Scala analysis: xen10-wilson-purvi-03b-03
Purvi modulation 3 from Figure 3b, Al-Farabi (8/7 49/48 8/7)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 9/7 435.084095 septimal major third, BP third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 12/7 933.129094 septimal major sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 8/7 231.1741 septimal whole tone 2: 9/8 203.9100 major whole tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 9/8 203.9100 major whole tone 5: 8/7 231.1741 septimal whole tone 6: 49/48 35.6968 slendro diesis, septimal 1/6-tone 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 3 8/7 231.174 cents septimal whole tone 2: 4 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 3: 2 21/16 470.781 cents narrow fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 72/49 666.258 cents Arabic lute grave fifth 4: 1 49/36 533.742 cents Arabic lute acute fourth 4: 4 3/2 701.955 cents perfect fifth 4: 2 32/21 729.219 cents wide fifth 5: 1 49/32 737.652 cents 5: 2 14/9 764.916 cents septimal minor sixth 5: 4 12/7 933.129 cents septimal major sixth 6: 3 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/14 1137.039 cents septimal major seventh 6: 1 96/49 1164.303 cents 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 : 231.2 435.1 498.0 702.0 933.1 968.8 1200.0 231.2 : 203.9 266.9 470.8 702.0 737.7 968.8 1200.0 435.1 : 63.0 266.9 498.0 533.7 764.9 996.1 1200.0 498.0 : 203.9 435.1 470.8 702.0 933.1 1137.0 1200.0 702.0 : 231.2 266.9 498.0 729.2 933.1 996.1 1200.0 933.1 : 35.7 266.9 498.0 702.0 764.9 968.8 1200.0 968.8 : 231.2 462.3 666.3 729.2 933.1 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 231.1741 cents 384/343, 195.4773 cents 49/48, 35.6968 cents 2: 266.8709 .. 462.3482 cents 384/343, 195.4773 cents 49/48, 35.6968 cents 3: 470.7809 .. 666.2582 cents 384/343, 195.4773 cents 1029/1024, 8.4327 cents 4: 533.7418 .. 729.2191 cents 384/343, 195.4773 cents 2401/2592,-132.5164 cents 5: 737.6518 .. 933.1291 cents 384/343, 195.4773 cents 1029/1024, 8.4327 cents 6: 968.8259 .. 1164.3032 cents 384/343, 195.4773 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 4.802350 Largest / Average step : 1.348516 Largest / Smallest step : 6.476043 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 173.44213 cents, oct.: 1214.09491 cents Scale is not proper Step pattern alph. order: ABCBADA Step pattern size order : DCBCDAD Scale is a Constant Structure, by a margin of 8.43272 cents Scale diversity : 1.245352 Lumma stability : 0.133044 Lumma impropriety factor : 0.110430 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 : 4 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1029/1024, 8.4327 cents Most common triad is 0.0 266.871 498.045 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 5 = 71.4286% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 195.4773 cents: 1 -- Rational properties -- Prime limit : 7 Odd number limit : 49 (O: 49 U: 49) Highest odd numerator or denominator: 9 Scale harmonicity : 0.029787 Average absolute harmonicity : 0.253511 Specific harmonicity : 0.177472 Fundamental : 1/84, -6.3923 octaves, 3.1146 Hz. Guide tone : 504, 8.9773 octaves, 131859.285 Hz. Exponens Consonantiae : 4.233600E+04, 15.36960 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 38.0, average 5.42857 Mersenne's string divisions : 351120 Sum of van Prooijen's expressibility: 4.44378, average 0.63483 Sum of Tenney's harmonic distance : 9.07733, average 1.29676 Vogel's harmonic complexity : 12.00000 Wille's k value : 73 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 75.07902, average 2.68139 Lattice compactness (without 2's) : 41.83447, average 1.49409 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.71429 11 1 3: -1 .. 2 0.42857 5 2 7: -1 .. 1 -0.28571 4 4 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 10 22| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 12 18|
FIT/MODE
7: 1 1 0 2 1 0 2 N T3 SD: 88.3737 c. M: 155.1879 c. 8: 2 1 0 2 1 0 2 N SD: 46.9204 c. M:-68.8259 c. 9: 2 1 1 1 2 0 2 N T3 SD: 29.8590 c. M:-35.4926 c. 10: 2 2 0 2 2 0 2 N M DE S SD: 22.5088 c. M:-44.9159 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 24.7263 c. M: 35.0841 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 14: 3 2 1 2 3 0 3 N SD: 16.9593 c. M:-25.9688 c. 17: 3 3 1 3 3 1 3 N M DE S SD: 12.8591 c. M:-19.4094 c. Safi al-Din's maqam `Ussaq 22: 4 4 1 4 4 1 4 N M DE S SD: 8.2408 c. M:-12.9923 c. 27: 5 5 1 5 5 1 5 N M DE S SD: 7.7053 c. M:-9.3603 c. 31: 6 5 2 5 6 1 6 N SD: 4.7643 c. M: 9.2776 c. 36: 7 6 2 6 7 1 7 N SD: 1.6935 c. M:-2.1592 c. 77: 15 13 4 13 15 2 15 N SD: 1.6769 c. M:-2.5921 c. 94: 18 16 5 16 18 3 18 N SD: 0.9611 c. M:-1.3869 c. 99: 19 17 5 17 19 3 19 N SD: 0.8871 c. M:-1.2795 c. 130: 25 22 7 22 25 4 25 N SD: 0.6417 c. M: 1.2379 c. 135: 26 23 7 23 26 4 26 N SD: 0.2434 c. M:-0.4715 c. 171: 33 29 9 29 33 5 33 N SD: 0.2536 c. M:-0.4049 c. 265: 51 45 14 45 51 8 51 N SD: 0.2203 c. M: 0.3671 c. 306: 59 52 16 52 59 9 59 N SD: 0.1534 c. M:-0.2100 c. 400: 77 68 21 68 77 12 77 N SD: 0.1124 c. M:-0.1741 c. 436: 84 74 23 74 84 13 84 N SD: 0.1128 c. M: 0.2217 c. 535: 103 91 28 91 103 16 103 N SD: 0.0988 c. M:-0.1461 c. 571: 110 97 30 97 110 17 110 N SD: 0.0289 c. M: 0.0578 c. 706: 136 120 37 120 136 21 136 N SD: 0.0239 c. M:-0.0434 c. 1277: 246 217 67 217 246 38 246 N SD: 0.0046 c. M:-0.0073 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: 16.2568 cents 4 x 5 x 6 x 7:8 S SD: 12.1926 cents 5:6 x 7:8 x 9:10 S SD: 34.1361 cents 6:7 x 8:9:10:11:12 S SD: 16.7821 cents 7:8:9 x 11:12 x 14 SD: 16.1074 cents 8:9:10:11:12 x 14:16 S SD: 12.8667 cents 9:10 x 12:14:15:16:18 S SD: 16.2143 cents 10:11:13 x 15:17:18:20 SD: 14.2720 cents 11:13:14:15:17:19 x 22 SD: 14.9374 cents 12:14:15:16:18 x 21:24 S SD: 10.0731 cents 13:15:17 x 20:22:23:26 SD: 10.4266 cents 14:16:18:19:21:24:25:28 SD: 6.6428 cents 15:17:19:20:23 x 26:30 SD: 8.4982 cents 16:18 x 21:24:27:28:32 S SD: 7.8705 cents 18:21:23:24:27:31:32:36 SD: 6.6952 cents 19:22:24:25:29 x 33:38 SD: 9.2108 cents 20:23:26:27:30:34:35:40 SD: 4.8544 cents 21:24:27:28:32:36:37:42 SD: 4.2405 cents 24:27:31:32:36:41:42:48 SD: 4.1491 cents 28:32:36:37:42:48:49:56 SD: 2.2181 cents 36:41:46:48:54:62:63:72 SD: 2.0953 cents 42:48:54:56:63:72:74:84 SD: 1.6767 cents 48:55:62:64:72:82:84:96 SD: 1.5680 cents 56:64:72:75:84:96:98:112 SD: 1.1016 cents 84:96:108:112:126:144:147:168 S SD: 0.0000 cents