Scala analysis: xen10-wilson-purvi-04-03
Purvi modulation 3 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: 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: 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: 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: 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: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 3 9/8 203.910 cents major whole tone 1: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 81/64 407.820 cents Pythagorean major third 2: 2 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: 2 14/9 764.916 cents septimal minor sixth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 2 12/7 933.129 cents septimal major sixth 6: 2 7/4 968.826 cents harmonic seventh 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 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: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 435.1 498.0 702.0 933.1 996.1 1200.0 203.9 : 231.2 294.1 498.0 729.2 792.2 996.1 1200.0 435.1 : 63.0 266.9 498.0 561.0 764.9 968.8 1200.0 498.0 : 203.9 435.1 498.0 702.0 905.9 1137.0 1200.0 702.0 : 231.2 294.1 498.0 702.0 933.1 996.1 1200.0 933.1 : 63.0 266.9 470.8 702.0 764.9 968.8 1200.0 996.1 : 203.9 407.8 639.0 702.0 905.9 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: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 174.41585 cents, oct.: 1220.91093 cents Scale is not proper Scale is a mode of a 1277-tone equal temperament with octave 2/1 degrees: 217 463 530 747 993 1060 1277 Least number of segments generator : 639 of 600.470 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 747 of 701.958 cents and inv. generated superset size: 72 = 65 more = 1028.571% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABCA Step pattern size order : MLSMLSM Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.378117 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 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: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale is Hypodorian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords Scale contains a complete diamond : 1 3 9 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 : 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 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 168.2132 cents: 1 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 9 Scale harmonicity : 0.035775 Average absolute harmonicity : 0.263579 Specific harmonicity : 0.200148 Fundamental : 1/504, -8.9773 octaves, 0.5191 Hz. Guide tone : 144, 7.1699 octaves, 37674.081 Hz. Exponens Consonantiae : 7.257600E+04, 16.14720 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 46.0, average 6.57143 Mersenne's string divisions : 2713200 Sum of van Prooijen's expressibility: 4.66207, average 0.66601 Sum of Tenney's harmonic distance : 9.89768, average 1.41395 Vogel's harmonic complexity : 16.00000 Wille's k value : 283 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 92.07766, average 3.28849 Lattice compactness (without 2's) : 51.81272, average 1.85045 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.71429 13 1 3: -2 .. 2 0.42857 9 4 7: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 1 / 7 = 0.14286 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 2 0 1 1 1 1 N T3 SD: 45.8015 c. M:-79.2016 c. 9: 1 2 0 2 2 0 2 N T3 S SD: 54.7833 c. M: 98.0450 c. 10: 2 2 0 2 2 0 2 N M DE S SD: 29.2665 c. M:-44.9159 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 18.3873 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: 2 3 1 2 3 1 2 P T3 SD: 19.9093 c. M:-32.4814 c. Unicycle Gestures 17: 3 3 1 3 3 1 3 N M DE S SD: 8.6804 c. M: 15.4820 c. Safi al-Din's maqam `Ussaq 19: 3 4 1 3 4 1 3 N SD: 10.5090 c. M:-14.4363 c. 22: 4 4 1 4 4 1 4 N M DE S SD: 8.8249 c. M:-14.2718 c. 24: 4 5 1 4 5 1 4 N SD: 8.8264 c. M:-16.8709 c. 31: 5 6 2 5 6 2 5 N SD: 7.2827 c. M:-10.3616 c. 36: 6 7 2 6 7 2 6 N SD: 2.4298 c. M:-3.9100 c. 41: 7 8 2 7 8 2 7 N SD: 2.0638 c. M:-3.9403 c. 58: 10 11 3 10 11 3 10 N SD: 1.9657 c. M:-2.9865 c. 77: 13 15 4 13 15 4 13 N SD: 1.1767 c. M:-1.9358 c. 94: 16 18 5 16 18 5 16 N SD: 0.6389 c. M: 1.2142 c. 135: 23 26 7 23 26 7 23 N SD: 0.3738 c. M:-0.5344 c. 171: 29 33 9 29 33 9 29 N SD: 0.2519 c. M:-0.4012 c. 265: 45 51 14 45 51 14 45 N SD: 0.1966 c. M: 0.3671 c. 306: 52 59 16 52 59 16 52 N SD: 0.1109 c. M:-0.2100 c. 400: 68 77 21 68 77 21 68 N SD: 0.0793 c. M: 0.1291 c. 571: 97 110 30 97 110 30 97 N SD: 0.0420 c. M: 0.0578 c. 706: 120 136 37 120 136 37 120 N SD: 0.0377 c. M:-0.0560 c. 877: 149 169 46 149 169 46 149 N SD: 0.0310 c. M:-0.0522 c. 1277: 217 246 67 217 246 67 217 N SD: 0.0037 c. M:-0.0054 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: 13.9684 cents 5:6 x 7:8 x 9:10 S SD: 36.0915 cents 6:7 x 8:9:10:11:12 S SD: 15.9693 cents 7:8:9 x 11:12 x 14 SD: 17.0053 cents 8:9:10:11:12 x 14:16 S SD: 12.8667 cents 9:10 x 12:14:15:16:18 S SD: 13.7489 cents 10:11:13 x 15:17:18:20 SD: 8.4196 cents 12:14:15:16:18 x 21:24 S SD: 14.0297 cents 13:15:17 x 20:22:23:26 SD: 12.1014 cents 14:16:18:19:21:24:25:28 SD: 5.9620 cents 16:18 x 21:24:27:28:32 S SD: 7.8705 cents 17:19:22:23:26:29:30:34 SD: 6.7922 cents 18:20:23:24:27:31:32:36 SD: 3.6179 cents 24:27:31:32:36:41:43:48 SD: 2.3978 cents 32:36:41:43:48:55:57:64 SD: 2.2563 cents 42:47:54:56:63:72:75:84 SD: 1.7132 cents 56:63:72:75:84:96:100:112 SD: 1.5580 cents 63:71:81:84:95:108:112:126 SD: 1.3760 cents 66:74:85:88:99:113:117:132 SD: 1.2089 cents 80:90:103:107:120:137:142:160 SD: 0.9640 cents 98:110:126:131:147:168:174:196 SD: 0.9011 cents 102:115:131:136:153:175:181:204 SD: 0.7812 cents 112:126:144:149:168:192:199:224 SD: 0.5696 cents 126:142:162:168:189:216:224:252 SD: 0.4358 cents 144:162:185:192:216:247:256:288 SD: 0.2386 cents 312:351:401:416:468:535:555:624 SD: 0.1849 cents 336:378:432:448:504:576:597:672 SD: 0.1381 cents 360:405:463:480:540:617:640:720 SD: 0.0954 cents 504:567:648:672:756:864:896:1008 S SD: 0.0000 cents