Scala analysis: xen10-wilson-purvi-06a-06
Purvi modulation 6 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: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 81/50 835.192576 acute minor 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: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 10/9 182.4037 minor whole tone 3: 10/9 182.4037 minor whole tone 4: 9/8 203.9100 major whole tone 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 10/9 182.4037 minor whole tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 4 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 3 6/5 315.641 cents minor third 2: 1 243/200 337.148 cents acute minor third 2: 2 100/81 364.807 cents grave major third 2: 1 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: 1 8/5 813.686 cents minor sixth 5: 2 81/50 835.193 cents acute minor sixth 5: 1 400/243 862.852 cents grave major sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 50/27 1066.762 cents grave 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 : 133.2 315.6 498.0 702.0 835.2 1017.6 1200.0 133.2 : 182.4 364.8 568.7 702.0 884.4 1066.8 1200.0 315.6 : 182.4 386.3 519.6 702.0 884.4 1017.6 1200.0 498.0 : 203.9 337.1 519.6 702.0 835.2 1017.6 1200.0 702.0 : 133.2 315.6 498.0 631.3 813.7 996.1 1200.0 835.2 : 182.4 364.8 498.0 680.4 862.9 1066.8 1200.0 1017.6: 182.4 315.6 498.0 680.4 884.4 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 203.9100 cents 25/24, 70.6724 cents 27/25, 133.2376 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 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 .. 884.3587 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 6: 996.0900 .. 1066.7624 cents 25/24, 70.6724 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.286638 Largest / Average step : 1.189475 Largest / Smallest step : 1.530424 Median interval of one step : 10/9, 182.4037 cents, amount: 4 Most common interval of one step : 10/9, 182.4037 cents, amount: 4 Least squares average step : 169.62868 cents, oct.: 1187.40079 cents Scale is strictly proper Step pattern alph. order: ABBCABB Step pattern size order : SMMLSMM Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.349275 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.646638 Rothenberg efficiency : 0.478912 redundancy: 0.521088 Efficiency x scale size : 3.352381 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 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 triad is 0.0 701.955 1017.596 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords 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 subharmonic part : 2 at degree 2 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 70.6724 cents: 5 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.034325 Average absolute harmonicity : 0.251503 Specific harmonicity : 0.176535 Fundamental : 1/150, -7.2288 octaves, 1.7442 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 4.860000E+04, 15.56867 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 111.5, average 15.92857 Mersenne's string divisions : 7867860 Sum of van Prooijen's expressibility: 5.94730, average 0.84961 Sum of Tenney's harmonic distance : 11.72546, average 1.67507 Vogel's harmonic complexity : 14.28571 Wille's k value : 121 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 77.27819, average 2.75994 Lattice compactness (without 2's) : 64.60840, average 2.30744 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.28571 6 1 3: -1 .. 4 1.42857 12 2 5: -2 .. 0 -0.85714 6 4 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 18 / 7 = 2.57143 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: 21.8077 c. M:-38.1910 c. Lebeng 12: 1 2 2 2 1 2 2 P M ME S SD: 20.3722 c. M: 35.1926 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 17: 2 2 3 3 2 2 3 SP D3 S SD: 17.7477 c. M: 33.2883 c. 19: 2 3 3 3 2 3 3 SP M ME S SD: 7.5787 c. M: 14.1399 c. Nineteen-tone Phrygian 26: 3 4 4 4 3 4 4 SP M ME S SD: 6.4717 c. M:-9.6473 c. 27: 3 4 4 5 3 4 4 SP T3 SD: 6.4939 c. M:-9.2519 c. 34: 4 5 5 6 4 5 5 SP T3 SD: 6.2554 c. M:-11.8662 c. 39: 4 6 6 7 4 6 6 SP SD: 6.0559 c. M: 10.1607 c. 45: 5 7 7 7 5 7 7 SP M DE S SD: 6.0773 c. M:-8.6217 c. 46: 5 7 7 8 5 7 7 SP SD: 1.9371 c. M: 2.8028 c. 53: 6 8 8 9 6 8 8 SP SD: 1.5450 c. M:-2.6115 c. 72: 8 11 11 12 8 11 11 SP SD: 1.3641 c. M: 1.9550 c. 99: 11 15 15 17 11 15 15 SP SD: 0.7816 c. M:-1.1711 c. 118: 13 18 18 20 13 18 18 SP SD: 0.7019 c. M: 1.2943 c. 125: 14 19 19 21 14 19 19 SP SD: 0.8752 c. M:-1.1624 c. 152: 17 23 23 26 17 23 23 SP SD: 0.8689 c. M:-1.6495 c. 164: 18 25 25 28 18 25 25 SP SD: 0.8613 c. M: 1.5303 c. 171: 19 26 26 29 19 26 26 SP SD: 0.1338 c. M:-0.2006 c. 388: 43 59 59 66 43 59 59 SP SD: 0.1417 c. M: 0.2479 c. 441: 49 67 67 75 49 67 67 SP SD: 0.0965 c. M:-0.1816 c. 559: 62 85 85 95 62 85 85 SP SD: 0.0827 c. M: 0.1428 c. 612: 68 93 93 104 68 93 93 SP SD: 0.0587 c. M:-0.1015 c. 783: 87 119 119 133 87 119 119 SP SD: 0.0545 c. M:-0.0958 c. 829: 92 126 126 141 92 126 126 SP SD: 0.0656 c. M: 0.0957 c. 954: 106 145 145 162 106 145 145 SP SD: 0.0611 c. M:-0.0958 c. 1000: 111 152 152 170 111 152 152 SP SD: 0.0321 c. M:-0.0450 c. 1171: 130 178 178 199 130 178 178 SP SD: 0.0106 c. M: 0.0181 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: 16.3887 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 17.4324 cents 6 x 7:8:9:10:11:12 S SD: 12.6984 cents 7 x 8:9 x 11:13:14 SD: 25.9257 cents 8:9:10:11:12:13:14:16 S SD: 17.6324 cents 9:10:11:12:14:15:16:18 S SD: 14.4775 cents 10:11:12:13:15:16:18:20 SD: 8.3211 cents 14:15:17:19:21:23:25:28 SD: 6.8922 cents 16:17:19:21:24:26:29:32 SD: 6.4584 cents 20:22:24:27:30:32:36:40 S SD: 6.2827 cents 21:23:25:28:32:34:38:42 SD: 5.7258 cents 24:26:29:32:36:39:43:48 SD: 2.3256 cents 36:39:43:48:54:58:65:72 SD: 2.0810 cents 40:43:48:53:60:65:72:80 SD: 2.0742 cents 50:54:60:67:75:81:90:100 SD: 1.2335 cents 60:65:72:80:90:97:108:120 SD: 0.9167 cents 90:97:108:120:135:146:162:180 SD: 0.6119 cents 126:136:151:168:189:204:227:252 SD: 0.4438 cents 150:162:180:200:225:243:270:300 SD: 0.0000 cents