Scala analysis: ragisyn3
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: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 9/8 203.910002 major 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: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 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 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: 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 : 70.7 203.9 337.1 386.3 519.6 568.7 702.0 751.1 884.4 1017.6 1066.8 1200.0 70.7 : 133.2 266.5 315.6 448.9 498.0 631.3 680.4 813.7 946.9 996.1 1129.3 1200.0 203.9 : 133.2 182.4 315.6 364.8 498.0 547.2 680.4 813.7 862.9 996.1 1066.8 1200.0 337.1 : 49.2 182.4 231.6 364.8 414.0 547.2 680.4 729.6 862.9 933.5 1066.8 1200.0 386.3 : 133.2 182.4 315.6 364.8 498.0 631.3 680.4 813.7 884.4 1017.6 1150.8 1200.0 519.6 : 49.2 182.4 231.6 364.8 498.0 547.2 680.4 751.1 884.4 1017.6 1066.8 1200.0 568.7 : 133.2 182.4 315.6 448.9 498.0 631.3 702.0 835.2 968.4 1017.6 1150.8 1200.0 702.0 : 49.2 182.4 315.6 364.8 498.0 568.7 702.0 835.2 884.4 1017.6 1066.8 1200.0 751.1 : 133.2 266.5 315.6 448.9 519.6 652.8 786.0 835.2 968.4 1017.6 1150.8 1200.0 884.4 : 133.2 182.4 315.6 386.3 519.6 652.8 702.0 835.2 884.4 1017.6 1066.8 1200.0 1017.6: 49.2 182.4 253.1 386.3 519.6 568.7 702.0 751.1 884.4 933.5 1066.8 1200.0 1066.8: 133.2 203.9 337.1 470.4 519.6 652.8 702.0 835.2 884.4 1017.6 1150.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.1661 .. 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: 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: 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 : 98.82690 cents, oct.: 1185.92276 cents Scale is not proper Step pattern alph. order: ABBCBCBCBBCB Step pattern size order : MLLSLSLSLLSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 13.39901 cents Scale diversity : 1.402901 Lumma stability : 0.256087 Lumma impropriety factor : 0.152195 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 : 6, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 8.3333% Scale is differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 5 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 243 Scale harmonicity : 0.016667 Average absolute harmonicity : 0.165697 Specific harmonicity : 0.106862 Fundamental : 1/16200, -13.9837 octaves, 0.0161 Hz. Guide tone : 60750, 15.8906 octaves, 15893753.092 Hz. Exponens Consonantiae : 9.841500E+08, 29.87430 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 460.5, average 38.37500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.92467, average 1.16039 Sum of Tenney's harmonic distance : 27.05297, average 2.25441 Vogel's harmonic complexity : 27.33333 Wille's k value : 9841 Wilson's harmonic complexity : 52 Rectangular lattice diameter : 14 Triangular lattice diameter : 9 Lattice compactness : 318.54298, average 4.08388 Lattice compactness (without 2's) : 268.03610, average 3.43636 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.08333 17 1 3: -4 .. 5 0.16667 24 2 5: -2 .. 3 0.58333 15 9 Average exponent except 2's : 9 / 12 = 0.75000 Average absolute exponent except 2's: 39 / 12 = 3.25000 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: 25.5856 c. M:-48.8789 c. Twelve-tone Chromatic (1/11-comma) 14: 1 1 2 1 1 1 1 1 1 2 0 2 N D3 SD: 24.3273 c. M:-42.2577 c. 15: 1 1 2 1 1 1 2 0 2 2 0 2 N D3 SD: 23.5727 c. M: 43.9100 c. 16: 1 2 2 0 2 1 1 1 2 2 0 2 N SD: 21.0873 c. M:-37.8524 c. 17: 1 2 2 0 2 1 2 0 2 2 1 2 N SD: 23.2131 c. M: 45.2388 c. 18: 1 2 2 1 2 1 2 0 2 2 1 2 N T3 SD: 16.6468 c. M:-31.3783 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 9.8972 c. M: 21.3581 c. Meantone Chromatic (1/3-comma) 27: 2 3 3 1 3 1 3 1 3 3 1 3 N SD: 11.5859 c. M:-18.4080 c. 28: 2 3 3 1 3 1 3 2 3 3 1 3 N SD: 11.5166 c. M:-20.3074 c. 29: 2 3 3 1 4 1 3 1 3 4 1 3 N SD: 11.1143 c. M:-18.3797 c. 30: 2 3 3 2 3 1 4 1 3 3 2 3 P SD: 11.4315 c. M:-18.0450 c. 31: 2 3 4 1 3 2 3 1 4 3 2 3 N SD: 10.8492 c. M:-17.1085 c. 32: 2 3 4 1 4 1 4 1 3 4 1 4 N SD: 10.7304 c. M: 21.8587 c. 34: 2 4 4 1 4 1 4 1 4 4 1 4 N SD: 7.3299 c. M:-15.7936 c. 38: 2 4 5 1 4 2 4 2 4 4 2 4 N SD: 8.2852 c. M: 14.4363 c. 46: 3 5 5 2 5 2 5 2 5 5 2 5 N SD: 3.9859 c. M:-7.5884 c. 53: 3 6 6 2 6 2 6 2 6 6 2 6 N SD: 2.0444 c. M: 3.9513 c. 99: 6 11 11 4 11 4 11 4 11 11 4 11 N SD: 1.3529 c. M:-2.2464 c. 118: 7 13 13 5 13 5 13 5 13 13 5 13 N SD: 0.8223 c. M: 1.5544 c. 171: 10 19 19 7 19 7 19 7 19 19 7 19 N SD: 0.2751 c. M: 0.4970 c. 388: 23 43 43 16 43 16 43 16 43 43 16 43 N SD: 0.2513 c. M:-0.4616 c. 441: 26 49 49 18 49 18 49 18 49 49 18 49 N SD: 0.1223 c. M:-0.2674 c. 559: 33 62 62 23 62 23 62 23 62 62 23 62 N SD: 0.1145 c. M:-0.2205 c. 612: 36 68 68 25 68 25 68 25 68 68 25 68 N SD: 0.0737 c. M: 0.1407 c. 1000: 59 111 111 41 111 41 111 41 111 111 41 111 N SD: 0.0678 c. M:-0.1276 c. 1171: 69 130 130 48 130 48 130 48 130 130 48 130 N SD: 0.0195 c. M:-0.0364 c. 1783: 105 198 198 73 198 73 198 73 198 198 73 198 N SD: 0.0179 c. M:-0.0369 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 7 x x 8 x 9 x 10 x 11:12 S SD: 11.4617 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.4677 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.8961 cents 9 x 10:11 x 12 x x 14:15:16:17:18 S SD: 6.6831 cents 10 x 11:12 x x 14:15 x 17:18:19:20 SD: 9.1142 cents 11 x 12:13:14:15 x x 17:18:20 x 22 SD: 10.9901 cents 12 x 14 x 15:16:17:18:19:20 x 22:24 S SD: 9.8628 cents 13:14:15:16 x x 18 x 20:22:23:24:26 S SD: 9.5680 cents 14:15:16:17:18:19 x 21:22:23:25:26:28 SD: 7.8226 cents 15:16:17:18:19:20:21 x 23:25:27:28:30 SD: 5.6070 cents 16:17:18:19:20 x 22:24:25:27:29:30:32 SD: 6.1524 cents 17:18:19 x 21:23:24 x 26:28:31 x 34 SD: 6.4115 cents 18:19:20:22:23:24:25:27:28:30:32:33:36 SD: 5.2437 cents 19:20:21:23:24:26 x x 29:32:34:35:38 SD: 5.5370 cents 20:21:23:24:25:27:28:30:31:33:36:37:40 SD: 4.2935 cents 21:22:24 x 26:28:29 x 32:35:38:39:42 SD: 4.7577 cents 22:23:25:27:28:30:31:33:34:37:40:41:44 SD: 4.7295 cents 23:24:26:28:29:31:32 x 35:38:41:43:46 SD: 3.7514 cents 24:25:27:29:30:32:33:36:37:40:43:44:48 SD: 2.9182 cents 32:33:36:39:40:43:44:48:49:53:58:59:64 SD: 2.8854 cents 39:41:44:47:49:53:54:59:60:65:70:72:78 SD: 2.6532 cents 40:42:45:49:50:54:56:60:62:67:72:74:80 SD: 2.2319 cents 46:48:52:56:58:62:64:69:71:77:83:85:92 SD: 1.7076 cents 48:50:54:58:60:65:67:72:74:80:86:89:96 SD: 1.3590 cents 72:75:81:87:90:97:100:108:111:120:130:133:144 SD: 1.0331 cents 80:83:90:97:100:108:111:120:123:133:144:148:160 SD: 0.9385 cents 88:92:99:107:110:119:122:132:136:147:158:163:176 SD: 0.8361 cents 96:100:108:117:120:130:133:144:148:160:173:178:192 SD: 0.7790 cents 116:121:131:141:145:157:161:174:179:193:209:215:232 SD: 0.7679 cents 120:125:135:146:150:162:167:180:185:200:216:222:240 SD: 0.4048 cents 144:150:162:175:180:194:200:216:222:240:259:267:288 SD: 0.3938 cents 168:175:189:204:210:227:233:252:259:280:302:311:336 SD: 0.3548 cents 216:225:243:262:270:292:300:324:333:360:389:400:432 SD: 0.3522 cents 232:242:261:282:290:313:322:348:358:387:418:430:464 SD: 0.3344 cents 240:250:270:292:300:324:333:360:370:400:432:444:480 SD: 0.3188 cents 264:275:297:321:330:356:367:396:407:440:475:489:528 SD: 0.2840 cents 265:276:298:322:331:358:368:398:409:442:477:491:530 SD: 0.2786 cents 280:292:315:340:350:378:389:420:432:467:504:519:560 SD: 0.2563 cents 288:300:324:350:360:389:400:432:444:480:518:533:576 SD: 0.2190 cents 360:375:405:437:450:486:500:540:556:600:648:667:720 SD: 0.1896 cents 432:450:486:525:540:583:600:648:667:720:778:800:864 SD: 0.1193 cents 480:500:540:583:600:648:667:720:741:800:864:889:960 SD: 0.1026 cents 576:600:648:700:720:778:800:864:889:960:1037:1067:1152 SD: 0.0986 cents 600:625:675:729:750:810:833:900:926:1000:1080:1111:1200 SD: 0.0606 cents