Scala analysis: max4
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: 7/6 266.870906 septimal minor third 2: 6/5 315.641287 minor third 3: 5/4 386.313714 major 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: 7/6 266.8709 septimal minor third 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 16/15 111.7313 minor diatonic semitone 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: 1 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: 2 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 21/20 84.467 cents minor semitone 2: 4 15/14 119.443 cents major diatonic semitone 2: 2 10/9 182.404 cents minor whole tone 2: 2 28/25 196.198 cents middle second 2: 1 7/6 266.871 cents septimal minor third 2: 1 6/5 315.641 cents minor third 2: 1 4/3 498.045 cents perfect fourth 3: 1 35/32 155.140 cents septimal neutral second 3: 1 9/8 203.910 cents major whole tone 3: 4 8/7 231.174 cents septimal whole tone 3: 2 7/6 266.871 cents septimal minor third 3: 1 6/5 315.641 cents minor third 3: 1 5/4 386.314 cents major third 3: 1 49/36 533.742 cents Arabic lute acute fourth 3: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 7/6 266.871 cents septimal minor third 4: 2 25/21 301.847 cents BP second, quasi-equal minor third 4: 4 6/5 315.641 cents minor third 4: 1 5/4 386.314 cents major third 4: 1 4/3 498.045 cents perfect fourth 4: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 10/7 617.488 cents Euler's tritone 5: 2 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 32/25 427.373 cents classic diminished fourth 5: 1 4/3 498.045 cents perfect fourth 5: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 36/25 631.283 cents classic diminished fifth 5: 2 35/24 653.185 cents septimal semi-diminished fifth 5: 1 32/21 729.219 cents wide fifth 6: 1 5/4 386.314 cents major third 6: 2 9/7 435.084 cents septimal major third, BP third 6: 2 4/3 498.045 cents perfect 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: 2 3/2 701.955 cents perfect fifth 6: 2 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: 2 48/35 546.815 cents septimal semi-augmented fourth 7: 1 25/18 568.717 cents classic augmented fourth 7: 1 10/7 617.488 cents Euler's tritone 7: 1 3/2 701.955 cents perfect fifth 7: 1 25/16 772.627 cents classic augmented fifth 7: 2 8/5 813.686 cents minor sixth 7: 1 80/49 848.662 cents smaller approximation to neutral sixth 7: 2 49/30 849.383 cents larger approximation to neutral sixth 8: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 8: 2 10/7 617.488 cents Euler's tritone 8: 1 3/2 701.955 cents perfect fifth 8: 1 8/5 813.686 cents minor sixth 8: 4 5/3 884.359 cents major sixth, BP sixth 8: 2 42/25 898.153 cents quasi-equal major sixth 8: 1 12/7 933.129 cents septimal major sixth 9: 1 35/24 653.185 cents septimal semi-diminished fifth 9: 1 72/49 666.258 cents Arabic lute grave fifth 9: 1 8/5 813.686 cents minor 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 16/9 996.090 cents Pythagorean minor seventh 9: 1 64/35 1044.860 cents septimal neutral seventh 10: 1 3/2 701.955 cents perfect fifth 10: 1 5/3 884.359 cents major sixth, BP sixth 10: 1 12/7 933.129 cents septimal major sixth 10: 2 25/14 1003.802 cents middle minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 4 28/15 1080.557 cents grave major seventh 10: 1 40/21 1115.533 cents acute major seventh 11: 1 12/7 933.129 cents septimal major sixth 11: 1 7/4 968.826 cents harmonic seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 2 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: 1 96/49 1164.303 cents 11: 1 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 7.81818 = 86/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 266.9 315.6 386.3 498.0 582.5 617.5 702.0 813.7 884.4 933.1 968.8 1200.0 266.9 : 48.8 119.4 231.2 315.6 350.6 435.1 546.8 617.5 666.3 702.0 933.1 1200.0 315.6 : 70.7 182.4 266.9 301.8 386.3 498.0 568.7 617.5 653.2 884.4 1151.2 1200.0 386.3 : 111.7 196.2 231.2 315.6 427.4 498.0 546.8 582.5 813.7 1080.6 1129.3 1200.0 498.0 : 84.5 119.4 203.9 315.6 386.3 435.1 470.8 702.0 968.8 1017.6 1088.3 1200.0 582.5 : 35.0 119.4 231.2 301.8 350.6 386.3 617.5 884.4 933.1 1003.8 1115.5 1200.0 617.5 : 84.5 196.2 266.9 315.6 351.3 582.5 849.4 898.2 968.8 1080.6 1165.0 1200.0 702.0 : 111.7 182.4 231.2 266.9 498.0 764.9 813.7 884.4 996.1 1080.6 1115.5 1200.0 813.7 : 70.7 119.4 155.1 386.3 653.2 702.0 772.6 884.4 968.8 1003.8 1088.3 1200.0 884.4 : 48.8 84.5 315.6 582.5 631.3 702.0 813.7 898.2 933.1 1017.6 1129.3 1200.0 933.1 : 35.7 266.9 533.7 582.5 653.2 764.9 849.4 884.4 968.8 1080.6 1151.2 1200.0 968.8 : 231.2 498.0 546.8 617.5 729.2 813.7 848.7 933.1 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 .. 266.8709 cents 343/300, 231.8953 cents 50/49, 34.9756 cents 2: 84.4672 .. 498.0450 cents 80/63, 413.5778 cents 9/10,-182.4037 cents 3: 155.1396 .. 546.8154 cents 1536/1225, 391.6758 cents 105/128,-342.9054 cents 4: 266.8709 .. 617.4878 cents 60/49, 350.6169 cents 245/288,-279.9445 cents 5: 350.6169 .. 729.2191 cents 56/45, 378.6022 cents 6/7,-266.8709 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: 582.5122 .. 933.1291 cents 60/49, 350.6169 cents 6/7,-266.8709 cents 9: 653.1846 .. 1044.8604 cents 1536/1225, 391.6758 cents 245/288,-279.9445 cents 10: 701.9550 .. 1115.5328 cents 80/63, 413.5778 cents 105/128,-342.9054 cents 11: 933.1291 .. 1165.0244 cents 343/300, 231.8953 cents 9/10,-182.4037 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 : 7/6, 266.8709 cents Average / Smallest step : 2.859135 Largest / Average step : 2.668709 Largest / Smallest step : 7.630199 Median interval of one step : 77.56981 cents, amount: 0 Least squares average step : 99.13468 cents, oct.: 1189.61616 cents Scale is not proper Step pattern alph. order: ABCDEFEDCBGH Step pattern size order : HCDFEAEFDCBG Scale is not a Constant Structure Scale diversity : 1.495785 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 : 9 Mean interval variety : 7.81818 = 86/11 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 6 Most common triad is 0.0 315.641 582.512 cents, amount: 2 Number of recognisable fifths : 5, 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 11 Formal octave complements present : 11 = 91.6667% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 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 : 0.188208 Specific harmonicity : 0.138427 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 : 64.0, average 5.33333 Mersenne's string divisions : 116396280 Sum of van Prooijen's expressibility: 7.97561, average 0.66463 Sum of Tenney's harmonic distance : 16.09852, average 1.34154 Vogel's harmonic complexity : 17.91667 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 201.57388, average 2.58428 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 0.33333 16 1 3: -1 .. 1 0.00000 6 2 5: -1 .. 1 0.00000 6 4 7: -1 .. 1 0.08333 5 5 Average exponent except 2's : 1 / 12 = 0.08333 Average absolute exponent except 2's: 17 / 12 = 1.41667
FIT/MODE
12: 3 0 1 1 1 0 1 1 1 0 1 2 N SD: 19.6853 c. M: 33.1291 c. 15: 3 1 1 1 1 1 1 1 1 1 0 3 N SD: 17.3192 c. M:-26.8709 c. 19: 4 1 1 2 1 1 1 2 1 1 0 4 N SD: 11.0899 c. M: 21.4575 c. 22: 5 1 1 2 2 0 2 2 1 1 1 4 N SD: 10.2546 c. M:-17.4878 c. 27: 6 1 2 2 2 1 2 2 2 1 1 5 N SD: 7.6833 c. M: 13.6863 c. 31: 7 1 2 3 2 1 2 3 2 1 1 6 N SD: 3.7390 c. M: 5.9639 c. 53: 12 2 3 5 4 1 4 5 3 2 2 10 N SD: 3.5693 c. M:-6.1671 c. 68: 15 3 4 6 5 2 5 6 4 3 2 13 N SD: 2.2138 c. M:-3.9274 c. 72: 16 3 4 7 5 2 5 7 4 3 2 14 N SD: 1.6735 c. M: 2.9804 c. 99: 22 4 6 9 7 3 7 9 6 4 3 19 N SD: 0.8896 c. M:-1.5651 c. 140: 31 6 8 13 10 4 10 13 8 6 4 27 N SD: 0.9053 c. M: 1.5016 c. 171: 38 7 10 16 12 5 12 16 10 7 5 33 N SD: 0.2276 c. M: 0.4049 c. 270: 60 11 16 25 19 8 19 25 16 11 8 52 N SD: 0.2349 c. M:-0.3530 c. 441: 98 18 26 41 31 13 31 41 26 18 13 85 N SD: 0.1306 c. M: 0.2042 c. 612: 136 25 36 57 43 18 43 57 36 25 18 118 N SD: 0.1227 c. M: 0.2042 c. 935: 208 38 55 87 66 27 66 87 55 38 28 180 N SD: 0.0980 c. M:-0.1616 c. 1106: 246 45 65 103 78 32 78 103 65 45 33 213 N SD: 0.0741 c. M:-0.1280 c. 1236: 275 50 73 115 87 36 87 115 73 50 37 238 N SD: 0.0822 c. M:-0.1194 c. 1277: 284 52 75 119 90 37 90 119 75 52 38 246 N SD: 0.0704 c. M:-0.1033 c. 1376: 306 56 81 128 97 40 97 128 81 56 41 265 N SD: 0.0496 c. M:-0.0799 c. 1547: 344 63 91 144 109 45 109 144 91 63 46 298 N SD: 0.0398 c. M: 0.0665 c. 1578: 351 64 93 147 111 46 111 147 93 64 47 304 N SD: 0.0366 c. M:-0.0539 c. 1848: 411 75 109 172 130 54 130 172 109 75 55 356 N SD: 0.0364 c. M: 0.0569 c. 2019: 449 82 119 188 142 59 142 188 119 82 60 389 N SD: 0.0286 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: 0.0000 cents 5 x 6 x x 7 x x 8 x x 9:10 S SD: 9.7541 cents 6:7 x x 8 x x 9 x 10 x 11:12 S SD: 13.4228 cents 7:8 x 9 x x 10 x 11 x 12 x 14 S SD: 11.3357 cents 8:9 x 10 x 11 x 12:13 x x 14:16 S SD: 10.7453 cents 9 x 11 x 12 x 13 x 14:15 x 16:18 SD: 9.5799 cents 10 x 12 x 13:14 x 15:16 x 17:18:20 S SD: 8.3942 cents 11:13 x 14:15 x 16:17 x 18:19 x 22 SD: 11.0466 cents 12:14 x 15:16 x 17:18:19:20 x 21:24 S SD: 2.5784 cents 13:15 x 16:17:18:19:20:21 x 22:23:26 SD: 8.4824 cents 14:16:17:18:19 x 20:21:22:23:24:25:28 SD: 8.0435 cents 15 x 18:19:20:21 x 23:24:25 x 26:30 SD: 5.2683 cents 16 x 19:20:21:22:23:24:26:27 x 28:32 SD: 5.7831 cents 17:20 x 21:23:24 x 26:27:28:29:30:34 SD: 5.8938 cents 18:21:22:23:24:25:26:27:29:30:31:32:36 SD: 5.2467 cents 19:22:23:24:25 x 27:29:30:32 x 33:38 SD: 5.7175 cents 20:23:24:25:27:28:29:30:32:33:34:35:40 SD: 3.9617 cents 21 x 25:26:28:29:30:32:34:35:36:37:42 SD: 4.3864 cents 22:26 x 28:29:31 x 33:35:37:38:39:44 SD: 5.4787 cents 23:27:28:29:31:32:33:35:37:38:39:40:46 SD: 4.4835 cents 24:28:29:30:32 x 34:36:38:40:41:42:48 S SD: 2.4365 cents 27 x 32:34:36:38:39:41:43:45:46:47:54 SD: 3.8465 cents 28:33:34:35:37:39:40:42:45:47:48:49:56 SD: 2.9574 cents 29:34:35:36:39:41 x 44:46:48:50:51:58 SD: 3.8071 cents 30:35:36:38:40:42:43:45:48:50:51:53:60 SD: 2.6851 cents 35:41:42:44:47:49:50:53:56:58:60:61:70 SD: 2.2310 cents 36:42:43:45:48:50:51:54:58:60:62:63:72 SD: 2.1606 cents 40:47:48:50:53:56:57:60:64:67:69:70:80 SD: 1.8245 cents 48:56:58:60:64:67:69:72:77:80:82:84:96 SD: 1.5435 cents 56:65:67:70:75:78:80:84:90:93:96:98:112 SD: 1.5383 cents 60:70:72:75:80:84:86:90:96:100:103:105:120 SD: 0.5202 cents 120:140:144:150:160:168:171:180:192:200:206:210:240 SD: 0.4129 cents 168:196:202:210:224:235:240:252:269:280:288:294:336 SD: 0.3292 cents 180:210:216:225:240:252:257:270:288:300:309:315:360 SD: 0.2157 cents 240:280:288:300:320:336:343:360:384:400:411:420:480 SD: 0.1619 cents 360:420:432:450:480:504:514:540:576:600:617:630:720 SD: 0.0869 cents 420:490:504:525:560:588:600:630:672:700:720:735:840 S SD: 0.0000 cents