Scala analysis: ragisyn9
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: 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: 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: 2187/2000 154.7439 Gorgo limma 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: 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: 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: 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: 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 : 49.2 182.4 315.6 364.8 498.0 547.2 702.0 751.1 884.4 1017.6 1066.8 1200.0 49.2 : 133.2 266.5 315.6 448.9 498.0 652.8 702.0 835.2 968.4 1017.6 1150.8 1200.0 182.4 : 133.2 182.4 315.6 364.8 519.6 568.7 702.0 835.2 884.4 1017.6 1066.8 1200.0 315.6 : 49.2 182.4 231.6 386.3 435.5 568.7 702.0 751.1 884.4 933.5 1066.8 1200.0 364.8 : 133.2 182.4 337.1 386.3 519.6 652.8 702.0 835.2 884.4 1017.6 1150.8 1200.0 498.0 : 49.2 203.9 253.1 386.3 519.6 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 547.2 : 154.7 203.9 337.1 470.4 519.6 652.8 702.0 835.2 968.4 1017.6 1150.8 1200.0 702.0 : 49.2 182.4 315.6 364.8 498.0 547.2 680.4 813.7 862.9 996.1 1045.3 1200.0 751.1 : 133.2 266.5 315.6 448.9 498.0 631.3 764.5 813.7 946.9 996.1 1150.8 1200.0 884.4 : 133.2 182.4 315.6 364.8 498.0 631.3 680.4 813.7 862.9 1017.6 1066.8 1200.0 1017.6: 49.2 182.4 231.6 364.8 498.0 547.2 680.4 729.6 884.4 933.5 1066.8 1200.0 1066.8: 133.2 182.4 315.6 448.9 498.0 631.3 680.4 835.2 884.4 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: 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: 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 : 98.13208 cents, oct.: 1177.58494 cents Scale is not proper Step pattern alph. order: ABBABACABBAB Step pattern size order : SMMSMSLSMMSM Scale is a Constant Structure, by a margin of 13.39901 cents Scale diversity : 1.366040 Lumma stability : 0.220243 Lumma impropriety factor : 0.116351 Rothenberg efficiency : 0.372679 redundancy: 0.627321 Efficiency x scale size : 4.472150 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 Scale contains two identical disjunct hexachords Best fifths form a closed circle Scale contains a complete diamond : 3 5 9 Formal octave complements present : 7 = 58.3333% Scale is 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: 729 Scale harmonicity : 0.019634 Average absolute harmonicity : 0.169585 Specific harmonicity : 0.107260 Fundamental : 1/7290, -12.8317 octaves, 0.0359 Hz. Guide tone : 9000, 13.1357 octaves, 2354630.088 Hz. Exponens Consonantiae : 6.561000E+07, 25.96741 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 1376.5, average 114.70833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.94576, average 1.24548 Sum of Tenney's harmonic distance : 30.10952, average 2.50913 Vogel's harmonic complexity : 24.83333 Wille's k value : 5467 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 12 Triangular lattice diameter : 8 Lattice compactness : 302.73565, average 3.88123 Lattice compactness (without 2's) : 274.63606, average 3.52098 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.91667 13 1 3: -6 .. 2 -1.83333 30 2 5: -1 .. 3 1.08333 17 9 Average exponent except 2's :-9 / 12 =-0.75000 Average absolute exponent except 2's: 47 / 12 = 3.91667 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: 30.5769 c. M:-52.7889 c. Twelve-tone Chromatic (1/11-comma) 13: 1 1 1 1 1 1 2 0 2 1 1 1 P D3 SD: 28.0383 c. M:-43.1416 c. 14: 1 1 2 0 2 0 2 1 1 2 0 2 N D3 SD: 24.1910 c. M: 38.1910 c. 15: 1 1 2 1 1 1 2 0 2 2 0 2 N D3 SD: 21.8530 c. M:-35.1926 c. 16: 1 1 2 1 2 0 2 1 2 2 0 2 N SD: 21.5818 c. M: 32.4037 c. 18: 1 2 2 0 2 1 2 1 2 2 1 2 N T3 SD: 20.9782 c. M: 35.2883 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 9.7621 c. M:-21.2099 c. Meantone Chromatic (1/3-comma) 24: 1 3 2 1 3 1 3 1 3 2 1 3 P T3 SD: 11.6411 c. M: 17.5963 c. 26: 1 3 3 1 3 1 3 1 3 3 1 3 N M DE SD: 6.8722 c. M: 12.6596 c. Meantone Chromatic (4/9-comma) 27: 1 3 3 1 3 1 4 1 3 3 1 3 N SD: 6.9021 c. M: 13.8778 c. 45: 2 5 5 2 5 2 5 2 5 5 2 5 N M DE SD: 6.4322 c. M:-12.7889 c. Meantone Chromatic (2/5-comma) 46: 2 5 5 2 5 2 6 2 5 5 2 5 N SD: 2.4435 c. M:-5.4006 c. 53: 2 6 6 2 6 2 7 2 6 6 2 6 N SD: 2.3339 c. M: 3.9513 c. 72: 3 8 8 3 8 3 9 3 8 8 3 8 N SD: 1.4339 c. M:-2.7889 c. 99: 4 11 11 4 11 4 13 4 11 11 4 11 N SD: 0.8448 c. M: 1.7566 c. 171: 7 19 19 7 19 7 22 7 19 19 7 19 N SD: 0.1403 c. M: 0.2439 c. 441: 18 49 49 18 49 18 57 18 49 49 18 49 N SD: 0.1267 c. M: 0.2724 c. 559: 23 62 62 23 62 23 72 23 62 62 23 62 N SD: 0.1251 c. M:-0.2205 c. 612: 25 68 68 25 68 25 79 25 68 68 25 68 N SD: 0.0881 c. M: 0.1523 c. 783: 32 87 87 32 87 32 101 32 87 87 32 87 N SD: 0.0793 c. M: 0.1633 c. 829: 34 92 92 34 92 34 107 34 92 92 34 92 N SD: 0.0722 c. M:-0.1454 c. 1000: 41 111 111 41 111 41 129 41 111 111 41 111 N SD: 0.0370 c. M:-0.0789 c. 1171: 48 130 130 48 130 48 151 48 130 130 48 130 N SD: 0.0150 c. M:-0.0317 c. 1342: 55 149 149 55 149 55 173 55 149 149 55 149 N SD: 0.0148 c. M:-0.0318 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: 13.3254 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 14.3674 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.6302 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 17.3020 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 9.4407 cents 9 x 10 x 11:12 x x 14:15:16:17:18 S SD: 5.7702 cents 10 x 11:12 x 13:14:15 x 17:18:19:20 SD: 9.0404 cents 11 x 12:13:14 x 15 x 17:18:20 x 22 SD: 9.6084 cents 12 x 13:14:15:16 x 18:19:20 x 22:24 S SD: 9.3225 cents 13 x 14 x 16:17:18 x 20:22:23:24:26 S SD: 8.6024 cents 14 x 16:17 x x 19:21:22:23:25:26:28 SD: 7.8259 cents 15:16:17:18:19:20:21 x 23:25:27:28:30 SD: 8.4425 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 6.7994 cents 17:18:19:20:21 x 23 x 26:28:31 x 34 SD: 8.2374 cents 18:19:20 x 22:24:25:27:28:30:32:33:36 SD: 5.5264 cents 19:20:21:23 x 25:26 x 29:32:34:35:38 SD: 5.7487 cents 20:21:22:24:25:27 x 30:31:33:36:37:40 SD: 4.8425 cents 21:22:23:25:26:28:29 x 32:35:38:39:42 SD: 4.5827 cents 23:24:26 x 28:31:32 x 35:38:41:43:46 SD: 6.6353 cents 24:25:27:29:30:32:33:36:37:40:43:44:48 SD: 3.6498 cents 26:27:29:31:32:35:36:39:40:43:47:48:52 SD: 2.9863 cents 30:31:33:36:37:40:41:45:46:50:54:56:60 SD: 2.2338 cents 35:36:39:42:43:47:48:53:54:58:63:65:70 SD: 2.1080 cents 46:47:51:55:57:61:63:69:71:77:83:85:92 SD: 1.7111 cents 54:56:60:65:67:72:74:81:83:90:97:100:108 SD: 1.5749 cents 60:62:67:72:74:80:82:90:93:100:108:111:120 SD: 1.2837 cents 64:66:71:77:79:85:88:96:99:107:115:119:128 SD: 1.2124 cents 70:72:78:84:86:93:96:105:108:117:126:130:140 SD: 1.1276 cents 72:74:80:86:89:96:99:108:111:120:130:133:144 SD: 0.9836 cents 81:83:90:97:100:108:111:122:125:135:146:150:162 SD: 0.9130 cents 90:93:100:108:111:120:123:135:139:150:162:167:180 SD: 0.8969 cents 99:102:110:119:122:132:136:149:153:165:178:183:198 SD: 0.7682 cents 108:111:120:130:133:144:148:162:167:180:194:200:216 SD: 0.7356 cents 110:113:122:132:136:147:151:165:170:183:198:204:220 SD: 0.6589 cents 134:138:149:161:165:179:184:201:207:223:241:248:268 SD: 0.6252 cents 135:139:150:162:167:180:185:203:208:225:243:250:270 SD: 0.5451 cents 144:148:160:173:178:192:198:216:222:240:259:267:288 SD: 0.5138 cents 162:167:180:194:200:216:222:243:250:270:292:300:324 SD: 0.4810 cents 170:175:189:204:210:227:233:255:262:283:306:315:340 SD: 0.3918 cents 180:185:200:216:222:240:247:270:278:300:324:333:360 SD: 0.2799 cents 210:216:233:252:259:280:288:315:324:350:378:389:420 SD: 0.2614 cents 234:241:260:281:289:312:321:351:361:390:421:433:468 SD: 0.2383 cents 306:315:340:367:378:408:420:459:472:510:551:567:612 SD: 0.2057 cents 315:324:350:378:389:420:432:473:486:525:567:583:630 SD: 0.1872 cents 350:360:389:420:432:467:480:525:540:583:630:648:700 SD: 0.1567 cents 414:426:460:497:511:552:568:621:639:690:745:767:828 SD: 0.1081 cents 486:500:540:583:600:648:667:729:750:810:875:900:972 SD: 0.0935 cents