Scala analysis: xen10-wilson-purvi-08a-04
Purvi modulation 4 from Figure 8a, Ptolemy (12/11 22/21 7/6), (7/6 12/11 22/21)
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: 14/11 417.507964 undecimal diminished fourth or major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 18/11 852.592059 undecimal neutral sixth 6: 21/11 1119.462965 undecimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 9/8 203.9100 major whole tone 2: 112/99 213.5980 3: 22/21 80.5370 undecimal minor semitone 4: 9/8 203.9100 major whole tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 7/6 266.8709 septimal minor third 7: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 1: 1 7/6 266.871 cents septimal minor third 2: 2 33/28 284.447 cents undecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 44/27 845.453 cents neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 56/33 915.553 cents 6: 1 12/7 933.129 cents septimal major sixth 6: 1 99/56 986.402 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 21/11 1119.463 cents undecimal major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 417.5 498.0 702.0 852.6 1119.5 1200.0 203.9 : 213.6 294.1 498.0 648.7 915.6 996.1 1200.0 417.5 : 80.5 284.4 435.1 702.0 782.5 986.4 1200.0 498.0 : 203.9 354.5 621.4 702.0 905.9 1119.5 1200.0 702.0 : 150.6 417.5 498.0 702.0 915.6 996.1 1200.0 852.6 : 266.9 347.4 551.3 764.9 845.5 1049.4 1200.0 1119.5: 80.5 284.4 498.0 578.6 782.5 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 266.8709 cents 49/44, 186.3339 cents 22/21, 80.5370 cents 2: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 99/98, 17.5761 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 915.5530 cents 392/363, 133.0609 cents 99/98, 17.5761 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 99/98, 17.5761 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.128568 Largest / Average step : 1.556747 Largest / Smallest step : 3.313642 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 176.57585 cents, oct.: 1236.03095 cents Scale is not proper Step pattern alph. order: ABCADEC Step pattern size order : CDACBEA Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.581147 Lumma stability : 0.192815 Lumma impropriety factor : 0.035697 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 243/242, 7.1391 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 Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 21 Scale harmonicity : 0.024115 Average absolute harmonicity : 0.244837 Specific harmonicity : 0.118851 Fundamental : 1/264, -8.0444 octaves, 0.9910 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 6.652800E+04, 16.02167 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 59.0, average 8.42857 Mersenne's string divisions : 8282400 Sum of van Prooijen's expressibility: 5.31349, average 0.75907 Sum of Tenney's harmonic distance : 10.86349, average 1.55193 Vogel's harmonic complexity : 16.57143 Wille's k value : 148 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 72.58084, average 2.59217 Lattice compactness (without 2's) : 46.50078, average 1.66074 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.14286 9 1 3: -1 .. 2 0.71429 7 3 7: 0 .. 1 0.28571 2 11: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 21 26| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 21 23| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 46.9609 c. M: 90.8915 c. Lebeng 8: 1 2 0 2 1 1 1 P D3 S SD: 47.2853 c. M: 69.4630 c. 9: 1 2 0 2 1 2 1 N D3 SD: 55.6764 c. M: 98.0450 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 31.5703 c. M: 57.5080 c. Sethares Neutral, Beatles-7, Dichotic-7 11: 2 2 1 1 2 2 1 P D3 S SD: 29.9411 c. M:-47.4095 c. 12: 2 2 1 2 1 3 1 P D3 SD: 22.2781 c. M: 52.5921 c. Harmonic Major, Mischung 2, Mela Sarasangi, Raga Anand Leela, Haripriya, Nat Bhairav, Simhavahini, Ethiopian, Tabahaniotikos: Greece 14: 2 3 1 2 2 3 1 P T3 SD: 15.8226 c. M: 32.4814 c. 17: 3 3 1 3 2 4 1 N SD: 6.0757 c. M:-9.9488 c. 31: 5 6 2 5 4 7 2 N SD: 5.8626 c. M: 10.3616 c. 41: 7 7 3 7 5 9 3 N SD: 4.2903 c. M: 7.7519 c. 46: 8 8 3 8 6 10 3 N SD: 3.9291 c. M:-8.2775 c. 48: 8 9 3 8 6 11 3 N SD: 4.0785 c. M:-7.4920 c. 58: 10 10 4 10 7 13 4 N SD: 2.6924 c. M: 4.3162 c. 72: 12 13 5 12 9 16 5 N SD: 2.3354 c. M: 3.9100 c. 87: 15 15 6 15 11 19 6 N SD: 2.3535 c. M: 3.7149 c. 89: 15 16 6 15 11 20 6 N SD: 1.4365 c. M: 3.1539 c. 101: 17 18 7 17 13 22 7 N SD: 1.8295 c. M:-2.8535 c. 106: 18 19 7 18 13 24 7 N SD: 1.5140 c. M: 3.5355 c. 118: 20 21 8 20 15 26 8 N SD: 0.7649 c. M:-1.6452 c. 135: 23 24 9 23 17 30 9 N SD: 0.4374 c. M:-0.7413 c. 224: 38 40 15 38 28 50 15 N SD: 0.3735 c. M: 0.8063 c. 342: 58 61 23 58 43 76 23 N SD: 0.1969 c. M: 0.4012 c. 359: 61 64 24 61 45 80 24 N SD: 0.1894 c. M:-0.3193 c. 477: 81 85 32 81 60 106 32 N SD: 0.1172 c. M:-0.2381 c. 701: 119 125 47 119 88 156 47 N SD: 0.1248 c. M: 0.2010 c. 836: 142 149 56 142 105 186 56 N SD: 0.1026 c. M:-0.1954 c. 877: 149 156 59 149 110 195 59 N SD: 0.1131 c. M: 0.1927 c. 894: 152 159 60 152 112 199 60 N SD: 0.1089 c. M: 0.2431 c. 1012: 172 180 68 172 127 225 68 N SD: 0.0609 c. M: 0.1167 c. 1147: 195 204 77 195 144 255 77 N SD: 0.0599 c. M:-0.1005 c. 1354: 230 241 91 230 170 301 91 N SD: 0.0611 c. M: 0.1129 c. 1371: 233 244 92 233 172 305 92 N SD: 0.0319 c. M: 0.0756 c. 1489: 253 265 100 253 187 331 100 N SD: 0.0360 c. M:-0.0607 c. 1713: 291 305 115 291 215 381 115 N SD: 0.0343 c. M: 0.0571 c. 1848: 314 329 124 314 232 411 124 N SD: 0.0132 c. M:-0.0245 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: 10.5889 cents 4 x 5 x 6:7 x 8 S SD: 30.0867 cents 5 x 6:7 x 8 x 10 S SD: 34.4830 cents 6:7 x 8:9:10:11:12 S SD: 16.5724 cents 7:8:9 x x 11:13:14 SD: 18.1630 cents 8:9:10:11:12:13:15:16 SD: 10.0303 cents 10:11:13 x 15:16:19:20 SD: 11.1092 cents 12:14:15:16:18:20:23:24 SD: 11.0595 cents 13:15 x 17:20:21:25:26 SD: 12.5068 cents 14:16:18:19:21:23:27:28 SD: 6.9210 cents 18:20:23:24:27:29:34:36 SD: 5.6671 cents 22:25:28:29:33:36:42:44 SD: 3.7640 cents 30:34:38:40:45:49:57:60 SD: 2.5157 cents 48:54:61:64:72:79:92:96 SD: 1.7697 cents 54:61:69:72:81:88:103:108 SD: 1.7546 cents 58:65:74:77:87:95:111:116 SD: 1.6850 cents 63:71:80:84:95:103:120:126 SD: 1.6035 cents 66:74:84:88:99:108:126:132 SD: 0.8341 cents 88:99:112:117:132:144:168:176 SD: 0.7036 cents 96:108:122:128:144:157:183:192 SD: 0.5402 cents 144:162:183:192:216:236:275:288 SD: 0.5365 cents 162:182:206:216:243:265:309:324 SD: 0.4665 cents 168:189:214:224:252:275:321:336 SD: 0.3083 cents 198:223:252:264:297:324:378:396 SD: 0.2774 cents 264:297:336:352:396:432:504:528 SD: 0.0000 cents