Scala analysis: xen10-wilson-purvi-03b-05
Purvi modulation 5 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: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 14/9 764.915905 septimal minor 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: 49/48 35.6968 slendro diesis, septimal 1/6-tone 3: 8/7 231.1741 septimal whole tone 4: 9/8 203.9100 major whole tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 9/8 203.9100 major whole 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 : 231.2 266.9 498.0 702.0 764.9 968.8 1200.0 231.2 : 35.7 266.9 470.8 533.7 737.7 968.8 1200.0 266.9 : 231.2 435.1 498.0 702.0 933.1 1164.3 1200.0 498.0 : 203.9 266.9 470.8 702.0 933.1 968.8 1200.0 702.0 : 63.0 266.9 498.0 729.2 764.9 996.1 1200.0 764.9 : 203.9 435.1 666.3 702.0 933.1 1137.0 1200.0 968.8 : 231.2 462.3 498.0 729.2 933.1 996.1 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 : 165.03147 cents, oct.: 1155.22029 cents Scale is not proper Step pattern alph. order: ABACDCA Step pattern size order : DADCBCD 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 0.0 701.955 933.129 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 2 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 5 = 71.4286% Scale is 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 195.4773 cents: 6 -- 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 : 0.253645 Specific harmonicity : 0.177472 Fundamental : 1/252, -7.9773 octaves, 1.0382 Hz. Guide tone : 168, 7.3923 octaves, 43953.095 Hz. Exponens Consonantiae : 4.233600E+04, 15.36960 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 38.5, average 5.50000 Mersenne's string divisions : 345345 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 : 16.14286 Wille's k value : 220 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 0.42857 11 1 3: -2 .. 1 -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 1 1 0 2 1 N T3 SD: 53.0679 c. M: 79.2016 c. 9: 2 0 2 1 1 1 2 N T3 SD: 29.8590 c. M:-35.4926 c. 10: 2 0 2 2 0 2 2 N M DE S SD: 22.5088 c. M: 44.9159 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 24.7263 c. M:-35.0841 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 14: 3 0 3 2 1 2 3 N SD: 16.9593 c. M:-25.9688 c. 17: 3 1 3 3 1 3 3 N M DE S SD: 12.8591 c. M:-19.4094 c. Seventeen-tone Natural Minor 22: 4 1 4 4 1 4 4 N M DE S SD: 8.2408 c. M:-12.9923 c. Twenty-two tone Minor, Superpyth-7 27: 5 1 5 5 1 5 5 N M DE S SD: 7.7053 c. M: 9.3603 c. 31: 6 1 6 5 2 5 6 N SD: 4.7643 c. M:-9.2776 c. 36: 7 1 7 6 2 6 7 N SD: 1.6935 c. M:-2.1592 c. 77: 15 2 15 13 4 13 15 N SD: 1.6769 c. M:-2.5921 c. 94: 18 3 18 16 5 16 18 N SD: 0.9611 c. M:-1.3869 c. 99: 19 3 19 17 5 17 19 N SD: 0.8871 c. M: 1.2795 c. 130: 25 4 25 22 7 22 25 N SD: 0.6417 c. M:-1.2379 c. 135: 26 4 26 23 7 23 26 N SD: 0.2434 c. M: 0.4715 c. 171: 33 5 33 29 9 29 33 N SD: 0.2536 c. M:-0.4049 c. 265: 51 8 51 45 14 45 51 N SD: 0.2203 c. M:-0.3671 c. 306: 59 9 59 52 16 52 59 N SD: 0.1534 c. M: 0.2100 c. 400: 77 12 77 68 21 68 77 N SD: 0.1124 c. M:-0.1741 c. 436: 84 13 84 74 23 74 84 N SD: 0.1128 c. M:-0.2217 c. 535: 103 16 103 91 28 91 103 N SD: 0.0988 c. M:-0.1461 c. 571: 110 17 110 97 30 97 110 N SD: 0.0289 c. M:-0.0578 c. 706: 136 21 136 120 37 120 136 N SD: 0.0239 c. M: 0.0434 c. 1277: 246 38 246 217 67 217 246 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 x 5:6 S SD: 28.1557 cents 4 x x 5:6 x 7:8 S SD: 27.9328 cents 5 x 6:7 x 8:9:10 S SD: 23.8917 cents 6 x 7:8:9 x 11:12 SD: 16.1074 cents 7:8 x 9 x 11:12:14 SD: 14.8960 cents 8:9 x 11:12 x 14:16 SD: 11.9689 cents 9:10:11:12 x 14:16:18 S SD: 16.3368 cents 11 x 13:15 x 17:19:22 SD: 10.2996 cents 12 x 14:16:18:19:21:24 SD: 5.1070 cents 13:15 x 17 x 20:23:26 SD: 9.2272 cents 14:16 x 19:21:22:25:28 SD: 8.2851 cents 15:17:18:20 x 23:26:30 SD: 9.8368 cents 16:18:19:21:24:25:28:32 SD: 7.1215 cents 17:19:20:23 x 26:30:34 SD: 9.7337 cents 18 x 21:24:27:28:32:36 S SD: 4.5440 cents 19 x 22:25:29:30:33:38 SD: 8.2353 cents 20:23 x 27:30:31:35:40 SD: 4.1407 cents 25 x 29:33:38:39:44:50 SD: 5.3972 cents 26:30 x 35:39:40:46:52 SD: 5.9462 cents 27:31:32:36:41:42:47:54 SD: 5.2350 cents 28:32:33:37:42:44:49:56 SD: 4.1868 cents 29:33:34:39:44:45:51:58 SD: 4.1187 cents 30:34:35:40:45:47:53:60 SD: 3.5885 cents 32 x 37:43:48:50:56:64 SD: 3.6593 cents 34:39:40:45:51:53:60:68 SD: 3.6044 cents 36:41:42:48:54:56:63:72 SD: 0.8602 cents 84:96:98:112:126:131:147:168 SD: 0.6301 cents 120:137:140:160:180:187:210:240 SD: 0.5110 cents 132:151:154:176:198:205:231:264 SD: 0.4650 cents 168:192:196:224:252:261:294:336 SD: 0.3157 cents 204:233:238:272:306:317:357:408 SD: 0.3009 cents 216:247:252:288:324:336:378:432 SD: 0.1431 cents 252:288:294:336:378:392:441:504 S SD: 0.0000 cents