Scala analysis: xen10-wilson-purvi-06a-05
Purvi modulation 5 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: 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: 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: 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: 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 : 203.9 315.6 498.0 702.0 835.2 1017.6 1200.0 203.9 : 111.7 294.1 498.0 631.3 813.7 996.1 1200.0 315.6 : 182.4 386.3 519.6 702.0 884.4 1088.3 1200.0 498.0 : 203.9 337.1 519.6 702.0 905.9 1017.6 1200.0 702.0 : 133.2 315.6 498.0 702.0 813.7 996.1 1200.0 835.2 : 182.4 364.8 568.7 680.4 862.9 1066.8 1200.0 1017.6: 182.4 386.3 498.0 680.4 884.4 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 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 : 170.13349 cents, oct.: 1190.93441 cents Scale is strictly proper Step pattern alph. order: ABCADCC Step pattern size order : DACDBCC 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 : 1 at degree 0 Length of longest subharmonic part : 2 at degree 2 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 3 and 4 combined Limited inverse transpositions with margin 92.1787 cents: 3 6 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.032120 Average absolute harmonicity : 0.261778 Specific harmonicity : 0.195241 Fundamental : 1/600, -9.2288 octaves, 0.4360 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 1.944000E+05, 17.56867 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 94.0, average 13.42857 Mersenne's string divisions : 5144370 Sum of van Prooijen's expressibility: 5.47018, average 0.78145 Sum of Tenney's harmonic distance : 10.75348, average 1.53621 Vogel's harmonic complexity : 16.85714 Wille's k value : 337 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 83.76781, average 2.99171 Lattice compactness (without 2's) : 58.68910, average 2.09604 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.14286 9 1 3: -1 .. 4 1.28571 11 3 5: -2 .. 0 -0.57143 4 3 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 15 / 7 = 2.14286 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: 20.4434 c. M: 32.4814 c. Lebeng 12: 2 1 2 2 1 2 2 P M ME S SD: 16.1056 c. M: 35.1926 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 19: 3 2 3 3 2 3 3 SP M ME S SD: 8.9647 c. M: 14.4363 c. Nineteen-tone Natural Minor, Aeolian 33: 6 3 5 5 4 5 5 SP SD: 9.1395 c. M:-14.2718 c. 34: 6 3 5 6 4 5 5 SP SD: 6.2402 c. M:-11.8662 c. 39: 7 3 6 7 4 6 6 SP SD: 6.3824 c. M:-11.4746 c. 41: 7 4 6 7 5 6 6 SP SD: 6.2337 c. M:-13.5879 c. 45: 8 4 7 7 5 7 7 SP SD: 7.0440 c. M:-9.4233 c. 46: 8 4 7 8 5 7 7 SP SD: 2.4294 c. M:-4.7857 c. 53: 9 5 8 9 6 8 8 SP SD: 1.1897 c. M:-2.5433 c. 99: 17 9 15 17 11 15 15 SP SD: 1.1271 c. M:-2.1506 c. 118: 20 11 18 20 13 18 18 SP SD: 0.6152 c. M: 1.2943 c. 164: 28 15 25 28 18 25 25 SP SD: 0.7356 c. M: 1.0462 c. 171: 29 16 26 29 19 26 26 SP SD: 0.1990 c. M: 0.4012 c. 388: 66 36 59 66 43 59 59 SP SD: 0.1335 c. M:-0.2137 c. 441: 75 41 67 75 49 67 67 SP SD: 0.1105 c. M:-0.1816 c. 559: 95 52 85 95 62 85 85 SP SD: 0.0634 c. M: 0.1300 c. 612: 104 57 93 104 68 93 93 SP SD: 0.0465 c. M:-0.1015 c. 783: 133 73 119 133 87 119 119 SP SD: 0.0504 c. M: 0.0786 c. 1000: 170 93 152 170 111 152 152 SP SD: 0.0446 c. M:-0.0900 c. 1171: 199 109 178 199 130 178 178 SP SD: 0.0106 c. M:-0.0183 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 7:8 x 9 x 11:13:14 SD: 20.4080 cents 8:9:10:11:12:13:14:16 S SD: 14.4559 cents 9:10:11:12:14:15:16:18 S SD: 13.0271 cents 10:11:12:13:15:16:18:20 SD: 8.9184 cents 12 x 14:16:18:19:22:24 SD: 11.7362 cents 14:16:17:19:21:23:25:28 SD: 7.6674 cents 15:17:18:20:23:24:27:30 SD: 6.5053 cents 16:18:19:21:24:26:29:32 SD: 5.0386 cents 24:27:29:32:36:39:43:48 SD: 2.1971 cents 40:45:48:53:60:65:72:80 SD: 1.7278 cents 50:56:60:67:75:81:90:100 SD: 1.6538 cents 56:63:67:75:84:91:101:112 SD: 1.6057 cents 64:72:77:85:96:104:115:128 SD: 1.4547 cents 66:74:79:88:99:107:119:132 SD: 1.1376 cents 80:90:96:107:120:130:144:160 SD: 1.0846 cents 90:101:108:120:135:146:162:180 SD: 0.6991 cents 120:135:144:160:180:194:216:240 SD: 0.5094 cents 144:162:173:192:216:233:259:288 SD: 0.4544 cents 150:169:180:200:225:243:270:300 SD: 0.3661 cents 200:225:240:267:300:324:360:400 SD: 0.3090 cents 210:236:252:280:315:340:378:420 SD: 0.2995 cents 216:243:259:288:324:350:389:432 SD: 0.2363 cents 240:270:288:320:360:389:432:480 SD: 0.1272 cents 360:405:432:480:540:583:648:720 SD: 0.0848 cents 600:675:720:800:900:972:1080:1200 SD: 0.0000 cents