Scala analysis: eikobag
twelve note C(6, 3) combination product bag from <1 3 3 5 7 9>
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: 4/3 498.044999 perfect fourth 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 3/2 701.955001 perfect fifth 7: 14/9 764.915905 septimal minor sixth 8: 8/5 813.686286 minor sixth 9: 7/4 968.825906 harmonic seventh 10: 9/5 1017.596288 just minor seventh, BP 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: 10/9 182.4037 minor whole tone 5: 21/20 84.4672 minor semitone 6: 15/14 119.4428 major diatonic semitone 7: 28/27 62.9609 Archytas' 1/3-tone 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 35/32 155.1396 septimal neutral second 10: 36/35 48.7704 septimal diesis, 1/4-tone 11: 28/27 62.9609 Archytas' 1/3-tone 12: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 21/20 84.467 cents minor semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 35/32 155.140 cents septimal neutral second 1: 2 10/9 182.404 cents minor whole tone 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 10/9 182.404 cents minor whole tone 2: 4 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 3: 2 8/7 231.174 cents septimal whole tone 3: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 3: 4 7/6 266.871 cents septimal minor third 3: 2 6/5 315.641 cents minor third 3: 2 5/4 386.314 cents major third 3: 1 80/63 413.578 cents wide major third 4: 4 6/5 315.641 cents minor third 4: 2 5/4 386.314 cents major third 4: 2 9/7 435.084 cents septimal major third, BP third 4: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 4: 2 4/3 498.045 cents perfect fourth 5: 1 56/45 378.602 cents septimal narrow major third 5: 2 9/7 435.084 cents septimal major third, BP third 5: 2 21/16 470.781 cents narrow fourth 5: 4 4/3 498.045 cents perfect fourth 5: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 2 10/7 617.488 cents Euler's tritone 6: 2 4/3 498.045 cents perfect fourth 6: 2 27/20 519.551 cents acute fourth 6: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 2 35/24 653.185 cents septimal semi-diminished fifth 6: 2 40/27 680.449 cents grave fifth 6: 2 3/2 701.955 cents perfect fifth 7: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 1 10/7 617.488 cents Euler's tritone 7: 4 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 7: 2 14/9 764.916 cents septimal minor sixth 7: 1 45/28 821.398 cents septimale wide minor sixth 8: 2 3/2 701.955 cents perfect fifth 8: 2 54/35 750.725 cents septimal semi-augmented fifth 8: 2 14/9 764.916 cents septimal minor sixth 8: 2 8/5 813.686 cents minor sixth 8: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 63/40 786.422 cents narrow minor sixth 9: 2 8/5 813.686 cents minor sixth 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 4 12/7 933.129 cents septimal major sixth 9: 1 140/81 947.320 cents 9: 2 7/4 968.826 cents harmonic seventh 10: 2 12/7 933.129 cents septimal major sixth 10: 2 7/4 968.826 cents harmonic seventh 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 15/8 1088.269 cents classic major seventh 11: 2 9/5 1017.596 cents just minor seventh, BP seventh 11: 1 64/35 1044.860 cents septimal neutral seventh 11: 2 28/15 1080.557 cents grave major seventh 11: 2 40/21 1115.533 cents acute major seventh 11: 2 27/14 1137.039 cents septimal major seventh 11: 3 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.63636 = 62/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 84.5 266.9 315.6 498.0 582.5 702.0 764.9 813.7 968.8 1017.6 1080.6 1200.0 84.5 : 182.4 231.2 413.6 498.0 617.5 680.4 729.2 884.4 933.1 996.1 1115.5 1200.0 266.9 : 48.8 231.2 315.6 435.1 498.0 546.8 702.0 750.7 813.7 933.1 1017.6 1200.0 315.6 : 182.4 266.9 386.3 449.3 498.0 653.2 702.0 764.9 884.4 968.8 1151.2 1200.0 498.0 : 84.5 203.9 266.9 315.6 470.8 519.6 582.5 702.0 786.4 968.8 1017.6 1200.0 582.5 : 119.4 182.4 231.2 386.3 435.1 498.0 617.5 702.0 884.4 933.1 1115.5 1200.0 702.0 : 63.0 111.7 266.9 315.6 378.6 498.0 582.5 764.9 813.7 996.1 1080.6 1200.0 764.9 : 48.8 203.9 252.7 315.6 435.1 519.6 702.0 750.7 933.1 1017.6 1137.0 1200.0 813.7 : 155.1 203.9 266.9 386.3 470.8 653.2 702.0 884.4 968.8 1088.3 1151.2 1200.0 968.8 : 48.8 111.7 231.2 315.6 498.0 546.8 729.2 813.7 933.1 996.1 1044.9 1200.0 1017.6: 63.0 182.4 266.9 449.3 498.0 680.4 764.9 884.4 947.3 996.1 1151.2 1200.0 1080.6: 119.4 203.9 386.3 435.1 617.5 702.0 821.4 884.4 933.1 1088.3 1137.0 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: 111.7313 .. 266.8709 cents 35/32, 155.1396 cents 24/25,-70.6724 cents 3: 231.1741 .. 413.5778 cents 10/9, 182.4037 cents 48/49,-35.6968 cents 4: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 189/200,-97.9365 cents 5: 378.6022 .. 617.4878 cents 225/196, 238.8856 cents 14/15,-119.4428 cents 6: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 14/15,-119.4428 cents 7: 582.5122 .. 821.3978 cents 225/196, 238.8856 cents 14/15,-119.4428 cents 8: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 14/15,-119.4428 cents 9: 786.4222 .. 968.8259 cents 10/9, 182.4037 cents 189/200,-97.9365 cents 10: 933.1291 .. 1088.2687 cents 35/32, 155.1396 cents 48/49,-35.6968 cents 11: 1017.5963 .. 1151.2296 cents 175/162, 133.6333 cents 24/25,-70.6724 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 : 21/20, 84.4672 cents, amount: 2 Most common interval of one step : 36/35, 48.7704 cents, amount: 3 Least squares average step : 104.19543 cents, oct.: 1250.34518 cents Scale is not proper Step pattern alph. order: ABCBADECFCED Step pattern size order : CFAFCDBAEABD Scale is not a Constant Structure Scale diversity : 1.445357 Lumma stability : 0.081284 Lumma impropriety factor : 0.651213 Rothenberg efficiency : 0.356421 redundancy: 0.643579 Efficiency x scale size : 4.277056 Number of different interval sizes : 44 = 4.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.63636 = 62/11 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: 8 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 8, average 701.9550 cents Scale contains a complete diamond : 1 3 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 differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 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 Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 21 Scale harmonicity : 0.030910 Average absolute harmonicity : 0.178733 Specific harmonicity : 0.153804 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 504, 8.9773 octaves, 131859.285 Hz. Exponens Consonantiae : 9.072000E+04, 16.46913 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 98.0, average 8.16667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.29427, average 0.77452 Sum of Tenney's harmonic distance : 18.85210, average 1.57101 Vogel's harmonic complexity : 14.33333 Wille's k value : 157 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 209.37996, average 2.68436 Lattice compactness (without 2's) : 132.51645, average 1.69893 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.33333 16 1 3: -2 .. 2 0.00000 10 2 5: -1 .. 0 -0.50000 6 3 7: 0 .. 1 0.50000 6 6 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 22 / 12 = 1.83333 Scale is weakly epimorphic with val: <12 17 26 35| Scale is weakly epimorphic with val: <12 19 25 34| Scale is weakly epimorphic with val: <12 19 28 37| Scale is weakly epimorphic with val: <12 20 25 34| Scale is weakly epimorphic with val: <12 20 26 31| Scale is weakly epimorphic with val: <12 20 26 33| Scale is weakly epimorphic with val: <12 20 26 35| Scale is weakly epimorphic with val: <12 20 26 37| Scale is weakly epimorphic with val: <12 20 27 34| Scale is weakly epimorphic with val: <12 20 29 34| Scale is weakly epimorphic with val: <12 20 30 31| Scale is weakly epimorphic with val: <12 20 30 33| Scale is weakly epimorphic with val: <12 20 30 35| Scale is weakly epimorphic with val: <12 20 30 37| Scale is weakly epimorphic with val: <12 20 31 34|
FIT/MODE
12: 1 2 0 2 1 1 1 0 2 0 1 1 N D3 SD: 20.3605 c. M:-35.0841 c. 18: 1 3 1 2 2 1 1 1 2 1 1 2 N SD: 22.5697 c. M: 35.4926 c. 19: 1 3 1 3 1 2 1 1 2 1 1 2 N SD: 11.6219 c. M: 21.4575 c. 22: 2 3 1 3 2 2 1 1 3 1 1 2 N SD: 12.3612 c. M:-24.6237 c. 27: 2 4 1 4 2 3 1 1 4 1 1 3 N SD: 8.1630 c. M: 13.8905 c. 31: 2 5 1 5 2 3 2 1 4 1 2 3 N SD: 5.6439 c. M: 11.1447 c. 41: 3 6 2 6 3 4 2 2 5 2 2 4 N SD: 3.8900 c. M:-6.7940 c. 53: 4 8 2 8 4 5 3 2 7 2 3 5 N SD: 3.9731 c. M:-6.2353 c. 58: 4 9 2 9 4 6 3 2 8 2 3 6 N SD: 3.4870 c. M: 6.7897 c. 68: 5 10 3 10 5 7 3 3 9 3 3 7 N SD: 3.5308 c. M: 6.0924 c. 72: 5 11 3 11 5 7 4 3 9 3 4 7 N SD: 1.7291 c. M:-2.9804 c. 99: 7 15 4 15 7 10 5 4 13 4 5 10 N SD: 0.9806 c. M: 1.7693 c. 171: 12 26 7 26 12 17 9 7 22 7 9 17 N SD: 0.2086 c. M: 0.4049 c. 441: 31 67 18 67 31 44 23 18 57 18 23 44 N SD: 0.1590 c. M: 0.2901 c. 612: 43 93 25 93 43 61 32 25 79 25 32 61 N SD: 0.1315 c. M: 0.2100 c. 783: 55 119 32 119 55 78 41 32 101 32 41 78 N SD: 0.1314 c. M: 0.2435 c. 935: 66 142 38 142 66 93 49 38 121 38 49 93 N SD: 0.1173 c. M:-0.2387 c. 1065: 75 162 43 162 75 106 56 43 138 43 56 106 N SD: 0.1147 c. M:-0.1882 c. 1106: 78 168 45 168 78 110 58 45 143 45 58 110 N SD: 0.0853 c. M:-0.1621 c. 1236: 87 188 50 188 87 123 65 50 160 50 65 123 N SD: 0.0812 c. M:-0.1326 c. 1277: 90 194 52 194 90 127 67 52 165 52 67 127 N SD: 0.0715 c. M:-0.1060 c. 1407: 99 214 57 214 99 140 74 57 182 57 74 140 N SD: 0.0626 c. M:-0.1161 c. 1547: 109 235 63 235 109 154 81 63 200 63 81 154 N SD: 0.0570 c. M:-0.1154 c. 1578: 111 240 64 240 111 157 83 64 204 64 83 157 N SD: 0.0567 c. M: 0.1058 c. 1677: 118 255 68 255 118 167 88 68 217 68 88 167 N SD: 0.0489 c. M: 0.0906 c. 1848: 130 281 75 281 130 184 97 75 239 75 97 184 N SD: 0.0371 c. M: 0.0638 c. 2019: 142 307 82 307 142 201 106 82 261 82 106 201 N SD: 0.0358 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 3 x x x x x 4 S SD: 0.0000 cents 3 x x x 4 x x x 5 x x x 6 S SD: 23.5575 cents 4 x x 5 x x 6 x x 7 x x 8 S SD: 17.6681 cents 5 x x 6 x 7 x x 8 x 9 x 10 S SD: 0.0000 cents 6 x 7 x 8 x 9 x 10 x x 11:12 S SD: 12.8751 cents 7 x 8 x 9:10 x 11 x 12 x 13:14 S SD: 12.8756 cents 8 x 9:10 x 11:12 x 13:14 x 15:16 S SD: 12.9372 cents 9 x x 11:12:13 x 14 x x 16:17:18 SD: 9.9168 cents 10:11 x 12:13:14:15 x 16 x 18:19:20 S SD: 10.7418 cents 11:12:13 x 15 x x 17:18:19:20:21:22 SD: 11.3096 cents 12:13:14 x 16:17:18 x 19:21 x 22:24 SD: 7.5759 cents 13:14:15:16:17:18 x 20:21:23 x 24:26 SD: 8.4076 cents 14:15:16:17:19:20:21:22 x x 25:26:28 SD: 7.5214 cents 15:16 x 18:20:21 x 23:24:26:27:28:30 SD: 4.0476 cents 16:17 x 19:21:22:24:25:26:28:29:30:32 SD: 5.3380 cents 17:18:20 x 23:24 x 26:27:30:31:32:34 SD: 5.6728 cents 18:19:21:22:24:25:27:28:29 x 32:34:36 SD: 4.3681 cents 19:20:22:23:25:27:29 x 30:33:34:35:38 SD: 5.6361 cents 20:21:23:24:27:28:30:31:32:35:36:37:40 SD: 3.0760 cents 21:22 x 25:28:29:32:33:34:37:38:39:42 SD: 4.5815 cents 22:23:26 x 29:31:33:34:35:39:40:41:44 SD: 4.1726 cents 24:25:28:29:32:34:36:37:38:42:43:45:48 SD: 3.1703 cents 27:28 x 32:36:38:41:42:43:47:49:50:54 SD: 4.0659 cents 28:29:33:34:37:39:42:44:45:49:50:52:56 SD: 3.9509 cents 29:30:34:35:39:41:44:45:46:51:52:54:58 SD: 3.8308 cents 30:32:35:36:40:42:45:47:48:53:54:56:60 SD: 2.8437 cents 35:37:41:42:47:49:53:54:56:61:63:65:70 SD: 2.5530 cents 36:38:42:43:48:50:54:56:58:63:65:67:72 SD: 1.9310 cents 40:42:47:48:53:56:60:62:64:70:72:75:80 SD: 1.5975 cents 59:62:69:71:79:83:89:92:94:103:106:110:118 SD: 1.5948 cents 60:63:70:72:80:84:90:93:96:105:108:112:120 SD: 0.5162 cents 120:126:140:144:160:168:180:187:192:210:216:224:240 SD: 0.2574 cents 180:189:210:216:240:252:270:280:288:315:324:336:360 SD: 0.0000 cents