Scala analysis: ragisyn1
Ragasyn 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: 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: 250/243 49.1661 maximal diesis, Porcupine comma 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 1 2500/2187 231.570 cents 3: 2 125/108 253.076 cents semi-augmented whole tone 3: 8 6/5 315.641 cents minor third 3: 1 243/200 337.148 cents acute minor third 4: 4 100/81 364.807 cents grave major third 4: 4 5/4 386.314 cents major third 4: 4 162/125 448.879 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: 4 125/81 751.121 cents 8: 4 8/5 813.686 cents minor sixth 8: 4 81/50 835.193 cents acute minor sixth 9: 1 400/243 862.852 cents grave major sixth 9: 8 5/3 884.359 cents major sixth, BP sixth 9: 2 216/125 946.924 cents semi-augmented sixth 9: 1 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: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 49.2 182.4 315.6 364.8 498.0 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 49.2 : 133.2 266.5 315.6 448.9 519.6 652.8 702.0 835.2 968.4 1017.6 1150.8 1200.0 182.4 : 133.2 182.4 315.6 386.3 519.6 568.7 702.0 835.2 884.4 1017.6 1066.8 1200.0 315.6 : 49.2 182.4 253.1 386.3 435.5 568.7 702.0 751.1 884.4 933.5 1066.8 1200.0 364.8 : 133.2 203.9 337.1 386.3 519.6 652.8 702.0 835.2 884.4 1017.6 1150.8 1200.0 498.0 : 70.7 203.9 253.1 386.3 519.6 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 568.7 : 133.2 182.4 315.6 448.9 498.0 631.3 680.4 813.7 946.9 996.1 1129.3 1200.0 702.0 : 49.2 182.4 315.6 364.8 498.0 547.2 680.4 813.7 862.9 996.1 1066.8 1200.0 751.1 : 133.2 266.5 315.6 448.9 498.0 631.3 764.5 813.7 946.9 1017.6 1150.8 1200.0 884.4 : 133.2 182.4 315.6 364.8 498.0 631.3 680.4 813.7 884.4 1017.6 1066.8 1200.0 1017.6: 49.2 182.4 231.6 364.8 498.0 547.2 680.4 751.1 884.4 933.5 1066.8 1200.0 1066.8: 133.2 182.4 315.6 448.9 498.0 631.3 702.0 835.2 884.4 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 .. 448.8789 cents 6561/6250, 84.0714 cents 20000/19683, 27.6598 cents 5: 435.4799 .. 519.5513 cents 6561/6250, 84.0714 cents 78125/78732,-13.3990 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: 751.1211 .. 835.1926 cents 6561/6250, 84.0714 cents 78125/78732,-13.3990 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 : 98.33060 cents, oct.: 1179.96718 cents Scale is not proper Step pattern alph. order: ABBABCBABBAB Step pattern size order : SLLSLMLSLLSL Scale is a Constant Structure, by a margin of 13.39901 cents Scale diversity : 1.371265 Lumma stability : 0.256087 Lumma impropriety factor : 0.080507 Rothenberg efficiency : 0.393783 redundancy: 0.606217 Efficiency x scale size : 4.725397 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 78732/78125, 13.3990 cents Number of recognisable fifths : 7, average 701.9550 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Scale is fully connected 5-limit major-minor triadic 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 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 7 and 8 combined Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 5 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 243 Scale harmonicity : 0.021157 Average absolute harmonicity : 0.171759 Specific harmonicity : 0.118093 Fundamental : 1/2430, -11.2467 octaves, 0.1077 Hz. Guide tone : 4500, 12.1357 octaves, 1177315.044 Hz. Exponens Consonantiae : 1.093500E+07, 23.38245 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 533.5, average 44.45833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.48097, average 1.12341 Sum of Tenney's harmonic distance : 26.90000, average 2.24167 Vogel's harmonic complexity : 22.08333 Wille's k value : 1822 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 11 Triangular lattice diameter : 7 Lattice compactness : 272.63364, average 3.49530 Lattice compactness (without 2's) : 244.06442, average 3.12903 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.58333 11 1 3: -5 .. 2 -1.50000 26 2 5: -1 .. 3 1.00000 16 9 Average exponent except 2's :-6 / 12 =-0.50000 Average absolute exponent except 2's: 42 / 12 = 3.50000 Scale is weakly epimorphic with val: <12 17 31| Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 19 29|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 28.0049 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: 21.6854 c. M:-35.1926 c. 17: 1 2 1 1 2 1 2 1 2 1 1 2 P M ME SD: 21.0013 c. M: 33.2883 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 7.6038 c. M:-14.1399 c. Meantone Chromatic (1/3-comma) 27: 1 3 3 1 3 2 3 1 3 3 1 3 N SD: 6.1992 c. M: 9.2519 c. 34: 1 4 4 1 4 2 4 1 4 4 1 4 N SD: 7.1912 c. M: 13.8720 c. 45: 2 5 5 2 5 2 5 2 5 5 2 5 N M DE SD: 5.8375 c. M: 8.7174 c. Meantone Chromatic (2/5-comma) 46: 2 5 5 2 5 3 5 2 5 5 2 5 N SD: 2.8616 c. M:-5.4006 c. 53: 2 6 6 2 6 3 6 2 6 6 2 6 N SD: 2.1984 c. M: 3.9513 c. 72: 3 8 8 3 8 4 8 3 8 8 3 8 N SD: 1.3260 c. M: 2.0508 c. 99: 4 11 11 4 11 6 11 4 11 11 4 11 N SD: 0.7324 c. M: 1.1711 c. 171: 7 19 19 7 19 10 19 7 19 19 7 19 N SD: 0.1579 c. M: 0.2964 c. 441: 18 49 49 18 49 26 49 18 49 49 18 49 N SD: 0.0994 c. M: 0.1865 c. 612: 25 68 68 25 68 36 68 25 68 68 25 68 N SD: 0.0807 c. M: 0.1465 c. 730: 30 81 81 30 81 43 81 30 81 81 30 81 N SD: 0.0773 c. M:-0.1489 c. 901: 37 100 100 37 100 53 100 37 100 100 37 100 N SD: 0.0638 c. M:-0.1204 c. 1000: 41 111 111 41 111 59 111 41 111 111 41 111 N SD: 0.0439 c. M:-0.0826 c. 1171: 48 130 130 48 130 69 130 48 130 130 48 130 N SD: 0.0164 c. M:-0.0317 c. 1342: 55 149 149 55 149 79 149 55 149 149 55 149 N SD: 0.0123 c. M:-0.0212 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: 12.8136 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: 15.7196 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 9.6744 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: 8.2881 cents 11 x 12:13:14 x 15 x 17:18:20 x 22 SD: 10.3172 cents 12 x 13:14:15:16:17:18:19:20 x 22:24 S SD: 9.0636 cents 13 x 14 x 16:17:18 x 20:22:23:24:26 S SD: 8.4335 cents 14 x 16:17 x 19 x 21:22:23:25:26:28 SD: 8.2825 cents 15:16:17:18:19:20:21 x 23:25:27:28:30 SD: 7.9088 cents 16:17:18:19:20:21:22:24:25:27:29:30:32 SD: 6.9439 cents 17:18:19:20:21:23:24 x 26:28:31 x 34 SD: 7.9775 cents 18:19:20 x 22:24:25:27:28:30:32:33:36 SD: 5.1690 cents 19:20:21:23 x 25:26 x 29:32:34:35:38 SD: 6.2831 cents 20:21:22:24:25:27:28:30:31:33:36:37:40 SD: 4.5854 cents 21:22:23:25:26:28:29 x 32:35:38:39:42 SD: 4.5503 cents 23:24:26 x 28:31:32 x 35:38:41:43:46 SD: 6.1731 cents 24:25:27:29:30:32:33:36:37:40:43:44:48 SD: 3.9123 cents 26:27:29:31:32:35:36:39:40:43:47:48:52 SD: 2.7018 cents 30:31:33:36:37:40:42:45:46:50:54:56:60 SD: 2.4547 cents 34:35:38:41:42:45:47:51:52:57:61:63:68 SD: 2.3345 cents 36:37:40:43:44:48:50:54:56:60:65:67:72 SD: 2.1467 cents 39:40:43:47:48:52:54:59:60:65:70:72:78 SD: 2.0700 cents 44:45:49:53:54:59:61:66:68:73:79:81:88 SD: 1.9860 cents 46:47:51:55:57:61:64:69:71:77:83:85:92 SD: 1.7141 cents 54:56:60:65:67:72:75:81:83:90:97:100:108 SD: 1.5683 cents 60:62:67:72:74:80:83:90:93:100:108:111:120 SD: 1.3024 cents 64:66:71:77:79:85:89:96:99:107:115:119:128 SD: 1.1770 cents 70:72:78:84:86:93:97:105:108:117:126:130:140 SD: 1.1744 cents 72:74:80:86:89:96:100:108:111:120:130:133:144 SD: 0.9222 cents 90:93:100:108:111:120:125:135:139:150:162:167:180 SD: 0.7200 cents 110:113:122:132:136:147:153:165:170:183:198:204:220 SD: 0.6836 cents 134:138:149:161:165:179:186:201:207:223:241:248:268 SD: 0.6139 cents 136:140:151:163:168:181:189:204:210:227:245:252:272 SD: 0.4559 cents 144:148:160:173:178:192:200:216:222:240:259:267:288 SD: 0.3833 cents 170:175:189:204:210:227:236:255:262:283:306:315:340 SD: 0.3786 cents 180:185:200:216:222:240:250:270:278:300:324:333:360 SD: 0.2753 cents 234:241:260:281:289:312:325:351:361:390:421:433:468 SD: 0.2382 cents 270:278:300:324:333:360:375:405:417:450:486:500:540 SD: 0.2178 cents 306:315:340:367:378:408:425:459:472:510:551:567:612 SD: 0.1874 cents 324:333:360:389:400:432:450:486:500:540:583:600:648 SD: 0.1697 cents 350:360:389:420:432:467:486:525:540:583:630:648:700 SD: 0.1567 cents 414:426:460:497:511:552:575:621:639:690:745:767:828 SD: 0.1051 cents 486:500:540:583:600:648:675:729:750:810:875:900:972 SD: 0.0595 cents