Scala analysis: coherent_shrutis-schismaticTranp
complementing 11 shrutis: 96/95 transposition of coherent_shrutis.scl
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: 108/95 222.038273 3: 6/5 315.641287 minor third 4: 24/19 404.441985 smaller undevicesimal major third 5: 128/95 516.173270 6: 27/19 608.351986 7: 144/95 720.083272 8: 8/5 813.686286 minor sixth 9: 32/19 902.486984 19th subharmonic 10: 512/285 1014.218269 11: 36/19 1106.396986 smaller undevicesimal major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 19/18 93.6030 undevicesimal semitone 1: 16/15 111.7313 minor diatonic semitone 2: 81/76 110.3070 3: 19/18 93.6030 undevicesimal semitone 4: 20/19 88.8007 small undevicesimal semitone 5: 16/15 111.7313 minor diatonic semitone 6: 135/128 92.1787 major chroma, major limma 7: 16/15 111.7313 minor diatonic semitone 8: 19/18 93.6030 undevicesimal semitone 9: 20/19 88.8007 small undevicesimal semitone 10: 16/15 111.7313 minor diatonic semitone 11: 135/128 92.1787 major chroma, major limma 12: 19/18 93.6030 undevicesimal semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 20/19 88.801 cents small undevicesimal semitone 1: 2 135/128 92.179 cents major chroma, major limma 1: 3 19/18 93.603 cents undevicesimal semitone 1: 1 81/76 110.307 cents 1: 4 16/15 111.731 cents minor diatonic semitone 2: 2 10/9 182.404 cents minor whole tone 2: 1 285/256 185.782 cents 2: 2 64/57 200.532 cents 2: 4 9/8 203.910 cents major whole tone 2: 2 152/135 205.334 cents 2: 1 108/95 222.038 cents 3: 3 45/38 292.711 cents 3: 3 32/27 294.135 cents Pythagorean minor third 3: 3 19/16 297.513 cents 19th harmonic 3: 3 6/5 315.641 cents minor third 4: 4 5/4 386.314 cents major third 4: 3 24/19 404.442 cents smaller undevicesimal major third 4: 1 512/405 405.866 cents narrow diminished fourth 4: 1 81/64 407.820 cents Pythagorean major third 4: 3 19/15 409.244 cents undevicesimal ditone 5: 1 95/72 479.917 cents 5: 1 405/304 496.621 cents 5: 7 4/3 498.045 cents perfect fourth 5: 1 171/128 501.423 cents 5: 1 128/95 516.173 cents 5: 1 27/20 519.551 cents acute fourth 6: 1 80/57 586.846 cents 6: 2 45/32 590.224 cents diatonic tritone 6: 3 38/27 591.648 cents 6: 3 27/19 608.352 cents 6: 2 64/45 609.776 cents 2nd tritone 6: 1 57/40 613.154 cents 7: 1 40/27 680.449 cents grave fifth 7: 1 95/64 683.827 cents 7: 1 256/171 698.577 cents 7: 7 3/2 701.955 cents perfect fifth 7: 1 608/405 703.379 cents 7: 1 144/95 720.083 cents 8: 3 30/19 790.756 cents smaller undevicesimal minor sixth 8: 1 128/81 792.180 cents Pythagorean minor sixth 8: 1 405/256 794.134 cents wide augmented fifth 8: 3 19/12 795.558 cents undevicesimal minor sixth 8: 4 8/5 813.686 cents minor sixth 9: 3 5/3 884.359 cents major sixth, BP sixth 9: 3 32/19 902.487 cents 19th subharmonic 9: 3 27/16 905.865 cents Pythagorean major sixth 9: 3 76/45 907.289 cents 10: 1 95/54 977.962 cents 10: 2 135/76 994.666 cents 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 2 57/32 999.468 cents undevicesimal minor seventh 10: 1 512/285 1014.218 cents 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 11: 4 15/8 1088.269 cents classic major seventh 11: 1 152/81 1089.693 cents 11: 3 36/19 1106.397 cents smaller undevicesimal major seventh 11: 2 256/135 1107.821 cents octave - major chroma 11: 2 19/10 1111.199 cents undevicesimal major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.27273 = 58/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 222.0 315.6 404.4 516.2 608.4 720.1 813.7 902.5 1014.2 1106.4 1200.0 111.7 : 110.3 203.9 292.7 404.4 496.6 608.4 702.0 790.8 902.5 994.7 1088.3 1200.0 222.0 : 93.6 182.4 294.1 386.3 498.0 591.6 680.4 792.2 884.4 978.0 1089.7 1200.0 315.6 : 88.8 200.5 292.7 404.4 498.0 586.8 698.6 790.8 884.4 996.1 1106.4 1200.0 404.4 : 111.7 203.9 315.6 409.2 498.0 609.8 702.0 795.6 907.3 1017.6 1111.2 1200.0 516.2 : 92.2 203.9 297.5 386.3 498.0 590.2 683.8 795.6 905.9 999.5 1088.3 1200.0 608.4 : 111.7 205.3 294.1 405.9 498.0 591.6 703.4 813.7 907.3 996.1 1107.8 1200.0 720.1 : 93.6 182.4 294.1 386.3 479.9 591.6 702.0 795.6 884.4 996.1 1088.3 1200.0 813.7 : 88.8 200.5 292.7 386.3 498.0 608.4 702.0 790.8 902.5 994.7 1106.4 1200.0 902.5 : 111.7 203.9 297.5 409.2 519.6 613.2 702.0 813.7 905.9 1017.6 1111.2 1200.0 1014.2: 92.2 185.8 297.5 407.8 501.4 590.2 702.0 794.1 905.9 999.5 1088.3 1200.0 1106.4: 93.6 205.3 315.6 409.2 498.0 609.8 702.0 813.7 907.3 996.1 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 111.7313 cents 76/75, 22.9306 cents 20/19, 88.8007 cents 2: 182.4037 .. 222.0383 cents 486/475, 39.6346 cents 25/24, 70.6724 cents 3: 292.7107 .. 315.6413 cents 76/75, 22.9306 cents 25/24, 70.6724 cents 4: 386.3137 .. 409.2443 cents 76/75, 22.9306 cents 25/24, 70.6724 cents 5: 479.9167 .. 519.5513 cents 486/475, 39.6346 cents 25/24, 70.6724 cents 6: 586.8457 .. 613.1543 cents 3249/3200, 26.3086 cents 1600/1539, 67.2944 cents 7: 680.4487 .. 720.0833 cents 486/475, 39.6346 cents 1600/1539, 67.2944 cents 8: 790.7557 .. 813.6863 cents 76/75, 22.9306 cents 25/24, 70.6724 cents 9: 884.3587 .. 907.2893 cents 76/75, 22.9306 cents 25/24, 70.6724 cents 10: 977.9617 .. 1017.5963 cents 486/475, 39.6346 cents 25/24, 70.6724 cents 11: 1088.2687 .. 1111.1993 cents 76/75, 22.9306 cents 25/24, 70.6724 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 20/19, 88.8007 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.126117 Largest / Average step : 1.117313 Largest / Smallest step : 1.258225 Median interval of one step : 19/18, 93.6030 cents, amount: 3 Most common interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 101.13305 cents, oct.: 1213.59662 cents Scale is strictly proper Step pattern alph. order: ABCDAEACDAEC Step pattern size order : EDCAEBECAEBC Scale is a Constant Structure, by a margin of 67.29441 cents Scale diversity : 1.221983 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.731308 Rothenberg efficiency : 0.291919 redundancy: 0.708081 Efficiency x scale size : 3.503030 Number of different interval sizes : 58 = 5.27273 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.27273 = 58/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1216/1215, 1.4243 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 9, average 701.7379 cents Best fifths form a closed circle Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 8.3333% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 19 Odd number limit : 405 (O: 405 U: 405) Highest odd numerator or denominator: 285 Scale harmonicity : 0.016619 Average absolute harmonicity : 0.121744 Specific harmonicity : 0.076946 Fundamental : 1/285, -8.1548 octaves, 0.9180 Hz. Guide tone : 13824, 13.7549 octaves, 3616711.815 Hz. Exponens Consonantiae : 3.939840E+06, 21.90971 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 857.5, average 71.45833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 16.22967, average 1.35247 Sum of Tenney's harmonic distance : 34.14475, average 2.84540 Vogel's harmonic complexity : 17.33333 Wille's k value : 202 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 303.10037, average 3.88590 Lattice compactness (without 2's) : 154.52572, average 1.98110 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 9 3.41667 41 1 3: -1 .. 3 0.83333 14 5: -1 .. 0 -0.58333 7 3 19: -1 .. 0 -0.66667 8 8 Average exponent except 2's :-5 / 12 =-0.41667 Average absolute exponent except 2's: 29 / 12 = 2.41667 Scale is JI-epimorphic with val: <12 19 28 51| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.0988 c. M: 22.0383 c. Twelve-tone Chromatic (1/11-comma) 25: 2 3 2 1 3 2 2 2 2 2 2 2 P D3 SD: 12.6736 c. M: 20.4420 c. 27: 3 2 2 2 3 2 2 2 2 3 2 2 SP D3 SD: 11.3019 c. M:-21.6020 c. 28: 3 2 2 2 3 2 3 2 2 3 2 2 SP D3 SD: 10.6428 c. M: 18.7277 c. 30: 3 3 2 2 3 2 3 2 3 2 3 2 SP D3 SD: 10.7833 c. M:-17.9617 c. 32: 3 3 2 3 3 2 3 3 2 3 3 2 SP B ME S SD: 9.1621 c. M:-18.6030 c. Diminished-12 33: 3 3 3 2 3 3 3 2 3 3 2 3 SP D3 SD: 8.4747 c. M: 15.4879 c. 37: 3 4 3 2 4 3 3 3 3 3 3 3 SP D3 SD: 8.0880 c. M: 15.2528 c. 38: 4 3 3 3 3 3 4 3 3 3 3 3 SP B ME SD: 7.7701 c. M:-14.5845 c. 39: 4 3 3 3 4 3 3 3 3 4 3 3 SP D3 SD: 8.1677 c. M: 13.6863 c. 42: 4 4 3 3 4 3 4 3 4 3 4 3 SP D3 SD: 8.0032 c. M: 14.2183 c. 44: 4 4 4 3 4 3 4 4 3 4 4 3 SP D3 SD: 6.8613 c. M:-11.7848 c. 45: 4 4 4 3 4 4 4 3 4 4 3 4 SP D3 SD: 7.2548 c. M: 13.6863 c. 47: 4 5 3 4 4 4 4 4 3 5 3 4 SP D3 SD: 6.7323 c. M: 9.6036 c. 49: 4 5 4 3 5 4 4 4 4 4 4 4 SP D3 SD: 7.3053 c. M: 13.7721 c. 50: 5 4 4 4 5 3 5 4 4 4 4 4 SP D3 SD: 6.3288 c. M:-11.8267 c. 52: 5 5 4 4 4 4 5 4 4 5 4 4 SP D3 SD: 6.2817 c. M:-10.9426 c. 53: 5 5 4 4 5 4 5 4 4 5 4 4 SP D3 SD: 3.2305 c. M:-4.6497 c. 65: 6 6 5 5 6 5 6 5 5 6 5 5 SP D3 SD: 1.2295 c. M:-2.1284 c. 193: 18 18 15 14 18 15 18 15 14 18 15 15 SP SD: 0.9127 c. M:-1.7959 c. 205: 19 19 16 15 19 16 19 16 15 19 16 16 SP SD: 0.6847 c. M: 1.5353 c. 258: 24 24 20 19 24 20 24 20 19 24 20 20 SP SD: 0.5830 c. M:-1.2175 c. 270: 25 25 21 20 25 21 25 21 20 25 21 21 SP SD: 0.4236 c. M: 0.8849 c. 335: 31 31 26 25 31 26 31 26 25 31 26 26 SP SD: 0.4139 c. M: 0.6865 c. 460: 43 42 36 34 43 35 43 36 34 43 35 36 SP SD: 0.3136 c. M:-0.5643 c. 525: 49 48 41 39 49 40 49 41 39 49 40 41 SP SD: 0.3010 c. M:-0.6389 c. 600: 56 55 47 44 56 46 56 47 44 56 46 47 SP SD: 0.3027 c. M: 0.4870 c. 653: 61 60 51 48 61 50 61 51 48 61 50 51 SP SD: 0.2628 c. M:-0.4383 c. 665: 62 61 52 49 62 51 62 52 49 62 51 52 SP SD: 0.1602 c. M: 0.2317 c. 718: 67 66 56 53 67 55 67 56 53 67 55 56 SP SD: 0.1911 c. M:-0.2664 c. 730: 68 67 57 54 68 56 68 57 54 68 56 57 SP SD: 0.0684 c. M: 0.1328 c. 1718: 160 158 134 127 160 132 160 134 127 160 132 134 SP SD: 0.0427 c. M:-0.0805 c. 1783: 166 164 139 132 166 137 166 139 132 166 137 139 SP SD: 0.0389 c. M:-0.0608 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: 9.0641 cents 3 x x x x 4 x x x 5 x x 6 S SD: 8.5457 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 13.0330 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.2119 cents 6 x 7 x x 8 x 9 x 10:11 x 12 S SD: 10.8410 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.2820 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.1264 cents 9 x 10:11 x 12:13:14 x 15:16:17:18 S SD: 8.8913 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 8.1284 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 8.9043 cents 12:13:14 x 15:16:17:18:19:20:22:23:24 S SD: 7.0619 cents 13:14:15:16 x x 18:20:21:22:23:25:26 SD: 8.5111 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 5.9101 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 4.1270 cents 26:28:30:31:33:35:37:39:42:44:47:49:52 SD: 3.7364 cents 28:30:32:34:35:38:40:42:45:47:50:53:56 SD: 3.4000 cents 29:31:33:35:37:39:41:44:46:49:52:55:58 SD: 2.3223 cents 35:37:40:42:44:47:50:53:56:59:63:66:70 SD: 2.0328 cents 45:48:51:54:57:61:64:68:72:76:81:85:90 SD: 1.3320 cents 60:64:68:72:76:81:85:91:96:101:108:114:120 SD: 0.9430 cents 95:101:108:114:120:128:135:144:152:160:171:180:190 SD: 0.5525 cents 152:162:173:182:192:205:216:230:243:256:273:288:304 SD: 0.4902 cents 161:172:183:193:203:217:229:244:258:271:289:305:322 SD: 0.4834 cents 167:178:190:200:211:225:237:253:267:281:300:316:334 SD: 0.4674 cents 181:193:206:217:229:244:257:274:290:305:325:343:362 SD: 0.4544 cents 190:203:216:228:240:256:270:288:304:320:341:360:380 SD: 0.2758 cents 225:240:256:270:284:303:320:341:360:379:404:426:450 SD: 0.2515 cents 240:256:273:288:303:323:341:364:384:404:431:455:480 SD: 0.2501 cents 270:288:307:324:341:364:384:409:432:455:485:512:540 SD: 0.2282 cents 285:304:324:342:360:384:405:432:456:480:512:540:570 SD: 0.0000 cents