Scala analysis: harm12s
Harmonics 1 to 12 and subharmonics mixed
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 8/7 231.174094 septimal whole tone 3: 5/4 386.313714 major third 4: 4/3 498.044999 perfect fourth 5: 11/8 551.317942 undecimal semi-augmented fourth 6: 16/11 648.682058 undecimal semi-diminished fifth 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 7/4 968.825906 harmonic seventh 10: 16/9 996.089998 Pythagorean minor seventh 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 9/8 203.9100 major whole tone 2: 64/63 27.2641 septimal comma, Archytas' comma 3: 35/32 155.1396 septimal neutral second 4: 16/15 111.7313 minor diatonic semitone 5: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 6: 128/121 97.3641 undecimal semitone 7: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 8: 16/15 111.7313 minor diatonic semitone 9: 35/32 155.1396 septimal neutral second 10: 64/63 27.2641 septimal comma, Archytas' comma 11: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 2 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 128/121 97.364 cents undecimal semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 35/32 155.140 cents septimal neutral second 1: 2 9/8 203.910 cents major whole tone 2: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 2 10/9 182.404 cents minor whole tone 2: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 81/64 407.820 cents Pythagorean major third 3: 1 9/8 203.910 cents major whole tone 3: 2 64/55 262.368 cents 3: 2 32/27 294.135 cents Pythagorean minor third 3: 2 77/64 320.144 cents Keemun minor third 3: 2 5/4 386.314 cents major third 3: 2 9/7 435.084 cents septimal major third, BP third 4: 2 6/5 315.641 cents minor third 4: 2 11/9 347.408 cents undecimal neutral third 4: 2 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 64/49 462.348 cents 2 septatones or septatonic major third 4: 2 4/3 498.045 cents perfect fourth 4: 2 45/32 590.224 cents diatonic tritone 5: 1 32/25 427.373 cents classic diminished fourth 5: 2 128/99 444.772 cents 5: 2 21/16 470.781 cents narrow fourth 5: 2 11/8 551.318 cents undecimal semi-augmented fourth 5: 2 10/7 617.488 cents Euler's tritone 5: 2 3/2 701.955 cents perfect fifth 6: 2 4/3 498.045 cents perfect fourth 6: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 2 16/11 648.682 cents undecimal semi-diminished fifth 6: 2 32/21 729.219 cents wide fifth 6: 2 99/64 755.228 cents 6: 1 25/16 772.627 cents classic augmented fifth 7: 2 64/45 609.776 cents 2nd tritone 7: 2 3/2 701.955 cents perfect fifth 7: 1 49/32 737.652 cents 7: 2 11/7 782.492 cents undecimal augmented fifth 7: 2 18/11 852.592 cents undecimal neutral sixth 7: 2 5/3 884.359 cents major sixth, BP sixth 8: 2 14/9 764.916 cents septimal minor sixth 8: 2 8/5 813.686 cents minor sixth 8: 2 128/77 879.856 cents 8: 2 27/16 905.865 cents Pythagorean major sixth 8: 2 55/32 937.632 cents 8: 1 16/9 996.090 cents Pythagorean minor seventh 9: 1 128/81 792.180 cents Pythagorean minor sixth 9: 2 12/7 933.129 cents septimal major sixth 9: 2 7/4 968.826 cents harmonic seventh 9: 2 9/5 1017.596 cents just minor seventh, BP seventh 9: 2 20/11 1034.996 cents large minor seventh 9: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 2 64/35 1044.860 cents septimal neutral seventh 10: 2 15/8 1088.269 cents classic major seventh 10: 1 121/64 1102.636 cents two (undecimal semi-augmented fourth) 10: 2 64/33 1146.727 cents 33rd subharmonic 10: 2 63/32 1172.736 cents octave - septimal comma Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 203.9 231.2 386.3 498.0 551.3 648.7 702.0 813.7 968.8 996.1 1200.0 203.9 : 27.3 182.4 294.1 347.4 444.8 498.0 609.8 764.9 792.2 996.1 1200.0 231.2 : 155.1 266.9 320.1 417.5 470.8 582.5 737.7 764.9 968.8 1172.7 1200.0 386.3 : 111.7 165.0 262.4 315.6 427.4 582.5 609.8 813.7 1017.6 1044.9 1200.0 498.0 : 53.3 150.6 203.9 315.6 470.8 498.0 702.0 905.9 933.1 1088.3 1200.0 551.3 : 97.4 150.6 262.4 417.5 444.8 648.7 852.6 879.9 1035.0 1146.7 1200.0 648.7 : 53.3 165.0 320.1 347.4 551.3 755.2 782.5 937.6 1049.4 1102.6 1200.0 702.0 : 111.7 266.9 294.1 498.0 702.0 729.2 884.4 996.1 1049.4 1146.7 1200.0 813.7 : 155.1 182.4 386.3 590.2 617.5 772.6 884.4 937.6 1035.0 1088.3 1200.0 968.8 : 27.3 231.2 435.1 462.3 617.5 729.2 782.5 879.9 933.1 1044.9 1200.0 996.1 : 203.9 407.8 435.1 590.2 702.0 755.2 852.6 905.9 1017.6 1172.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 203.9100 cents 567/512, 176.6459 cents 64/63, 27.2641 cents 2: 150.6371 .. 407.8200 cents 297/256, 257.1829 cents 32/33,-53.2729 cents 3: 203.9100 .. 435.0841 cents 8/7, 231.1741 cents 8/9,-203.9100 cents 4: 315.6413 .. 590.2237 cents 75/64, 274.5824 cents 14/15,-119.4428 cents 5: 427.3726 .. 701.9550 cents 75/64, 274.5824 cents 1024/1125,-162.8511 cents 6: 498.0450 .. 772.6274 cents 75/64, 274.5824 cents 8/9,-203.9100 cents 7: 609.7763 .. 884.3587 cents 75/64, 274.5824 cents 1024/1125,-162.8511 cents 8: 764.9159 .. 996.0900 cents 8/7, 231.1741 cents 14/15,-119.4428 cents 9: 792.1800 .. 1049.3629 cents 297/256, 257.1829 cents 8/9,-203.9100 cents 10: 996.0900 .. 1172.7359 cents 567/512, 176.6459 cents 32/33,-53.2729 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 4.001267 Largest / Average step : 1.869175 Largest / Smallest step : 7.479068 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 106.26397 cents, oct.: 1168.90369 cents Scale is not proper Step pattern alph. order: ABCDEFEDCBA Step pattern size order : FAEDBCBDEAF Scale is not a Constant Structure Scale diversity : 1.557860 Lumma stability : 0.045440 Lumma impropriety factor : 0.748938 Rothenberg efficiency : 0.270523 redundancy: 0.729477 Efficiency x scale size : 2.975758 Number of different interval sizes : 56 = 5.60000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 6.00000 = 6 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 385/384, 4.5026 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 11 = 100.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 11 Odd number limit : 121 (O: 121 U: 121) Highest odd numerator or denominator: 11 Scale harmonicity : 0.011441 Average absolute harmonicity : 0.198958 Specific harmonicity : 0.126048 Fundamental : 1/27720, -14.7586 octaves, 0.0094 Hz. Guide tone : 55440, 15.7586 octaves, 14504521.340 Hz. Exponens Consonantiae : 1.536797E+09, 30.51728 octaves Euler's gradus suavitatis : 56 Sum of Mann's harmonic distance : 75.5, average 6.86364 Mersenne's string divisions : 218243025 Sum of van Prooijen's expressibility: 8.03365, average 0.73033 Sum of Tenney's harmonic distance : 16.46249, average 1.49659 Vogel's harmonic complexity : 32.54545 Wille's k value : 19057 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 10 Triangular lattice diameter : 4 Lattice compactness : 245.04855, average 3.71286 Lattice compactness (without 2's) : 104.77394, average 1.58748 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.54545 28 1 3: -2 .. 2 0.00000 6 4 5: -1 .. 1 0.00000 2 2 7: -1 .. 1 0.00000 2 2 11: -1 .. 1 0.00000 2 2 Average exponent except 2's : 0 / 11 = 0.00000 Average absolute exponent except 2's: 12 / 11 = 1.09091 Scale is weakly epimorphic with val: <11 15 24 32 38| Scale is weakly epimorphic with val: <11 15 24 32 39| Scale is weakly epimorphic with val: <11 15 24 34 38| Scale is weakly epimorphic with val: <11 15 24 34 39| Scale is weakly epimorphic with val: <11 15 27 32 35| Scale is weakly epimorphic with val: <11 15 27 34 35| Scale is weakly epimorphic with val: <11 15 28 32 35| Scale is weakly epimorphic with val: <11 15 28 34 35| Scale is weakly epimorphic with val: <11 16 24 29 36| Scale is weakly epimorphic with val: <11 16 24 29 41| Scale is weakly epimorphic with val: <11 16 24 30 37| Scale is weakly epimorphic with val: <11 16 24 30 40| Scale is weakly epimorphic with val: <11 16 25 29 35| Scale is weakly epimorphic with val: <11 16 25 31 37| Scale is weakly epimorphic with val: <11 16 25 31 40| Scale is weakly epimorphic with val: <11 16 26 30 35| Scale is weakly epimorphic with val: <11 16 26 31 36| Scale is weakly epimorphic with val: <11 16 26 31 41| Scale is weakly epimorphic with val: <11 16 29 30 35| Scale is weakly epimorphic with val: <11 16 29 31 36| Scale is weakly epimorphic with val: <11 16 29 31 41| Scale is weakly epimorphic with val: <11 17 24 29 36| Scale is weakly epimorphic with val: <11 17 24 29 41| Scale is weakly epimorphic with val: <11 17 24 30 37| Scale is weakly epimorphic with val: <11 17 24 30 40| Scale is weakly epimorphic with val: <11 17 25 29 35| Scale is weakly epimorphic with val: <11 17 25 31 37| Scale is weakly epimorphic with val: <11 17 25 31 40| Scale is weakly epimorphic with val: <11 17 26 30 35| Scale is weakly epimorphic with val: <11 17 26 31 36| Scale is weakly epimorphic with val: <11 17 26 31 41| Scale is weakly epimorphic with val: <11 17 29 30 35| Scale is weakly epimorphic with val: <11 17 29 31 36| Scale is weakly epimorphic with val: <11 17 29 31 41| Scale is weakly epimorphic with val: <11 18 24 32 38| Scale is weakly epimorphic with val: <11 18 24 32 39| Scale is weakly epimorphic with val: <11 18 24 34 38| Scale is weakly epimorphic with val: <11 18 24 34 39| Scale is weakly epimorphic with val: <11 18 27 32 35| Scale is weakly epimorphic with val: <11 18 27 34 35| Scale is weakly epimorphic with val: <11 18 28 32 35| Scale is weakly epimorphic with val: <11 18 28 34 35| Scale is weakly epimorphic with val: <11 19 24 32 37| Scale is weakly epimorphic with val: <11 19 24 32 40| Scale is weakly epimorphic with val: <11 19 24 34 37| Scale is weakly epimorphic with val: <11 19 24 34 40| Scale is weakly epimorphic with val: <11 19 26 32 35| Scale is weakly epimorphic with val: <11 19 26 34 35| Scale is weakly epimorphic with val: <11 19 29 32 35| Scale is weakly epimorphic with val: <11 19 29 34 35|
FIT/MODE
11: 2 0 2 1 0 1 0 1 2 0 2 N I SD: 30.6283 c. M: 50.0499 c. 12: 2 0 2 1 0 1 1 1 2 0 2 N SD: 25.8667 c. M: 51.3179 c. 13: 2 1 1 1 1 1 1 1 1 1 2 N D3 I SD: 27.2904 c. M:-45.7490 c. 15: 3 0 2 1 1 1 1 1 2 0 3 N I SD: 18.9194 c. M:-36.0900 c. 16: 3 0 2 2 0 2 0 2 2 0 3 N I SD: 19.2123 c. M:-26.9550 c. 17: 3 0 2 2 1 1 1 2 2 0 3 N I SD: 17.8214 c. M: 33.3725 c. 19: 3 1 2 2 1 1 1 2 2 1 3 N I SD: 13.9330 c. M:-21.4575 c. 22: 4 0 3 2 1 2 1 2 3 0 4 N I SD: 9.3224 c. M:-14.2718 c. 31: 5 1 4 3 1 3 1 3 4 1 5 N I SD: 6.3821 c. M:-10.3616 c. 41: 7 1 5 4 2 3 2 4 5 1 7 N I SD: 3.4848 c. M: 5.8259 c. 46: 8 1 6 4 2 4 2 4 6 1 8 N I SD: 3.7839 c. M: 4.9906 c. 63: 11 1 8 6 3 5 3 6 8 1 11 N I SD: 3.7183 c. M:-5.6138 c. 72: 12 2 9 7 3 6 3 7 9 2 12 N I SD: 2.5006 c. M:-3.9100 c. 87: 15 2 11 8 4 7 4 8 11 2 15 N I SD: 2.0124 c. M:-3.3087 c. 94: 16 2 12 9 4 8 4 9 12 2 16 N I SD: 1.8521 c. M: 3.3350 c. 118: 20 3 15 11 5 10 5 11 15 3 20 N I SD: 1.5054 c. M:-2.7242 c. 130: 22 3 17 12 6 10 6 12 17 3 22 N I SD: 1.3020 c. M:-2.5282 c. 152: 26 3 20 14 7 12 7 14 20 3 26 N I SD: 1.2970 c. M: 2.2267 c. 176: 30 4 23 16 8 14 8 16 23 4 30 N I SD: 1.1462 c. M: 2.3226 c. 178: 30 4 23 17 8 14 8 17 23 4 30 N I SD: 1.5783 c. M: 2.0441 c. 181: 31 4 23 17 8 15 8 17 23 4 31 N I SD: 1.2271 c. M: 1.7833 c. 183: 31 4 24 17 8 15 8 17 24 4 31 N I SD: 0.8365 c. M:-1.6659 c. 224: 38 5 29 21 10 18 10 21 29 5 38 N I SD: 0.5025 c. M: 0.8170 c. 270: 46 6 35 25 12 22 12 25 35 6 46 N I SD: 0.3099 c. M:-0.5344 c. 342: 58 8 44 32 15 28 15 32 44 8 58 N I SD: 0.3519 c. M: 0.4407 c. 472: 80 11 61 44 21 38 21 44 61 11 80 N I SD: 0.3103 c. M:-0.5202 c. 494: 84 11 64 46 22 40 22 46 64 11 84 N I SD: 0.1926 c. M:-0.4049 c. 612: 104 14 79 57 27 50 27 57 79 14 104 N I SD: 0.1679 c. M: 0.3376 c. 742: 126 17 96 69 33 60 33 69 96 17 126 N I SD: 0.1366 c. M: 0.2092 c. 836: 142 19 108 78 37 68 37 78 108 19 142 N I SD: 0.1083 c. M: 0.1893 c. 1106: 188 25 143 103 49 90 49 103 143 25 188 N I SD: 0.0791 c. M: 0.1425 c. 1236: 210 28 160 115 55 100 55 115 160 28 210 N I SD: 0.0854 c. M:-0.1384 c. 1354: 230 31 175 126 60 110 60 126 175 31 230 N I SD: 0.0843 c. M:-0.1405 c. 1578: 268 36 204 147 70 128 70 147 204 36 268 N I SD: 0.0517 c. M:-0.1077 c. 1848: 314 42 239 172 82 150 82 172 239 42 314 N I SD: 0.0239 c. M: 0.0499 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 4 x x x 5 x x 6 S SD: 23.5575 cents 4 x x 5 x x x 6 x 7 x 8 S SD: 0.0000 cents 5 x x 6 x 7 x x 8 x 9:10 S SD: 16.0377 cents 6 x 7 x 8 x x 9:10 x 11:12 S SD: 15.9050 cents 7 x 8:9 x x 10 x 11:12 x 14 S SD: 12.4710 cents 8:9 x 10 x 11 x 12:13:14 x 16 S SD: 3.8345 cents 9:10 x 11:12 x 13 x 14 x 16:18 S SD: 9.5834 cents 10:11 x x 13:14 x 15:16 x 18:20 SD: 9.9698 cents 11:12:13:14 x 15:16:17:18:19:20:22 S SD: 11.6603 cents 12 x 14:15:16 x 17:18:19:21 x 24 SD: 7.5929 cents 13 x 15:16:17:18:19:20:21 x 23:26 SD: 7.5398 cents 14 x 16:18 x 19:20:21:22 x 25:28 SD: 8.7467 cents 15:17 x 19:20:21:22:23:24:26:27:30 SD: 6.3666 cents 16:18 x 20:21:22:23:24:26:28 x 32 S SD: 4.8180 cents 17:19 x 21:23 x 25:26:27 x 30:34 SD: 6.8518 cents 18:20:21:23:24:25:26:27:29 x 32:36 SD: 6.1453 cents 20 x 23:25:27:28:29:30:32:35:36:40 SD: 4.5209 cents 21 x 24:26:28:29:31:32:34:37 x 42 SD: 5.3115 cents 22 x 25:28:29:30:32:33:35 x 39:44 SD: 4.7007 cents 23:26 x 29:31:32:33:35:37:40:41:46 SD: 4.9689 cents 24:27 x 30:32:33:35:36:38:42:43:48 SD: 2.3031 cents 25:28:29:31:33:34:36:38:40:44 x 50 SD: 5.0064 cents 26:29:30:33:35:36:38:39:42 x 46:52 SD: 4.5022 cents 27:30:31:34:36:37:39:41:43:47:48:54 SD: 3.4849 cents 28 x 32:35:37:39:41:42:45:49:50:56 SD: 3.1505 cents 29 x 33:36:39:40:42:44:46:51:52:58 SD: 3.7616 cents 30:34 x 38:40:41:44:45:48 x 53:60 SD: 3.7252 cents 31:35 x 39:41:43:45:47:50:54:55:62 SD: 3.4833 cents 32:36:37:40:43:44:47:48:51:56:57:64 SD: 2.7705 cents 34:38:39:43:45:47:49:51:54 x 60:68 SD: 3.7547 cents 35:39:40:44:47:48:51:53:56:61:62:70 SD: 2.7442 cents 36 x 41:45:48:50:52:54:58:63:64:72 SD: 2.5062 cents 37 x 42:46:49:51:54:56:59:65:66:74 SD: 2.7744 cents 38:43 x 48:51:52:55:57:61:67:68:76 SD: 3.2110 cents 39:44:45:49:52:54:57:59:62:68:69:78 SD: 2.9355 cents 40:45:46:50:53:55:58:60:64:70:71:80 SD: 1.4961 cents 44 x 50:55:59:61:64:66:70:77:78:88 SD: 2.2762 cents 45:51 x 56:60:62:65:68:72:79:80:90 SD: 2.3955 cents 48:54:55:60:64:66:70:72:77:84:85:96 SD: 0.9392 cents 52 x 59:65:69:72:76:78:83:91:92:104 SD: 2.2980 cents 53:60:61:66:71:73:77:80:85:93:94:106 SD: 2.1549 cents 54:61:62:68:72:74:79:81:86:95:96:108 SD: 2.1506 cents 55:62:63:69:73:76:80:83:88:96:98:110 SD: 1.6955 cents 56:63:64:70:75:77:81:84:90:98:100:112 SD: 1.5000 cents 63:71:72:79:84:87:92:95:101:110:112:126 SD: 1.4461 cents 64:72:73:80:85:88:93:96:102:112:114:128 SD: 0.9857 cents 72:81:82:90:96:99:105:108:115:126:128:144 SD: 0.7362 cents 104:117:119:130:139:143:151:156:166:182:185:208 SD: 0.6416 cents 112:126:128:140:149:154:163:168:179:196:199:224 SD: 0.4123 cents 168:189:192:210:224:231:244:252:269:294:299:336 SD: 0.3154 cents 216:243:247:270:288:297:314:324:346:378:384:432 SD: 0.2230 cents 240:270:274:300:320:330:349:360:384:420:427:480 SD: 0.2090 cents 280:315:320:350:373:385:407:420:448:490:498:560 SD: 0.1892 cents 288:324:329:360:384:396:419:432:461:504:512:576 SD: 0.1025 cents 504:567:576:630:672:693:733:756:806:882:896:1008 SD: 0.0805 cents 552:621:631:690:736:759:803:828:883:966:981:1104 SD: 0.0756 cents