Scala analysis: xen10-wilson-purvi-06a-02
Purvi modulation 2 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: 5/4 386.313714 major 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: 50/27 1066.762425 grave major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 1: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 10/9 182.4037 minor whole tone 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
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: 2 6/5 315.641 cents minor third 2: 1 243/200 337.148 cents acute minor third 2: 1 100/81 364.807 cents grave major third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 1 81/50 835.193 cents acute minor sixth 5: 1 400/243 862.852 cents grave major sixth 5: 2 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: 5 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 386.3 498.0 702.0 884.4 1066.8 1200.0 203.9 : 182.4 294.1 498.0 680.4 862.9 996.1 1200.0 386.3 : 111.7 315.6 498.0 680.4 813.7 1017.6 1200.0 498.0 : 203.9 386.3 568.7 702.0 905.9 1088.3 1200.0 702.0 : 182.4 364.8 498.0 702.0 884.4 996.1 1200.0 884.4 : 182.4 315.6 519.6 702.0 813.7 1017.6 1200.0 1066.8: 133.2 337.1 519.6 631.3 835.2 1017.6 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 : 175.00615 cents, oct.: 1225.04303 cents Scale is strictly proper Step pattern alph. order: ABCABBD Step pattern size order : DCADCCB Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.442956 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.574950 Rothenberg efficiency : 0.436735 redundancy: 0.563265 Efficiency x scale size : 3.057143 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.00000 = 4 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 contains a complete diamond : 1 3 Length of longest harmonic part : 2 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 Limited inverse transpositions with margin 92.1787 cents: 2 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.032120 Average absolute harmonicity : 0.268889 Specific harmonicity : 0.197044 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 900, 9.8138 octaves, 235463.009 Hz. Exponens Consonantiae : 1.944000E+05, 17.56867 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 63.0, average 9.00000 Mersenne's string divisions : 471240 Sum of van Prooijen's expressibility: 4.73779, average 0.67683 Sum of Tenney's harmonic distance : 9.62315, average 1.37474 Vogel's harmonic complexity : 13.71429 Wille's k value : 121 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 85.06292, average 3.03796 Lattice compactness (without 2's) : 56.58644, average 2.02094 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.28571 10 1 3: -3 .. 2 -0.28571 8 3 5: 0 .. 2 0.57143 4 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 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: 28.4612 c. M: 43.4566 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 26.1563 c. M: 44.3587 c. Sethares Neutral, Beatles-7, Dichotic-7 12: 2 2 1 2 2 2 1 P M ME S SD: 14.9266 c. M:-33.2376 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 16: 3 2 2 2 3 2 2 SP M ME S SD: 19.0921 c. M:-26.9550 c. Antiphrygian 19: 3 3 2 3 3 3 2 SP M ME S SD: 7.6979 c. M: 14.4363 c. Nineteen-tone Major, Ionian 34: 6 5 3 6 5 5 4 SP SD: 4.8298 c. M: 7.9389 c. 46: 8 7 4 8 7 7 5 SP SD: 3.2484 c. M:-4.9906 c. 53: 9 8 5 9 8 8 6 SP SD: 1.2320 c. M: 2.6115 c. 99: 17 15 9 17 15 15 11 SP SD: 1.1733 c. M:-2.1506 c. 118: 20 18 11 20 18 18 13 SP SD: 0.4842 c. M:-1.0342 c. 171: 29 26 16 29 26 26 19 SP SD: 0.2373 c. M: 0.4012 c. 388: 66 59 36 66 59 59 43 SP SD: 0.1860 c. M:-0.2842 c. 441: 75 67 41 75 67 67 49 SP SD: 0.0925 c. M:-0.1716 c. 559: 95 85 52 95 85 85 62 SP SD: 0.0713 c. M:-0.1428 c. 612: 104 93 57 104 93 93 68 SP SD: 0.0430 c. M: 0.0958 c. 730: 124 111 68 124 111 111 81 SP SD: 0.0487 c. M:-0.0869 c. 1171: 199 178 109 199 178 178 130 SP SD: 0.0148 c. M:-0.0228 c. 1783: 303 271 166 303 271 271 198 SP SD: 0.0111 c. M: 0.0210 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 6:7 x 8 S SD: 21.1168 cents 5 x 6:7 x 8:9:10 S SD: 27.9580 cents 6:7 x 8:9:10:11:12 S SD: 10.8868 cents 7:8:9 x 11:12:13:14 SD: 18.2658 cents 8:9:10:11:12:13:15:16 SD: 10.3230 cents 10:11 x 13:15:17:19:20 SD: 13.5244 cents 12:14:15:16:18:20:22:24 S SD: 9.3316 cents 15:17:19:20:23:25:28:30 SD: 6.8916 cents 16:18:20:21:24:27:30:32 S SD: 5.8351 cents 24:27:30:32:36:40:44:48 S SD: 2.4856 cents 40:45:50:53:60:67:74:80 SD: 1.9968 cents 48:54:60:64:72:80:89:96 SD: 0.3090 cents 120:135:150:160:180:200:222:240 SD: 0.2474 cents 168:189:210:224:252:280:311:336 SD: 0.0883 cents 216:243:270:288:324:360:400:432 SD: 0.0000 cents