Scala analysis: tamil_vi
Vilarippalai scale in Tamil music, Vidyasankar Sundaresan
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 10/9 182.403712 minor whole tone 3: 32/27 294.134997 Pythagorean minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 45/32 590.223716 diatonic tritone 7: 40/27 680.448711 grave fifth 8: 128/81 792.179997 Pythagorean minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 16/9 996.089998 Pythagorean minor 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: 256/243 90.2250 limma, Pythagorean minor second 2: 135/128 92.1787 major chroma, major limma 3: 16/15 111.7313 minor diatonic semitone 4: 135/128 92.1787 major chroma, major limma 5: 16/15 111.7313 minor diatonic semitone 6: 135/128 92.1787 major chroma, major limma 7: 256/243 90.2250 limma, Pythagorean minor second 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: 135/128 92.1787 major chroma, major limma 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 5 135/128 92.179 cents major chroma, major limma 1: 5 16/15 111.731 cents minor diatonic semitone 2: 2 10/9 182.404 cents minor whole tone 2: 2 4096/3645 201.956 cents narrow diminished third 2: 8 9/8 203.910 cents major whole tone 3: 6 32/27 294.135 cents Pythagorean minor third 3: 3 1215/1024 296.089 cents wide augmented second 3: 3 6/5 315.641 cents minor third 4: 4 5/4 386.314 cents major third 4: 4 512/405 405.866 cents narrow diminished fourth 4: 4 81/64 407.820 cents Pythagorean major third 5: 10 4/3 498.045 cents perfect fourth 5: 1 10935/8192 499.999 cents fourth + schisma, 5-limit approximation to ET fourth 5: 1 27/20 519.551 cents acute fourth 6: 6 45/32 590.224 cents diatonic tritone 6: 6 64/45 609.776 cents 2nd tritone 7: 1 40/27 680.449 cents grave fifth 7: 1 16384/10935 700.001 cents fifth - schisma, 5-limit approximation to ET fifth 7: 10 3/2 701.955 cents perfect fifth 8: 4 128/81 792.180 cents Pythagorean minor sixth 8: 4 405/256 794.134 cents wide augmented fifth 8: 4 8/5 813.686 cents minor sixth 9: 3 5/3 884.359 cents major sixth, BP sixth 9: 3 2048/1215 903.911 cents narrow diminished seventh 9: 6 27/16 905.865 cents Pythagorean major sixth 10: 8 16/9 996.090 cents Pythagorean minor seventh 10: 2 3645/2048 998.044 cents wide augmented sixth 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 11: 5 15/8 1088.269 cents classic major seventh 11: 5 256/135 1107.821 cents octave - major chroma 11: 2 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.90909 = 32/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 90.2 182.4 294.1 386.3 498.0 590.2 680.4 792.2 884.4 996.1 1088.3 1200.0 90.2 : 92.2 203.9 296.1 407.8 500.0 590.2 702.0 794.1 905.9 998.0 1109.8 1200.0 182.4 : 111.7 203.9 315.6 407.8 498.0 609.8 702.0 813.7 905.9 1017.6 1107.8 1200.0 294.1 : 92.2 203.9 296.1 386.3 498.0 590.2 702.0 794.1 905.9 996.1 1088.3 1200.0 386.3 : 111.7 203.9 294.1 405.9 498.0 609.8 702.0 813.7 903.9 996.1 1107.8 1200.0 498.0 : 92.2 182.4 294.1 386.3 498.0 590.2 702.0 792.2 884.4 996.1 1088.3 1200.0 590.2 : 90.2 202.0 294.1 405.9 498.0 609.8 700.0 792.2 903.9 996.1 1107.8 1200.0 680.4 : 111.7 203.9 315.6 407.8 519.6 609.8 702.0 813.7 905.9 1017.6 1109.8 1200.0 792.2 : 92.2 203.9 296.1 407.8 498.0 590.2 702.0 794.1 905.9 998.0 1088.3 1200.0 884.4 : 111.7 203.9 315.6 405.9 498.0 609.8 702.0 813.7 905.9 996.1 1107.8 1200.0 996.1 : 92.2 203.9 294.1 386.3 498.0 590.2 702.0 794.1 884.4 996.1 1088.3 1200.0 1088.3: 111.7 202.0 294.1 405.9 498.0 609.8 702.0 792.2 903.9 996.1 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 111.7313 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 2: 182.4037 .. 203.9100 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 3: 294.1350 .. 315.6413 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 4: 386.3137 .. 407.8200 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 5: 498.0450 .. 519.5513 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 6: 590.2237 .. 609.7763 cents 2048/2025, 19.5526 cents 25/24, 70.6724 cents 7: 680.4487 .. 701.9550 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 8: 792.1800 .. 813.6863 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 9: 884.3587 .. 905.8650 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 10: 996.0900 .. 1017.5963 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 11: 1088.2687 .. 1109.7750 cents 81/80, 21.5063 cents 25/24, 70.6724 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.108340 Largest / Average step : 1.117313 Largest / Smallest step : 1.238363 Median interval of one step : 135/128, 92.1787 cents, amount: 5 Least squares average step : 98.93219 cents, oct.: 1187.18630 cents Scale is strictly proper Scale is 3-distributional even Step pattern alph. order: ABCBCBACBCBC Step pattern size order : SMLMLMSLMLML Scale is a Constant Structure, by a margin of 70.67243 cents Scale diversity : 1.148093 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.804487 Rothenberg efficiency : 0.514153 redundancy: 0.485847 Efficiency x scale size : 6.169841 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.90909 = 32/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 10 Most common triad is 0.0 498.045 701.955 cents, amount: 8 Number of recognisable fifths : 11, average 701.7774 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties -- Prime limit : 5 Odd number limit : 10935 (O: 10935 U: 10935) Highest odd numerator or denominator: 243 Scale harmonicity : 0.026270 Average absolute harmonicity : 0.167484 Specific harmonicity : 0.151596 Fundamental : 1/7776, -12.9248 octaves, 0.0336 Hz. Guide tone : 11520, 13.4919 octaves, 3013926.512 Hz. Exponens Consonantiae : 8.957952E+07, 26.41667 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 502.5, average 41.87500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.76967, average 1.14747 Sum of Tenney's harmonic distance : 27.98696, average 2.33225 Vogel's harmonic complexity : 19.75000 Wille's k value : 5467 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 8 Triangular lattice diameter : 8 Lattice compactness : 408.73333, average 5.24017 Lattice compactness (without 2's) : 199.66483, average 2.55981 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 8 1.75000 41 1 3: -5 .. 2 -1.50000 24 5 5: 0 .. 1 0.50000 6 6 Average exponent except 2's :-12 / 12 =-1.00000 Average absolute exponent except 2's: 30 / 12 = 2.50000 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: 11.4282 c. M:-19.5513 c. Twelve-tone Chromatic (1/11-comma) 26: 2 2 2 2 3 2 2 2 2 3 2 2 SP D3 S SD: 12.2088 c. M:-19.4236 c. 28: 2 2 3 2 3 2 2 2 3 2 2 3 SP D3 SD: 11.6517 c. M: 20.7514 c. 29: 2 2 3 2 3 2 2 3 2 3 2 3 SP M ME SD: 10.9879 c. M: 18.3797 c. 30: 2 3 2 3 2 3 2 3 2 3 2 3 SP B ME SD: 10.7490 c. M: 18.0450 c. 32: 2 3 3 2 3 3 2 3 3 3 2 3 SP D3 SD: 9.9711 c. M:-16.4100 c. 34: 2 3 3 3 3 3 2 3 3 3 3 3 SP B ME SD: 9.6534 c. M: 19.6368 c. 35: 3 2 4 2 4 2 3 3 3 3 3 3 SP D3 SD: 9.4132 c. M:-16.2407 c. 37: 3 3 3 3 3 3 3 3 3 4 3 3 SP M ME SD: 8.8901 c. M:-14.4340 c. 39: 3 3 4 3 3 3 3 4 3 3 3 4 SP D3 SD: 8.3759 c. M:-13.6863 c. 41: 3 3 4 3 4 3 3 4 3 4 3 4 SP M ME SD: 4.4526 c. M: 7.2780 c. 53: 4 4 5 4 5 4 4 5 4 5 4 5 SP M ME SD: 0.9859 c. M: 1.5445 c. 118: 9 9 11 9 11 9 9 11 9 11 9 11 SP M DE SD: 0.6646 c. M:-1.3004 c. 171: 13 13 16 13 16 13 13 16 13 16 13 16 SP M DE SD: 0.5235 c. M:-1.0031 c. 224: 17 17 21 17 21 17 17 21 17 21 17 21 SP M DE SD: 0.5529 c. M: 0.9380 c. 323: 24 25 30 25 30 25 24 30 25 30 25 30 SP D3 SD: 0.5224 c. M: 1.0609 c. 335: 25 26 31 26 31 26 25 31 26 31 26 31 SP D3 SD: 0.4763 c. M:-0.8211 c. 376: 28 29 35 29 35 29 28 35 29 35 29 35 SP D3 SD: 0.4544 c. M: 0.8633 c. 388: 29 30 36 30 36 30 29 36 30 36 30 36 SP D3 SD: 0.3092 c. M: 0.5343 c. 441: 33 34 41 34 41 34 33 41 34 41 34 41 SP D3 SD: 0.2126 c. M: 0.4291 c. 494: 37 38 46 38 46 38 37 46 38 46 38 46 SP D3 SD: 0.1883 c. M: 0.3465 c. 506: 38 39 47 39 47 39 38 47 39 47 39 47 SP D3 SD: 0.1755 c. M:-0.2901 c. 559: 42 43 52 43 52 43 42 52 43 52 43 52 SP D3 SD: 0.0673 c. M:-0.1162 c. 612: 46 47 57 47 57 47 46 57 47 57 47 57 SP D3 SD: 0.0330 c. M: 0.0566 c. 1171: 88 90 109 90 109 90 88 109 90 109 90 109 SP D3 SD: 0.0259 c. M: 0.0457 c. 1783: 134 137 166 137 166 137 134 166 137 166 137 166 SP D3 SD: 0.0197 c. M: 0.0399 c. 1901: 143 146 177 146 177 146 143 177 146 177 146 177 SP D3 SD: 0.0234 c. M:-0.0433 c. 2395: 180 184 223 184 223 184 180 223 184 223 184 223 SP D3 SD: 0.0203 c. M: 0.0371 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: 10.7531 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: 8.6813 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.6080 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.6915 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.9735 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.9296 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 7.3210 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.6384 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 9.7522 cents 12 x 13:14:15:16:17:18:19:20:21:23:24 SD: 6.7376 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 8.9359 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.5665 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.2526 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.0099 cents 27:28:30:32:34:36:38:40:43:45:48:51:54 SD: 2.9502 cents 33:35:37:39:41:44:46:49:52:55:59:62:66 SD: 2.4942 cents 36:38:40:43:45:48:51:53:57:60:64:68:72 SD: 2.1224 cents 39:41:43:46:49:52:55:58:62:65:69:73:78 SD: 2.0318 cents 48:51:53:57:60:64:68:71:76:80:85:90:96 SD: 1.9967 cents 52:55:58:62:65:69:73:77:82:87:92:98:104 SD: 1.8327 cents 54:57:60:64:68:72:76:80:85:90:96:101:108 SD: 1.2935 cents 69:73:77:82:86:92:97:102:109:115:123:129:138 SD: 1.2352 cents 71:75:79:84:89:95:100:105:112:118:126:133:142 SD: 1.0523 cents 72:76:80:85:90:96:101:107:114:120:128:135:144 SD: 0.8984 cents 81:85:90:96:101:108:114:120:128:135:144:152:162 SD: 0.6886 cents 108:114:120:128:135:144:152:160:171:180:192:203:216 SD: 0.5470 cents 135:142:150:160:169:180:190:200:213:225:240:253:270 SD: 0.4081 cents 189:199:210:224:236:252:266:280:299:315:336:354:378 SD: 0.3052 cents 207:218:230:245:259:276:291:307:327:345:368:388:414 SD: 0.3026 cents 243:256:270:288:304:324:342:360:384:405:432:456:486 SD: 0.2056 cents 297:313:330:352:371:396:418:440:469:495:528:557:594 SD: 0.1942 cents 351:370:390:416:439:468:494:520:555:585:624:658:702 SD: 0.1914 cents 360:379:400:427:450:480:506:533:569:600:640:675:720 SD: 0.1909 cents 372:392:413:441:465:496:523:551:588:620:661:698:744 SD: 0.1885 cents 396:417:440:469:495:528:557:587:626:660:704:743:792 SD: 0.1856 cents 432:455:480:512:540:576:608:640:683:720:768:810:864 SD: 0.1424 cents 504:531:560:597:630:672:709:747:796:840:896:945:1008 SD: 0.1407 cents 519:547:577:615:649:692:730:769:820:865:923:973:1038 SD: 0.1403 cents 540:569:600:640:675:720:759:800:853:900:960:1013:1080 SD: 0.1188 cents 567:597:630:672:709:756:797:840:896:945:1008:1063:1134 SD: 0.1150 cents 576:607:640:683:720:768:810:853:910:960:1024:1080:1152 SD: 0.1064 cents 600:632:667:711:750:800:844:889:948:1000:1067:1125:1200 SD: 0.1044 cents