Scala analysis: xen10-wilson-purvi-08b-06
Purvi modulation 6 from Figure 8b, Ptolemy (7/6 22/21 12/11), (22/21 12/11 7/6)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 44/27 845.452940 neutral sixth 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: 7/6 266.8709 septimal minor third 2: 22/21 80.5370 undecimal minor semitone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole tone 5: 88/81 143.4979 2nd undecimal neutral second 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 21/16 470.781 cents narrow fourth 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 32/21 729.219 cents wide fifth 5: 2 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 6: 1 21/11 1119.463 cents undecimal major seventh 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 : 266.9 347.4 498.0 702.0 845.5 996.1 1200.0 266.9 : 80.5 231.2 435.1 578.6 729.2 933.1 1200.0 347.4 : 150.6 354.5 498.0 648.7 852.6 1119.5 1200.0 498.0 : 203.9 347.4 498.0 702.0 968.8 1049.4 1200.0 702.0 : 143.5 294.1 498.0 764.9 845.5 996.1 1200.0 845.5 : 150.6 354.5 621.4 702.0 852.6 1056.5 1200.0 996.1 : 203.9 470.8 551.3 702.0 905.9 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 266.8709 cents 49/44, 186.3339 cents 22/21, 80.5370 cents 2: 231.1741 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.128568 Largest / Average step : 1.556747 Largest / Smallest step : 3.313642 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Least squares average step : 170.48176 cents, oct.: 1193.37232 cents Scale is not proper Step pattern alph. order: ABCDECD Step pattern size order : EACDBCD Scale is a Constant Structure, by a margin of 27.26409 cents Scale diversity : 1.600163 Lumma stability : 0.134228 Lumma impropriety factor : 0.154686 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 : 243/242, 7.1391 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 class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.022658 Average absolute harmonicity : 0.249119 Specific harmonicity : 0.137778 Fundamental : 1/54, -5.7549 octaves, 4.8449 Hz. Guide tone : 3696, 11.8517 octaves, 966968.089 Hz. Exponens Consonantiae : 1.995840E+05, 17.60664 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 72.0, average 10.28571 Mersenne's string divisions : 1938300 Sum of van Prooijen's expressibility: 5.22634, average 0.74662 Sum of Tenney's harmonic distance : 11.01043, average 1.57292 Vogel's harmonic complexity : 11.71429 Wille's k value : 40 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 82.35355, average 2.94120 Lattice compactness (without 2's) : 50.80682, average 1.81453 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.00000 11 1 3: -3 .. 1 -1.14286 10 3 7: 0 .. 1 0.14286 1 1 11: 0 .. 1 0.28571 2 2 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 22 22| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 18 25| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 2 0 1 1 1 1 1 N T3 SD: 32.7629 c. M:-75.9862 c. 10: 2 1 1 2 1 1 2 P D3 I SD: 20.2275 c. M: 36.0900 c. 14: 3 1 2 2 2 2 2 P T3 SD: 16.1889 c. M:-32.4814 c. 17: 4 1 2 3 2 2 3 N SD: 7.2253 c. M:-15.4820 c. 24: 5 2 3 4 3 3 4 P SD: 6.9174 c. M: 16.8709 c. 31: 7 2 4 5 4 4 5 N SD: 5.5643 c. M:-10.3616 c. 41: 9 3 5 7 5 5 7 N SD: 2.3589 c. M:-3.8116 c. 72: 16 5 9 12 9 9 12 N SD: 2.6824 c. M:-4.5471 c. 77: 17 5 10 13 9 10 13 N SD: 2.4556 c. M: 4.5508 c. 87: 19 6 11 15 10 11 15 N SD: 2.9201 c. M: 4.8019 c. 89: 20 6 11 15 11 11 15 N SD: 2.3229 c. M:-3.9853 c. 94: 21 6 12 16 11 12 16 N SD: 1.5811 c. M: 2.8997 c. 118: 26 8 15 20 14 15 20 N SD: 1.2594 c. M: 2.4641 c. 125: 28 8 16 21 15 16 21 N SD: 1.4842 c. M:-2.3100 c. 135: 30 9 17 23 16 17 23 N SD: 0.5394 c. M: 1.0085 c. 176: 39 12 22 30 21 22 30 N SD: 0.4830 c. M: 0.9618 c. 301: 67 20 38 51 36 38 51 N SD: 0.3716 c. M:-0.5877 c. 311: 69 21 39 53 37 39 53 N SD: 0.4029 c. M: 0.6330 c. 342: 76 23 43 58 41 43 58 N SD: 0.2107 c. M:-0.4012 c. 359: 80 24 45 61 43 45 61 N SD: 0.2370 c. M:-0.5386 c. 477: 106 32 60 81 57 60 81 N SD: 0.1489 c. M: 0.2381 c. 494: 110 33 62 84 59 62 84 N SD: 0.1487 c. M:-0.3356 c. 535: 119 36 67 91 64 67 91 N SD: 0.1476 c. M:-0.2556 c. 670: 149 45 84 114 80 84 114 N SD: 0.1298 c. M: 0.2691 c. 701: 156 47 88 119 84 88 119 N SD: 0.1410 c. M:-0.2010 c. 836: 186 56 105 142 100 105 142 N SD: 0.0596 c. M:-0.1147 c. 1012: 225 68 127 172 121 127 172 N SD: 0.0348 c. M: 0.0725 c. 1848: 411 124 232 314 221 232 314 N SD: 0.0082 c. M:-0.0139 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: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 11.8769 cents 5 x 6:7 x 8:9:10 S SD: 19.6117 cents 6:7 x 8:9:10:11:12 S SD: 10.9945 cents 7:8 x 9 x 11:12:14 SD: 22.9491 cents 8:9:10:11:12:13:14:16 S SD: 13.6152 cents 9 x 11:12:14:15:16:18 SD: 12.3353 cents 10 x 12:13:15:16:18:20 SD: 11.0578 cents 11:13 x 15:17:18:20:22 SD: 13.1745 cents 12:14:15:16:18:20:21:24 S SD: 8.7722 cents 14:16:17:19:21:23:25:28 SD: 7.2784 cents 15 x 18:20:23:24:27:30 SD: 10.4464 cents 16:19:20:21:24:26:28:32 SD: 8.9938 cents 17:20:21:23:26:28:30:34 SD: 7.5868 cents 18:21:22:24:27:29:32:36 SD: 2.8265 cents 30:35:37:40:45:49:53:60 SD: 2.7801 cents 36:42:44:48:54:59:64:72 SD: 1.4012 cents 54:63:66:72:81:88:96:108 SD: 0.0000 cents