Scala analysis: genum1125
Transposed genus(1125) minus a note; permutation epimorphic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 6/5 315.641287 minor third 3: 5/4 386.313714 major third 4: 32/25 427.372572 classic diminished fourth 5: 45/32 590.223716 diatonic tritone 6: 3/2 701.955001 perfect fifth 7: 8/5 813.686286 minor sixth 8: 9/5 1017.596288 just minor seventh, BP seventh 9: 15/8 1088.268715 classic major seventh 10: 48/25 1129.327573 classic diminished octave 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 9/8 203.9100 major whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 128/125 41.0589 minor diesis, diesis 5: 1125/1024 162.8511 double augmented prime 6: 16/15 111.7313 minor diatonic semitone 7: 16/15 111.7313 minor diatonic semitone 8: 9/8 203.9100 major whole tone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 128/125 41.0589 minor diesis, diesis 11: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 128/125 41.059 cents minor diesis, diesis 1: 3 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 16/15 111.731 cents minor diatonic semitone 1: 1 1125/1024 162.851 cents double augmented prime 1: 2 9/8 203.910 cents major whole tone 2: 3 16/15 111.731 cents minor diatonic semitone 2: 1 10/9 182.404 cents minor whole tone 2: 1 9/8 203.910 cents major whole tone 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 3 75/64 274.582 cents classic augmented second 2: 2 6/5 315.641 cents minor third 3: 1 10/9 182.404 cents minor whole tone 3: 1 256/225 223.463 cents Neapolitan diminished third 3: 1 75/64 274.582 cents classic augmented second 3: 3 6/5 315.641 cents minor third 3: 4 5/4 386.314 cents major third 3: 1 32/25 427.373 cents classic diminished fourth 4: 4 5/4 386.314 cents major third 4: 4 32/25 427.373 cents classic diminished fourth 4: 1 125/96 456.986 cents classic augmented third 4: 1 4/3 498.045 cents perfect fourth 4: 1 45/32 590.224 cents diatonic tritone 5: 6 4/3 498.045 cents perfect fourth 5: 1 512/375 539.104 cents double diminished fifth 5: 2 45/32 590.224 cents diatonic tritone 5: 1 36/25 631.283 cents classic diminished fifth 5: 1 375/256 660.896 cents double augmented fourth 6: 1 512/375 539.104 cents double diminished fifth 6: 1 25/18 568.717 cents classic augmented fourth 6: 2 64/45 609.776 cents 2nd tritone 6: 1 375/256 660.896 cents double augmented fourth 6: 6 3/2 701.955 cents perfect fifth 7: 1 64/45 609.776 cents 2nd tritone 7: 1 3/2 701.955 cents perfect fifth 7: 1 192/125 743.014 cents classic diminished sixth 7: 4 25/16 772.627 cents classic augmented fifth 7: 4 8/5 813.686 cents minor sixth 8: 1 25/16 772.627 cents classic augmented fifth 8: 4 8/5 813.686 cents minor sixth 8: 3 5/3 884.359 cents major sixth, BP sixth 8: 1 128/75 925.418 cents diminished seventh 8: 1 225/128 976.537 cents augmented sixth 8: 1 9/5 1017.596 cents just minor seventh, BP seventh 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 3 128/75 925.418 cents diminished seventh 9: 1 225/128 976.537 cents augmented sixth 9: 1 16/9 996.090 cents Pythagorean minor seventh 9: 1 9/5 1017.596 cents just minor seventh, BP seventh 9: 3 15/8 1088.269 cents classic major seventh 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 1 2048/1125 1037.149 cents double diminished octave 10: 3 15/8 1088.269 cents classic major seventh 10: 3 48/25 1129.328 cents classic diminished octave 10: 2 125/64 1158.941 cents classic augmented seventh, octave - minor diesis Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.40000 = 27/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 203.9 315.6 386.3 427.4 590.2 702.0 813.7 1017.6 1088.3 1129.3 1200.0 203.9 : 111.7 182.4 223.5 386.3 498.0 609.8 813.7 884.4 925.4 996.1 1200.0 315.6 : 70.7 111.7 274.6 386.3 498.0 702.0 772.6 813.7 884.4 1088.3 1200.0 386.3 : 41.1 203.9 315.6 427.4 631.3 702.0 743.0 813.7 1017.6 1129.3 1200.0 427.4 : 162.9 274.6 386.3 590.2 660.9 702.0 772.6 976.5 1088.3 1158.9 1200.0 590.2 : 111.7 223.5 427.4 498.0 539.1 609.8 813.7 925.4 996.1 1037.1 1200.0 702.0 : 111.7 315.6 386.3 427.4 498.0 702.0 813.7 884.4 925.4 1088.3 1200.0 813.7 : 203.9 274.6 315.6 386.3 590.2 702.0 772.6 813.7 976.5 1088.3 1200.0 1017.6: 70.7 111.7 182.4 386.3 498.0 568.7 609.8 772.6 884.4 996.1 1200.0 1088.3: 41.1 111.7 315.6 427.4 498.0 539.1 702.0 813.7 925.4 1129.3 1200.0 1129.3: 70.7 274.6 386.3 457.0 498.0 660.9 772.6 884.4 1088.3 1158.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 203.9100 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 2: 111.7313 .. 315.6413 cents 9/8, 203.9100 cents 128/135,-92.1787 cents 3: 182.4037 .. 427.3726 cents 144/125, 244.9689 cents 25/27,-133.2376 cents 4: 386.3137 .. 590.2237 cents 9/8, 203.9100 cents 125/128,-41.0589 cents 5: 498.0450 .. 660.8961 cents 1125/1024, 162.8511 cents 128/135,-92.1787 cents 6: 539.1039 .. 701.9550 cents 1125/1024, 162.8511 cents 131072/140625,-121.7923 cents 7: 609.7763 .. 813.6863 cents 9/8, 203.9100 cents 128/135,-92.1787 cents 8: 772.6274 .. 1017.5963 cents 144/125, 244.9689 cents 125/128,-41.0589 cents 9: 884.3587 .. 1088.2687 cents 9/8, 203.9100 cents 25/27,-133.2376 cents 10: 996.0900 .. 1158.9411 cents 1125/1024, 162.8511 cents 128/135,-92.1787 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 2.656940 Largest / Average step : 1.869175 Largest / Smallest step : 4.966285 Median interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 116.58249 cents, oct.: 1282.40741 cents Scale is not proper Step pattern alph. order: ABCDEBBACDC Step pattern size order : ECBADCCEBAB Scale is not a Constant Structure Scale diversity : 1.403933 Lumma stability : 0.068431 Lumma impropriety factor : 0.578206 Rothenberg efficiency : 0.434199 redundancy: 0.565801 Efficiency x scale size : 4.776190 Number of different interval sizes : 32 = 3.20000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.40000 = 27/5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 8 Most common triad is 0.0 386.314 813.686 cents, amount: 5 Number of recognisable fifths : 7, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 27.2727% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 5 Odd number limit : 1125 (O: 1125 U: 1125) Highest odd numerator or denominator: 45 Scale harmonicity : 0.028958 Average absolute harmonicity : 0.186627 Specific harmonicity : 0.155485 Fundamental : 1/800, -9.6439 octaves, 0.3270 Hz. Guide tone : 1440, 10.4919 octaves, 376740.814 Hz. Exponens Consonantiae : 1.152000E+06, 20.13571 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 151.0, average 13.72727 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.10770, average 0.91888 Sum of Tenney's harmonic distance : 20.18975, average 1.83543 Vogel's harmonic complexity : 15.90909 Wille's k value : 562 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 270.45101, average 4.09774 Lattice compactness (without 2's) : 117.50346, average 1.78036 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 5 0.00000 28 1 3: 0 .. 2 0.90909 10 2 5: -2 .. 1 -0.36364 10 8 Average exponent except 2's : 6 / 11 = 0.54545 Average absolute exponent except 2's: 20 / 11 = 1.81818 Scale is weakly epimorphic with val: <11 16 29| Scale is weakly epimorphic with val: <11 17 26| = patent
FIT/MODE
11: 2 1 0 1 1 1 1 2 1 0 1 N T3 SD: 34.9358 c. M: 59.0410 c. 12: 2 1 1 0 2 1 1 2 1 0 1 N T3 SD: 15.9276 c. M: 29.3276 c. 19: 3 2 1 1 2 2 2 3 1 1 1 N SD: 11.2032 c. M: 21.8027 c. 22: 4 2 1 1 3 2 2 4 1 1 1 N SD: 10.5572 c. M:-18.7673 c. 28: 5 2 2 1 4 2 3 5 1 1 2 N SD: 11.0540 c. M: 16.8401 c. 31: 5 3 2 1 4 3 3 5 2 1 2 N SD: 6.4263 c. M: 11.1447 c. 34: 6 3 2 1 5 3 3 6 2 1 2 N SD: 4.9387 c. M:-9.7763 c. 53: 9 5 3 2 7 5 5 9 3 2 3 N SD: 1.5796 c. M:-2.8161 c. 65: 11 6 4 2 9 6 6 11 4 2 4 N SD: 1.6971 c. M: 3.1737 c. 87: 15 8 5 3 12 8 8 15 5 3 5 N SD: 1.8210 c. M:-3.0934 c. 118: 20 11 7 4 16 11 11 20 7 4 7 N SD: 0.3618 c. M: 0.6471 c. 289: 49 27 17 10 39 27 27 49 17 10 17 N SD: 0.3022 c. M: 0.6043 c. 323: 55 30 19 11 44 30 30 55 19 11 19 N SD: 0.2564 c. M:-0.4884 c. 376: 64 35 22 13 51 35 35 64 22 13 22 N SD: 0.2803 c. M:-0.4888 c. 441: 75 41 26 15 60 41 41 75 26 15 26 N SD: 0.1285 c. M:-0.2525 c. 494: 84 46 29 17 67 46 46 84 29 17 29 N SD: 0.1300 c. M:-0.2271 c. 559: 95 52 33 19 76 52 52 95 33 19 33 N SD: 0.1013 c. M: 0.1812 c. 612: 104 57 36 21 83 57 57 104 36 21 36 N SD: 0.0457 c. M:-0.0842 c. 730: 124 68 43 25 99 68 68 124 43 25 43 N SD: 0.0452 c. M: 0.0867 c. 1171: 199 109 69 40 159 109 109 199 69 40 69 N SD: 0.0265 c. M: 0.0455 c. 1783: 303 166 105 61 242 166 166 303 105 61 105 N SD: 0.0095 c. M:-0.0175 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 4 x x 5 x x x 6 S SD: 33.3153 cents 4 x x 5 x x 6 x 7 x x 8 S SD: 12.1926 cents 5 x 6 x x 7 x 8:9 x x 10 S SD: 1.5423 cents 6 x 7 x 8 x 9:10:11 x x 12 S SD: 19.2764 cents 7:8 x x 9:10 x 11 x 13 x 14 SD: 8.8092 cents 8:9 x 10 x 11:12:13:14:15 x 16 S SD: 8.4896 cents 9:10:11 x 12:13 x 14:16:17 x 18 S SD: 13.4762 cents 10:11:12 x 13:14:15:16:18 x 19:20 S SD: 5.6897 cents 11:12:13 x 14:15:17:18:20 x 21:22 SD: 11.6834 cents 12 x 14:15 x 17:18:19:22 x 23:24 SD: 7.7948 cents 13:15 x 16:17:18:20:21:23:24:25:26 SD: 9.2466 cents 14:16:17 x 18:20:21:22:25:26:27:28 SD: 5.8849 cents 15:17:18 x 19:21:23:24:27:28:29:30 SD: 4.6928 cents 16:18:19:20 x 23:24:26:29:30:31:32 SD: 5.3733 cents 18:20:22 x 23:25:27:29:32:34:35:36 SD: 5.6500 cents 19:21:23:24 x 27:29:30:34:36 x 38 SD: 6.7485 cents 20:23:24:25:26:28:30:32:36 x 38:40 SD: 5.0561 cents 22:25:26 x 28:31:33:35:40:41:42:44 SD: 4.1461 cents 23:26:28:29 x 32:35:37:41:43:44:46 SD: 4.8092 cents 24:27:29:30:31:34:36:38:43:45:46:48 SD: 2.8105 cents 25:28:30:31:32:35:38:40:45:47:48:50 SD: 2.6650 cents 26:29:31 x 33:37:39:42:47:49:50:52 SD: 3.7388 cents 29:33:35:36:37:41:44:46:52:54:56:58 SD: 3.6960 cents 30:34:36 x 38:42:45:48:54:56:58:60 SD: 2.7466 cents 32:36:38:40:41:45:48:51:58:60:61:64 SD: 2.3632 cents 39:44:47:49:50:55:59:62:70:73:75:78 SD: 2.1724 cents 40:45:48:50:51:56:60:64:72:75:77:80 SD: 1.0190 cents 64:72:77:80:82:90:96:102:115:120:123:128 SD: 0.8179 cents 96:108:115:120:123:135:144:154:173:180:184:192 SD: 0.6114 cents 120:135:144:150:154:169:180:192:216:225:230:240 SD: 0.5446 cents 135:152:162:169:173:190:203:216:243:253:259:270 SD: 0.5407 cents 136:153:163:170:174:191:204:218:245:255:261:272 SD: 0.4361 cents 160:180:192:200:205:225:240:256:288:300:307:320 SD: 0.1847 cents 200:225:240:250:256:281:300:320:360:375:384:400 SD: 0.1400 cents 360:405:432:450:461:506:540:576:648:675:691:720 SD: 0.1131 cents 440:495:528:550:563:619:660:704:792:825:845:880 SD: 0.0925 cents 600:675:720:750:768:844:900:960:1080:1125:1152:1200 SD: 0.0466 cents