Scala analysis: xen10-wilson-purvi-11a-04
Purvi modulation 4 from Figure 11a, Archytas (28/27 36/35 5/4), (5/4 28/27 36/35)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 14/9 764.915905 septimal minor sixth 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 9/8 203.9100 major whole tone 2: 280/243 245.3646 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 9/8 203.9100 major whole tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 5/4 386.3137 major third 7: 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: 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: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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: 2 54/35 750.725 cents septimal semi-augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 2 140/81 947.320 cents 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 : 203.9 449.3 498.0 702.0 764.9 1151.2 1200.0 203.9 : 245.4 294.1 498.0 561.0 947.3 996.1 1200.0 449.3 : 48.8 252.7 315.6 702.0 750.7 954.6 1200.0 498.0 : 203.9 266.9 653.2 702.0 905.9 1151.2 1200.0 702.0 : 63.0 449.3 498.0 702.0 947.3 996.1 1200.0 764.9 : 386.3 435.1 639.0 884.4 933.1 1137.0 1200.0 1151.2: 48.8 252.7 498.0 546.8 750.7 813.7 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: 252.6804 .. 449.2746 cents 2450/2187, 196.5942 cents 162/175,-133.6333 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 750.7254 .. 947.3196 cents 2450/2187, 196.5942 cents 162/175,-133.6333 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 162/175,-133.6333 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 : 175.25980 cents, oct.: 1226.81857 cents Scale is not proper Step pattern alph. order: ABCADEC Step pattern size order : CDACBEA Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.470169 Lumma stability : 0.081284 Lumma impropriety factor : 0.416298 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 2 and 3 combined 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 : 0.250162 Specific harmonicity : 0.147436 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 1260, 10.2992 octaves, 329648.212 Hz. Exponens Consonantiae : 2.721600E+05, 18.05410 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 85.0, average 12.14286 Mersenne's string divisions : 134906730 Sum of van Prooijen's expressibility: 5.95086, average 0.85012 Sum of Tenney's harmonic distance : 11.89084, average 1.69869 Vogel's harmonic complexity : 14.14286 Wille's k value : 121 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 86.91806, average 3.10422 Lattice compactness (without 2's) : 63.29777, average 2.26063 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.14286 9 1 3: -3 .. 2 -0.71429 11 3 5: 0 .. 1 0.28571 2 7: 0 .. 1 0.42857 3 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 18 21| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 12 16 21| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 2 0 1 0 3 0 N SD: 45.4508 c. M: 79.2016 c. 8: 1 2 0 2 0 3 0 N SD: 38.0310 c. M: 53.9100 c. 10: 2 2 0 2 0 4 0 N D3 SD: 32.2795 c. M:-48.7704 c. 11: 2 2 1 1 1 4 0 N SD: 32.1734 c. M:-48.7704 c. 12: 2 3 0 2 1 4 0 N SD: 29.7740 c. M:-50.7254 c. 13: 2 3 0 2 1 4 1 N SD: 32.8732 c. M: 55.8012 c. 14: 2 3 1 2 1 4 1 N SD: 22.0987 c. M: 36.9439 c. 17: 3 3 1 3 1 5 1 N D3 SD: 13.9637 c. M: 25.7452 c. Seventeen-tone Harmonic Major 19: 3 4 1 3 1 6 1 N SD: 9.4136 c. M: 14.4363 c. 22: 4 4 1 4 1 7 1 N D3 SD: 8.5123 c. M:-14.2718 c. 24: 4 5 1 4 1 8 1 N SD: 5.9456 c. M: 14.9159 c. 34: 6 7 1 6 2 11 1 N SD: 8.4418 c. M:-13.4763 c. 39: 7 8 1 7 2 12 2 N SD: 8.6977 c. M: 12.7681 c. 41: 7 8 2 7 2 13 2 N SD: 5.5726 c. M: 10.2502 c. 45: 8 9 2 7 3 14 2 N SD: 7.0266 c. M:-9.4233 c. 46: 8 9 2 8 2 15 2 N SD: 4.6291 c. M: 8.3942 c. 48: 8 10 2 8 3 15 2 N SD: 4.2537 c. M:-10.0841 c. 53: 9 11 2 9 3 17 2 N SD: 2.6403 c. M:-4.8954 c. 72: 12 15 3 12 4 23 3 N SD: 2.0013 c. M: 3.9100 c. 77: 13 16 3 13 4 25 3 N SD: 1.4851 c. M:-2.6734 c. 94: 16 19 4 16 5 30 4 N SD: 1.3419 c. M: 2.4661 c. 99: 17 20 4 17 5 32 4 N SD: 1.1514 c. M:-2.1506 c. 118: 20 24 5 20 6 38 5 N SD: 1.3564 c. M: 2.2040 c. 147: 25 30 6 25 8 47 6 N SD: 0.9323 c. M:-2.4310 c. 152: 26 31 6 26 8 49 6 N SD: 0.9259 c. M:-1.4020 c. 171: 29 35 7 29 9 55 7 N SD: 0.2357 c. M: 0.4012 c. 441: 75 90 18 75 23 142 18 N SD: 0.1924 c. M: 0.2950 c. 494: 84 101 20 84 26 159 20 N SD: 0.1458 c. M:-0.2663 c. 612: 104 125 25 104 32 197 25 N SD: 0.1565 c. M: 0.2550 c. 665: 113 136 27 113 35 214 27 N SD: 0.0788 c. M:-0.1969 c. 836: 142 171 34 142 44 269 34 N SD: 0.0713 c. M:-0.1559 c. 935: 159 191 38 159 49 301 38 N SD: 0.0771 c. M:-0.1542 c. 1007: 171 206 41 171 53 324 41 N SD: 0.0866 c. M: 0.1364 c. 1106: 188 226 45 188 58 356 45 N SD: 0.0504 c. M: 0.0884 c. 1277: 217 261 52 217 67 411 52 N SD: 0.0511 c. M: 0.0969 c. 1354: 230 277 55 230 71 436 55 N SD: 0.0488 c. M: 0.0710 c. 1771: 301 362 72 301 93 570 72 N SD: 0.0379 c. M:-0.0756 c. 1848: 314 378 75 314 97 595 75 N SD: 0.0400 c. M:-0.0760 c. 1942: 330 397 79 330 102 625 79 N SD: 0.0358 c. M:-0.0686 c. 2019: 343 413 82 343 106 650 82 N SD: 0.0336 c. M:-0.0567 c. 2118: 360 433 86 360 111 682 86 N SD: 0.0357 c. M:-0.0560 c. 2289: 389 468 93 389 120 737 93 N SD: 0.0193 c. M: 0.0404 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 5 x 6 S SD: 39.8143 cents 4 x 5 x 6 x x 8 S SD: 20.9870 cents 5:6 x 7 x 8 x 10 S SD: 37.0786 cents 6:7 x 8:9 x x 12 S SD: 15.7402 cents 7:8:9 x x 11 x 14 SD: 8.8516 cents 8:9:10:11:12 x x 16 S SD: 16.4949 cents 9:10 x 12 x 14 x 18 SD: 5.3766 cents 10:11:13 x 15:16:19:20 SD: 12.3817 cents 11:12:14:15 x 17:21:22 SD: 13.4341 cents 12:14 x 16:18:19:23:24 SD: 12.3867 cents 13:15:17 x x 20:25:26 SD: 10.7381 cents 14:16:18:19:21:22:27:28 SD: 6.9897 cents 15:17:19:20 x 23:29:30 SD: 8.3077 cents 16:18:21 x 24:25:31:32 SD: 3.9453 cents 17:19:22:23 x 26:33:34 SD: 6.7611 cents 18:20:23:24:27:28:35:36 SD: 4.7014 cents 19:21 x 25:29:30:37:38 SD: 9.1981 cents 20:23:26:27:30:31:39:40 SD: 6.3848 cents 22:25 x 29:33:34:43:44 SD: 5.0052 cents 24:27:31:32:36:37:47:48 SD: 2.9668 cents 34:38:44:45:51:53:66:68 SD: 2.5646 cents 40:45:52:53:60:62:78:80 SD: 2.0453 cents 48:54:62:64:72:75:93:96 SD: 1.6672 cents 54:61:70:72:81:84:105:108 SD: 1.0157 cents 72:81:93:96:108:112:140:144 SD: 0.8849 cents 88:99:114:117:132:137:171:176 SD: 0.7661 cents 112:126:145:149:168:174:218:224 SD: 0.7539 cents 126:142:163:168:189:196:245:252 SD: 0.6672 cents 128:144:166:171:192:199:249:256 SD: 0.5256 cents 144:162:187:192:216:224:280:288 SD: 0.4412 cents 162:182:210:216:243:252:315:324 SD: 0.3395 cents 216:243:280:288:324:336:420:432 SD: 0.0000 cents