Scala analysis: cxi1
First 11/5 <11 17 26 31| permutation epimorphic scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 9/7 435.084095 septimal major third, BP third 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 3/2 701.955001 perfect fifth 7: 8/5 813.686286 minor sixth 8: 12/7 933.129094 septimal major sixth 9: 7/4 968.825906 harmonic seventh 10: 15/8 1088.268715 classic major seventh 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 15/14 119.4428 major diatonic semitone 2: 28/25 196.1985 middle second 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 49/45 147.4281 BP minor semitone 6: 15/14 119.4428 major diatonic semitone 7: 16/15 111.7313 minor diatonic semitone 8: 15/14 119.4428 major diatonic semitone 9: 49/48 35.6968 slendro diesis, septimal 1/6-tone 10: 15/14 119.4428 major diatonic semitone 11: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 4 15/14 119.443 cents major diatonic semitone 1: 1 49/45 147.428 cents BP minor semitone 1: 1 28/25 196.198 cents middle second 2: 1 15/14 119.443 cents major diatonic semitone 2: 2 35/32 155.140 cents septimal neutral second 2: 1 28/25 196.198 cents middle second 2: 4 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 6/5 315.641 cents minor third 3: 3 7/6 266.871 cents septimal minor third 3: 1 75/64 274.582 cents classic augmented second 3: 2 6/5 315.641 cents minor third 3: 2 60/49 350.617 cents smaller approximation to neutral third 3: 1 56/45 378.602 cents septimal narrow major third 3: 1 5/4 386.314 cents major third 3: 1 32/25 427.373 cents classic diminished fourth 4: 5 5/4 386.314 cents 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 98/75 463.069 cents 4: 2 4/3 498.045 cents perfect fourth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 5: 2 4/3 498.045 cents perfect fourth 5: 2 75/56 505.757 cents marvelous fourth 5: 1 49/36 533.742 cents Arabic lute acute fourth 5: 2 48/35 546.815 cents septimal semi-augmented fourth 5: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 10/7 617.488 cents Euler's tritone 6: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 3 10/7 617.488 cents Euler's tritone 6: 2 35/24 653.185 cents septimal semi-diminished fifth 6: 1 72/49 666.258 cents Arabic lute grave fifth 6: 2 112/75 694.243 cents marvelous fifth 6: 2 3/2 701.955 cents perfect fifth 7: 1 35/24 653.185 cents septimal semi-diminished fifth 7: 2 3/2 701.955 cents perfect fifth 7: 1 75/49 736.931 cents BP fifth 7: 1 14/9 764.916 cents septimal minor sixth 7: 1 25/16 772.627 cents classic augmented fifth 7: 5 8/5 813.686 cents minor sixth 8: 1 25/16 772.627 cents classic augmented fifth 8: 1 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 8: 2 49/30 849.383 cents larger approximation to neutral sixth 8: 2 5/3 884.359 cents major sixth, BP sixth 8: 1 128/75 925.418 cents diminished seventh 8: 3 12/7 933.129 cents septimal major sixth 9: 1 5/3 884.359 cents major sixth, BP sixth 9: 2 12/7 933.129 cents septimal major sixth 9: 4 7/4 968.826 cents harmonic seventh 9: 1 25/14 1003.802 cents middle minor seventh 9: 2 64/35 1044.860 cents septimal neutral seventh 9: 1 28/15 1080.557 cents grave major seventh 10: 1 25/14 1003.802 cents middle minor seventh 10: 1 90/49 1052.572 cents 10: 4 28/15 1080.557 cents grave major seventh 10: 2 15/8 1088.269 cents classic major seventh 10: 1 48/25 1129.328 cents classic diminished octave 10: 1 35/18 1151.230 cents septimal semi-diminished octave 10: 1 96/49 1164.303 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.40000 = 32/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 119.4 315.6 386.3 435.1 582.5 702.0 813.7 933.1 968.8 1088.3 1200.0 119.4 : 196.2 266.9 315.6 463.1 582.5 694.2 813.7 849.4 968.8 1080.6 1200.0 315.6 : 70.7 119.4 266.9 386.3 498.0 617.5 653.2 772.6 884.4 1003.8 1200.0 386.3 : 48.8 196.2 315.6 427.4 546.8 582.5 702.0 813.7 933.1 1129.3 1200.0 435.1 : 147.4 266.9 378.6 498.0 533.7 653.2 764.9 884.4 1080.6 1151.2 1200.0 582.5 : 119.4 231.2 350.6 386.3 505.8 617.5 736.9 933.1 1003.8 1052.6 1200.0 702.0 : 111.7 231.2 266.9 386.3 498.0 617.5 813.7 884.4 933.1 1080.6 1200.0 813.7 : 119.4 155.1 274.6 386.3 505.8 702.0 772.6 821.4 968.8 1088.3 1200.0 933.1 : 35.7 155.1 266.9 386.3 582.5 653.2 702.0 849.4 968.8 1080.6 1200.0 968.8 : 119.4 231.2 350.6 546.8 617.5 666.3 813.7 933.1 1044.9 1164.3 1200.0 1088.3: 111.7 231.2 427.4 498.0 546.8 694.2 813.7 925.4 1044.9 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 196.1985 cents 192/175, 160.5017 cents 49/48, 35.6968 cents 2: 119.4428 .. 315.6413 cents 28/25, 196.1985 cents 375/392,-76.7557 cents 3: 266.8709 .. 427.3726 cents 192/175, 160.5017 cents 35/36,-48.7704 cents 4: 386.3137 .. 546.8154 cents 192/175, 160.5017 cents 125/128,-41.0589 cents 5: 498.0450 .. 617.4878 cents 15/14, 119.4428 cents 35/36,-48.7704 cents 6: 582.5122 .. 701.9550 cents 15/14, 119.4428 cents 49/50,-34.9756 cents 7: 653.1846 .. 813.6863 cents 192/175, 160.5017 cents 35/36,-48.7704 cents 8: 772.6274 .. 933.1291 cents 192/175, 160.5017 cents 125/128,-41.0589 cents 9: 884.3587 .. 1080.5572 cents 28/25, 196.1985 cents 35/36,-48.7704 cents 10: 1003.8015 .. 1164.3032 cents 192/175, 160.5017 cents 375/392,-76.7557 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 28/25, 196.1985 cents Average / Smallest step : 3.056041 Largest / Average step : 1.798486 Largest / Smallest step : 5.496247 Median interval of one step : 15/14, 119.4428 cents, amount: 4 Most common interval of one step : 15/14, 119.4428 cents, amount: 4 Least squares average step : 112.12895 cents, oct.: 1233.41850 cents Scale is not proper Step pattern alph. order: ABCDEAFAGAF Step pattern size order : EGCBFEDEAED Scale is not a Constant Structure Scale diversity : 1.512366 Lumma stability : 0.059495 Lumma impropriety factor : 0.388072 Rothenberg efficiency : 0.317867 redundancy: 0.682133 Efficiency x scale size : 3.496537 Number of different interval sizes : 46 = 4.60000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.40000 = 32/5 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 6 Number of recognisable fifths : 6, average 699.3845 cents Scale contains a complete diamond : 1 5 Length of longest harmonic part : 2 at degree 5 Length of longest subharmonic part : 2 at degree 6 Formal octave complements present : 3 = 27.2727% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 7 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 15 Scale harmonicity : 0.022369 Average absolute harmonicity : 0.181975 Specific harmonicity : 0.132066 Fundamental : 1/280, -8.1293 octaves, 0.9344 Hz. Guide tone : 2520, 11.2992 octaves, 659296.425 Hz. Exponens Consonantiae : 7.056000E+05, 19.42849 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 75.5, average 6.86364 Mersenne's string divisions : 1304812080 Sum of van Prooijen's expressibility: 8.41575, average 0.76507 Sum of Tenney's harmonic distance : 16.57564, average 1.50688 Vogel's harmonic complexity : 16.09091 Wille's k value : 262 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 183.01997, average 2.77303 Lattice compactness (without 2's) : 105.05057, average 1.59168 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 -0.18182 16 1 3: 0 .. 2 0.63636 7 1 5: -1 .. 1 0.00000 6 4 7: -1 .. 1 -0.09091 5 5 Average exponent except 2's : 6 / 11 = 0.54545 Average absolute exponent except 2's: 18 / 11 = 1.63636 Scale is weakly epimorphic with val: <11 17 26 31| = patent
FIT/MODE
11: 1 2 0 1 1 1 1 1 1 1 1 N T3 SD: 35.2652 c. M: 60.4018 c. 12: 1 2 1 0 2 1 1 1 1 1 1 N D3 SD: 20.7689 c. M: 35.0841 c. 17: 2 2 1 1 2 2 1 2 1 1 2 N D3 SD: 23.4106 c. M: 37.2157 c. 19: 2 3 1 1 2 2 2 2 0 2 2 N G SD: 11.0026 c. M: 21.4575 c. 22: 2 4 1 1 3 2 2 2 1 2 2 N SD: 8.7973 c. M:-17.4878 c. 31: 3 5 2 1 4 3 3 3 1 3 3 N SD: 4.2797 c. M: 9.2776 c. 41: 4 7 2 2 5 4 4 4 1 4 4 N SD: 4.1179 c. M:-6.3099 c. 53: 5 9 3 2 7 5 5 5 2 5 5 N SD: 3.7510 c. M: 6.2353 c. 68: 7 11 4 3 8 7 6 7 2 7 6 N SD: 3.3395 c. M:-6.0924 c. 72: 7 12 4 3 9 7 7 7 2 7 7 N SD: 2.3960 c. M: 4.9354 c. 94: 9 16 5 4 12 9 9 9 3 9 9 N SD: 2.8928 c. M:-4.7218 c. 99: 10 16 6 4 12 10 9 10 3 10 9 N SD: 1.3252 c. M:-2.6404 c. 130: 13 21 8 5 16 13 12 13 4 13 12 N SD: 1.0336 c. M: 1.7951 c. 140: 14 23 8 6 17 14 13 14 4 14 13 N SD: 0.9510 c. M:-2.0588 c. 171: 17 28 10 7 21 17 16 17 5 17 16 N SD: 0.2759 c. M: 0.5494 c. 441: 44 72 26 18 54 44 41 44 13 44 41 N SD: 0.1676 c. M:-0.2901 c. 612: 61 100 36 25 75 61 57 61 18 61 57 N SD: 0.1294 c. M:-0.2100 c. 935: 93 153 55 38 115 93 87 93 28 93 87 N SD: 0.0867 c. M:-0.1616 c. 1106: 110 181 65 45 136 110 103 110 33 110 103 N SD: 0.0661 c. M:-0.1280 c. 1277: 127 209 75 52 157 127 119 127 38 127 119 N SD: 0.0725 c. M:-0.1033 c. 1376: 137 225 81 56 169 137 128 137 41 137 128 N SD: 0.0585 c. M:-0.1034 c. 1407: 140 230 83 57 173 140 131 140 42 140 131 N SD: 0.0554 c. M: 0.1161 c. 1547: 154 253 91 63 190 154 144 154 46 154 144 N SD: 0.0400 c. M:-0.0807 c. 1718: 171 281 101 70 211 171 160 171 51 171 160 N SD: 0.0437 c. M:-0.0747 c. 1848: 184 302 109 75 227 184 172 184 55 184 172 N SD: 0.0358 c. M: 0.0569 c. 2019: 201 330 119 82 248 201 188 201 60 201 188 N SD: 0.0242 c. M: 0.0456 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 3 x x x x 4 S SD: 0.0000 cents 3 x x x 4 x x x 5 x x 6 S SD: 26.5469 cents 4 x x 5 x x 6 x x 7 x 8 S SD: 0.0000 cents 5 x 6 x x 7 x 8 x 9 x 10 S SD: 9.7541 cents 6 x 7 x 8 x 9 x 10 x 11:12 S SD: 16.8612 cents 7 x 8 x 9:10 x 11:12 x 13:14 S SD: 14.0011 cents 8:9 x 10 x 11:12:13 x 14:15:16 S SD: 11.7448 cents 9:10:11 x 12:13 x 14:15:16:17:18 S SD: 14.7105 cents 10:11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4539 cents 11:12:13 x 14:15:17:18:19 x 21:22 SD: 10.7640 cents 12:13:14:15 x 17:18:19 x 21:23:24 SD: 7.8101 cents 13:14 x 16:17:18:20:21:22:23:24:26 S SD: 7.6151 cents 14:15:17 x 18:20:21:22:24:25:26:28 SD: 6.4140 cents 15:16:18:19 x 21:23:24 x 26:28:30 SD: 5.4058 cents 18:19:22 x 23:25:27:29:31:32:34:36 SD: 5.5642 cents 19:20:23:24 x 27:29:30 x 33:36:38 SD: 7.1108 cents 20:21:24:25:26:28:30:32:34:35:38:40 SD: 4.3834 cents 22:24:26 x 28:31:33:35:38:39:41:44 SD: 5.4626 cents 23:25:28:29:30:32:35:37:39:40:43:46 SD: 5.3092 cents 24:26:29:30:31:34:36:38:41:42:45:48 SD: 3.3502 cents 25:27:30:31:32:35:38:40:43:44:47:50 SD: 3.0433 cents 26:28:31 x 33:36:39:42:45:46:49:52 SD: 4.5307 cents 27:29:32:34:35:38:41:43:46:47:51:54 SD: 3.8646 cents 28:30:34:35:36:39:42:45:48:49:53:56 SD: 2.6142 cents 32:34:38:40:41:45:48:51:55:56:60:64 SD: 2.4060 cents 40:43:48:50:51:56:60:64:69:70:75:80 SD: 1.7235 cents 52:56:62:65:67:73:78:83:89:91:98:104 SD: 1.6814 cents 55:59:66:69:71:77:83:88:94:96:103:110 SD: 1.4498 cents 56:60:67:70:72:78:84:90:96:98:105:112 SD: 1.1660 cents 60:64:72:75:77:84:90:96:103:105:113:120 SD: 1.0542 cents 80:86:96:100:103:112:120:128:137:140:150:160 SD: 0.5907 cents 112:120:134:140:144:157:168:179:192:196:210:224 SD: 0.5396 cents 140:150:168:175:180:196:210:224:240:245:263:280 SD: 0.2995 cents 200:214:240:250:257:280:300:320:343:350:375:400 SD: 0.2367 cents 280:300:336:350:360:392:420:448:480:490:525:560 SD: 0.0000 cents