Scala analysis: max6
31 intervals 26 triads 6 tetrads 2 pentads smallest step 50/49
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: 4/3 498.044999 perfect fourth 5: 7/5 582.512193 septimal or Huygens' tritone, BP 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: 10/9 182.4037 minor whole tone 5: 21/20 84.4672 minor semitone 6: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 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: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 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: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 2 8/7 231.174 cents septimal whole tone 2: 2 21/20 84.467 cents minor semitone 2: 3 15/14 119.443 cents major diatonic semitone 2: 1 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 1 8/7 231.174 cents septimal whole tone 2: 3 7/6 266.871 cents septimal minor third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 3: 1 35/32 155.140 cents septimal neutral second 3: 1 9/8 203.910 cents major whole tone 3: 2 8/7 231.174 cents septimal whole tone 3: 2 7/6 266.871 cents septimal minor third 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 3 6/5 315.641 cents minor third 3: 2 4/3 498.045 cents perfect fourth 4: 1 7/6 266.871 cents septimal minor third 4: 1 25/21 301.847 cents BP second, quasi-equal minor third 4: 2 6/5 315.641 cents minor third 4: 1 60/49 350.617 cents smaller approximation to neutral third 4: 1 49/40 351.338 cents larger approximation to neutral third 4: 2 5/4 386.314 cents major third 4: 1 4/3 498.045 cents perfect 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 60/49 350.617 cents smaller approximation to neutral third 5: 1 49/40 351.338 cents larger approximation to neutral third 5: 2 5/4 386.314 cents major third 5: 1 9/7 435.084 cents septimal major third, BP third 5: 2 4/3 498.045 cents perfect fourth 5: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 10/7 617.488 cents Euler's tritone 5: 1 32/21 729.219 cents wide fifth 6: 1 5/4 386.314 cents major third 6: 1 9/7 435.084 cents septimal major third, BP third 6: 1 21/16 470.781 cents narrow fourth 6: 1 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: 1 35/24 653.185 cents septimal semi-diminished fifth 6: 1 32/21 729.219 cents wide fifth 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 8/5 813.686 cents minor sixth 7: 1 21/16 470.781 cents narrow fourth 7: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 7: 3 10/7 617.488 cents Euler's tritone 7: 2 3/2 701.955 cents perfect fifth 7: 1 14/9 764.916 cents septimal minor sixth 7: 2 8/5 813.686 cents minor sixth 7: 1 80/49 848.662 cents smaller approximation to neutral sixth 7: 1 49/30 849.383 cents larger 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 3/2 701.955 cents perfect fifth 8: 2 8/5 813.686 cents minor sixth 8: 1 80/49 848.662 cents smaller approximation to neutral sixth 8: 1 49/30 849.383 cents larger approximation to neutral sixth 8: 2 5/3 884.359 cents major sixth, BP sixth 8: 1 42/25 898.153 cents quasi-equal major sixth 8: 1 12/7 933.129 cents septimal major sixth 9: 2 3/2 701.955 cents perfect fifth 9: 3 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 2 12/7 933.129 cents septimal major sixth 9: 2 7/4 968.826 cents harmonic seventh 9: 1 16/9 996.090 cents Pythagorean minor seventh 9: 1 64/35 1044.860 cents septimal neutral seventh 10: 1 49/32 737.652 cents 10: 3 12/7 933.129 cents septimal major sixth 10: 1 7/4 968.826 cents harmonic seventh 10: 1 25/14 1003.802 cents middle minor seventh 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 10: 3 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 9/5 1017.596 cents just minor seventh, BP seventh 11: 1 15/8 1088.269 cents classic major seventh 11: 2 40/21 1115.533 cents acute major seventh 11: 1 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 11: 1 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 8.18182 = 90/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 231.2 266.9 315.6 498.0 582.5 617.5 702.0 813.7 884.4 933.1 968.8 1200.0 231.2 : 35.7 84.5 266.9 351.3 386.3 470.8 582.5 653.2 702.0 737.7 968.8 1200.0 266.9 : 48.8 231.2 315.6 350.6 435.1 546.8 617.5 666.3 702.0 933.1 1164.3 1200.0 315.6 : 182.4 266.9 301.8 386.3 498.0 568.7 617.5 653.2 884.4 1115.5 1151.2 1200.0 498.0 : 84.5 119.4 203.9 315.6 386.3 435.1 470.8 702.0 933.1 968.8 1017.6 1200.0 582.5 : 35.0 119.4 231.2 301.8 350.6 386.3 617.5 848.7 884.4 933.1 1115.5 1200.0 617.5 : 84.5 196.2 266.9 315.6 351.3 582.5 813.7 849.4 898.2 1080.6 1165.0 1200.0 702.0 : 111.7 182.4 231.2 266.9 498.0 729.2 764.9 813.7 996.1 1080.6 1115.5 1200.0 813.7 : 70.7 119.4 155.1 386.3 617.5 653.2 702.0 884.4 968.8 1003.8 1088.3 1200.0 884.4 : 48.8 84.5 315.6 546.8 582.5 631.3 813.7 898.2 933.1 1017.6 1129.3 1200.0 933.1 : 35.7 266.9 498.0 533.7 582.5 764.9 849.4 884.4 968.8 1080.6 1151.2 1200.0 968.8 : 231.2 462.3 498.0 546.8 729.2 813.7 848.7 933.1 1044.9 1115.5 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 231.1741 cents 28/25, 196.1985 cents 50/49, 34.9756 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: 350.6169 .. 729.2191 cents 56/45, 378.6022 cents 25/28,-196.1985 cents 6: 386.3137 .. 813.6863 cents 32/25, 427.3726 cents 105/128,-342.9054 cents 7: 470.7809 .. 849.3831 cents 56/45, 378.6022 cents 105/128,-342.9054 cents 8: 653.1846 .. 933.1291 cents 288/245, 279.9445 cents 25/28,-196.1985 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 .. 1165.0244 cents 28/25, 196.1985 cents 147/160,-146.7069 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.859135 Largest / Average step : 2.311741 Largest / Smallest step : 6.609579 Median interval of one step : 77.56981 cents, amount: 0 Least squares average step : 98.60352 cents, oct.: 1183.24223 cents Scale is not proper Step pattern alph. order: ABCDEFEGHCBA Step pattern size order : HBCGEAEFDCBH Scale is not a Constant Structure Scale diversity : 1.491817 Lumma stability : 0.058293 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 : 8 Highest interval variety : 12 Mean interval variety : 8.18182 = 90/11 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 7/6, 266.8709 cents & inv., amount: 6 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 7 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 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 -- 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 : 0.184559 Specific harmonicity : 0.134990 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 : 67.0, average 5.58333 Mersenne's string divisions : 38798760 Sum of van Prooijen's expressibility: 8.12174, average 0.67681 Sum of Tenney's harmonic distance : 16.54568, average 1.37881 Vogel's harmonic complexity : 17.33333 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 201.15934, average 2.57897 Lattice compactness (without 2's) : 123.63296, average 1.58504 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.75000 17 1 3: -1 .. 1 0.00000 6 2 5: -1 .. 1 -0.08333 5 3 7: -1 .. 1 0.00000 6 6 Average exponent except 2's :-1 / 12 =-0.08333 Average absolute exponent except 2's: 17 / 12 = 1.41667 Scale is weakly epimorphic with val: <12 17 30 32| Scale is weakly epimorphic with val: <12 19 30 34| Scale is weakly epimorphic with val: <12 20 30 35|
FIT/MODE
12: 2 1 0 2 1 0 1 1 1 0 1 2 N SD: 21.2811 c. M: 33.1291 c. 15: 3 0 1 2 1 1 1 1 1 1 0 3 N SD: 17.0539 c. M:-26.8709 c. 19: 4 0 1 3 1 1 1 2 1 1 0 4 N SD: 12.5233 c. M:-21.4575 c. 22: 4 1 1 3 2 0 2 2 1 1 1 4 N SD: 10.8416 c. M:-17.4878 c. 26: 5 1 1 4 2 0 2 3 1 1 1 5 N SD: 10.8113 c. M:-17.4878 c. 27: 5 1 1 4 2 1 2 2 2 1 1 5 N SD: 7.0782 c. M: 13.6863 c. 31: 6 1 1 5 2 1 2 3 2 1 1 6 N SD: 3.7452 c. M: 5.9639 c. 58: 11 2 2 9 4 2 4 5 4 2 2 11 N SD: 3.6707 c. M: 6.7897 c. 68: 13 2 3 10 5 2 5 6 4 3 2 13 N SD: 2.2027 c. M:-3.9274 c. 72: 14 2 3 11 5 2 5 7 4 3 2 14 N SD: 1.5649 c. M:-2.9804 c. 99: 19 3 4 15 7 3 7 9 6 4 3 19 N SD: 0.8065 c. M: 1.5651 c. 140: 27 4 6 21 10 4 10 13 8 6 4 27 N SD: 0.8916 c. M: 1.5016 c. 171: 33 5 7 26 12 5 12 16 10 7 5 33 N SD: 0.2352 c. M:-0.4049 c. 270: 52 8 11 41 19 8 19 25 16 11 8 52 N SD: 0.2124 c. M: 0.3530 c. 441: 85 13 18 67 31 13 31 41 26 18 13 85 N SD: 0.1330 c. M: 0.2042 c. 935: 180 28 38 142 66 27 66 87 55 38 28 180 N SD: 0.1081 c. M:-0.1616 c. 1106: 213 33 45 168 78 32 78 103 65 45 33 213 N SD: 0.0751 c. M:-0.1280 c. 1236: 238 37 50 188 87 36 87 115 73 50 37 238 N SD: 0.0834 c. M:-0.1194 c. 1277: 246 38 52 194 90 37 90 119 75 52 38 246 N SD: 0.0647 c. M:-0.1033 c. 1376: 265 41 56 209 97 40 97 128 81 56 41 265 N SD: 0.0530 c. M:-0.0799 c. 1407: 271 42 57 214 99 41 99 131 83 57 42 271 N SD: 0.0521 c. M: 0.0801 c. 1547: 298 46 63 235 109 45 109 144 91 63 46 298 N SD: 0.0397 c. M: 0.0665 c. 1578: 304 47 64 240 111 46 111 147 93 64 47 304 N SD: 0.0366 c. M:-0.0539 c. 1848: 356 55 75 281 130 54 130 172 109 75 55 356 N SD: 0.0334 c. M: 0.0569 c. 2019: 389 60 82 307 142 59 142 188 119 82 60 389 N SD: 0.0295 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 4 x x x x 5 x x 6 S SD: 0.0000 cents 4 x x 5 x x x 6 x x x 7:8 S SD: 17.6681 cents 5 x x 6 x 7 x x 8 x x 9:10 S SD: 9.7541 cents 6 x 7 x 8 x 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: 11.7108 cents 8:9 x 10 x 11 x 12:13 x x 14:16 S SD: 12.3151 cents 9:10 x 11:12 x 13 x 14:15 x 16:18 S SD: 10.3648 cents 10:11 x 12:13:14 x 15:16 x 17:18:20 S SD: 10.4752 cents 11 x 13 x 15 x 16:17 x 18:19 x 22 SD: 11.8120 cents 12 x 14 x 16 x 17:18:19:20 x 21:24 S SD: 2.9008 cents 13:15 x 16:17:18:19:20:21 x 22:23:26 SD: 9.1128 cents 14:16 x 17:19 x 20:21:22:23:24:25:28 SD: 6.4619 cents 15:17 x 18:20:21 x 23:24:25 x 26:30 SD: 4.8841 cents 16:18 x 19:21:22:23:24:26:27 x 28:32 SD: 6.3935 cents 17:19:20 x 23:24 x 26:27:28:29:30:34 SD: 6.7418 cents 18 x 21:22:24:25:26:27:29:30:31:32:36 SD: 4.5601 cents 19 x 22:23:25 x 27:29:30:32 x 33:38 SD: 6.0250 cents 20:23 x 24:27:28:29:30:32:33:34:35:40 SD: 3.8094 cents 21:24 x 25:28:29:30:32:34:35:36:37:42 SD: 4.1197 cents 22:25:26 x 29:31 x 33:35:37:38:39:44 SD: 4.6107 cents 23:26:27:28:31:32:33:35:37:38:39:40:46 SD: 4.5856 cents 24:27:28:29:32 x 34:36:38:40:41:42:48 SD: 3.4756 cents 25 x 29:30:33:35:36:38:40:42:43:44:50 SD: 3.4475 cents 26:30 x 31:35:36:37:39:42:43:45:46:52 SD: 4.2339 cents 27:31 x 32:36:38:39:41:43:45:46:47:54 SD: 3.7383 cents 28:32:33:34:37:39:40:42:45:47:48:49:56 SD: 2.9574 cents 29:33:34:35:39:41 x 44:46:48:50:51:58 SD: 3.7108 cents 30:34:35:36:40:42:43:45:48:50:51:53:60 SD: 2.2396 cents 32 x 37:38:43:45:46:48:51:53:55:56:64 SD: 3.0302 cents 35:40:41:42:47:49:50:53:56:58:60:61:70 SD: 2.0740 cents 40:46:47:48:53:56:57:60:64:67:69:70:80 SD: 2.0339 cents 42:48:49:50:56:59:60:63:67:70:72:74:84 SD: 1.6441 cents 48:55:56:58:64:67:69:72:77:80:82:84:96 SD: 1.5884 cents 56:64:65:67:75:78:80:84:90:93:96:98:112 SD: 1.5383 cents 60:69:70:72:80:84:86:90:96:100:103:105:120 SD: 1.0385 cents 84:96:98:101:112:118:120:126:134:140:144:147:168 SD: 0.7118 cents 120:137:140:144:160:168:171:180:192:200:206:210:240 SD: 0.4394 cents 168:192:196:202:224:235:240:252:269:280:288:294:336 SD: 0.3292 cents 180:206:210:216:240:252:257:270:288:300:309:315:360 SD: 0.2943 cents 210:240:245:252:280:294:300:315:336:350:360:368:420 SD: 0.1962 cents 300:343:350:360:400:420:429:450:480:500:514:525:600 SD: 0.1756 cents 360:411:420:432:480:504:514:540:576:600:617:630:720 SD: 0.1736 cents 390:446:455:468:520:546:557:585:624:650:669:683:780 SD: 0.1721 cents 420:480:490:504:560:588:600:630:672:700:720:735:840 S SD: 0.0000 cents