Scala analysis: xen10-wilson-purvi-08c-07
Purvi modulation 7 from Figure 8c, Ptolemy (22/21 7/6 12/11), (12/11 7/6 22/21)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 14/11 417.507964 undecimal diminished fourth or major third 3: 4/3 498.044999 perfect fourth 4: 14/9 764.915905 septimal minor sixth 5: 56/33 915.552963 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: 7/6 266.8709 septimal minor third 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 22/21 80.5370 undecimal minor semitone 4: 7/6 266.8709 septimal minor third 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 9/8 203.9100 major whole tone 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: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 33/28 284.447 cents undecimal minor third 2: 2 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: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 56/33 915.553 cents 5: 1 7/4 968.826 cents harmonic seventh 6: 2 12/7 933.129 cents septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 266.9 417.5 498.0 764.9 915.6 1119.5 1200.0 266.9 : 150.6 231.2 498.0 648.7 852.6 933.1 1200.0 417.5 : 80.5 347.4 498.0 702.0 782.5 1049.4 1200.0 498.0 : 266.9 417.5 621.4 702.0 968.8 1119.5 1200.0 764.9 : 150.6 354.5 435.1 702.0 852.6 933.1 1200.0 915.6 : 203.9 284.4 551.3 702.0 782.5 1049.4 1200.0 1119.5: 80.5 347.4 498.0 578.6 845.5 996.1 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: 231.1741 .. 417.5080 cents 49/44, 186.3339 cents 48/49,-35.6968 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 .. 968.8259 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 48/49,-35.6968 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 : 12/11, 150.6371 cents, amount: 2 Least squares average step : 181.07306 cents, oct.: 1267.51140 cents Scale is not proper Step pattern alph. order: ABCABDC Step pattern size order : DBADBCA Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.579325 Lumma stability : 0.163522 Lumma impropriety factor : 0.095191 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 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 Number of recognisable fifths : 4, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord Best fifths form a closed circle All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 33 Scale harmonicity : 0.024711 Average absolute harmonicity : 0.205925 Specific harmonicity : 0.116785 Fundamental : 1/198, -7.6294 octaves, 1.3213 Hz. Guide tone : 168, 7.3923 octaves, 43953.095 Hz. Exponens Consonantiae : 3.326400E+04, 15.02167 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 96.0, average 13.71429 Mersenne's string divisions : 447064800 Sum of van Prooijen's expressibility: 6.15859, average 0.87980 Sum of Tenney's harmonic distance : 12.92167, average 1.84595 Vogel's harmonic complexity : 17.57143 Wille's k value : 115 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 64.81037, average 2.31466 Lattice compactness (without 2's) : 43.53000, average 1.55464 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.00000 9 1 3: -2 .. 1 -0.57143 6 1 7: 0 .. 1 0.71429 5 2 11: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 18 26| Scale is JI-epimorphic with val: <7 11 19 24| 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: 68.5478 c. M: 95.4423 c. Lebeng 8: 2 1 0 2 1 1 1 N D3 SD: 37.3231 c. M: 69.4630 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 28.9983 c. M: 52.7963 c. 12: 3 1 1 3 1 2 1 N T3 S SD: 21.5787 c. M:-35.0841 c. 13: 3 1 1 3 2 2 1 N SD: 25.7999 c. M: 48.2772 c. 14: 3 2 1 3 2 2 1 P T3 SD: 13.6043 c. M:-27.3042 c. 17: 4 2 1 4 2 3 1 N SD: 8.6870 c. M:-15.4820 c. 31: 7 4 2 7 4 5 2 N SD: 7.4640 c. M:-13.4793 c. 39: 9 5 2 9 5 6 3 N SD: 8.6487 c. M:-13.2613 c. 41: 9 5 3 9 5 7 3 N SD: 5.4570 c. M: 8.2359 c. 46: 10 6 3 10 6 8 3 N SD: 4.2037 c. M: 8.3942 c. 55: 12 7 4 12 7 9 4 N SD: 3.7073 c. M: 6.7357 c. 58: 13 7 4 13 7 10 4 N SD: 2.7474 c. M: 5.2081 c. 63: 14 8 4 14 8 11 4 N SD: 2.3862 c. M:-4.3466 c. 72: 16 9 5 16 9 12 5 N SD: 1.5444 c. M: 2.7963 c. 89: 20 11 6 20 11 15 6 N SD: 1.8385 c. M:-3.6234 c. 118: 26 15 8 26 15 20 8 N SD: 1.3131 c. M: 2.4641 c. 135: 30 17 9 30 17 23 9 N SD: 0.3155 c. M:-0.5370 c. 342: 76 43 23 76 43 58 23 N SD: 0.1541 c. M:-0.2365 c. 477: 106 60 32 106 60 81 32 N SD: 0.1227 c. M: 0.2042 c. 877: 195 110 59 195 110 149 59 N SD: 0.1183 c. M: 0.1927 c. 1012: 225 127 68 225 127 172 68 N SD: 0.0896 c. M: 0.1379 c. 1147: 255 144 77 255 144 195 77 N SD: 0.0842 c. M: 0.1382 c. 1236: 275 155 83 275 155 210 83 N SD: 0.0712 c. M:-0.1326 c. 1354: 301 170 91 301 170 230 91 N SD: 0.0738 c. M: 0.1129 c. 1371: 305 172 92 305 172 233 92 N SD: 0.0442 c. M:-0.0875 c. 1506: 335 189 101 335 189 256 101 N SD: 0.0376 c. M:-0.0614 c. 1713: 381 215 115 381 215 291 115 N SD: 0.0310 c. M:-0.0578 c. 1848: 411 232 124 411 232 314 124 N SD: 0.0188 c. M:-0.0315 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: 31.4805 cents 3 x x 4 x 5 x 6 S SD: 10.3981 cents 4 x 5 x 6:7 x 8 S SD: 22.0442 cents 5:6 x 7:8 x x 10 S SD: 27.2624 cents 6:7 x 8:9:10:11:12 S SD: 16.5422 cents 7:8:9 x 11:12:13:14 SD: 11.1582 cents 9 x 11:12:14:15:17:18 SD: 13.1512 cents 10:12:13 x 16:17:19:20 SD: 13.1046 cents 11:13:14:15:17:19:21:22 SD: 7.9267 cents 12:14:15:16:19:20:23:24 SD: 7.7356 cents 13:15 x 17:20:22:25:26 SD: 7.5358 cents 18:21:23:24:28:31:34:36 SD: 4.6074 cents 23:27:29:31:36:39:44:46 SD: 4.1830 cents 29:34:37:39:45:49:55:58 SD: 3.2440 cents 30:35:38:40:47:51:57:60 SD: 2.4659 cents 36:42:46:48:56:61:69:72 SD: 1.4333 cents 54:63:69:72:84:92:103:108 SD: 1.4023 cents 66:77:84:88:103:112:126:132 SD: 0.8017 cents 96:112:122:128:149:163:183:192 SD: 0.7719 cents 102:119:130:136:159:173:195:204 SD: 0.7252 cents 132:154:168:176:205:224:252:264 SD: 0.4018 cents 162:189:206:216:252:275:309:324 SD: 0.3192 cents 198:231:252:264:308:336:378:396 S SD: 0.0000 cents