Scala analysis: xen10-wilson-purvi-11b-03
Purvi modulation 3 from Figure 11b, Archytas (5/4 36/35 28/27), (36/35 28/27 5/4)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 16/15 111.731285 minor diatonic semitone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 54/35 750.725382 septimal semi-augmented fifth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 5/4 386.3137 major third 4: 9/8 203.9100 major whole tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 280/243 245.3646 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 280/243 245.365 cents 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 45/32 590.224 cents diatonic tritone 3: 1 6/5 315.641 cents minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 3: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 64/45 609.776 cents 2nd tritone 5: 2 54/35 750.725 cents septimal semi-augmented fifth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 140/81 947.320 cents 5: 1 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 243/140 954.635 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/14 1137.039 cents septimal major seventh 6: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 48.8 111.7 498.0 702.0 750.7 996.1 1200.0 48.8 : 63.0 449.3 653.2 702.0 947.3 1151.2 1200.0 111.7 : 386.3 590.2 639.0 884.4 1088.3 1137.0 1200.0 498.0 : 203.9 252.7 498.0 702.0 750.7 813.7 1200.0 702.0 : 48.8 294.1 498.0 546.8 609.8 996.1 1200.0 750.7 : 245.4 449.3 498.0 561.0 947.3 1151.2 1200.0 996.1 : 203.9 252.7 315.6 702.0 905.9 954.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 590.2237 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 162.17396 cents, oct.: 1135.21774 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : ABECADC Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.594117 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 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: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents 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 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 35 Scale harmonicity : 0.028556 Average absolute harmonicity : 0.250178 Specific harmonicity : 0.149615 Fundamental : 1/630, -9.2992 octaves, 0.4153 Hz. Guide tone : 432, 8.7549 octaves, 113022.244 Hz. Exponens Consonantiae : 2.721600E+05, 18.05410 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 115.5, average 16.50000 Mersenne's string divisions : 102841725 Sum of van Prooijen's expressibility: 6.17271, average 0.88182 Sum of Tenney's harmonic distance : 13.07377, average 1.86768 Vogel's harmonic complexity : 17.57143 Wille's k value : 472 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 92.57356, average 3.30620 Lattice compactness (without 2's) : 62.47592, average 2.23128 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.85714 15 1 3: -2 .. 3 0.28571 10 3 5: -1 .. 0 -0.42857 3 1 7: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 0 1 2 1 0 2 1 N T3 SD: 40.9727 c. M: 65.0111 c. 8: 0 1 2 2 0 2 1 N SD: 40.2962 c. M:-53.9100 c. 10: 0 1 3 2 0 2 2 N SD: 27.6320 c. M: 48.7704 c. 12: 0 1 4 2 0 3 2 N SD: 27.0242 c. M: 50.7254 c. 14: 1 0 5 2 1 3 2 N SD: 24.0622 c. M:-36.9439 c. 16: 1 0 6 2 1 3 3 N SD: 23.7115 c. M: 36.7313 c. 17: 1 1 5 3 1 3 3 N SD: 17.3139 c. M:-29.4452 c. 19: 1 1 6 3 1 4 3 N SD: 10.5811 c. M:-14.5845 c. 22: 1 1 7 4 1 4 4 N SD: 8.5569 c. M: 14.2718 c. 24: 1 1 8 4 1 5 4 N SD: 4.8195 c. M: 11.7313 c. 41: 2 2 13 7 2 8 7 N SD: 5.7369 c. M:-10.2502 c. 43: 2 2 14 7 2 9 7 N SD: 4.8873 c. M:-8.5612 c. 46: 2 2 15 8 2 9 8 N SD: 4.3761 c. M: 7.3835 c. 53: 2 3 17 9 2 11 9 N SD: 1.9644 c. M: 3.5556 c. 77: 3 4 25 13 3 16 13 N SD: 1.7226 c. M: 2.6734 c. 94: 4 5 30 16 4 19 16 N SD: 1.7534 c. M:-3.1623 c. 99: 4 5 32 17 4 20 17 N SD: 1.4449 c. M: 2.6404 c. 118: 5 6 38 20 5 24 20 N SD: 1.0717 c. M:-2.0771 c. 142: 6 7 46 24 6 29 24 N SD: 1.2514 c. M:-1.9338 c. 147: 6 8 47 25 6 30 25 N SD: 0.9783 c. M:-2.5544 c. 152: 6 8 49 26 6 31 26 N SD: 0.9776 c. M: 1.4020 c. 171: 7 9 55 29 7 35 29 N SD: 0.3141 c. M:-0.5494 c. 323: 13 17 104 55 13 66 55 N SD: 0.3020 c. M: 0.4732 c. 419: 17 22 135 71 17 86 71 N SD: 0.2996 c. M:-0.5687 c. 441: 18 23 142 75 18 90 75 N SD: 0.1702 c. M:-0.2950 c. 494: 20 26 159 84 20 101 84 N SD: 0.1055 c. M: 0.1874 c. 665: 27 35 214 113 27 136 113 N SD: 0.0618 c. M:-0.1484 c. 1106: 45 58 356 188 45 226 188 N SD: 0.0511 c. M:-0.0884 c. 1354: 55 71 436 230 55 277 230 N SD: 0.0470 c. M:-0.0695 c. 1600: 65 84 515 272 65 327 272 N SD: 0.0439 c. M: 0.0900 c. 1771: 72 93 570 301 72 362 301 N SD: 0.0363 c. M:-0.0700 c. 1966: 80 103 633 334 80 402 334 N SD: 0.0358 c. M:-0.0597 c. 2019: 82 106 650 343 82 413 343 N SD: 0.0331 c. M: 0.0567 c. 2289: 93 120 737 389 93 468 389 N SD: 0.0279 c. M: 0.0668 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x x 5:6 S SD: 37.2438 cents 4 x x 5:6 x 7:8 S SD: 28.7524 cents 5 x x 7 x 8:9:10 SD: 26.8809 cents 6 x 7:8:9 x 11:12 SD: 32.8063 cents 7 x 8:9 x 11:12:14 SD: 30.4656 cents 8 x 9:11:12 x 14:16 SD: 21.9802 cents 9 x 10:12 x 14:16:18 S SD: 14.4166 cents 10 x 11:13:15 x 18:20 SD: 14.4522 cents 11 x 12:15 x 17:20:22 SD: 13.4899 cents 12 x 13:16:18:19:21:24 SD: 9.8231 cents 13 x 14:17 x 20:23:26 SD: 7.7423 cents 14 x 15:19:21:22:25:28 SD: 7.5774 cents 15 x 16:20 x 23:27:30 SD: 4.8060 cents 16 x 17:21:24:25:28:32 SD: 7.4764 cents 17 x 18:23 x 26:30:34 SD: 6.9134 cents 18 x 19:24:27:28:32:36 SD: 3.8370 cents 19 x 20:25 x 29:34:38 SD: 7.8198 cents 20 x 21:27:30:31:36:40 SD: 6.9368 cents 21 x 22:28 x 32:37:42 SD: 8.1895 cents 22:23 x 29:33:34:39:44 SD: 5.8182 cents 23:24:25:31 x 35:41:46 SD: 8.5414 cents 24:25:26:32:36:37:43:48 SD: 5.3136 cents 26:27:28:35:39:40:46:52 SD: 4.3269 cents 28:29:30:37:42:43:50:56 SD: 3.4050 cents 30:31:32:40:45:46:53:60 SD: 2.4606 cents 42:43:45:56:63:65:75:84 SD: 2.0797 cents 60:62:64:80:90:93:107:120 SD: 1.7904 cents 62:64:66:83:93:96:110:124 SD: 1.7478 cents 64:66:68:85:96:99:114:128 SD: 1.7130 cents 66:68:70:88:99:102:117:132 SD: 1.6814 cents 70:72:75:93:105:108:124:140 SD: 1.6672 cents 72:74:77:96:108:111:128:144 SD: 0.6976 cents 134:138:143:179:201:207:238:268 SD: 0.6842 cents 136:140:145:181:204:210:242:272 SD: 0.5943 cents 138:142:147:184:207:213:245:276 SD: 0.4959 cents 180:185:192:240:270:278:320:360 SD: 0.3180 cents 210:216:224:280:315:324:373:420 SD: 0.2209 cents 346:356:369:461:519:534:615:692 SD: 0.2204 cents 348:358:371:464:522:537:619:696 SD: 0.1965 cents 378:389:403:504:567:583:672:756 SD: 0.1960 cents 390:401:416:520:585:602:693:780 SD: 0.1889 cents 418:430:446:557:627:645:743:836 SD: 0.1758 cents 420:432:448:560:630:648:747:840 SD: 0.1104 cents 558:574:595:744:837:861:992:1116 SD: 0.0901 cents