Scala analysis: majsyn3
648/625 and 81/80 Fokker block, Gene Ward Smith.
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: 6/5 315.641287 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: 25/16 772.627428 classic augmented fifth 9: 5/3 884.358713 major sixth, BP sixth 10: 9/5 1017.596288 just minor seventh, BP seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 16/15 111.7313 minor diatonic semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 16/15 111.7313 minor diatonic semitone 10: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 250/243 49.166 cents maximal diesis, Porcupine comma 1: 4 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 16/15 111.731 cents minor diatonic semitone 1: 4 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 6 10/9 182.404 cents minor whole tone 2: 4 9/8 203.910 cents major whole tone 2: 2 144/125 244.969 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: 2 100/81 364.807 cents grave major third 4: 6 5/4 386.314 cents major third 4: 2 32/25 427.373 cents classic diminished fourth 4: 2 162/125 448.879 cents 5: 1 125/96 456.986 cents classic augmented third 5: 8 4/3 498.045 cents perfect fourth 5: 3 27/20 519.551 cents acute fourth 6: 6 25/18 568.717 cents classic augmented fourth 6: 6 36/25 631.283 cents classic diminished fifth 7: 3 40/27 680.449 cents grave fifth 7: 8 3/2 701.955 cents perfect fifth 7: 1 192/125 743.014 cents classic diminished sixth 8: 2 125/81 751.121 cents 8: 2 25/16 772.627 cents classic augmented fifth 8: 6 8/5 813.686 cents minor sixth 8: 2 81/50 835.193 cents acute minor sixth 9: 9 5/3 884.359 cents major sixth, BP sixth 9: 3 216/125 946.924 cents semi-augmented sixth 10: 2 125/72 955.031 cents classic augmented sixth 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 6 9/5 1017.596 cents just minor seventh, BP seventh 11: 4 50/27 1066.762 cents grave major seventh 11: 3 15/8 1088.269 cents classic major seventh 11: 4 48/25 1129.328 cents classic diminished octave 11: 1 243/125 1150.834 cents octave - maximal diesis Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 70.7 203.9 315.6 386.3 519.6 568.7 702.0 772.6 884.4 1017.6 1088.3 1200.0 70.7 : 133.2 245.0 315.6 448.9 498.0 631.3 702.0 813.7 946.9 1017.6 1129.3 1200.0 203.9 : 111.7 182.4 315.6 364.8 498.0 568.7 680.4 813.7 884.4 996.1 1066.8 1200.0 315.6 : 70.7 203.9 253.1 386.3 457.0 568.7 702.0 772.6 884.4 955.0 1088.3 1200.0 386.3 : 133.2 182.4 315.6 386.3 498.0 631.3 702.0 813.7 884.4 1017.6 1129.3 1200.0 519.6 : 49.2 182.4 253.1 364.8 498.0 568.7 680.4 751.1 884.4 996.1 1066.8 1200.0 568.7 : 133.2 203.9 315.6 448.9 519.6 631.3 702.0 835.2 946.9 1017.6 1150.8 1200.0 702.0 : 70.7 182.4 315.6 386.3 498.0 568.7 702.0 813.7 884.4 1017.6 1066.8 1200.0 772.6 : 111.7 245.0 315.6 427.4 498.0 631.3 743.0 813.7 946.9 996.1 1129.3 1200.0 884.4 : 133.2 203.9 315.6 386.3 519.6 631.3 702.0 835.2 884.4 1017.6 1088.3 1200.0 1017.6: 70.7 182.4 253.1 386.3 498.0 568.7 702.0 751.1 884.4 955.0 1066.8 1200.0 1088.3: 111.7 182.4 315.6 427.4 498.0 631.3 680.4 813.7 884.4 996.1 1129.3 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 .. 244.9689 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 3: 253.0761 .. 315.6413 cents 648/625, 62.5651 cents 15625/15552, 8.1073 cents 4: 364.8074 .. 448.8789 cents 6561/6250, 84.0714 cents 250/243, 49.1661 cents 5: 456.9861 .. 519.5513 cents 648/625, 62.5651 cents 15625/15552, 8.1073 cents 6: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 7: 680.4487 .. 743.0139 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 8: 751.1211 .. 835.1926 cents 6561/6250, 84.0714 cents 15625/15552, 8.1073 cents 9: 884.3587 .. 946.9239 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 10: 955.0311 .. 1017.5963 cents 648/625, 62.5651 cents 15625/15552, 8.1073 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 : 16/15, 111.7313 cents, amount: 3 Least squares average step : 99.35628 cents, oct.: 1192.27539 cents Scale is strictly proper Step pattern alph. order: ABCABDBACBAC Step pattern size order : BDCBDADBCDBC Scale is a Constant Structure, by a margin of 8.10728 cents Scale diversity : 1.349256 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.354799 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 : 8, average 701.9550 cents Best fifths form a closed circle Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 3 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined 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 : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.026643 Average absolute harmonicity : 0.176368 Specific harmonicity : 0.148141 Fundamental : 1/720, -9.4919 octaves, 0.3634 Hz. Guide tone : 1350, 10.3987 octaves, 353194.513 Hz. Exponens Consonantiae : 9.720000E+05, 19.89060 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 135.0, average 11.25000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.28379, average 0.94032 Sum of Tenney's harmonic distance : 21.38897, average 1.78241 Vogel's harmonic complexity : 17.58333 Wille's k value : 562 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 250.09555, average 3.20635 Lattice compactness (without 2's) : 174.79285, average 2.24093 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.41667 21 1 3: -2 .. 3 0.50000 14 2 5: -1 .. 2 0.50000 12 9 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 26 / 12 = 2.16667 Scale is weakly epimorphic with val: <12 17 26| Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 20 25| Scale is weakly epimorphic with val: <12 20 27| Scale is weakly epimorphic with val: <12 20 29| Scale is weakly epimorphic with val: <12 20 31|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.5139 c. M:-31.2826 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 1 1 2 0 2 1 1 2 1 1 P D3 SD: 22.1934 c. M:-40.4487 c. 16: 1 2 1 1 2 1 1 1 2 2 1 1 N D3 S SD: 21.8458 c. M:-36.7313 c. 19: 1 2 2 1 2 1 2 1 2 2 1 2 P M ME SD: 9.3776 c. M: 14.7327 c. Meantone Chromatic (1/3-comma) 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 8.1969 c. M: 16.3255 c. Meantone Chromatic (53/220-comma) 33: 2 4 3 2 3 2 3 2 3 4 2 3 P SD: 9.8193 c. M:-14.2718 c. 34: 2 4 3 2 4 1 4 2 3 4 2 3 P SD: 4.8851 c. M:-9.8605 c. 46: 3 5 4 3 5 2 5 3 4 5 3 4 SP SD: 5.0874 c. M:-9.9813 c. 53: 3 6 5 3 6 2 6 3 5 6 3 5 P SD: 1.6709 c. M: 2.8161 c. 99: 6 11 9 6 11 4 11 6 9 11 6 9 SP SD: 1.6774 c. M:-3.1301 c. 118: 7 13 11 7 13 5 13 7 11 13 7 11 SP SD: 0.4866 c. M: 0.9072 c. 171: 10 19 16 10 19 7 19 10 16 19 10 16 SP SD: 0.3602 c. M: 0.6976 c. 289: 17 32 27 17 32 12 32 17 27 32 17 27 SP SD: 0.2755 c. M: 0.5201 c. 441: 26 49 41 26 49 18 49 26 41 49 26 41 SP SD: 0.1090 c. M:-0.1766 c. 559: 33 62 52 33 62 23 62 33 52 62 33 52 SP SD: 0.1017 c. M:-0.1812 c. 612: 36 68 57 36 68 25 68 36 57 68 36 57 SP SD: 0.0532 c. M: 0.0900 c. 730: 43 81 68 43 81 30 81 43 68 81 43 68 SP SD: 0.0480 c. M: 0.0992 c. 1171: 69 130 109 69 130 48 130 69 109 130 69 109 SP SD: 0.0233 c. M:-0.0455 c. 1342: 79 149 125 79 149 55 149 79 125 149 79 125 SP SD: 0.0267 c. M: 0.0492 c. 1783: 105 198 166 105 198 73 198 105 166 198 105 166 SP SD: 0.0108 c. M:-0.0225 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: 8.6629 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.3417 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.9762 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.4802 cents 9 x 10:11 x 12 x x 14:15:16:17:18 S SD: 6.3975 cents 10 x 11:12 x x 14:15:16:17:18:19:20 S SD: 7.9279 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 9.5955 cents 12 x x 14:15:16:17:18:19:20:22:23:24 S SD: 8.3661 cents 13:14:15 x 16 x 18 x 20:22:23:24:26 S SD: 10.5534 cents 14:15:16:17:18:19 x 21:22:23:25:26:28 SD: 7.7065 cents 15:16:17:18:19:20:21 x 23:25:27:28:30 SD: 5.8574 cents 16:17:18:19:20 x 22:24:25:27:29:30:32 SD: 4.4654 cents 19:20:21:23:24:26 x 29:30:32:34:36:38 SD: 6.0103 cents 20:21:23:24:25:27:28:30:31:33:36:38:40 SD: 4.4491 cents 23:24:26:28:29:31:32:35:36:38:41:43:46 SD: 3.8249 cents 24:25:27:29:30:32:33:36:38:40:43:45:48 SD: 3.2266 cents 25:26:28:30:31:34:35:38:39:42:45:47:50 SD: 3.0722 cents 31:32:35:37:39:42:43:47:48:52:56:58:62 SD: 3.0108 cents 32:33:36:38:40:43:44:48:50:53:58:60:64 SD: 2.9581 cents 39:41:44:47:49:53:54:59:61:65:70:73:78 SD: 2.3916 cents 40:42:45:48:50:54:56:60:63:67:72:75:80 SD: 2.1171 cents 46:48:52:55:58:62:64:69:72:77:83:86:92 SD: 1.8024 cents 48:50:54:58:60:65:67:72:75:80:86:90:96 SD: 1.4698 cents 64:67:72:77:80:86:89:96:100:107:115:120:128 SD: 1.1852 cents 72:75:81:86:90:97:100:108:113:120:130:135:144 SD: 1.0693 cents 80:83:90:96:100:108:111:120:125:133:144:150:160 SD: 0.6969 cents 96:100:108:115:120:130:133:144:150:160:173:180:192 SD: 0.6471 cents 120:125:135:144:150:162:167:180:188:200:216:225:240 SD: 0.4803 cents 144:150:162:173:180:194:200:216:225:240:259:270:288 SD: 0.3585 cents 216:225:243:259:270:292:300:324:338:360:389:405:432 SD: 0.3204 cents 240:250:270:288:300:324:333:360:375:400:432:450:480 SD: 0.1443 cents 360:375:405:432:450:486:500:540:563:600:648:675:720 SD: 0.1282 cents 480:500:540:576:600:648:667:720:750:800:864:900:960 SD: 0.0721 cents