Scala analysis: carl
Carl's 5-limit transversal
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: 125/108 253.076139 semi-augmented whole tone 4: 5/4 386.313714 major third 5: 25/18 568.717426 classic augmented fourth 6: 625/432 639.389853 7: 3/2 701.955001 perfect fifth 8: 5/3 884.358713 major sixth, BP sixth 9: 125/72 955.031140 classic augmented sixth 10: 625/324 1137.434852 octave - major diesis 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 648/625 62.5651 major diesis 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 250/243 49.1661 maximal diesis, Porcupine comma 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 10/9 182.4037 minor whole tone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 648/625 62.5651 major diesis 8: 10/9 182.4037 minor whole tone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 10/9 182.4037 minor whole tone 11: 648/625 62.5651 major diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 250/243 49.166 cents maximal diesis, Porcupine comma 1: 2 648/625 62.565 cents major diesis 1: 3 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 10/9 182.404 cents minor whole tone 2: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 2 10/9 182.404 cents minor whole tone 2: 1 9/8 203.910 cents major whole tone 2: 2 144/125 244.969 cents classic diminished third 2: 3 125/108 253.076 cents semi-augmented whole tone 2: 1 6/5 315.641 cents minor third 3: 1 125/108 253.076 cents semi-augmented whole tone 3: 1 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 3: 6 6/5 315.641 cents minor third 3: 1 100/81 364.807 cents grave major third 3: 1 5/4 386.314 cents major third 3: 1 625/486 435.480 cents 4: 1 6/5 315.641 cents minor third 4: 3 5/4 386.314 cents major third 4: 1 625/486 435.480 cents 4: 2 162/125 448.879 cents 4: 4 4/3 498.045 cents perfect fourth 5: 1 162/125 448.879 cents 5: 2 4/3 498.045 cents perfect fourth 5: 1 27/20 519.551 cents acute fourth 5: 1 864/625 560.610 cents 5: 5 25/18 568.717 cents classic augmented fourth 5: 1 36/25 631.283 cents classic diminished fifth 6: 1 25/18 568.717 cents classic augmented fourth 6: 5 36/25 631.283 cents classic diminished fifth 6: 1 625/432 639.390 cents 6: 1 40/27 680.449 cents grave fifth 6: 2 3/2 701.955 cents perfect fifth 6: 1 125/81 751.121 cents 7: 4 3/2 701.955 cents perfect fifth 7: 2 125/81 751.121 cents 7: 1 972/625 764.520 cents 7: 3 8/5 813.686 cents minor sixth 7: 1 5/3 884.359 cents major sixth, BP sixth 8: 1 972/625 764.520 cents 8: 1 8/5 813.686 cents minor sixth 8: 1 81/50 835.193 cents acute minor sixth 8: 6 5/3 884.359 cents major sixth, BP sixth 8: 1 1250/729 933.525 cents 8: 1 216/125 946.924 cents semi-augmented sixth 9: 1 5/3 884.359 cents major sixth, BP sixth 9: 3 216/125 946.924 cents semi-augmented sixth 9: 2 125/72 955.031 cents classic augmented sixth 9: 1 16/9 996.090 cents Pythagorean minor seventh 9: 2 9/5 1017.596 cents just minor seventh, BP seventh 9: 2 50/27 1066.762 cents grave major seventh 10: 3 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 50/27 1066.762 cents grave major seventh 10: 3 48/25 1129.328 cents classic diminished octave 10: 2 625/324 1137.435 cents octave - major diesis 10: 1 243/125 1150.834 cents octave - maximal diesis Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.60000 = 28/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 70.7 203.9 253.1 386.3 568.7 639.4 702.0 884.4 955.0 1137.4 1200.0 70.7 : 133.2 182.4 315.6 498.0 568.7 631.3 813.7 884.4 1066.8 1129.3 1200.0 203.9 : 49.2 182.4 364.8 435.5 498.0 680.4 751.1 933.5 996.1 1066.8 1200.0 253.1 : 133.2 315.6 386.3 448.9 631.3 702.0 884.4 946.9 1017.6 1150.8 1200.0 386.3 : 182.4 253.1 315.6 498.0 568.7 751.1 813.7 884.4 1017.6 1066.8 1200.0 568.7 : 70.7 133.2 315.6 386.3 568.7 631.3 702.0 835.2 884.4 1017.6 1200.0 639.4 : 62.6 245.0 315.6 498.0 560.6 631.3 764.5 813.7 946.9 1129.3 1200.0 702.0 : 182.4 253.1 435.5 498.0 568.7 702.0 751.1 884.4 1066.8 1137.4 1200.0 884.4 : 70.7 253.1 315.6 386.3 519.6 568.7 702.0 884.4 955.0 1017.6 1200.0 955.0 : 182.4 245.0 315.6 448.9 498.0 631.3 813.7 884.4 946.9 1129.3 1200.0 1137.4: 62.6 133.2 266.5 315.6 448.9 631.3 702.0 764.5 946.9 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.1661 .. 182.4037 cents 27/25, 133.2376 cents 250/243, 49.1661 cents 2: 133.2376 .. 315.6413 cents 10/9, 182.4037 cents 243/250,-49.1661 cents 3: 253.0761 .. 435.4799 cents 10/9, 182.4037 cents 625/648,-62.5651 cents 4: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 2916/3125,-119.8386 cents 5: 448.8789 .. 631.2826 cents 10/9, 182.4037 cents 243/250,-49.1661 cents 6: 568.7174 .. 751.1211 cents 10/9, 182.4037 cents 625/648,-62.5651 cents 7: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 243/250,-49.1661 cents 8: 764.5201 .. 946.9239 cents 10/9, 182.4037 cents 2916/3125,-119.8386 cents 9: 884.3587 .. 1066.7624 cents 10/9, 182.4037 cents 625/648,-62.5651 cents 10: 1017.5963 .. 1150.8339 cents 27/25, 133.2376 cents 243/250,-49.1661 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 250/243, 49.1661 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 2.218822 Largest / Average step : 1.672034 Largest / Smallest step : 3.709946 Median interval of one step : 25/24, 70.6724 cents, amount: 3 Least squares average step : 107.94681 cents, oct.: 1187.41490 cents Scale is not proper Step pattern alph. order: ABCBDAEDADE Step pattern size order : CDADECBECEB Scale is not a Constant Structure Scale diversity : 1.387112 Lumma stability : 0.081944 Lumma impropriety factor : 0.520031 Rothenberg efficiency : 0.404762 redundancy: 0.595238 Efficiency x scale size : 4.452381 Number of different interval sizes : 36 = 3.60000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.60000 = 28/5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 8 Most common triad is 0.0 315.641 884.359 cents, amount: 6 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 = 9.0909% 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 -- Rational properties -- Prime limit : 5 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 625 Scale harmonicity : 0.021459 Average absolute harmonicity : 0.168343 Specific harmonicity : 0.114771 Fundamental : 1/1296, -10.3399 octaves, 0.2019 Hz. Guide tone : 11250, 13.4576 octaves, 2943287.610 Hz. Exponens Consonantiae : 1.458000E+07, 23.79749 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 1285.0, average 116.81818 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.41076, average 1.40098 Sum of Tenney's harmonic distance : 29.66736, average 2.69703 Vogel's harmonic complexity : 19.72727 Wille's k value : 937 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 237.97334, average 3.60566 Lattice compactness (without 2's) : 190.55687, average 2.88723 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.81818 22 1 3: -4 .. 2 -1.18182 19 2 5: 0 .. 4 1.81818 20 8 Average exponent except 2's : 7 / 11 = 0.63636 Average absolute exponent except 2's: 39 / 11 = 3.54545 Scale is weakly epimorphic with val: <11 15 29| Scale is weakly epimorphic with val: <11 16 28| Scale is weakly epimorphic with val: <11 17 27| Scale is weakly epimorphic with val: <11 18 26| Scale is weakly epimorphic with val: <11 19 25|
FIT/MODE
11: 1 1 0 2 1 1 0 2 1 1 1 N T3 SD: 32.2466 c. M:-50.0499 c. 12: 1 1 1 1 2 0 1 2 1 1 1 N D3 SD: 29.3362 c. M:-46.9239 c. 13: 1 1 1 1 2 1 1 2 0 2 1 N D3 SD: 24.6895 c. M:-38.7182 c. 14: 1 1 1 1 2 1 1 2 1 2 1 N D3 SD: 29.2159 c. M: 54.4317 c. 15: 1 2 0 2 2 1 1 2 1 2 1 N T3 SD: 15.0679 c. M:-36.0900 c. 18: 1 2 1 2 3 1 1 2 1 3 1 N SD: 18.8564 c. M:-31.3783 c. 19: 1 2 1 2 3 1 1 3 1 3 1 N SD: 6.6853 c. M: 14.4363 c. 34: 2 4 1 4 5 2 2 5 2 5 2 N SD: 4.4991 c. M: 8.0231 c. 53: 3 6 2 6 8 3 3 8 3 8 3 N SD: 3.1562 c. M: 5.4276 c. 72: 4 8 3 8 11 4 4 11 4 11 4 N SD: 3.5365 c. M: 6.0565 c. 84: 5 9 4 9 13 5 4 13 5 13 4 N SD: 2.8865 c. M:-5.4223 c. 90: 5 10 4 10 14 5 5 13 6 13 5 N SD: 3.5151 c. M:-4.9689 c. 94: 6 10 4 10 15 5 5 14 6 14 5 N SD: 3.0953 c. M:-5.9233 c. 99: 6 11 4 11 15 6 5 15 6 15 5 N SD: 1.7922 c. M:-3.0344 c. 118: 7 13 5 13 18 7 6 18 7 18 6 N SD: 0.8303 c. M:-1.5482 c. 152: 9 17 6 17 23 9 8 23 9 23 8 N SD: 0.5586 c. M:-1.3532 c. 171: 10 19 7 19 26 10 9 26 10 26 9 N SD: 0.4547 c. M: 0.7934 c. 270: 16 30 11 30 41 16 14 41 16 41 14 N SD: 0.3744 c. M:-0.6101 c. 289: 17 32 12 32 44 17 15 44 17 44 15 N SD: 0.1990 c. M: 0.4498 c. 441: 26 49 18 49 67 26 23 67 26 67 23 N SD: 0.0734 c. M:-0.1716 c. 730: 43 81 30 81 111 43 38 111 43 111 38 N SD: 0.0531 c. M:-0.0994 c. 1171: 69 130 48 130 178 69 61 178 69 178 61 N SD: 0.0361 c. M:-0.0636 c. 1342: 79 149 55 149 204 79 70 204 79 204 70 N SD: 0.0273 c. M: 0.0456 c. 1783: 105 198 73 198 271 105 93 271 105 271 93 N SD: 0.0137 c. M: 0.0260 c.
FIT/HARMONIC
1 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 4 S SD: 0.0000 cents 3 x x x x 4 x x 5 x x 6 S SD: 23.5575 cents 4 x x x 5 x x 6 x 7 x 8 S SD: 3.4487 cents 5 x x 6 x 7 x x 8:9 x 10 S SD: 22.8155 cents 6 x x 7 x 8 x 9:10 x x 12 S SD: 14.4012 cents 7 x x 8:9 x 10:11 x 12 x 14 S SD: 16.9180 cents 8 x 9 x 10:11 x 12:13:14:15:16 S SD: 8.6886 cents 9 x 10 x 11 x 13:14:15:16:17:18 SD: 11.8308 cents 10 x 11:12:13:14 x 15:17 x 19:20 SD: 13.7457 cents 11 x 12:13:14:15:16:17:18:19:21:22 SD: 10.1457 cents 12 x x 14:15:17 x 18:20:21:23:24 SD: 5.1227 cents 13:14 x 15:16:18:19:20:22:23:25:26 SD: 9.0146 cents 14:15 x 16:18:19:20:21:23:24:27:28 SD: 9.1757 cents 15:16:17 x 19:21:22:23:25:26:29:30 SD: 6.7790 cents 16:17:18:19:20:22:23:24:27:28:31:32 SD: 5.9522 cents 18:19:20:21:23:25:26:27:30:31:35:36 SD: 4.9941 cents 20:21 x 23:25:28:29:30:33:35:39:40 SD: 3.6921 cents 21:22 x 24:26:29:30:32:35:36:41:42 SD: 5.5563 cents 22:23:25 x 28:31:32:33:37:38:42:44 SD: 5.1703 cents 23:24:26:27:29:32:33:35:38:40:44:46 SD: 4.2502 cents 24:25:27:28:30:33:35:36:40:42:46:48 SD: 2.8707 cents 28:29 x 32:35:39:41:42:47:49:54:56 SD: 3.7140 cents 30:31:34:35:38:42:43:45:50:52:58:60 SD: 3.5747 cents 31:32:35:36:39:43:45:47:52:54:60:62 SD: 2.8968 cents 38:40:43:44:48:53:55:57:63:66:73:76 SD: 2.7996 cents 39:41:44:45:49:54:56:59:65:68:75:78 SD: 2.7026 cents 40:42:45:46:50:56:58:60:67:69:77:80 SD: 2.4567 cents 44:46:50:51:55:61:64:66:73:76:85:88 SD: 2.2109 cents 48:50:54:56:60:67:69:72:80:83:93:96 SD: 2.0212 cents 49:51:55:57:61:68:71:74:82:85:95:98 SD: 1.8606 cents 56:58:63:65:70:78:81:84:93:97:108:112 SD: 1.2908 cents 72:75:81:83:90:100:104:108:120:125:139:144 SD: 0.6908 cents 96:100:108:111:120:133:139:144:160:167:185:192 SD: 0.5653 cents 144:150:162:167:180:200:208:216:240:250:278:288 SD: 0.4222 cents 192:200:216:222:240:267:278:288:320:333:370:384 SD: 0.3590 cents 208:217:234:241:260:289:301:312:347:361:401:416 SD: 0.3551 cents 216:225:243:250:270:300:313:324:360:375:417:432 SD: 0.2813 cents 240:250:270:278:300:333:347:360:400:417:463:480 SD: 0.2584 cents 280:292:315:324:350:389:405:420:467:486:540:560 SD: 0.2283 cents 312:325:351:361:390:433:451:468:520:542:602:624 SD: 0.2152 cents 336:350:378:389:420:467:486:504:560:583:648:672 SD: 0.1592 cents 408:425:459:472:510:567:590:612:680:708:787:816 SD: 0.1584 cents 432:450:486:500:540:600:625:648:720:750:833:864 SD: 0.0630 cents