Scala analysis: xen10-wilson-purvi-04-04
Purvi modulation 4 from Figure 4, Archytas (8/7 9/8 28/27) all 6 permutations
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: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 12/7 933.129094 septimal major sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 9/8 203.9100 major whole tone 2: 256/243 90.2250 limma, Pythagorean minor second 3: 9/8 203.9100 major whole tone 4: 9/8 203.9100 major whole tone 5: 8/7 231.1741 septimal whole tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 4 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 3 32/27 294.135 cents Pythagorean minor third 2: 2 81/64 407.820 cents Pythagorean major third 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 5 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 4: 1 112/81 561.006 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 2 128/81 792.180 cents Pythagorean minor sixth 5: 3 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 4 16/9 996.090 cents Pythagorean minor seventh 6: 1 243/128 1109.775 cents Pythagorean major seventh 6: 1 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.66667 = 11/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 294.1 498.0 702.0 933.1 996.1 1200.0 203.9 : 90.2 294.1 498.0 729.2 792.2 996.1 1200.0 294.1 : 203.9 407.8 639.0 702.0 905.9 1109.8 1200.0 498.0 : 203.9 435.1 498.0 702.0 905.9 996.1 1200.0 702.0 : 231.2 294.1 498.0 702.0 792.2 996.1 1200.0 933.1 : 63.0 266.9 470.8 561.0 764.9 968.8 1200.0 996.1 : 203.9 407.8 498.0 702.0 905.9 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 231.1741 cents 54/49, 168.2132 cents 28/27, 62.9609 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 470.7809 .. 638.9941 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 4: 561.0059 .. 729.2191 cents 54/49, 168.2132 cents 6272/6561,-77.9882 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 6: 968.8259 .. 1137.0391 cents 54/49, 168.2132 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.722778 Largest / Average step : 1.348516 Largest / Smallest step : 3.671709 Median interval of one step : 9/8, 203.9100 cents, amount: 4 Most common interval of one step : 9/8, 203.9100 cents, amount: 4 Least squares average step : 172.40229 cents, oct.: 1206.81602 cents Scale is not proper Step pattern alph. order: ABAACDA Step pattern size order : CBCCDAC Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.447201 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 Rothenberg efficiency : 0.496599 redundancy: 0.503401 Efficiency x scale size : 3.476190 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.66667 = 11/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 64/63, 27.2641 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 5 = 71.4286% Scale is n-1 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 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.031627 Average absolute harmonicity : 0.265422 Specific harmonicity : 0.206896 Fundamental : 1/1512, -10.5622 octaves, 0.1730 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 4.354560E+05, 18.73217 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 67.5, average 9.64286 Mersenne's string divisions : 10004925 Sum of van Prooijen's expressibility: 5.13919, average 0.73417 Sum of Tenney's harmonic distance : 11.03485, average 1.57641 Vogel's harmonic complexity : 18.57143 Wille's k value : 850 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 108.37030, average 3.87037 Lattice compactness (without 2's) : 58.76409, average 2.09872 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 1.42857 18 1 3: -3 .. 2 -0.28571 10 5 7: -1 .. 0 -0.14286 1 1 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 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 1 1 1 SP B ME I SD: 39.2526 c. M: 75.9862 c. Lebeng 10: 2 0 2 2 2 0 2 N M DE I SD: 31.4162 c. M: 54.1350 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 12.9292 c. M: 33.1291 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 17: 3 1 3 3 3 1 3 N M DE I SD: 8.7240 c. M: 15.4820 c. Supra-7 24: 4 2 4 4 5 1 4 N SD: 7.1439 c. M:-16.8709 c. 36: 6 3 6 6 7 2 6 N SD: 3.2218 c. M:-5.8650 c. 41: 7 3 7 7 8 2 7 N SD: 1.5305 c. M:-3.4563 c. 77: 13 6 13 13 15 4 13 N SD: 1.3056 c. M:-1.9689 c. 94: 16 7 16 16 18 5 16 N SD: 0.5399 c. M: 1.2142 c. 135: 23 10 23 23 26 7 23 N SD: 0.4470 c. M: 0.8017 c. 171: 29 13 29 29 33 9 29 N SD: 0.3394 c. M:-0.6018 c. 212: 36 16 36 36 41 11 36 N SD: 0.3344 c. M:-0.8332 c. 265: 45 20 45 45 51 14 45 N SD: 0.1593 c. M: 0.2989 c. 306: 52 23 52 52 59 16 52 N SD: 0.0778 c. M:-0.2042 c. 400: 68 30 68 68 77 21 68 N SD: 0.0888 c. M: 0.1350 c. 571: 97 43 97 97 110 30 97 N SD: 0.0483 c. M:-0.0857 c. 706: 120 53 120 120 136 37 120 N SD: 0.0465 c. M: 0.0840 c. 877: 149 66 149 149 169 46 149 N SD: 0.0337 c. M:-0.0522 c. 971: 165 73 165 165 187 51 165 N SD: 0.0268 c. M: 0.0704 c. 1277: 217 96 217 217 246 67 217 N SD: 0.0048 c. M: 0.0081 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: 24.0316 cents 5 x 6:7:8 x 9:10 S SD: 28.6661 cents 6 x 7:8:9:10:11:12 S SD: 12.8667 cents 7:8 x 9:11:12 x 14 SD: 21.1600 cents 8:9 x 11:12 x 14:16 SD: 11.9689 cents 10:11:12:13:15:17:18:20 SD: 9.6571 cents 12 x 14:16:18 x 21:24 S SD: 7.7114 cents 13:15 x 17:20:22:23:26 SD: 12.4064 cents 14:16:17:19:21:24:25:28 SD: 8.4579 cents 15:17:18:20:23:26:27:30 SD: 7.6959 cents 16:18:19:21:24:27:28:32 SD: 6.7634 cents 18:20:21:24:27:31:32:36 SD: 5.0906 cents 22:25:26:29:33:38:39:44 SD: 4.3176 cents 31:35:37:41:47:53:55:62 SD: 3.9379 cents 32:36:38:43:48:55:57:64 SD: 2.1410 cents 42:47:50:56:63:72:75:84 SD: 2.0368 cents 48:54:57:64:72:82:85:96 SD: 1.3820 cents 64:72:76:85:96:110:114:128 SD: 1.3478 cents 66:74:78:88:99:113:117:132 SD: 1.3355 cents 72:81:85:96:108:123:128:144 SD: 1.2950 cents 80:90:95:107:120:137:142:160 SD: 1.0219 cents 96:108:114:128:144:165:171:192 SD: 0.9378 cents 102:115:121:136:153:175:181:204 SD: 0.7676 cents 112:126:133:149:168:192:199:224 SD: 0.7466 cents 120:135:142:160:180:206:213:240 SD: 0.6457 cents 136:153:161:181:204:233:242:272 SD: 0.6021 cents 144:162:171:192:216:247:256:288 SD: 0.5033 cents 162:182:192:216:243:278:288:324 SD: 0.4242 cents 168:189:199:224:252:288:299:336 SD: 0.3085 cents 216:243:256:288:324:370:384:432 SD: 0.1909 cents 378:425:448:504:567:648:672:756 SD: 0.1454 cents 432:486:512:576:648:741:768:864 SD: 0.1431 cents 480:540:569:640:720:823:853:960 SD: 0.1162 cents 594:668:704:792:891:1018:1056:1188 SD: 0.1157 cents