Scala analysis: xen03-wilson-negative-12
Negative, linear-mapped intonational system, 12 notes
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: 9/8 203.910002 major whole tone 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 64/45 609.776284 2nd tritone 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 27/16 905.865003 Pythagorean major sixth 10: 9/5 1017.596288 just minor seventh, BP seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 135/128 92.1787 major chroma, major limma 3: 16/15 111.7313 minor diatonic semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma 8: 16/15 111.7313 minor diatonic semitone 9: 135/128 92.1787 major chroma, major limma 10: 16/15 111.7313 minor diatonic semitone 11: 25/24 70.6724 classic chromatic semitone, minor chroma 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 135/128 92.179 cents major chroma, major limma 1: 7 16/15 111.731 cents minor diatonic semitone 2: 4 10/9 182.404 cents minor whole tone 2: 6 9/8 203.910 cents major whole tone 2: 2 256/225 223.463 cents Neapolitan diminished third 3: 2 75/64 274.582 cents classic augmented second 3: 4 32/27 294.135 cents Pythagorean minor third 3: 1 1215/1024 296.089 cents wide augmented second 3: 5 6/5 315.641 cents minor third 4: 6 5/4 386.314 cents major third 4: 2 512/405 405.866 cents narrow diminished fourth 4: 2 81/64 407.820 cents Pythagorean major third 4: 2 32/25 427.373 cents classic diminished fourth 5: 1 675/512 478.492 cents wide augmented third 5: 9 4/3 498.045 cents perfect fourth 5: 2 27/20 519.551 cents acute fourth 6: 1 25/18 568.717 cents classic augmented fourth 6: 5 45/32 590.224 cents diatonic tritone 6: 5 64/45 609.776 cents 2nd tritone 6: 1 36/25 631.283 cents classic diminished fifth 7: 2 40/27 680.449 cents grave fifth 7: 9 3/2 701.955 cents perfect fifth 7: 1 1024/675 721.508 cents narrow diminished sixth 8: 2 25/16 772.627 cents classic augmented fifth 8: 2 128/81 792.180 cents Pythagorean minor sixth 8: 2 405/256 794.134 cents wide augmented fifth 8: 6 8/5 813.686 cents minor sixth 9: 5 5/3 884.359 cents major sixth, BP sixth 9: 1 2048/1215 903.911 cents narrow diminished seventh 9: 4 27/16 905.865 cents Pythagorean major sixth 9: 2 128/75 925.418 cents diminished seventh 10: 2 225/128 976.537 cents augmented sixth 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 4 9/5 1017.596 cents just minor seventh, BP seventh 11: 7 15/8 1088.269 cents classic major seventh 11: 3 256/135 1107.821 cents octave - major chroma 11: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 203.9 315.6 386.3 498.0 609.8 702.0 813.7 905.9 1017.6 1088.3 1200.0 111.7 : 92.2 203.9 274.6 386.3 498.0 590.2 702.0 794.1 905.9 976.5 1088.3 1200.0 203.9 : 111.7 182.4 294.1 405.9 498.0 609.8 702.0 813.7 884.4 996.1 1107.8 1200.0 315.6 : 70.7 182.4 294.1 386.3 498.0 590.2 702.0 772.6 884.4 996.1 1088.3 1200.0 386.3 : 111.7 223.5 315.6 427.4 519.6 631.3 702.0 813.7 925.4 1017.6 1129.3 1200.0 498.0 : 111.7 203.9 315.6 407.8 519.6 590.2 702.0 813.7 905.9 1017.6 1088.3 1200.0 609.8 : 92.2 203.9 296.1 407.8 478.5 590.2 702.0 794.1 905.9 976.5 1088.3 1200.0 702.0 : 111.7 203.9 315.6 386.3 498.0 609.8 702.0 813.7 884.4 996.1 1107.8 1200.0 813.7 : 92.2 203.9 274.6 386.3 498.0 590.2 702.0 772.6 884.4 996.1 1088.3 1200.0 905.9 : 111.7 182.4 294.1 405.9 498.0 609.8 680.4 792.2 903.9 996.1 1107.8 1200.0 1017.6: 70.7 182.4 294.1 386.3 498.0 568.7 680.4 792.2 884.4 996.1 1088.3 1200.0 1088.3: 111.7 223.5 315.6 427.4 498.0 609.8 721.5 813.7 925.4 1017.6 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 111.7313 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 2: 182.4037 .. 223.4626 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 3: 274.5824 .. 315.6413 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 5: 478.4924 .. 519.5513 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 6: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 7: 680.4487 .. 721.5076 cents 128/125, 41.0589 cents 250/243, 49.1661 cents 8: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 9: 884.3587 .. 925.4176 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 10: 976.5374 .. 1017.5963 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 11: 1088.2687 .. 1129.3276 cents 128/125, 41.0589 cents 25/24, 70.6724 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.414979 Largest / Average step : 1.117313 Largest / Smallest step : 1.580974 Median interval of one step : 16/15, 111.7313 cents, amount: 7 Most common interval of one step : 16/15, 111.7313 cents, amount: 7 Least squares average step : 100.43614 cents, oct.: 1205.23369 cents Scale is strictly proper Step pattern alph. order: ABACAABABACA Step pattern size order : LMLSLLMLMLSL Scale is a Constant Structure, by a margin of 49.16614 cents Scale diversity : 1.316122 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.605705 Rothenberg efficiency : 0.415708 redundancy: 0.584292 Efficiency x scale size : 4.988492 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 9 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 9, average 701.9550 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Scale contains a complete diamond : 1 3 15 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 58.3333% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 45 Scale harmonicity : 0.027675 Average absolute harmonicity : 0.193011 Specific harmonicity : 0.168192 Fundamental : 1/720, -9.4919 octaves, 0.3634 Hz. Guide tone : 8640, 13.0768 octaves, 2260444.884 Hz. Exponens Consonantiae : 6.220800E+06, 22.56867 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 142.5, average 11.87500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.39640, average 0.86637 Sum of Tenney's harmonic distance : 20.60339, average 1.71695 Vogel's harmonic complexity : 15.58333 Wille's k value : 607 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 322.18350, average 4.13056 Lattice compactness (without 2's) : 156.00167, average 2.00002 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 6 0.33333 30 1 3: -2 .. 3 0.50000 14 4 5: -1 .. 1 -0.25000 7 7 Average exponent except 2's : 3 / 12 = 0.25000 Average absolute exponent except 2's: 21 / 12 = 1.75000 Scale is JI-epimorphic with val: <12 19 28| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.6343 c. M: 17.5963 c. Twelve-tone Chromatic (1/11-comma) 29: 3 2 3 1 3 3 2 3 2 3 1 3 P SD: 10.6807 c. M:-16.8865 c. 31: 3 2 3 2 3 3 2 3 2 3 2 3 SP M ME SD: 7.6050 c. M: 15.5424 c. 33: 3 3 3 2 3 3 2 3 3 3 2 3 SP D3 SD: 9.3674 c. M:-14.2718 c. 34: 3 3 3 2 3 3 3 3 3 3 2 3 SP D3 S SD: 6.0688 c. M:-11.7821 c. 41: 4 3 4 2 4 4 3 4 3 4 2 4 SP SD: 4.4538 c. M:-6.7940 c. 53: 5 4 5 3 5 5 4 5 4 5 3 5 SP SD: 1.0875 c. M:-1.5445 c. 118: 11 9 11 7 11 11 9 11 9 11 7 11 SP SD: 0.3879 c. M: 0.7803 c. 171: 16 13 16 10 16 16 13 16 13 16 10 16 SP SD: 0.4121 c. M:-0.7500 c. 289: 27 22 27 17 27 27 22 27 22 27 17 27 SP SD: 0.3596 c. M: 0.6747 c. 323: 30 25 30 19 30 30 25 30 25 30 19 30 SP SD: 0.3197 c. M:-0.6365 c. 376: 35 29 35 22 35 35 29 35 29 35 22 35 SP SD: 0.2692 c. M:-0.5180 c. 388: 36 30 36 23 36 36 30 36 30 36 23 36 SP SD: 0.2774 c. M: 0.4979 c. 441: 41 34 41 26 41 41 34 41 34 41 26 41 SP SD: 0.1447 c. M:-0.2574 c. 494: 46 38 46 29 46 46 38 46 38 46 29 46 SP SD: 0.1146 c. M:-0.2175 c. 559: 52 43 52 33 52 52 43 52 43 52 33 52 SP SD: 0.0730 c. M: 0.1162 c. 612: 57 47 57 36 57 57 47 57 47 57 36 57 SP SD: 0.0305 c. M:-0.0508 c. 1171: 109 90 109 69 109 109 90 109 90 109 69 109 SP SD: 0.0227 c. M: 0.0410 c. 1783: 166 137 166 105 166 166 137 166 137 166 105 166 SP SD: 0.0119 c. M:-0.0239 c. 2395: 223 184 223 141 223 223 184 223 184 223 141 223 SP SD: 0.0124 c. M:-0.0238 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: 7.1688 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 12.1926 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.4528 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.3417 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.2740 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.6315 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.3584 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.9765 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 10.4841 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 7.2688 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 9.1045 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 6.8621 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 4.8607 cents 16:17:18:19:20:21:23:24:26:27:29:30:32 SD: 4.0174 cents 24:26:27:29:30:32:34:36:38:41:43:45:48 SD: 3.4904 cents 30:32:34:36:38:40:43:45:48:51:54:56:60 SD: 2.7554 cents 32:34:36:38:40:43:46:48:51:54:58:60:64 SD: 2.7483 cents 39:42:44:47:49:52:55:59:62:66:70:73:78 SD: 2.6927 cents 40:43:45:48:50:53:57:60:64:68:72:75:80 SD: 1.8143 cents 45:48:51:54:56:60:64:68:72:76:81:84:90 SD: 1.7628 cents 48:51:54:58:60:64:68:72:77:81:86:90:96 SD: 1.4911 cents 60:64:68:72:75:80:85:90:96:101:108:113:120 SD: 1.4103 cents 64:68:72:77:80:85:91:96:102:108:115:120:128 SD: 1.0777 cents 80:85:90:96:100:107:114:120:128:135:144:150:160 SD: 0.7751 cents 90:96:101:108:113:120:128:135:144:152:162:169:180 SD: 0.7722 cents 104:111:117:125:130:139:148:156:166:176:187:195:208 SD: 0.7079 cents 105:112:118:126:131:140:149:158:168:177:189:197:210 SD: 0.6661 cents 120:128:135:144:150:160:171:180:192:203:216:225:240 SD: 0.4537 cents 135:144:152:162:169:180:192:203:216:228:243:253:270 SD: 0.4533 cents 176:188:198:211:220:235:250:264:282:297:317:330:352 SD: 0.4301 cents 192:205:216:230:240:256:273:288:307:324:346:360:384 SD: 0.3473 cents 224:239:252:269:280:299:319:336:358:378:403:420:448 SD: 0.3265 cents 225:240:253:270:281:300:320:338:360:380:405:422:450 SD: 0.2882 cents 240:256:270:288:300:320:341:360:384:405:432:450:480 SD: 0.1410 cents 360:384:405:432:450:480:512:540:576:608:648:675:720 SD: 0.1187 cents 480:512:540:576:600:640:683:720:768:810:864:900:960 SD: 0.0704 cents