11 6 11 4 11 4 11 11 4 11 N SD: 0.8717 c. M:-1.6608 c. 118: 5 13 13 7 13 5 13 5 13 13 5 13 N SD: 0.8446 c. M:-1.6813 c. 171: 7 19 19 10 19 7 19 7 19 19 7 19 N SD: 0.1901 c. M: 0.3488 c. 441: 18 49 49 26 49 18 49 18 49 49 18 49 N SD: 0.0982 c. M: 0.1865 c. 612: 25 68 68 36 68 25 68 25 68 68 25 68 N SD: 0.0777 c. M: 0.1465 c. 730: 30 81 81 43 81 30 81 30 81 81 30 81 N SD: 0.0736 c. M:-0.1489 c. 783: 32 87 87 46 87 32 87 32 87 87 32 87 N SD: 0.0881 c. M: 0.1633 c. 901: 37 100 100 53 100 37 100 37 100 100 37 100 N SD: 0.0658 c. M: 0.1284 c. 1000: 41 111 111 59 111 41 111 41 111 111 41 111 N SD: 0.0507 c. M:-0.0863 c. 1171: 48 130 130 69 130 48 130 48 130 130 48 130 N SD: 0.0174 c. M:-0.0317 c. 1342: 55 149 149 79 149 55 149 55 149 149 55 149 N SD: 0.0143 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: 12.8136 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.3450 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: 7.1805 cents 10 x 11:12 x x 14:15 x 17:18:19:20 SD: 7.5447 cents 11 x 12:13:14:15 x x 17:18:20 x 22 SD: 8.1985 cents 12 x 13:14:15:16:17:18:19:20 x 22:24 S SD: 9.0636 cents 13 x 14 x 16 x 18 x 20:22:23:24:26 S SD: 9.1198 cents 14 x 16:17:18:19 x 21:22:23:25:26:28 SD: 8.4141 cents 15:16:17:18:19:20:21 x 23:25:27:28:30 SD: 7.3755 cents 16:17:18:19:20 x 22:24:25:27:29:30:32 SD: 6.8860 cents 17:18:19:20:21:23:24 x 26:28:31 x 34 SD: 7.8474 cents 18:19:20:22:23:24:25:27:28:30:32:33:36 SD: 6.3736 cents 19:20:21:23:24:26 x x 29:32:34:35:38 SD: 6.0337 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 3.8213 cents 21:22:23:25:26:28:29 x 32:35:38:39:42 SD: 5.1570 cents 23:24:26:28:29:31:32 x 35:38:41:43:46 SD: 5.5485 cents 24:25:27:29:30:32:33:36:37:40:43:44:48 SD: 3.9123 cents 26:27:29:31:33:35:36:39:40:43:47:48:52 SD: 3.1964 cents 28:29:31:34:35:38:39:42:43:47:50:52:56 SD: 2.8109 cents 34:35:38:41:43:46:47:51:52:57:61:63:68 SD: 2.6935 cents 35:36:39:42:44:47:49:53:54:58:63:65:70 SD: 2.3404 cents 36:37:40:43:45:49:50:54:56:60:65:67:72 SD: 1.9759 cents 44:45:49:53:55:59:61:66:68:73:79:81:88 SD: 1.8695 cents 54:56:60:65:68:73:75:81:83:90:97:100:108 SD: 1.7648 cents 60:62:67:72:75:81:83:90:93:100:108:111:120 SD: 1.2943 cents 64:66:71:77:80:86:89:96:99:107:115:119:128 SD: 1.2305 cents 72:74:80:86:90:97:100:108:111:120:130:133:144 SD: 0.9520 cents 80:82:89:96:100:108:111:120:123:133:144:148:160 SD: 0.8812 cents 100:103:111:120:125:135:139:150:154:167:180:185:200 SD: 0.5062 cents 136:140:151:163:170:184:189:204:210:227:245:252:272 SD: 0.4783 cents 144:148:160:173:180:194:200:216:222:240:259:267:288 SD: 0.4502 cents 180:185:200:216:225:243:250:270:278:300:324:333:360 SD: 0.2345 cents 280:288:311:336:350:378:389:420:432:467:504:519:560 SD: 0.1873 cents 380:391:422:456:475:513:528:570:586:633:684:704:760 SD: 0.1731 cents 420:432:467:504:525:567:583:630:648:700:756:778:840 SD: 0.1459 cents 440:453:489:528:550:594:611:660:679:733:792:815:880 SD: 0.1337 cents 460:473:511:552:575:621:639:690:710:767:828:852:920 SD: 0.1125 cents 560:576:622:672:700:756:778:840:864:933:1008:1037:1120 SD: 0.0960 cents