Scala analysis: cxi2
Second 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: 7/6 266.870906 septimal minor third 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major 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: 49/45 147.4281 BP minor semitone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 28/25 196.1985 middle second 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 : 119.4 266.9 315.6 386.3 582.5 702.0 813.7 933.1 968.8 1088.3 1200.0 119.4 : 147.4 196.2 266.9 463.1 582.5 694.2 813.7 849.4 968.8 1080.6 1200.0 266.9 : 48.8 119.4 315.6 435.1 546.8 666.3 702.0 821.4 933.1 1052.6 1200.0 315.6 : 70.7 266.9 386.3 498.0 617.5 653.2 772.6 884.4 1003.8 1151.2 1200.0 386.3 : 196.2 315.6 427.4 546.8 582.5 702.0 813.7 933.1 1080.6 1129.3 1200.0 582.5 : 119.4 231.2 350.6 386.3 505.8 617.5 736.9 884.4 933.1 1003.8 1200.0 702.0 : 111.7 231.2 266.9 386.3 498.0 617.5 764.9 813.7 884.4 1080.6 1200.0 813.7 : 119.4 155.1 274.6 386.3 505.8 653.2 702.0 772.6 968.8 1088.3 1200.0 933.1 : 35.7 155.1 266.9 386.3 533.7 582.5 653.2 849.4 968.8 1080.6 1200.0 968.8 : 119.4 231.2 350.6 498.0 546.8 617.5 813.7 933.1 1044.9 1164.3 1200.0 1088.3: 111.7 231.2 378.6 427.4 498.0 694.2 813.7 925.4 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 : 111.13164 cents, oct.: 1222.44807 cents Scale is not proper Step pattern alph. order: ABCDEAFAGAF Step pattern size order : EFBCGEDEAED 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 : 5 = 45.4545% Scale is n-1 differentially coherent in interval class 1 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 -- 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 : 0.182671 Specific harmonicity : 0.132268 Fundamental : 1/840, -9.7142 octaves, 0.3115 Hz. Guide tone : 840, 9.7142 octaves, 219765.475 Hz. Exponens Consonantiae : 7.056000E+05, 19.42849 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 74.0, average 6.72727 Mersenne's string divisions : 326203020 Sum of van Prooijen's expressibility: 8.30661, average 0.75515 Sum of Tenney's harmonic distance : 16.39955, average 1.49087 Vogel's harmonic complexity : 19.45455 Wille's k value : 787 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 183.04121, average 2.77335 Lattice compactness (without 2's) : 104.22872, average 1.57922 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 -0.27273 17 1 3: -1 .. 1 0.36364 6 1 5: -1 .. 1 0.00000 6 4 7: -1 .. 1 0.09091 5 5 Average exponent except 2's : 5 / 11 = 0.45455 Average absolute exponent except 2's: 17 / 11 = 1.54545 Scale is weakly epimorphic with val: <11 17 26 31| = patent
FIT/MODE
11: 1 1 1 0 2 1 1 1 1 1 1 N T3 SD: 38.1969 c. M: 60.4018 c. 12: 1 2 0 1 2 1 1 1 1 1 1 N D3 SD: 20.4750 c. M: 33.1291 c. 18: 2 2 1 1 3 2 1 2 1 1 2 N SD: 18.1147 c. M:-31.3783 c. 19: 2 2 1 1 3 2 2 2 0 2 2 N G SD: 11.6193 c. M: 21.4575 c. 22: 2 3 1 1 4 2 2 2 1 2 2 N SD: 8.9645 c. M:-17.4878 c. 31: 3 4 1 2 5 3 3 3 1 3 3 N SD: 3.4665 c. M: 5.9639 c. 68: 7 8 3 4 11 7 6 7 2 7 6 N SD: 2.8643 c. M:-5.8489 c. 72: 7 9 3 4 12 7 7 7 2 7 7 N SD: 2.3379 c. M: 4.9354 c. 87: 9 10 4 5 14 9 8 9 2 9 8 N SD: 2.9557 c. M: 4.8019 c. 94: 9 12 4 5 16 9 9 9 3 9 9 N SD: 2.8989 c. M:-4.7218 c. 99: 10 12 4 6 16 10 9 10 3 10 9 N SD: 1.2692 c. M:-2.6404 c. 130: 13 16 5 8 21 13 12 13 4 13 12 N SD: 0.9952 c. M: 1.7951 c. 140: 14 17 6 8 23 14 13 14 4 14 13 N SD: 0.8005 c. M:-1.5016 c. 171: 17 21 7 10 28 17 16 17 5 17 16 N SD: 0.2826 c. M: 0.5494 c. 441: 44 54 18 26 72 44 41 44 13 44 41 N SD: 0.1557 c. M:-0.2851 c. 612: 61 75 25 36 100 61 57 61 18 61 57 N SD: 0.1285 c. M: 0.2042 c. 935: 93 115 38 55 153 93 87 93 28 93 87 N SD: 0.0901 c. M:-0.1616 c. 1106: 110 136 45 65 181 110 103 110 33 110 103 N SD: 0.0670 c. M:-0.1280 c. 1236: 123 152 50 73 202 123 115 123 37 123 115 N SD: 0.0834 c. M:-0.1194 c. 1277: 127 157 52 75 209 127 119 127 38 127 119 N SD: 0.0725 c. M:-0.1033 c. 1376: 137 169 56 81 225 137 128 137 41 137 128 N SD: 0.0519 c. M:-0.1034 c. 1407: 140 173 57 83 230 140 131 140 42 140 131 N SD: 0.0493 c. M: 0.0801 c. 1547: 154 190 63 91 253 154 144 154 46 154 144 N SD: 0.0332 c. M:-0.0665 c. 1578: 157 194 64 93 258 157 147 157 47 157 147 N SD: 0.0384 c. M: 0.0558 c. 1848: 184 227 75 109 302 184 172 184 55 184 172 N SD: 0.0355 c. M: 0.0569 c. 2019: 201 248 82 119 330 201 188 201 60 201 188 N SD: 0.0237 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 x 4 x x 5 x x 6 S SD: 32.5120 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 0.0000 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 9.7541 cents 6 x 7 x x 8:9 x 10 x 11:12 S SD: 17.5015 cents 7 x 8 x 9:10 x 11:12 x 13:14 S SD: 11.1791 cents 8 x 9 x 10:11:12:13 x 14:15:16 S SD: 9.4021 cents 9:10 x 11 x 13 x 14:15:16:17:18 SD: 14.5582 cents 10:11 x 12:13:14:15:16:17:18:19:20 S SD: 9.8998 cents 11:12:13 x 14:15:17:18:19 x 21:22 SD: 11.0272 cents 12:13:14 x 15:17:18:19 x 21:23:24 SD: 5.6242 cents 13:14:15 x 16:18:20:21:22:23:24:26 S SD: 7.2828 cents 15:16 x 18:19:21:23:24 x 26:28:30 SD: 5.4058 cents 16:17 x 19:20:22:24:26:27:28:30:32 SD: 5.4547 cents 17:18:20 x 21:24:26:27:29:30:32:34 SD: 5.3673 cents 19:20:22:23:24:27:29:30 x 33:36:38 SD: 6.5317 cents 20:21:23:24:25:28:30:32:34:35:38:40 SD: 4.6172 cents 21:23 x 25:26:29:32:34:36:37:39:42 SD: 6.3643 cents 22:24:26 x 28:31:33:35:38:39:41:44 SD: 5.8724 cents 23:25:27:28:29:32:35:37:39:40:43:46 SD: 4.8999 cents 24:26:28:29:30:34:36:38:41:42:45:48 SD: 3.2704 cents 25:27:29:30:31:35:38:40:43:44:47:50 SD: 3.0958 cents 27:29 x 32:34:38:41:43:46:47:51:54 SD: 4.0072 cents 28:30:33:34:35:39:42:45:48:49:53:56 SD: 3.0639 cents 30:32:35:36:38:42:45:48:51:53:56:60 SD: 3.0477 cents 32:34:37:38:40:45:48:51:55:56:60:64 SD: 2.7352 cents 40:43:47:48:50:56:60:64:69:70:75:80 SD: 1.5782 cents 55:59:64:66:69:77:83:88:94:96:103:110 SD: 1.3663 cents 60:64:70:72:75:84:90:96:103:105:113:120 SD: 1.0131 cents 80:86:93:96:100:112:120:128:137:140:150:160 SD: 0.7863 cents 100:107:117:120:125:140:150:160:171:175:188:200 SD: 0.7593 cents 112:120:131:134:140:157:168:179:192:196:210:224 SD: 0.6723 cents 120:129:140:144:150:168:180:192:206:210:225:240 SD: 0.5675 cents 140:150:163:168:175:196:210:224:240:245:263:280 SD: 0.4394 cents 168:180:196:202:210:235:252:269:288:294:315:336 SD: 0.3591 cents 180:193:210:216:225:252:270:288:309:315:338:360 SD: 0.3400 cents 200:214:233:240:250:280:300:320:343:350:375:400 SD: 0.3147 cents 240:257:280:288:300:336:360:384:411:420:450:480 SD: 0.1859 cents 280:300:327:336:350:392:420:448:480:490:525:560 SD: 0.1605 cents 360:386:420:432:450:504:540:576:617:630:675:720 SD: 0.1221 cents 420:450:490:504:525:588:630:672:720:735:788:840 SD: 0.0999 cents 480:514:560:576:600:672:720:768:823:840:900:960 SD: 0.0916 cents 560:600:653:672:700:784:840:896:960:980:1050:1120 SD: 0.0803 cents 600:643:700:720:750:840:900:960:1029:1050:1125:1200 SD: 0.0743 cents