Scala analysis: max2
31 intervals 26 triads 6 tetrads 2 pentads smallest step 49/48
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 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: 10/7 617.487807 Euler's tritone 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 12/7 933.129094 septimal major sixth 11: 7/4 968.825906 harmonic seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 8/7 231.1741 septimal whole tone 2: 49/48 35.6968 slendro diesis, septimal 1/6-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: 15/14 119.4428 major diatonic semitone 7: 21/20 84.4672 minor semitone 8: 16/15 111.7313 minor diatonic semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 36/35 48.7704 septimal diesis, 1/4-tone 11: 49/48 35.6968 slendro diesis, septimal 1/6-tone 12: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 2 8/7 231.174 cents septimal whole tone 2: 2 21/20 84.467 cents minor semitone 2: 2 15/14 119.443 cents major diatonic semitone 2: 2 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 1 9/8 203.910 cents major whole tone 2: 1 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 3: 2 35/32 155.140 cents septimal neutral second 3: 2 8/7 231.174 cents septimal whole tone 3: 1 7/6 266.871 cents septimal minor third 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 2 4/3 498.045 cents perfect fourth 4: 2 7/6 266.871 cents septimal minor third 4: 1 6/5 315.641 cents minor third 4: 1 60/49 350.617 cents smaller approximation to neutral third 4: 4 5/4 386.314 cents major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 1 49/36 533.742 cents Arabic lute acute fourth 4: 2 48/35 546.815 cents septimal semi-augmented fourth 5: 1 49/40 351.338 cents larger approximation to neutral third 5: 1 5/4 386.314 cents major third 5: 2 9/7 435.084 cents septimal major third, BP third 5: 4 4/3 498.045 cents perfect fourth 5: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 2 10/7 617.488 cents Euler's tritone 6: 2 21/16 470.781 cents narrow fourth 6: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 1 25/18 568.717 cents classic augmented fourth 6: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 10/7 617.488 cents Euler's tritone 6: 1 36/25 631.283 cents classic diminished fifth 6: 2 35/24 653.185 cents septimal semi-diminished fifth 6: 2 32/21 729.219 cents wide fifth 7: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 2 10/7 617.488 cents Euler's tritone 7: 4 3/2 701.955 cents perfect fifth 7: 2 14/9 764.916 cents septimal minor sixth 7: 1 8/5 813.686 cents minor sixth 7: 1 80/49 848.662 cents smaller approximation to neutral sixth 8: 2 35/24 653.185 cents septimal semi-diminished fifth 8: 1 72/49 666.258 cents Arabic lute grave fifth 8: 1 25/16 772.627 cents classic augmented fifth 8: 4 8/5 813.686 cents minor sixth 8: 1 49/30 849.383 cents larger approximation to neutral sixth 8: 1 5/3 884.359 cents major sixth, BP sixth 8: 2 12/7 933.129 cents septimal major sixth 9: 2 3/2 701.955 cents perfect fifth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 1 12/7 933.129 cents septimal major sixth 9: 2 7/4 968.826 cents harmonic seventh 9: 2 64/35 1044.860 cents septimal neutral seventh 10: 1 49/32 737.652 cents 10: 2 12/7 933.129 cents septimal major sixth 10: 1 7/4 968.826 cents harmonic seventh 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 1 25/14 1003.802 cents middle minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 28/15 1080.557 cents grave major seventh 10: 2 40/21 1115.533 cents acute major seventh 11: 2 7/4 968.826 cents harmonic seventh 11: 1 28/15 1080.557 cents grave major seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 1 40/21 1115.533 cents acute major seventh 11: 2 48/25 1129.328 cents classic diminished octave 11: 2 35/18 1151.230 cents septimal semi-diminished octave 11: 2 96/49 1164.303 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.90909 = 76/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 231.2 266.9 315.6 386.3 498.0 617.5 702.0 813.7 884.4 933.1 968.8 1200.0 231.2 : 35.7 84.5 155.1 266.9 386.3 470.8 582.5 653.2 702.0 737.7 968.8 1200.0 266.9 : 48.8 119.4 231.2 350.6 435.1 546.8 617.5 666.3 702.0 933.1 1164.3 1200.0 315.6 : 70.7 182.4 301.8 386.3 498.0 568.7 617.5 653.2 884.4 1115.5 1151.2 1200.0 386.3 : 111.7 231.2 315.6 427.4 498.0 546.8 582.5 813.7 1044.9 1080.6 1129.3 1200.0 498.0 : 119.4 203.9 315.6 386.3 435.1 470.8 702.0 933.1 968.8 1017.6 1088.3 1200.0 617.5 : 84.5 196.2 266.9 315.6 351.3 582.5 813.7 849.4 898.2 968.8 1080.6 1200.0 702.0 : 111.7 182.4 231.2 266.9 498.0 729.2 764.9 813.7 884.4 996.1 1115.5 1200.0 813.7 : 70.7 119.4 155.1 386.3 617.5 653.2 702.0 772.6 884.4 1003.8 1088.3 1200.0 884.4 : 48.8 84.5 315.6 546.8 582.5 631.3 702.0 813.7 933.1 1017.6 1129.3 1200.0 933.1 : 35.7 266.9 498.0 533.7 582.5 653.2 764.9 884.4 968.8 1080.6 1151.2 1200.0 968.8 : 231.2 462.3 498.0 546.8 617.5 729.2 848.7 933.1 1044.9 1115.5 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 231.1741 cents 384/343, 195.4773 cents 49/48, 35.6968 cents 2: 84.4672 .. 462.3482 cents 1280/1029, 377.8810 cents 147/160,-146.7069 cents 3: 155.1396 .. 498.0450 cents 128/105, 342.9054 cents 1715/2048,-307.2086 cents 4: 266.8709 .. 546.8154 cents 288/245, 279.9445 cents 7/8,-231.1741 cents 5: 351.3381 .. 617.4878 cents 400/343, 266.1497 cents 343/384,-195.4773 cents 6: 470.7809 .. 729.2191 cents 512/441, 258.4382 cents 147/160,-146.7069 cents 7: 582.5122 .. 848.6619 cents 400/343, 266.1497 cents 147/160,-146.7069 cents 8: 653.1846 .. 933.1291 cents 288/245, 279.9445 cents 343/384,-195.4773 cents 9: 701.9550 .. 1044.8604 cents 128/105, 342.9054 cents 7/8,-231.1741 cents 10: 737.6518 .. 1115.5328 cents 1280/1029, 377.8810 cents 1715/2048,-307.2086 cents 11: 968.8259 .. 1164.3032 cents 384/343, 195.4773 cents 147/160,-146.7069 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.801371 Largest / Average step : 2.311741 Largest / Smallest step : 6.476043 Median interval of one step : 77.56981 cents, amount: 0 Least squares average step : 97.26619 cents, oct.: 1167.19433 cents Scale is not proper Step pattern alph. order: ABCDEFGEDCBA Step pattern size order : GABCEFDECBAG Scale is not a Constant Structure Scale diversity : 1.505309 Lumma stability : 0.059495 Lumma impropriety factor : 0.859221 Rothenberg efficiency : 0.294078 redundancy: 0.705922 Efficiency x scale size : 3.528932 Number of different interval sizes : 52 = 4.72727 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.90909 = 76/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Number of recognisable fifths : 6, average 701.9550 cents Scale contains a complete diamond : 1 3 5 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 11 = 91.6667% Scale is 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 class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 7 Scale harmonicity : 0.022881 Average absolute harmonicity : 0.189486 Specific harmonicity : 0.142537 Fundamental : 1/420, -8.7142 octaves, 0.6229 Hz. Guide tone : 840, 9.7142 octaves, 219765.475 Hz. Exponens Consonantiae : 3.528000E+05, 18.42849 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 65.5, average 5.45833 Mersenne's string divisions : 116396280 Sum of van Prooijen's expressibility: 7.97561, average 0.66463 Sum of Tenney's harmonic distance : 16.30264, average 1.35855 Vogel's harmonic complexity : 17.41667 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 211.01892, average 2.70537 Lattice compactness (without 2's) : 119.90555, average 1.53725 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.58333 19 1 3: -1 .. 1 0.00000 6 2 5: -1 .. 1 0.08333 5 4 7: -1 .. 1 -0.08333 5 5 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 16 / 12 = 1.33333 Scale is weakly epimorphic with val: <12 21 25 31| Scale is weakly epimorphic with val: <12 21 26 32| Scale is weakly epimorphic with val: <12 21 28 34| Scale is weakly epimorphic with val: <12 21 29 35| Scale is weakly epimorphic with val: <12 21 31 37|
FIT/MODE
12: 2 1 0 1 1 1 1 1 1 0 1 2 N I SD: 21.0478 c. M: 33.1291 c. 15: 3 0 1 1 1 2 1 1 1 1 0 3 N SD: 16.2546 c. M:-26.8709 c. 19: 4 0 1 1 2 2 1 2 1 1 0 4 N SD: 12.0336 c. M:-21.4575 c. 22: 4 1 1 1 2 2 2 2 1 1 1 4 N I SD: 9.6819 c. M: 17.4878 c. 27: 5 1 1 2 2 3 2 2 2 1 1 5 N SD: 7.9902 c. M: 13.6863 c. 31: 6 1 1 2 3 3 2 3 2 1 1 6 N SD: 3.7131 c. M: 5.9639 c. 53: 10 2 2 3 5 5 4 5 3 2 2 10 N SD: 3.3850 c. M: 6.1671 c. 68: 13 2 3 4 6 7 5 6 4 3 2 13 N SD: 2.2710 c. M:-3.9274 c. 72: 14 2 3 4 7 7 5 7 4 3 2 14 N SD: 1.7700 c. M: 2.9804 c. 99: 19 3 4 6 9 10 7 9 6 4 3 19 N SD: 0.9025 c. M:-1.5651 c. 140: 27 4 6 8 13 14 10 13 8 6 4 27 N SD: 0.9028 c. M: 1.5016 c. 171: 33 5 7 10 16 17 12 16 10 7 5 33 N SD: 0.2553 c. M:-0.4049 c. 270: 52 8 11 16 25 27 19 25 16 11 8 52 N SD: 0.2202 c. M:-0.3530 c. 441: 85 13 18 26 41 44 31 41 26 18 13 85 N SD: 0.1221 c. M: 0.2042 c. 935: 180 28 38 55 87 93 66 87 55 38 28 180 N SD: 0.0975 c. M: 0.1616 c. 1106: 213 33 45 65 103 110 78 103 65 45 33 213 N SD: 0.0674 c. M: 0.1280 c. 1236: 238 37 50 73 115 123 87 115 73 50 37 238 N SD: 0.0877 c. M:-0.1194 c. 1277: 246 38 52 75 119 127 90 119 75 52 38 246 N SD: 0.0638 c. M: 0.1033 c. 1376: 265 41 56 81 128 137 97 128 81 56 41 265 N SD: 0.0518 c. M:-0.0799 c. 1547: 298 46 63 91 144 154 109 144 91 63 46 298 N SD: 0.0388 c. M: 0.0665 c. 1578: 304 47 64 93 147 157 111 147 93 64 47 304 N SD: 0.0366 c. M:-0.0539 c. 1848: 356 55 75 109 172 184 130 172 109 75 55 356 N SD: 0.0340 c. M: 0.0569 c. 2019: 389 60 82 119 188 201 142 188 119 82 60 389 N SD: 0.0268 c. M:-0.0456 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 x 7:8 S SD: 0.0000 cents 5 x x 6 x x 7 x 8 x x 9:10 S SD: 12.0031 cents 6 x 7 x x 8 x 9 x 10 x 11:12 S SD: 13.4228 cents 7:8 x x 9 x 10 x 11 x 12 x 14 S SD: 9.6489 cents 8:9 x x 10:11 x 12:13 x x 14:16 S SD: 9.3697 cents 9:10 x 11 x 12:13 x 14:15 x 16:18 S SD: 10.3648 cents 10:11 x 12 x 13:14:15:16 x 17:18:20 S SD: 11.1728 cents 11 x 13 x 14:15:16:17 x 18:19 x 22 SD: 11.0466 cents 12 x 14 x 15:16:17:18:19:20 x 21:24 S SD: 2.5784 cents 13:15 x x 16:17:19:20:21 x 22:23:26 SD: 9.1204 cents 14:16 x 17:18:19:20:21:22:23:24:25:28 SD: 7.3598 cents 15:17 x 18:19:20:21:23:24:25 x 26:30 SD: 6.0674 cents 16:18 x 19:20:21:23:24:26:27 x 28:32 SD: 5.5809 cents 17:19:20 x 21:23:24:26:27:28:29:30:34 SD: 6.5397 cents 18 x 21:22:23:24:26:27:29:30:31:32:36 SD: 5.5846 cents 19 x 22:23:24:25:27:29:30:32 x 33:38 SD: 5.7175 cents 20:23 x 24:25:27:29:30:32:33:34:35:40 SD: 3.8094 cents 21:24 x 25:26:28:30:32:34:35:36:37:42 SD: 3.8199 cents 22:25:26 x 28:29:31:33:35:37:38:39:44 SD: 5.4077 cents 23:26:27:28:29:31:33:35:37:38:39:40:46 SD: 4.6669 cents 24:27:28:29:30:32:34:36:38:40:41:42:48 S SD: 3.1860 cents 25 x 29:30:31:33:36:38:40:42:43:44:50 SD: 3.6719 cents 26:30 x 31:33:35:37:39:42:43:45:46:52 SD: 4.5470 cents 27:31 x 32:34:36:39:41:43:45:46:47:54 SD: 3.8254 cents 28:32:33:34:35:37:40:42:45:47:48:49:56 SD: 2.8639 cents 32 x 37:38:40:43:46:48:51:53:55:56:64 SD: 2.9480 cents 35:40:41:42:44:47:50:53:56:58:60:61:70 SD: 2.2310 cents 36:41:42:43:45:48:51:54:58:60:62:63:72 SD: 1.8969 cents 48:55:56:58:60:64:69:72:77:80:82:84:96 SD: 1.5291 cents 56:64:65:67:70:75:80:84:90:93:96:98:112 SD: 1.3498 cents 60:69:70:72:75:80:86:90:96:100:103:105:120 SD: 1.0385 cents 72:82:84:86:90:96:103:108:115:120:123:126:144 SD: 1.0270 cents 84:96:98:101:105:112:120:126:134:140:144:147:168 SD: 0.5164 cents 120:137:140:144:150:160:171:180:192:200:206:210:240 SD: 0.4394 cents 156:178:182:187:195:208:223:234:250:260:267:273:312 SD: 0.4391 cents 168:192:196:202:210:224:240:252:269:280:288:294:336 SD: 0.3054 cents 180:206:210:216:225:240:257:270:288:300:309:315:360 SD: 0.2943 cents 240:274:280:288:300:320:343:360:384:400:411:420:480 SD: 0.2210 cents 252:288:294:302:315:336:360:378:403:420:432:441:504 SD: 0.2039 cents 300:343:350:360:375:400:429:450:480:500:514:525:600 SD: 0.1756 cents 336:384:392:403:420:448:480:504:538:560:576:588:672 SD: 0.1290 cents 420:480:490:504:525:560:600:630:672:700:720:735:840 S SD: 0.0000 cents