Scala analysis: cv1
First 12/5 <12 19 28 34| epimorphic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 8/7 231.174094 septimal whole tone 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 7/4 968.825906 harmonic seventh 11: 28/15 1080.557192 grave major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 15/14 119.4428 major diatonic semitone 3: 49/48 35.6968 slendro diesis, septimal 1/6-tone 4: 15/14 119.4428 major diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 21/20 84.4672 minor semitone 11: 16/15 111.7313 minor diatonic semitone 12: 15/14 119.4428 major 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 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 21/20 84.467 cents minor semitone 1: 4 16/15 111.731 cents minor diatonic semitone 1: 4 15/14 119.443 cents major diatonic semitone 2: 3 35/32 155.140 cents septimal neutral second 2: 1 10/9 182.404 cents minor whole tone 2: 2 28/25 196.198 cents middle second 2: 1 9/8 203.910 cents major whole tone 2: 5 8/7 231.174 cents septimal whole tone 3: 4 7/6 266.871 cents septimal minor third 3: 1 75/64 274.582 cents classic augmented second 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 1 128/105 342.905 cents septimal neutral third 3: 1 60/49 350.617 cents smaller approximation to neutral third 4: 1 49/40 351.338 cents larger approximation to neutral third 4: 1 56/45 378.602 cents septimal narrow major third 4: 6 5/4 386.314 cents major third 4: 2 32/25 427.373 cents classic diminished fourth 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 64/49 462.348 cents 2 septatones or septatonic major third 5: 3 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 1 75/56 505.757 cents marvelous fourth 5: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 45/32 590.224 cents diatonic tritone 6: 1 64/45 609.776 cents 2nd tritone 6: 5 10/7 617.488 cents Euler's tritone 7: 2 35/24 653.185 cents septimal semi-diminished fifth 7: 1 112/75 694.243 cents marvelous fifth 7: 6 3/2 701.955 cents perfect fifth 7: 3 32/21 729.219 cents wide fifth 8: 1 49/32 737.652 cents 8: 1 14/9 764.916 cents septimal minor sixth 8: 2 25/16 772.627 cents classic augmented fifth 8: 6 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 8: 1 80/49 848.662 cents smaller approximation to neutral sixth 9: 1 49/30 849.383 cents larger approximation to neutral sixth 9: 1 105/64 857.095 cents septimal neutral sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 1 128/75 925.418 cents diminished seventh 9: 4 12/7 933.129 cents septimal major sixth 10: 5 7/4 968.826 cents harmonic seventh 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 2 25/14 1003.802 cents middle minor seventh 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 10: 3 64/35 1044.860 cents septimal neutral seventh 11: 4 28/15 1080.557 cents grave major seventh 11: 4 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: 1 96/49 1164.303 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.09091 = 56/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 231.2 266.9 386.3 498.0 582.5 702.0 813.7 884.4 968.8 1080.6 1200.0 111.7 : 119.4 155.1 274.6 386.3 470.8 590.2 702.0 772.6 857.1 968.8 1088.3 1200.0 231.2 : 35.7 155.1 266.9 351.3 470.8 582.5 653.2 737.7 849.4 968.8 1080.6 1200.0 266.9 : 119.4 231.2 315.6 435.1 546.8 617.5 702.0 813.7 933.1 1044.9 1164.3 1200.0 386.3 : 111.7 196.2 315.6 427.4 498.0 582.5 694.2 813.7 925.4 1044.9 1080.6 1200.0 498.0 : 84.5 203.9 315.6 386.3 470.8 582.5 702.0 813.7 933.1 968.8 1088.3 1200.0 582.5 : 119.4 231.2 301.8 386.3 498.0 617.5 729.2 848.7 884.4 1003.8 1115.5 1200.0 702.0 : 111.7 182.4 266.9 378.6 498.0 609.8 729.2 764.9 884.4 996.1 1080.6 1200.0 813.7 : 70.7 155.1 266.9 386.3 498.0 617.5 653.2 772.6 884.4 968.8 1088.3 1200.0 884.4 : 84.5 196.2 315.6 427.4 546.8 582.5 702.0 813.7 898.2 1017.6 1129.3 1200.0 968.8 : 111.7 231.2 342.9 462.3 498.0 617.5 729.2 813.7 933.1 1044.9 1115.5 1200.0 1080.6: 119.4 231.2 350.6 386.3 505.8 617.5 702.0 821.4 933.1 1003.8 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 119.4428 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 2: 155.1396 .. 231.1741 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 3: 266.8709 .. 350.6169 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 4: 351.3381 .. 462.3482 cents 2560/2401, 111.0101 cents 2401/2400, 0.7212 cents 5: 470.7809 .. 546.8154 cents 256/245, 76.0345 cents 1029/1024, 8.4327 cents 6: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 49/48, 35.6968 cents 7: 653.1846 .. 729.2191 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 8: 737.6518 .. 848.6619 cents 2560/2401, 111.0101 cents 1029/1024, 8.4327 cents 9: 849.3831 .. 933.1291 cents 360/343, 83.7460 cents 2401/2400, 0.7212 cents 10: 968.8259 .. 1044.8604 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1164.3032 cents 360/343, 83.7460 cents 49/48, 35.6968 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 : 15/14, 119.4428 cents Average / Smallest step : 2.801371 Largest / Average step : 1.194428 Largest / Smallest step : 3.346036 Median interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 98.86467 cents, oct.: 1186.37607 cents Scale is strictly proper Step pattern alph. order: ABCBADBAEDAB Step pattern size order : DEAEDCEDBCDE Scale is a Constant Structure, by a margin of 0.72120 cents Scale diversity : 1.508748 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.253235 Rothenberg efficiency : 0.285293 redundancy: 0.714707 Efficiency x scale size : 3.423521 Number of different interval sizes : 56 = 5.09091 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.09091 = 56/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2401/2400, 0.7212 cents Number of recognisable fifths : 7, average 700.8534 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 7 = 58.3333% 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 classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 7 Odd number limit : 105 (O: 105 U: 105) Highest odd numerator or denominator: 15 Scale harmonicity : 0.022369 Average absolute harmonicity : 0.186197 Specific harmonicity : 0.142546 Fundamental : 1/420, -8.7142 octaves, 0.6229 Hz. Guide tone : 1680, 10.7142 octaves, 439530.950 Hz. Exponens Consonantiae : 7.056000E+05, 19.42849 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 85.0, average 7.08333 Mersenne's string divisions : 480359880 Sum of van Prooijen's expressibility: 8.78373, average 0.73198 Sum of Tenney's harmonic distance : 17.60367, average 1.46697 Vogel's harmonic complexity : 17.66667 Wille's k value : 367 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 228.21395, average 2.92582 Lattice compactness (without 2's) : 116.42685, average 1.49265 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 0.75000 21 1 3: -1 .. 1 -0.33333 6 2 5: -1 .. 1 -0.16667 6 4 7: -1 .. 1 0.25000 5 5 Average exponent except 2's :-3 / 12 =-0.25000 Average absolute exponent except 2's: 17 / 12 = 1.41667 Scale is JI-epimorphic with val: <12 19 28 34| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 19.3425 c. M:-33.1291 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 0 2 1 1 2 1 1 1 1 2 N D3 SD: 20.5776 c. M: 40.5572 c. 19: 2 2 0 2 2 1 2 2 1 1 2 2 N SD: 12.2300 c. M:-21.4575 c. 22: 2 2 1 2 2 2 2 2 1 2 2 2 SP B ME SD: 9.4402 c. M:-17.4878 c. Jubilee-12 31: 3 3 1 3 3 2 3 3 2 2 3 3 P SD: 3.4571 c. M:-5.9639 c. 68: 6 7 2 7 6 5 7 6 4 5 6 7 P SD: 2.9452 c. M: 5.8489 c. 72: 7 7 2 7 7 5 7 7 4 5 7 7 P SD: 2.3904 c. M:-4.9354 c. 87: 8 9 2 9 8 6 9 8 5 6 8 9 N SD: 2.6804 c. M: 4.8019 c. 94: 9 9 3 9 9 7 9 9 5 7 9 9 SP SD: 2.7827 c. M:-4.7218 c. 99: 9 10 3 10 9 7 10 9 6 7 9 10 P SD: 1.2778 c. M: 2.6404 c. 130: 12 13 4 13 12 9 13 12 8 9 12 13 P SD: 0.9380 c. M:-1.7951 c. 140: 13 14 4 14 13 10 14 13 8 10 13 14 P SD: 0.7410 c. M: 1.5016 c. 171: 16 17 5 17 16 12 17 16 10 12 16 17 P SD: 0.2946 c. M:-0.5494 c. 270: 25 27 8 27 25 19 27 25 16 19 25 27 P SD: 0.3199 c. M: 0.6202 c. 441: 41 44 13 44 41 31 44 41 26 31 41 44 P SD: 0.1433 c. M: 0.2851 c. 612: 57 61 18 61 57 43 61 57 36 43 57 61 P SD: 0.1223 c. M: 0.2042 c. 935: 87 93 28 93 87 66 93 87 55 66 87 93 SP SD: 0.0973 c. M:-0.1616 c. 1106: 103 110 33 110 103 78 110 103 65 78 103 110 SP SD: 0.0672 c. M:-0.1280 c. 1236: 115 123 37 123 115 87 123 115 73 87 115 123 SP SD: 0.0783 c. M:-0.1194 c. 1277: 119 127 38 127 119 90 127 119 75 90 119 127 SP SD: 0.0694 c. M:-0.1033 c. 1376: 128 137 41 137 128 97 137 128 81 97 128 137 SP SD: 0.0583 c. M: 0.1034 c. 1407: 131 140 42 140 131 99 140 131 83 99 131 140 SP SD: 0.0443 c. M:-0.0801 c. 1547: 144 154 46 154 144 109 154 144 91 109 144 154 SP SD: 0.0339 c. M: 0.0665 c. 1578: 147 157 47 157 147 111 157 147 93 111 147 157 SP SD: 0.0373 c. M:-0.0558 c. 1848: 172 184 55 184 172 130 184 172 109 130 172 184 SP SD: 0.0339 c. M:-0.0569 c. 2019: 188 201 60 201 188 142 201 188 119 142 188 201 SP SD: 0.0251 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 7 x 8 S SD: 0.0000 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.7943 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 5.1990 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 10.9987 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 6.2454 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 11.3100 cents 10:11 x 12 x 13:14:15:16:17:18:19:20 S SD: 10.7845 cents 11:12 x 13:14:15 x 17 x 18:19:21:22 SD: 11.2247 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 4.4924 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 7.2634 cents 14:15:16 x 18:19:20:21:22:23:25:26:28 SD: 7.8706 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 5.7954 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 5.7052 cents 18:19 x 21:23:24:25:27:29:30:32:34:36 SD: 5.2013 cents 19:20 x 22:24:25:27:29:30:32:33:35:38 SD: 6.2166 cents 20:21:23 x 25:27:28:30:32:33:35:37:40 SD: 3.9270 cents 25:27 x 29:31:33:35:38:40:42:44:47:50 SD: 4.0882 cents 26:28:30 x 33:35:36:39:42:43:46:49:52 SD: 4.9574 cents 27:29:31:32:34:36:38:41:43:45:47:50:54 SD: 3.7155 cents 28:30:32:33:35:37:39:42:45:47:49:52:56 SD: 2.6056 cents 32:34 x 37:40:43:45:48:51:53:56:60:64 SD: 2.4916 cents 36:38:41:42:45:48:50:54:58:60:63:67:72 SD: 2.2444 cents 40:43:46:47:50:53:56:60:64:67:70:75:80 SD: 2.2072 cents 42:45:48:49:53:56:59:63:67:70:74:78:84 SD: 2.0516 cents 47:50:54:55:59:63:66:71:75:78:82:88:94 SD: 2.0070 cents 48:51:55:56:60:64:67:72:77:80:84:90:96 SD: 1.0947 cents 60:64:69:70:75:80:84:90:96:100:105:112:120 SD: 0.8989 cents 72:77:82:84:90:96:101:108:115:120:126:134:144 SD: 0.8498 cents 90:96:103:105:113:120:126:135:144:150:158:168:180 SD: 0.8115 cents 108:115:123:126:135:144:151:162:173:180:189:202:216 SD: 0.6788 cents 120:128:137:140:150:160:168:180:192:200:210:224:240 SD: 0.1504 cents 300:320:343:350:375:400:420:450:480:500:525:560:600 SD: 0.0601 cents 420:448:480:490:525:560:588:630:672:700:735:784:840 S SD: 0.0000 cents