Scala analysis: xen10-wilson-purvi-03a-02
Purvi modulation 2 from Figure 3a, Al-Farabi (8/7 8/7 49/48), (49/48 8/7 8/7)
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: 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: 96/49 1164.303188 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 49/48 35.6968 slendro diesis, septimal 1/6-tone 1: 9/8 203.9100 major whole tone 2: 8/7 231.1741 septimal 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: 8/7 231.1741 septimal whole tone 7: 49/48 35.6968 slendro diesis, septimal 1/6-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: 1 147/128 239.607 cents 2: 2 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean 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: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 256/147 960.393 cents 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: 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 : 203.9 435.1 498.0 702.0 933.1 1164.3 1200.0 203.9 : 231.2 294.1 498.0 729.2 960.4 996.1 1200.0 435.1 : 63.0 266.9 498.0 729.2 764.9 968.8 1200.0 498.0 : 203.9 435.1 666.3 702.0 905.9 1137.0 1200.0 702.0 : 231.2 462.3 498.0 702.0 933.1 996.1 1200.0 933.1 : 231.2 266.9 470.8 702.0 764.9 968.8 1200.0 1164.3: 35.7 239.6 470.8 533.7 737.7 968.8 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: 239.6068 .. 462.3482 cents 8192/7203, 222.7414 cents 1029/1024, 8.4327 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 .. 960.3932 cents 8192/7203, 222.7414 cents 1029/1024, 8.4327 cents 6: 968.8259 .. 1164.3032 cents 384/343, 195.4773 cents 1029/1024, 8.4327 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 : 181.62498 cents, oct.: 1271.37489 cents Scale is not proper Step pattern alph. order: ABCABBD Step pattern size order : CDBCDDA Scale is a Constant Structure, by a margin of 8.43272 cents Scale diversity : 1.315534 Lumma stability : 0.087604 Lumma impropriety factor : 0.110430 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 : 1029/1024, 8.4327 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 Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 3 = 42.8571% 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: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 147 (O: 147 U: 147) Highest odd numerator or denominator: 49 Scale harmonicity : 0.027344 Average absolute harmonicity : 0.253332 Specific harmonicity : 0.162044 Fundamental : 1/1176, -10.1997 octaves, 0.2225 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 3.386880E+05, 18.36960 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 106.0, average 15.14286 Mersenne's string divisions : 15736560 Sum of van Prooijen's expressibility: 5.39802, average 0.77115 Sum of Tenney's harmonic distance : 11.41178, average 1.63025 Vogel's harmonic complexity : 19.42857 Wille's k value : 661 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 95.55699, average 3.41275 Lattice compactness (without 2's) : 46.47818, average 1.65994 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 0.85714 14 1 3: -1 .. 2 0.85714 8 3 7: -2 .. 0 -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 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 2 0 1 1 2 0 N T3 SD: 46.1421 c. M:-79.2016 c. 8: 1 2 0 2 1 2 0 N T3 SD: 38.0173 c. M: 53.9100 c. 9: 2 1 1 1 2 2 0 N T3 SD: 35.7254 c. M:-62.7567 c. 10: 2 2 0 2 2 2 0 N M DE S SD: 29.1975 c. M:-44.9159 c. 12: 2 2 1 2 2 3 0 N SD: 22.7584 c. M:-35.6968 c. 14: 2 3 1 2 3 3 0 N SD: 20.6808 c. M:-35.6968 c. 17: 3 3 1 3 3 3 1 N M DE S SD: 15.5065 c. M: 34.8914 c. Seventeen-tone Major 18: 3 4 0 4 3 3 1 N SD: 23.7280 c. M:-31.5826 c. 19: 3 4 1 3 4 3 1 N T3 SD: 13.7258 c. M: 27.4611 c. 22: 4 4 1 4 4 4 1 N M DE S SD: 9.9766 c. M: 18.8486 c. Twenty-two tone Major 24: 4 5 1 4 5 4 1 N T3 SD: 10.2443 c. M:-16.8709 c. 27: 5 5 1 5 5 5 1 N M DE S SD: 9.7628 c. M:-18.3122 c. 28: 5 5 2 4 6 5 1 N SD: 10.8463 c. M:-16.2407 c. 29: 5 6 1 5 6 5 1 N T3 SD: 10.6569 c. M:-20.0883 c. 30: 5 6 1 5 6 6 1 N SD: 12.1772 c. M: 21.9550 c. 31: 5 6 2 5 6 6 1 N SD: 6.2448 c. M: 10.3616 c. 36: 6 7 2 6 7 7 1 N SD: 2.1255 c. M: 3.9100 c. 77: 13 15 4 13 15 15 2 N SD: 2.0168 c. M:-4.5280 c. 94: 16 18 5 16 18 18 3 N SD: 1.1652 c. M: 2.6011 c. 99: 17 19 5 17 19 19 3 N SD: 1.1377 c. M:-2.1506 c. 130: 22 25 7 22 25 25 4 N SD: 0.8239 c. M: 1.2379 c. 135: 23 26 7 23 26 26 4 N SD: 0.3190 c. M:-0.5344 c. 171: 29 33 9 29 33 33 5 N SD: 0.3057 c. M:-0.6091 c. 265: 45 51 14 45 51 51 8 N SD: 0.2758 c. M: 0.5296 c. 306: 52 59 16 52 59 59 9 N SD: 0.1883 c. M:-0.4027 c. 400: 68 77 21 68 77 77 12 N SD: 0.1351 c. M: 0.3032 c. 436: 74 84 23 74 84 84 13 N SD: 0.1478 c. M: 0.2403 c. 535: 91 103 28 91 103 103 16 N SD: 0.1213 c. M:-0.2021 c. 571: 97 110 30 97 110 110 17 N SD: 0.0378 c. M: 0.0578 c. 706: 120 136 37 120 136 136 21 N SD: 0.0312 c. M:-0.0560 c. 1277: 217 246 67 217 246 246 38 N SD: 0.0055 c. M: 0.0119 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 6:7 x 8 S SD: 15.1096 cents 5:6 x 7:8:9 x 10 S SD: 39.6168 cents 6:7 x 8:9:10 x 12 S SD: 15.9281 cents 7:8:9 x 11:12 x 14 SD: 17.0053 cents 8:9:10:11:12:14 x 16 S SD: 13.4276 cents 9:10 x 12:14:15 x 18 S SD: 16.4987 cents 10:11:13 x 15:17 x 20 SD: 9.1422 cents 11:12:14:15:17:19 x 22 SD: 14.4360 cents 12:14:15:16:18:21 x 24 S SD: 14.5458 cents 13:15:17 x 20:22:25:26 SD: 13.1650 cents 14:16:18:19:21:24:27:28 SD: 7.0358 cents 16:18 x 21:24:27:31:32 SD: 7.1839 cents 17:19:22:23:26:29:33:34 SD: 6.9295 cents 18:20:23:24:27:31:35:36 SD: 4.0715 cents 24:27:31:32:36:41:47:48 SD: 1.4341 cents 56:63:72:75:84:96:110:112 SD: 1.2757 cents 66:74:85:88:99:113:129:132 SD: 1.1446 cents 80:90:103:107:120:137:157:160 SD: 0.9771 cents 98:110:126:131:147:168:192:196 SD: 0.8440 cents 102:115:131:136:153:175:200:204 SD: 0.6663 cents 120:135:154:160:180:206:235:240 SD: 0.5827 cents 126:142:162:168:189:216:247:252 SD: 0.4587 cents 144:162:185:192:216:247:282:288 SD: 0.2616 cents 168:189:216:224:252:288:329:336 SD: 0.1074 cents