Scala analysis: xen03-wilson-acute-12
Acute, 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: 28/27 62.960904 Archytas' 1/3-tone 2: 9/8 203.910002 major whole tone 3: 7/6 266.870906 septimal minor third 4: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 5: 4/3 498.044999 perfect fourth 6: 112/81 561.005903 7: 3/2 701.955001 perfect fifth 8: 14/9 764.915905 septimal minor sixth 9: 27/16 905.865003 Pythagorean major sixth 10: 7/4 968.825906 harmonic seventh 11: 35/18 1151.229619 septimal semi-diminished octave 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 243/224 140.9491 Archytas' 2/3-tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 10/9 182.4037 minor whole tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 243/224 140.9491 Archytas' 2/3-tone 8: 28/27 62.9609 Archytas' 1/3-tone 9: 243/224 140.9491 Archytas' 2/3-tone 10: 28/27 62.9609 Archytas' 1/3-tone 11: 10/9 182.4037 minor whole tone 12: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 5 28/27 62.961 cents Archytas' 1/3-tone 1: 3 243/224 140.949 cents Archytas' 2/3-tone 1: 2 10/9 182.404 cents minor whole tone 2: 2 16/15 111.731 cents minor diatonic semitone 2: 6 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 2: 2 280/243 245.365 cents 3: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 3: 3 7/6 266.871 cents septimal minor third 3: 4 32/27 294.135 cents Pythagorean minor third 3: 1 2187/1792 344.859 cents 3: 2 5/4 386.314 cents major third 4: 2 6/5 315.641 cents minor third 4: 2 896/729 357.096 cents 4: 2 81/64 407.820 cents Pythagorean major third 4: 4 9/7 435.084 cents septimal major third, BP third 4: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 5: 1 729/560 456.590 cents 5: 1 21/16 470.781 cents narrow fourth 5: 9 4/3 498.045 cents perfect fourth 5: 1 45/32 590.224 cents diatonic tritone 6: 1 27/20 519.551 cents acute fourth 6: 1 48/35 546.815 cents septimal semi-augmented fourth 6: 4 112/81 561.006 cents 6: 4 81/56 638.994 cents 6: 1 35/24 653.185 cents septimal semi-diminished fifth 6: 1 40/27 680.449 cents grave fifth 7: 1 64/45 609.776 cents 2nd tritone 7: 9 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 7: 1 1120/729 743.410 cents 8: 2 54/35 750.725 cents septimal semi-augmented fifth 8: 4 14/9 764.916 cents septimal minor sixth 8: 2 128/81 792.180 cents Pythagorean minor sixth 8: 2 729/448 842.904 cents 8: 2 5/3 884.359 cents major sixth, BP sixth 9: 2 8/5 813.686 cents minor sixth 9: 1 3584/2187 855.141 cents 9: 4 27/16 905.865 cents Pythagorean major sixth 9: 3 12/7 933.129 cents septimal major sixth 9: 2 140/81 947.320 cents 10: 2 243/140 954.635 cents 10: 2 7/4 968.826 cents harmonic seventh 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 2 15/8 1088.269 cents classic major seventh 11: 2 9/5 1017.596 cents just minor seventh, BP seventh 11: 3 448/243 1059.051 cents 11: 5 27/14 1137.039 cents septimal major seventh 11: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.54545 = 50/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 63.0 203.9 266.9 449.3 498.0 561.0 702.0 764.9 905.9 968.8 1151.2 1200.0 63.0 : 140.9 203.9 386.3 435.1 498.0 639.0 702.0 842.9 905.9 1088.3 1137.0 1200.0 203.9 : 63.0 245.4 294.1 357.1 498.0 561.0 702.0 764.9 947.3 996.1 1059.1 1200.0 266.9 : 182.4 231.2 294.1 435.1 498.0 639.0 702.0 884.4 933.1 996.1 1137.0 1200.0 449.3 : 48.8 111.7 252.7 315.6 456.6 519.6 702.0 750.7 813.7 954.6 1017.6 1200.0 498.0 : 63.0 203.9 266.9 407.8 470.8 653.2 702.0 764.9 905.9 968.8 1151.2 1200.0 561.0 : 140.9 203.9 344.9 407.8 590.2 639.0 702.0 842.9 905.9 1088.3 1137.0 1200.0 702.0 : 63.0 203.9 266.9 449.3 498.0 561.0 702.0 764.9 947.3 996.1 1059.1 1200.0 764.9 : 140.9 203.9 386.3 435.1 498.0 639.0 702.0 884.4 933.1 996.1 1137.0 1200.0 905.9 : 63.0 245.4 294.1 357.1 498.0 561.0 743.4 792.2 855.1 996.1 1059.1 1200.0 968.8 : 182.4 231.2 294.1 435.1 498.0 680.4 729.2 792.2 933.1 996.1 1137.0 1200.0 1151.2: 48.8 111.7 252.7 315.6 498.0 546.8 609.8 750.7 813.7 954.6 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 182.4037 cents 175/162, 133.6333 cents 36/35, 48.7704 cents 2: 111.7313 .. 245.3646 cents 175/162, 133.6333 cents 24/25,-70.6724 cents 3: 252.6804 .. 386.3137 cents 175/162, 133.6333 cents 19683/19600, 7.3158 cents 4: 315.6413 .. 449.2746 cents 175/162, 133.6333 cents 24/25,-70.6724 cents 5: 456.5904 .. 590.2237 cents 175/162, 133.6333 cents 19683/19600, 7.3158 cents 6: 519.5513 .. 680.4487 cents 800/729, 160.8974 cents 24/25,-70.6724 cents 7: 609.7763 .. 743.4096 cents 175/162, 133.6333 cents 24/25,-70.6724 cents 8: 750.7254 .. 884.3587 cents 175/162, 133.6333 cents 19683/19600, 7.3158 cents 9: 813.6863 .. 947.3196 cents 175/162, 133.6333 cents 24/25,-70.6724 cents 10: 954.6354 .. 1088.2687 cents 175/162, 133.6333 cents 19683/19600, 7.3158 cents 11: 1017.5963 .. 1151.2296 cents 175/162, 133.6333 cents 24/25,-70.6724 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 2.050425 Largest / Average step : 1.824037 Largest / Smallest step : 3.740051 Median interval of one step : 28/27, 62.9609 cents, amount: 5 Most common interval of one step : 28/27, 62.9609 cents, amount: 5 Least squares average step : 99.78821 cents, oct.: 1197.45849 cents Scale is not proper Step pattern alph. order: ABACDABABACD Step pattern size order : BCBDABCBCBDA Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.504846 Lumma stability : 0.105670 Lumma impropriety factor : 0.353362 Rothenberg efficiency : 0.394186 redundancy: 0.605814 Efficiency x scale size : 4.730231 Number of different interval sizes : 50 = 4.54545 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.54545 = 50/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 19683/19600, 7.3158 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 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% Scale is differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 7 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 81 Scale harmonicity : 0.023067 Average absolute harmonicity : 0.173075 Specific harmonicity : 0.132639 Fundamental : 1/1296, -10.3399 octaves, 0.2019 Hz. Guide tone : 15120, 13.8842 octaves, 3955778.547 Hz. Exponens Consonantiae : 1.959552E+07, 24.22402 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 242.5, average 20.20833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.41227, average 1.03436 Sum of Tenney's harmonic distance : 24.43295, average 2.03608 Vogel's harmonic complexity : 18.25000 Wille's k value : 1093 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 299.69737, average 3.84227 Lattice compactness (without 2's) : 204.97398, average 2.62787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 -0.16667 22 1 3: -4 .. 3 -0.83333 22 4 5: 0 .. 1 0.16667 2 7: 0 .. 1 0.58333 7 7 Average exponent except 2's :-1 / 12 =-0.08333 Average absolute exponent except 2's: 31 / 12 = 2.58333 Scale is JI-epimorphic with val: <12 19 27 34| Scale is weakly epimorphic with val: <12 19 28 32|
FIT/MODE
12: 1 1 1 2 0 1 1 1 1 1 2 0 N T3 SD: 30.5527 c. M:-50.7254 c. 13: 1 1 1 2 0 1 2 0 2 0 2 1 N SD: 27.6680 c. M: 45.7490 c. 16: 1 2 1 2 1 0 2 1 2 1 2 1 N T3 SD: 21.2531 c. M: 36.0059 c. 17: 1 2 1 2 1 1 2 1 2 1 2 1 P M ME SD: 13.5154 c. M: 25.7452 c. Supra-12 19: 1 2 1 3 1 1 2 1 2 1 3 1 N SD: 12.2727 c. M: 21.6545 c. 22: 1 3 1 3 1 1 3 1 3 1 3 1 N M DE SD: 11.1103 c. M:-21.4077 c. Supra-12 24: 1 3 1 4 1 1 3 1 3 1 4 1 N SD: 10.0416 c. M: 18.8259 c. 27: 1 4 1 4 1 2 3 1 3 2 4 1 N SD: 11.6375 c. M: 18.5165 c. 32: 2 3 2 5 1 2 4 1 4 2 5 1 N SD: 9.4891 c. M: 16.4100 c. 36: 2 4 2 5 2 2 4 2 4 2 6 1 N SD: 7.0905 c. M: 15.9413 c. 38: 2 4 2 6 2 2 4 2 5 2 5 2 N SD: 9.4826 c. M: 14.4363 c. 41: 2 5 2 6 2 2 5 2 5 2 6 2 N SD: 4.8643 c. M: 10.2502 c. 45: 2 6 2 7 2 2 5 3 5 2 7 2 N SD: 6.5695 c. M: 9.6276 c. 53: 3 6 3 8 2 3 6 3 6 3 8 2 N SD: 3.4731 c. M:-5.0318 c. 72: 4 8 4 11 3 4 8 4 8 4 11 3 N SD: 3.0675 c. M: 5.8650 c. 77: 4 9 4 12 3 4 9 4 9 4 12 3 N SD: 1.5856 c. M:-2.6734 c. 94: 5 11 5 14 4 5 11 5 11 5 14 4 N SD: 1.2080 c. M: 2.4661 c. 152: 8 18 8 23 6 8 18 8 18 8 23 6 N SD: 1.2163 c. M:-2.2267 c. 171: 9 20 9 26 7 9 20 9 20 9 26 7 N SD: 0.3100 c. M: 0.6018 c. 400: 21 47 21 61 16 21 47 21 47 21 61 16 N SD: 0.3170 c. M:-0.7704 c. 441: 23 52 23 67 18 23 52 23 52 23 67 18 N SD: 0.2476 c. M: 0.4617 c. 494: 26 58 26 75 20 26 58 26 58 26 75 20 N SD: 0.2089 c. M:-0.4049 c. 571: 30 67 30 87 23 30 67 30 67 30 87 23 N SD: 0.1914 c. M:-0.4627 c. 612: 32 72 32 93 25 32 72 32 72 32 93 25 N SD: 0.1704 c. M: 0.2550 c. 665: 35 78 35 101 27 35 78 35 78 35 101 27 N SD: 0.1286 c. M:-0.1971 c. 836: 44 98 44 127 34 44 98 44 98 44 127 34 N SD: 0.1172 c. M:-0.2381 c. 935: 49 110 49 142 38 49 110 49 110 49 142 38 N SD: 0.1135 c. M:-0.2313 c. 1012: 53 119 53 154 41 53 119 53 119 53 154 41 N SD: 0.0897 c. M:-0.1538 c. 1106: 58 130 58 168 45 58 130 58 130 58 168 45 N SD: 0.0577 c. M:-0.1024 c. 1183: 62 139 62 180 48 62 139 62 139 62 180 48 N SD: 0.0648 c. M: 0.1023 c. 1277: 67 150 67 194 52 67 150 67 150 67 194 52 N SD: 0.0392 c. M: 0.0969 c. 1848: 97 217 97 281 75 97 217 97 217 97 281 75 N SD: 0.0337 c. M:-0.0760 c. 1942: 102 228 102 295 79 102 228 102 228 102 295 79 N SD: 0.0482 c. M:-0.0721 c. 2019: 106 237 106 307 82 106 237 106 237 106 307 82 N SD: 0.0403 c. M: 0.0701 c. 2289: 120 269 120 348 93 120 269 120 269 120 348 93 N SD: 0.0308 c. M: 0.0623 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: 15.7402 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 17.4335 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 13.8932 cents 7 x 8 x 9 x 10 x 11:12 x x 14 S SD: 12.0037 cents 8 x 9 x 10 x 11:12 x x 14 x 16 S SD: 10.6170 cents 9 x 10:11 x 12 x x 14:15:16 x 18 S SD: 12.9004 cents 10 x 11:12:13 x 14:15:16:17:18:19:20 S SD: 10.4412 cents 11 x 12:13:14 x 15 x 17 x 19:21:22 SD: 10.1345 cents 12 x x 14 x 16:17:18:19:20:21:23:24 SD: 6.8363 cents 13:14 x 15:17 x 18 x 20:22:23:25:26 SD: 8.5954 cents 14:15:16 x 18:19 x 21:22:24:25:27:28 SD: 8.6895 cents 15:16:17:18:19:20:21 x 23:25:26:29:30 SD: 8.3524 cents 16:17:18:19:21 x 22:24:25:27:28:31:32 SD: 5.2670 cents 17:18:19:20:22:23:24 x 26:29:30:33:34 SD: 6.4336 cents 18:19:20:21:23:24:25:27:28:30:32:35:36 SD: 4.7779 cents 19:20:21:22 x 25:26:29:30:32:33:37:38 SD: 6.0234 cents 20:21 x 23:26:27:28:30:31:34:35:39:40 SD: 4.3203 cents 22:23:25:26 x 29:30:33:34:37:39:43:44 SD: 4.7312 cents 23:24:26:27:30:31:32:35:36:39:40:45:46 SD: 3.6476 cents 24:25:27:28:31:32:33:36:37:41:42:47:48 SD: 2.6820 cents 34:35:38:40:44:45:47:51:53:57:60:66:68 SD: 2.6801 cents 36:37:41:42:47:48:50:54:56:61:63:70:72 SD: 2.5741 cents 42:44:47:49:54:56:58:63:65:71:74:82:84 SD: 2.4647 cents 47:49:53:55:61:63:65:71:73:79:82:91:94 SD: 1.8693 cents 48:50:54:56:62:64:66:72:75:81:84:93:96 SD: 1.4180 cents 54:56:61:63:70:72:75:81:84:91:95:105:108 SD: 1.1759 cents 78:81:88:91:101:104:108:117:121:132:137:152:156 SD: 0.9882 cents 84:87:95:98:109:112:116:126:131:142:147:163:168 SD: 0.9776 cents 96:100:108:112:124:128:133:144:149:162:168:187:192 SD: 0.9638 cents 102:106:115:119:132:136:141:153:159:172:179:198:204 SD: 0.7583 cents 108:112:122:126:140:144:149:162:168:182:189:210:216 SD: 0.7030 cents 112:116:126:131:145:149:155:168:174:189:196:218:224 SD: 0.6151 cents 128:133:144:149:166:171:177:192:199:216:224:249:256 SD: 0.5266 cents 138:143:155:161:179:184:191:207:215:233:242:268:276 SD: 0.5211 cents 144:149:162:168:187:192:199:216:224:243:252:280:288 SD: 0.4203 cents 162:168:182:189:210:216:224:243:252:273:284:315:324 SD: 0.3782 cents 192:199:216:224:249:256:265:288:299:324:336:373:384 SD: 0.3489 cents 216:224:243:252:280:288:299:324:336:365:378:420:432 SD: 0.2550 cents 240:249:270:280:311:320:332:360:373:405:420:467:480 SD: 0.1954 cents 378:392:425:441:490:504:523:567:588:638:662:735:756 SD: 0.1683 cents 384:398:432:448:498:512:531:576:597:648:672:747:768 SD: 0.1462 cents 432:448:486:504:560:576:597:648:672:729:756:840:864 SD: 0.0805 cents