Scala analysis: thirds
Major and minor 3rds paralleogram.
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: 10/9 182.403712 minor whole tone 3: 6/5 315.641287 minor third 4: 5/4 386.313714 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: 8/5 813.686286 minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 125/72 955.031140 classic augmented sixth 11: 48/25 1129.327573 classic diminished octave 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 16/15 111.7313 minor diatonic semitone 3: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 16/15 111.7313 minor diatonic semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 25/24 70.6724 classic chromatic semitone, minor chroma 11: 3456/3125 174.2964 12: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 16/15 111.731 cents minor diatonic semitone 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 3456/3125 174.296 cents 2: 2 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 2: 4 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 4 144/125 244.969 cents classic diminished third 3: 3 125/108 253.076 cents semi-augmented whole tone 3: 9 6/5 315.641 cents minor third 4: 8 5/4 386.314 cents major third 4: 4 32/25 427.373 cents classic diminished fourth 5: 3 125/96 456.986 cents classic augmented third 5: 6 4/3 498.045 cents perfect fourth 5: 1 27/20 519.551 cents acute fourth 5: 2 864/625 560.610 cents 6: 6 25/18 568.717 cents classic augmented fourth 6: 6 36/25 631.283 cents classic diminished fifth 7: 2 625/432 639.390 cents 7: 1 40/27 680.449 cents grave fifth 7: 6 3/2 701.955 cents perfect fifth 7: 3 192/125 743.014 cents classic diminished sixth 8: 4 25/16 772.627 cents classic augmented fifth 8: 8 8/5 813.686 cents minor sixth 9: 9 5/3 884.359 cents major sixth, BP sixth 9: 3 216/125 946.924 cents semi-augmented sixth 10: 4 125/72 955.031 cents classic augmented sixth 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 4 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 1152/625 1058.655 cents 11: 1 3125/1728 1025.704 cents 11: 2 50/27 1066.762 cents grave major seventh 11: 3 15/8 1088.269 cents classic major seventh 11: 6 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 70.7 182.4 315.6 386.3 498.0 568.7 702.0 813.7 884.4 955.0 1129.3 1200.0 70.7 : 111.7 245.0 315.6 427.4 498.0 631.3 743.0 813.7 884.4 1058.7 1129.3 1200.0 182.4 : 133.2 203.9 315.6 386.3 519.6 631.3 702.0 772.6 946.9 1017.6 1088.3 1200.0 315.6 : 70.7 182.4 253.1 386.3 498.0 568.7 639.4 813.7 884.4 955.0 1066.8 1200.0 386.3 : 111.7 182.4 315.6 427.4 498.0 568.7 743.0 813.7 884.4 996.1 1129.3 1200.0 498.0 : 70.7 203.9 315.6 386.3 457.0 631.3 702.0 772.6 884.4 1017.6 1088.3 1200.0 568.7 : 133.2 245.0 315.6 386.3 560.6 631.3 702.0 813.7 946.9 1017.6 1129.3 1200.0 702.0 : 111.7 182.4 253.1 427.4 498.0 568.7 680.4 813.7 884.4 996.1 1066.8 1200.0 813.7 : 70.7 141.3 315.6 386.3 457.0 568.7 702.0 772.6 884.4 955.0 1088.3 1200.0 884.4 : 70.7 245.0 315.6 386.3 498.0 631.3 702.0 813.7 884.4 1017.6 1129.3 1200.0 955.0 : 174.3 245.0 315.6 427.4 560.6 631.3 743.0 813.7 946.9 1058.7 1129.3 1200.0 1129.3: 70.7 141.3 253.1 386.3 457.0 568.7 639.4 772.6 884.4 955.0 1025.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 174.2964 cents 82944/78125, 103.6240 cents 25/24, 70.6724 cents 2: 141.3449 .. 244.9689 cents 82944/78125, 103.6240 cents 1953125/1990656,-32.9516 cents 3: 253.0761 .. 315.6413 cents 648/625, 62.5651 cents 15625/15552, 8.1073 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 5: 456.9861 .. 560.6101 cents 82944/78125, 103.6240 cents 3125/3072, 29.6136 cents 6: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 15625/15552, 8.1073 cents 7: 639.3899 .. 743.0139 cents 82944/78125, 103.6240 cents 15625/15552, 8.1073 cents 8: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 3125/3072, 29.6136 cents 9: 884.3587 .. 946.9239 cents 648/625, 62.5651 cents 25/24, 70.6724 cents 10: 955.0311 .. 1058.6551 cents 82944/78125, 103.6240 cents 15625/15552, 8.1073 cents 11: 1025.7036 .. 1129.3276 cents 82944/78125, 103.6240 cents 1953125/1990656,-32.9516 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 3456/3125, 174.2964 cents Average / Smallest step : 1.414979 Largest / Average step : 1.742964 Largest / Smallest step : 2.466258 Median interval of one step : 91.20186 cents, amount: 0 Most common interval of one step : 25/24, 70.6724 cents, amount: 6 Least squares average step : 99.36232 cents, oct.: 1192.34781 cents Scale is not proper Step pattern alph. order: ABCABACBAADA Step pattern size order : ABCABACBAADA Scale is a Constant Structure, by a margin of 8.10728 cents Scale diversity : 1.308102 Lumma stability : 0.311955 Lumma impropriety factor : 0.054919 Rothenberg efficiency : 0.439743 redundancy: 0.560257 Efficiency x scale size : 5.276912 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 9 Most common triad is 0.0 315.641 884.359 cents, amount: 6 Number of recognisable fifths : 6, average 701.9550 cents Best fifths form a closed circle Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 9 = 75.0000% Scale is n-1 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 Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 10-11 -- Rational properties -- Prime limit : 5 Odd number limit : 3125 (O: 3125 U: 3125) Highest odd numerator or denominator: 125 Scale harmonicity : 0.021277 Average absolute harmonicity : 0.182892 Specific harmonicity : 0.132403 Fundamental : 1/1800, -10.8138 octaves, 0.1453 Hz. Guide tone : 6000, 12.5507 octaves, 1569753.392 Hz. Exponens Consonantiae : 1.080000E+07, 23.36453 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 218.5, average 18.20833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.99510, average 0.91626 Sum of Tenney's harmonic distance : 22.13370, average 1.84447 Vogel's harmonic complexity : 20.16667 Wille's k value : 1562 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 277.27585, average 3.55482 Lattice compactness (without 2's) : 174.05798, average 2.23151 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.16667 22 1 3: -2 .. 1 -0.50000 12 2 5: -2 .. 3 0.50000 14 9 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 26 / 12 = 2.16667 Scale is weakly epimorphic with val: <12 17 26| Scale is weakly epimorphic with val: <12 17 28| Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 20 29| Scale is weakly epimorphic with val: <12 21 28|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 22.1777 c. M:-44.9689 c. Twelve-tone Chromatic (1/11-comma) 15: 1 1 2 1 1 1 2 1 1 1 2 1 P B ME SD: 12.3844 c. M: 22.4037 c. Augene-12 19: 1 2 2 1 2 1 2 2 1 1 3 1 N D3 SD: 6.0173 c. M: 7.6627 c. 34: 2 3 4 2 3 2 4 3 2 2 5 2 N SD: 2.9148 c. M: 5.9331 c. 53: 3 5 6 3 5 3 6 5 3 3 8 3 N SD: 2.0036 c. M: 4.0877 c. 84: 5 8 9 5 8 5 9 8 5 5 12 5 N SD: 1.7309 c. M:-3.3106 c. 87: 5 8 10 5 8 5 10 8 5 5 13 5 N SD: 1.9616 c. M: 3.3070 c. 99: 6 9 11 6 9 6 11 9 6 6 14 6 N SD: 1.4117 c. M:-2.5446 c. 118: 7 11 13 7 11 7 13 11 7 7 17 7 N SD: 0.4852 c. M:-0.9011 c. 152: 9 14 17 9 14 9 17 14 9 9 22 9 N SD: 0.4680 c. M: 0.8248 c. 171: 10 16 19 10 16 10 19 16 10 10 25 10 N SD: 0.3377 c. M: 0.6452 c. 270: 16 25 30 16 25 16 30 25 16 16 39 16 N SD: 0.3067 c. M:-0.5244 c. 289: 17 27 32 17 27 17 32 27 17 17 42 17 N SD: 0.1528 c. M:-0.2952 c. 441: 26 41 49 26 41 26 49 41 26 26 64 26 N SD: 0.0663 c. M: 0.0908 c. 612: 36 57 68 36 57 36 68 57 36 36 89 36 N SD: 0.0637 c. M: 0.1292 c. 730: 43 68 81 43 68 43 81 68 43 43 106 43 N SD: 0.0321 c. M:-0.0620 c. 1171: 69 109 130 69 109 69 130 109 69 69 170 69 N SD: 0.0250 c. M:-0.0500 c. 1342: 79 125 149 79 125 79 149 125 79 79 195 79 N SD: 0.0218 c. M: 0.0386 c. 1783: 105 166 198 105 166 105 198 166 105 105 259 105 N SD: 0.0080 c. M: 0.0145 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: 3.4487 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 x 12 S SD: 9.7541 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 15.5899 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.2477 cents 9 x 10:11 x 12 x x 14:15:16:17:18 S SD: 9.5797 cents 10 x 11:12 x 13:14:15:16:17 x 19:20 SD: 6.9550 cents 11 x 12:13:14 x 15:17 x 18:19:21:22 SD: 9.6517 cents 12 x 13:14:15:16:17:18:19:20:21:23:24 SD: 7.0436 cents 13 x 14 x 16:17:18:20:21:22:23:25:26 SD: 9.3695 cents 14:15:16:17:18:19 x 21:22:23:24:27:28 SD: 9.3716 cents 15:16:17:18:19:20:21:23:24:25:26:29:30 SD: 5.9956 cents 16:17:18:19:20:21:22:24:26:27:28:31:32 SD: 5.6719 cents 18:19:20:22:23:24:25:27:29:30:31:35:36 SD: 5.1366 cents 20:21:22:24:25:27:28:30:32:33:35:38:40 SD: 3.6964 cents 24:25:27:29:30:32:33:36:38:40:42:46:48 SD: 3.1587 cents 28:29:31:34:35:37:39:42:45:47:49:54:56 SD: 2.9850 cents 36:38:40:43:45:48:50:54:58:60:63:69:72 SD: 2.5457 cents 42:44:47:50:53:56:58:63:67:70:73:81:84 SD: 2.4960 cents 44:46:49:53:55:59:61:66:70:73:76:84:88 SD: 1.9344 cents 45:47:50:54:56:60:63:68:72:75:78:86:90 SD: 1.8754 cents 48:50:53:58:60:64:67:72:77:80:83:92:96 SD: 1.6943 cents 52:54:58:62:65:69:72:78:83:87:90:100:104 SD: 1.6506 cents 54:56:60:65:68:72:75:81:86:90:94:104:108 SD: 1.5930 cents 60:63:67:72:75:80:83:90:96:100:104:115:120 SD: 1.5132 cents 64:67:71:77:80:85:89:96:102:107:111:123:128 SD: 1.2739 cents 72:75:80:86:90:96:100:108:115:120:125:138:144 SD: 0.7575 cents 100:104:111:120:125:133:139:150:160:167:174:192:200 SD: 0.6366 cents 120:125:133:144:150:160:167:180:192:200:208:230:240 SD: 0.5742 cents 144:150:160:173:180:192:200:216:230:240:250:276:288 SD: 0.3918 cents 200:208:222:240:250:267:278:300:320:333:347:384:400 SD: 0.3865 cents 216:225:240:259:270:288:300:324:346:360:375:415:432 SD: 0.2230 cents 288:300:320:346:360:384:400:432:461:480:500:553:576 SD: 0.1785 cents 360:375:400:432:450:480:500:540:576:600:625:691:720 SD: 0.0418 cents