Scala analysis: 12_max7
32 7-limit dyads in 12 notes, Paul Hahn.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 7/6 266.870906 septimal minor third 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP 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: 7/4 968.825906 harmonic seventh 11: 28/15 1080.557192 grave major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 21/20 84.4672 minor semitone 2: 10/9 182.4037 minor whole tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 21/20 84.4672 minor semitone 11: 16/15 111.7313 minor diatonic semitone 12: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 21/20 84.467 cents minor semitone 1: 3 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 35/32 155.140 cents septimal neutral second 2: 2 10/9 182.404 cents minor whole tone 2: 2 28/25 196.198 cents middle second 2: 2 9/8 203.910 cents major whole tone 2: 3 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 3: 1 8/7 231.174 cents septimal whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 2 25/21 301.847 cents BP second, quasi-equal minor third 3: 5 6/5 315.641 cents minor third 3: 1 5/4 386.314 cents major third 4: 1 6/5 315.641 cents minor third 4: 1 56/45 378.602 cents septimal narrow major third 4: 5 5/4 386.314 cents major third 4: 1 63/50 400.108 cents quasi-equal major third 4: 1 80/63 413.578 cents wide major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 4/3 498.045 cents perfect fourth 5: 1 9/7 435.084 cents septimal major third, BP third 5: 2 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 1 75/56 505.757 cents marvelous fourth 5: 1 48/35 546.815 cents septimal semi-augmented fourth 5: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 48/35 546.815 cents septimal semi-augmented fourth 6: 1 25/18 568.717 cents classic augmented fourth 6: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 4 10/7 617.488 cents Euler's tritone 6: 1 36/25 631.283 cents classic diminished fifth 6: 1 35/24 653.185 cents septimal semi-diminished fifth 7: 1 10/7 617.488 cents Euler's tritone 7: 1 35/24 653.185 cents septimal semi-diminished fifth 7: 1 112/75 694.243 cents marvelous fifth 7: 6 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 7: 1 14/9 764.916 cents septimal minor sixth 8: 1 3/2 701.955 cents perfect fifth 8: 1 14/9 764.916 cents septimal minor sixth 8: 1 25/16 772.627 cents classic augmented fifth 8: 1 63/40 786.422 cents narrow minor sixth 8: 1 100/63 799.892 cents quasi-equal minor sixth 8: 5 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 8: 1 5/3 884.359 cents major sixth, BP sixth 9: 1 8/5 813.686 cents minor sixth 9: 5 5/3 884.359 cents major sixth, BP sixth 9: 2 42/25 898.153 cents quasi-equal major sixth 9: 3 12/7 933.129 cents septimal major sixth 9: 1 7/4 968.826 cents harmonic seventh 10: 1 12/7 933.129 cents septimal major sixth 10: 3 7/4 968.826 cents harmonic seventh 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 2 25/14 1003.802 cents middle minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 64/35 1044.860 cents septimal neutral seventh 10: 1 28/15 1080.557 cents grave major seventh 11: 1 9/5 1017.596 cents just minor seventh, BP seventh 11: 2 28/15 1080.557 cents grave major seventh 11: 3 15/8 1088.269 cents classic major seventh 11: 3 40/21 1115.533 cents acute major seventh 11: 2 48/25 1129.328 cents classic diminished octave 11: 1 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.36364 = 70/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 84.5 266.9 315.6 386.3 498.0 582.5 702.0 813.7 884.4 968.8 1080.6 1200.0 84.5 : 182.4 231.2 301.8 413.6 498.0 617.5 729.2 799.9 884.4 996.1 1115.5 1200.0 266.9 : 48.8 119.4 231.2 315.6 435.1 546.8 617.5 702.0 813.7 933.1 1017.6 1200.0 315.6 : 70.7 182.4 266.9 386.3 498.0 568.7 653.2 764.9 884.4 968.8 1151.2 1200.0 386.3 : 111.7 196.2 315.6 427.4 498.0 582.5 694.2 813.7 898.2 1080.6 1129.3 1200.0 498.0 : 84.5 203.9 315.6 386.3 470.8 582.5 702.0 786.4 968.8 1017.6 1088.3 1200.0 582.5 : 119.4 231.2 301.8 386.3 498.0 617.5 702.0 884.4 933.1 1003.8 1115.5 1200.0 702.0 : 111.7 182.4 266.9 378.6 498.0 582.5 764.9 813.7 884.4 996.1 1080.6 1200.0 813.7 : 70.7 155.1 266.9 386.3 470.8 653.2 702.0 772.6 884.4 968.8 1088.3 1200.0 884.4 : 84.5 196.2 315.6 400.1 582.5 631.3 702.0 813.7 898.2 1017.6 1129.3 1200.0 968.8 : 111.7 231.2 315.6 498.0 546.8 617.5 729.2 813.7 933.1 1044.9 1115.5 1200.0 1080.6: 119.4 203.9 386.3 435.1 505.8 617.5 702.0 821.4 933.1 1003.8 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 182.4037 cents 175/162, 133.6333 cents 36/35, 48.7704 cents 2: 119.4428 .. 266.8709 cents 49/45, 147.4281 cents 27/28,-62.9609 cents 3: 231.1741 .. 386.3137 cents 35/32, 155.1396 cents 48/49,-35.6968 cents 4: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 24/25,-70.6724 cents 5: 435.0841 .. 582.5122 cents 49/45, 147.4281 cents 27/28,-62.9609 cents 6: 546.8154 .. 653.1846 cents 1225/1152, 106.3692 cents 48/49,-35.6968 cents 7: 617.4878 .. 764.9159 cents 49/45, 147.4281 cents 48/49,-35.6968 cents 8: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 27/28,-62.9609 cents 9: 813.6863 .. 968.8259 cents 35/32, 155.1396 cents 24/25,-70.6724 cents 10: 933.1291 .. 1080.5572 cents 49/45, 147.4281 cents 48/49,-35.6968 cents 11: 1017.5963 .. 1151.2296 cents 175/162, 133.6333 cents 27/28,-62.9609 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 2.050425 Largest / Average step : 1.824037 Largest / Smallest step : 3.740051 Median interval of one step : 98.09924 cents, amount: 0 Least squares average step : 99.15766 cents, oct.: 1189.89190 cents Scale is not proper Step pattern alph. order: ABCDEAFEDAEF Step pattern size order : CFABDCEDBCDE Scale is not a Constant Structure Scale diversity : 1.457716 Lumma stability : 0.081284 Lumma impropriety factor : 0.446646 Rothenberg efficiency : 0.313850 redundancy: 0.686150 Efficiency x scale size : 3.766198 Number of different interval sizes : 50 = 4.54545 / class Number of one step interval sizes : 6 Highest interval variety : 8 Mean interval variety : 6.36364 = 70/11 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Most common triad is 0.0 498.045 884.359 cents, amount: 3 Number of recognisable fifths : 8, average 700.9911 cents Scale contains a complete diamond : 1 3 5 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 2 at degree 10 Formal octave complements present : 7 = 58.3333% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is differentially coherent in interval classes 5 and 6 combined Scale is n-1 differentially coherent in interval classes 6 and 7 combined Scale is n-1 differentially coherent in interval classes 7 and 8 combined Scale is n-1 differentially coherent in interval classes 8 and 9 combined Scale is n-1 differentially coherent in interval classes 9 and 10 combined -- Rational properties -- Prime limit : 7 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 21 Scale harmonicity : 0.029923 Average absolute harmonicity : 0.185728 Specific harmonicity : 0.148737 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 840, 9.7142 octaves, 219765.475 Hz. Exponens Consonantiae : 5.040000E+04, 15.62114 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 88.0, average 7.33333 Mersenne's string divisions : 635314680 Sum of van Prooijen's expressibility: 8.78373, average 0.73198 Sum of Tenney's harmonic distance : 17.57564, average 1.46464 Vogel's harmonic complexity : 11.50000 Wille's k value : 52 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 208.06457, average 2.66749 Lattice compactness (without 2's) : 121.32582, average 1.55546 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.08333 17 1 3: -1 .. 1 -0.08333 7 2 5: -1 .. 1 -0.25000 7 4 7: 0 .. 1 0.41667 5 5 Average exponent except 2's : 1 / 12 = 0.08333 Average absolute exponent except 2's: 19 / 12 = 1.58333 Scale is weakly epimorphic with val: <12 17 26 37|
FIT/MODE
12: 1 2 0 1 1 1 1 1 1 1 1 1 N T3 SD: 17.9491 c. M:-33.1291 c. 19: 1 3 1 1 2 1 2 2 1 1 2 2 N SD: 11.4595 c. M: 21.4575 c. 26: 2 4 1 1 3 2 2 3 1 2 2 3 N SD: 11.9394 c. M: 19.0187 c. 27: 2 4 1 2 2 2 3 2 2 2 2 3 N SD: 8.6527 c. M: 13.8905 c. 31: 2 5 1 2 3 2 3 3 2 2 3 3 N SD: 4.1647 c. M: 7.0478 c. 41: 3 6 2 2 4 3 4 4 2 3 4 4 N SD: 4.0173 c. M:-6.3099 c. 53: 4 8 2 3 5 4 5 5 3 4 5 5 N SD: 3.7374 c. M:-6.2353 c. 68: 5 10 3 4 6 5 7 6 4 5 6 7 N SD: 2.6614 c. M: 4.0866 c. 72: 5 11 3 4 7 5 7 7 4 5 7 7 N SD: 1.8682 c. M: 2.9804 c. 99: 7 15 4 6 9 7 10 9 6 7 9 10 N SD: 1.0103 c. M: 1.7693 c. 140: 10 21 6 8 13 10 14 13 8 10 13 14 N SD: 0.9239 c. M: 1.5016 c. 171: 12 26 7 10 16 12 17 16 10 12 16 17 N SD: 0.2351 c. M: 0.4049 c. 441: 31 67 18 26 41 31 44 41 26 31 41 44 N SD: 0.1346 c. M: 0.2851 c. 612: 43 93 25 36 57 43 61 57 36 43 57 61 N SD: 0.1171 c. M: 0.2042 c. 935: 66 142 38 55 87 66 93 87 55 66 87 93 N SD: 0.1106 c. M:-0.2387 c. 966: 68 147 39 57 90 68 96 90 57 68 90 96 N SD: 0.1104 c. M:-0.2098 c. 1065: 75 162 43 63 99 75 106 99 63 75 99 106 N SD: 0.1176 c. M:-0.1882 c. 1106: 78 168 45 65 103 78 110 103 65 78 103 110 N SD: 0.0833 c. M:-0.1621 c. 1236: 87 188 50 73 115 87 123 115 73 87 115 123 N SD: 0.0749 c. M:-0.1194 c. 1277: 90 194 52 75 119 90 127 119 75 90 119 127 N SD: 0.0764 c. M:-0.1060 c. 1376: 97 209 56 81 128 97 137 128 81 97 128 137 N SD: 0.0607 c. M:-0.1258 c. 1407: 99 214 57 83 131 99 140 131 83 99 131 140 N SD: 0.0487 c. M:-0.0801 c. 1547: 109 235 63 91 144 109 154 144 91 109 144 154 N SD: 0.0447 c. M:-0.0835 c. 1578: 111 240 64 93 147 111 157 147 93 111 147 157 N SD: 0.0403 c. M: 0.0565 c. 1848: 130 281 75 109 172 130 184 172 109 130 172 184 N SD: 0.0385 c. M: 0.0569 c. 2019: 142 307 82 119 188 142 201 188 119 142 188 201 N SD: 0.0329 c. M: 0.0690 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: 0.0000 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.7541 cents 6 x 7 x x 8 x 9 x 10 x 11:12 S SD: 5.1990 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 12.1234 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.4514 cents 9 x x 11 x 12:13 x 14:15:16:17:18 SD: 10.8096 cents 10:11 x 12 x 13:14:15:16:17:18:19:20 S SD: 11.3579 cents 11:12:13 x 14:15 x 17 x 18:19:21:22 SD: 12.7028 cents 12:13:14 x 15:16:17:18:19:20:21:22:24 S SD: 6.1984 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 8.1928 cents 15:16 x 18:19:20:21:23:24:25:26:28:30 SD: 4.9722 cents 16:17 x 19:20:21:22:24:26:27:28:30:32 SD: 5.5352 cents 17:18:20 x 21:23:24:26:27:28:30:32:34 SD: 5.6195 cents 18:19:21:22:23:24:25:27:29:30:32:34:36 SD: 5.2950 cents 20:21:23:24:25:27:28:30:32:33:35:37:40 SD: 3.3612 cents 21:22 x 25:26:28:29:32:34:35:37:39:42 SD: 4.4739 cents 22:23:26 x 28:29:31:33:35:37:39:41:44 SD: 4.8916 cents 23:24:27:28:29:31:32:35:37:38:40:43:46 SD: 4.2523 cents 24:25:28:29:30:32:34:36:38:40:42:45:48 SD: 2.8158 cents 27:28 x 32:34:36:38:41:43:45:47:50:54 SD: 4.0269 cents 28:29:33:34:35:37:39:42:45:47:49:52:56 SD: 3.6328 cents 30:32:35:36:38:40:42:45:48:50:53:56:60 SD: 3.2686 cents 32:34:37:38:40:43:45:48:51:53:56:60:64 SD: 3.1772 cents 35:37:41:42:44:47:49:53:56:58:61:65:70 SD: 2.5453 cents 36:38:42:43:45:48:50:54:58:60:63:67:72 SD: 1.8791 cents 40:42:47:48:50:53:56:60:64:67:70:75:80 SD: 1.6743 cents 55:58:64:66:69:73:77:83:88:92:96:103:110 SD: 1.6214 cents 60:63:70:72:75:80:84:90:96:100:105:112:120 S SD: 0.0000 cents