Scala analysis: xen10-wilson-purvi-06a-04
Purvi modulation 4 from Figure 6a, Al-Farabi (10/9 10/9 27/25), (27/25 10/9 10/9)
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: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 9/8 203.9100 major whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 10/9 182.4037 minor whole tone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 6/5 315.641 cents minor third 2: 3 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 2 27/20 519.551 cents acute fourth 3: 1 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 2 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 3 8/5 813.686 cents minor sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 50/27 1066.762 cents grave major seventh 6: 1 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 315.6 498.0 702.0 884.4 1017.6 1200.0 203.9 : 111.7 294.1 498.0 680.4 813.7 996.1 1200.0 315.6 : 182.4 386.3 568.7 702.0 884.4 1088.3 1200.0 498.0 : 203.9 386.3 519.6 702.0 905.9 1017.6 1200.0 702.0 : 182.4 315.6 498.0 702.0 813.7 996.1 1200.0 884.4 : 133.2 315.6 519.6 631.3 813.7 1017.6 1200.0 1017.6: 182.4 386.3 498.0 680.4 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 3: 498.0450 .. 568.7174 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 4: 631.2826 .. 701.9550 cents 25/24, 70.6724 cents 648/625, 62.5651 cents 5: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Most common interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 171.88942 cents, oct.: 1203.22594 cents Scale is strictly proper Step pattern alph. order: ABCACDC Step pattern size order : DACDCBC Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.405280 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.574950 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 3.266667 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 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 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 5 = 71.4286% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 27 (O: 27 U: 27) Highest odd numerator or denominator: 9 Scale harmonicity : 0.038760 Average absolute harmonicity : 0.271696 Specific harmonicity : 0.231660 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 2.160000E+04, 14.39874 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 32.5, average 4.64286 Mersenne's string divisions : 157080 Sum of van Prooijen's expressibility: 4.26067, average 0.60867 Sum of Tenney's harmonic distance : 8.32212, average 1.18887 Vogel's harmonic complexity : 12.00000 Wille's k value : 67 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 73.65731, average 2.63062 Lattice compactness (without 2's) : 48.18809, average 1.72100 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.00000 8 1 3: -1 .. 2 0.57143 8 3 5: -1 .. 1 -0.14286 3 3 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 21.3288 c. M: 32.4814 c. Lebeng 12: 2 1 2 2 2 1 2 P M ME I SD: 10.8355 c. M: 17.5963 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 19: 3 2 3 3 3 2 3 SP M ME I SD: 7.1976 c. M: 14.4363 c. Nineteen-tone Dorian 31: 5 3 5 5 5 3 5 SP M DE I SD: 7.1353 c. M: 11.1447 c. Intense Diatonic Phrygian, M.Dorian 34: 6 3 5 6 5 4 5 SP SD: 4.4044 c. M:-7.8547 c. 41: 7 4 6 7 6 5 6 SP SD: 4.2627 c. M:-6.7940 c. 46: 8 4 7 8 7 5 7 SP SD: 2.6157 c. M:-4.7857 c. 53: 9 5 8 9 8 6 8 SP SD: 0.8648 c. M: 1.3398 c. 118: 20 11 18 20 18 13 18 SP SD: 0.4008 c. M: 0.6471 c. 171: 29 16 26 29 26 19 26 SP SD: 0.2029 c. M: 0.4012 c. 388: 66 36 59 66 59 43 59 SP SD: 0.1396 c. M:-0.2137 c. 441: 75 41 67 75 67 49 67 SP SD: 0.0866 c. M:-0.1716 c. 559: 95 52 85 95 85 62 85 SP SD: 0.0497 c. M:-0.0778 c. 612: 104 57 93 104 93 68 93 SP SD: 0.0312 c. M:-0.0508 c. 1171: 199 109 178 199 178 130 178 SP SD: 0.0113 c. M:-0.0183 c. 1783: 303 166 271 303 271 198 271 SP SD: 0.0098 c. M:-0.0160 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 22.0266 cents 6 x 7:8:9:10:11:12 S SD: 9.7006 cents 7:8 x 9:11:12:13:14 SD: 21.4084 cents 8:9:10:11:12:13:14:16 S SD: 15.7353 cents 9:10:11:12:14:15:16:18 S SD: 10.9714 cents 10:11:12:13:15:17:18:20 SD: 9.6997 cents 12 x 14:16:18:20:22:24 S SD: 9.7006 cents 14:16:17:19:21:23:25:28 SD: 7.7101 cents 15:17:18:20:23:25:27:30 SD: 5.7341 cents 24:27:29:32:36:40:43:48 SD: 2.0607 cents 30:34:36:40:45:50:54:60 SD: 1.8252 cents 54:61:65:72:81:90:97:108 SD: 1.3682 cents 66:74:79:88:99:110:119:132 SD: 1.1224 cents 80:90:96:107:120:133:144:160 SD: 0.9893 cents 90:101:108:120:135:150:162:180 SD: 0.6114 cents 96:108:115:128:144:160:173:192 SD: 0.5163 cents 120:135:144:160:180:200:216:240 SD: 0.0000 cents