Scala analysis: xen10-wilson-purvi-08b-04
Purvi modulation 4 from Figure 8b, Ptolemy (7/6 22/21 12/11), (22/21 12/11 7/6)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 11/7 782.492036 undecimal augmented fifth 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: 22/21 80.5370 undecimal minor semitone 2: 7/6 266.8709 septimal minor third 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole tone 5: 22/21 80.5370 undecimal minor semitone 6: 112/99 213.5980 7: 9/8 203.9100 major whole tone
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 : 80.5 347.4 498.0 702.0 782.5 996.1 1200.0 80.5 : 266.9 417.5 621.4 702.0 915.6 1119.5 1200.0 347.4 : 150.6 354.5 435.1 648.7 852.6 933.1 1200.0 498.0 : 203.9 284.4 498.0 702.0 782.5 1049.4 1200.0 702.0 : 80.5 294.1 498.0 578.6 845.5 996.1 1200.0 782.5 : 213.6 417.5 498.0 764.9 915.6 1119.5 1200.0 996.1 : 203.9 284.4 551.3 702.0 905.9 986.4 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 : 166.90220 cents, oct.: 1168.31540 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : AEBCADC 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 fifths form a closed circle Best major 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 : 0.243275 Specific harmonicity : 0.118851 Fundamental : 1/126, -6.9773 octaves, 2.0764 Hz. Guide tone : 528, 9.0444 octaves, 138138.298 Hz. Exponens Consonantiae : 6.652800E+04, 16.02167 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 60.5, average 8.64286 Mersenne's string divisions : 270900 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 : 15.57143 Wille's k value : 94 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: -1 .. 4 1.00000 9 1 3: -2 .. 1 -0.71429 7 3 7: -1 .. 0 -0.28571 2 11: 0 .. 1 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: 0 2 1 1 1 1 1 N T3 SD: 44.1786 c. M: 80.5370 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 31.5703 c. M:-57.5080 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 20.5488 c. M: 47.4079 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 14: 1 3 2 2 1 3 2 P T3 SD: 15.8226 c. M:-32.4814 c. 17: 1 4 2 3 1 3 3 N SD: 6.0757 c. M: 9.9488 c. 31: 2 7 4 5 2 6 5 N SD: 5.8626 c. M:-10.3616 c. 41: 3 9 5 7 3 7 7 N SD: 4.2903 c. M:-7.7519 c. 46: 3 10 6 8 3 8 8 N SD: 3.9291 c. M: 8.2775 c. 48: 3 11 6 8 3 9 8 N SD: 4.0785 c. M: 7.4920 c. 58: 4 13 7 10 4 10 10 N SD: 2.6924 c. M:-4.3162 c. 72: 5 16 9 12 5 13 12 N SD: 2.3354 c. M:-3.9100 c. 87: 6 19 11 15 6 15 15 N SD: 2.3535 c. M:-3.7149 c. 89: 6 20 11 15 6 16 15 N SD: 1.4365 c. M:-3.1539 c. 101: 7 22 13 17 7 18 17 N SD: 1.8295 c. M: 2.8535 c. 106: 7 24 13 18 7 19 18 N SD: 1.5140 c. M:-3.5355 c. 118: 8 26 15 20 8 21 20 N SD: 0.7649 c. M: 1.6452 c. 135: 9 30 17 23 9 24 23 N SD: 0.4374 c. M: 0.7413 c. 224: 15 50 28 38 15 40 38 N SD: 0.3735 c. M:-0.8063 c. 342: 23 76 43 58 23 61 58 N SD: 0.1969 c. M:-0.4012 c. 359: 24 80 45 61 24 64 61 N SD: 0.1894 c. M: 0.3193 c. 477: 32 106 60 81 32 85 81 N SD: 0.1172 c. M: 0.2381 c. 701: 47 156 88 119 47 125 119 N SD: 0.1248 c. M:-0.2010 c. 836: 56 186 105 142 56 149 142 N SD: 0.1026 c. M: 0.1954 c. 877: 59 195 110 149 59 156 149 N SD: 0.1131 c. M:-0.1927 c. 894: 60 199 112 152 60 159 152 N SD: 0.1089 c. M:-0.2431 c. 1012: 68 225 127 172 68 180 172 N SD: 0.0609 c. M:-0.1167 c. 1147: 77 255 144 195 77 204 195 N SD: 0.0599 c. M: 0.1005 c. 1354: 91 301 170 230 91 241 230 N SD: 0.0611 c. M:-0.1129 c. 1371: 92 305 172 233 92 244 233 N SD: 0.0319 c. M:-0.0756 c. 1489: 100 331 187 253 100 265 253 N SD: 0.0360 c. M: 0.0607 c. 1713: 115 381 215 291 115 305 291 N SD: 0.0343 c. M:-0.0571 c. 1848: 124 411 232 314 124 329 314 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: 33.9556 cents 4 x 5 x 6 x 7:8 S SD: 11.8769 cents 5 x 6:7 x 8:9:10 S SD: 19.5749 cents 6 x 7:8:9 x 11:12 SD: 19.3124 cents 7 x x 9 x 11:12:14 SD: 22.2600 cents 8:9:10:11:12:13:14:16 S SD: 21.9852 cents 9:10:11:12 x 14:16:18 S SD: 17.2286 cents 10:11:12:13:15:16:18:20 SD: 15.3201 cents 11:12:13:15 x 17:20:22 SD: 18.3795 cents 12:13:15:16:18:19:21:24 SD: 10.8758 cents 13:14:16:17 x 20:23:26 SD: 11.7541 cents 14:15:17:19:21:22:25:28 SD: 7.3391 cents 18:19:22:24:27:28:32:36 SD: 3.1287 cents 36:38:44:48:54:57:64:72 SD: 2.6397 cents 40:42:49:53:60:63:71:80 SD: 1.8707 cents 58:61:71:77:87:91:103:116 SD: 1.5648 cents 63:66:77:84:95:99:112:126 SD: 1.3051 cents 80:84:98:107:120:126:142:160 SD: 1.3003 cents 81:85:99:108:122:127:144:162 SD: 1.2303 cents 82:86:100:109:123:129:146:164 SD: 1.0788 cents 84:88:103:112:126:132:149:168 SD: 0.9737 cents 86:90:105:115:129:135:153:172 SD: 0.8677 cents 108:113:132:144:162:170:192:216 SD: 0.5203 cents 126:132:154:168:189:198:224:252 SD: 0.0000 cents