Scala analysis: xen10-wilson-purvi-11c-03
Purvi modulation 3 from Figure 11c, Archytas (28/27 5/4 36/35), (36/35 5/4 28/27)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 81/70 252.680383 Al-Hwarizmi's lute middle finger 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 54/35 750.725382 septimal semi-augmented fifth 6: 27/14 1137.039096 septimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 9/8 203.9100 major whole tone 3: 280/243 245.3646 4: 9/8 203.9100 major whole tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 5/4 386.3137 major third 7: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 280/243 245.365 cents 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 9/7 435.084 cents septimal major third, BP third 2: 3 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 1 6/5 315.641 cents minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 3: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 3 54/35 750.725 cents septimal semi-augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 2 140/81 947.320 cents 5: 1 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 243/140 954.635 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/14 1137.039 cents septimal major seventh 6: 2 35/18 1151.230 cents septimal semi-diminished octave 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 : 48.8 252.7 498.0 702.0 750.7 1137.0 1200.0 48.8 : 203.9 449.3 653.2 702.0 1088.3 1151.2 1200.0 252.7 : 245.4 449.3 498.0 884.4 947.3 996.1 1200.0 498.0 : 203.9 252.7 639.0 702.0 750.7 954.6 1200.0 702.0 : 48.8 435.1 498.0 546.8 750.7 996.1 1200.0 750.7 : 386.3 449.3 498.0 702.0 947.3 1151.2 1200.0 1137.0: 63.0 111.7 315.6 561.0 764.9 813.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 449.2746 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 750.7254 .. 1088.2687 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 170.22820 cents, oct.: 1191.59738 cents Scale is not proper Step pattern alph. order: ABCBADE Step pattern size order : ACDCAEB Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.557433 Lumma stability : 0.081284 Lumma impropriety factor : 0.651213 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 19683/19600, 7.3158 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents 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 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: 81 Scale harmonicity : 0.030286 Average absolute harmonicity : 0.236385 Specific harmonicity : 0.138058 Fundamental : 1/210, -7.7142 octaves, 1.2458 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 6.804000E+04, 16.05410 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 183.5, average 26.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.38223, average 1.05460 Sum of Tenney's harmonic distance : 14.86627, average 2.12375 Vogel's harmonic complexity : 15.42857 Wille's k value : 202 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 85.77882, average 3.06353 Lattice compactness (without 2's) : 66.78325, average 2.38512 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.42857 9 1 3: -1 .. 4 1.71429 14 2 5: -1 .. 0 -0.42857 3 7: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 21 / 7 = 3.00000 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 18 19|
FIT/MODE
7: 0 1 2 1 0 2 1 N T3 SD: 60.3556 c. M: 108.4677 c. 8: 0 1 2 1 1 2 1 N T3 S SD: 68.8697 c. M: 102.6804 c. 9: 0 1 2 2 0 3 1 N SD: 75.1175 c. M: 119.3470 c. 10: 0 2 2 2 0 3 1 N SD: 32.4876 c. M: 57.0391 c. 12: 0 2 3 2 0 4 1 N SD: 36.0681 c. M: 52.6804 c. 13: 0 2 3 2 1 4 1 N SD: 42.2062 c. M: 68.0650 c. 14: 1 2 3 2 1 4 1 N SD: 20.2083 c. M:-36.9439 c. 17: 1 3 3 3 1 5 1 N T3 SD: 17.3548 c. M:-29.6726 c. 19: 1 3 4 3 1 6 1 N SD: 7.1977 c. M:-14.3875 c. 24: 1 4 5 4 1 8 1 N SD: 5.1388 c. M:-12.9609 c. 32: 1 6 6 6 1 10 2 N SD: 9.1909 c. M: 12.0391 c. 34: 1 6 7 6 1 11 2 N SD: 7.4968 c. M: 13.4763 c. 41: 2 7 8 7 2 13 2 N SD: 6.9252 c. M:-10.7343 c. 43: 2 7 9 7 2 14 2 N SD: 4.5869 c. M:-7.1470 c. 51: 2 9 10 9 2 16 3 N SD: 4.3851 c. M: 7.6273 c. 53: 2 9 11 9 2 17 3 N SD: 2.9900 c. M: 4.9636 c. 72: 3 12 15 12 3 23 4 N SD: 2.0908 c. M: 3.7058 c. 75: 3 13 15 13 3 24 4 N SD: 1.8001 c. M:-3.3196 c. 77: 3 13 16 13 3 25 4 N SD: 1.8343 c. M: 3.3297 c. 94: 4 16 19 16 4 30 5 N SD: 1.6527 c. M:-2.6388 c. 96: 4 16 20 16 4 31 5 N SD: 1.5620 c. M: 2.6804 c. 99: 4 17 20 17 4 32 5 N SD: 1.3116 c. M:-2.3548 c. 118: 5 20 24 20 5 38 6 N SD: 1.4119 c. M:-2.0771 c. 147: 6 25 30 25 6 47 8 N SD: 0.9095 c. M: 2.3452 c. 152: 6 26 31 26 6 49 8 N SD: 0.7019 c. M: 1.4020 c. 171: 7 29 35 29 7 55 9 N SD: 0.1960 c. M:-0.3524 c. 494: 20 84 101 84 20 159 26 N SD: 0.1194 c. M: 0.1970 c. 665: 27 113 136 113 27 214 35 N SD: 0.0810 c. M: 0.1970 c. 836: 34 142 171 142 34 269 44 N SD: 0.0808 c. M: 0.1970 c. 860: 35 146 176 146 35 277 45 N SD: 0.0978 c. M:-0.1702 c. 935: 38 159 191 159 38 301 49 N SD: 0.0818 c. M:-0.1538 c. 1012: 41 172 207 172 41 326 53 N SD: 0.0984 c. M: 0.1538 c. 1031: 42 175 211 175 42 332 54 N SD: 0.0943 c. M:-0.1142 c. 1106: 45 188 226 188 45 356 58 N SD: 0.0644 c. M:-0.1225 c. 1183: 48 201 242 201 48 381 62 N SD: 0.0659 c. M: 0.1022 c. 1277: 52 217 261 217 52 411 67 N SD: 0.0634 c. M:-0.0996 c. 1354: 55 230 277 230 55 436 71 N SD: 0.0496 c. M: 0.0954 c. 1429: 58 243 292 243 58 460 75 N SD: 0.0571 c. M:-0.0838 c. 1525: 62 259 312 259 62 491 80 N SD: 0.0472 c. M: 0.0902 c. 1600: 65 272 327 272 65 515 84 N SD: 0.0404 c. M:-0.0696 c. 1771: 72 301 362 301 72 570 93 N SD: 0.0356 c. M:-0.0582 c. 2289: 93 389 468 389 93 737 120 N SD: 0.0213 c. M:-0.0513 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: 44.5444 cents 4 x x 5:6 x x 8 S SD: 37.2438 cents 5 x 6:7 x 8 x 10 S SD: 30.6827 cents 6 x 7:8:9 x x 12 S SD: 3.5476 cents 7 x 8:9 x 11 x 14 SD: 18.4318 cents 8 x 9:11:12 x 15:16 SD: 17.4300 cents 9 x 10:12 x 14:17:18 SD: 16.0446 cents 10 x 12:13:15 x 19:20 SD: 16.1900 cents 11:12:13:15 x 17:21:22 SD: 19.3952 cents 12:13:14:16:18:19:23:24 SD: 14.5621 cents 13:14:15:17 x 20:25:26 SD: 14.4607 cents 14:15:16:19:21:22:27:28 SD: 12.2933 cents 15:16:17:20 x 23:29:30 SD: 12.2392 cents 16:17:19:21:24:25:31:32 SD: 11.4764 cents 17:18:20:23 x 26:33:34 SD: 10.9753 cents 18:19:21:24:27:28:35:36 SD: 7.3040 cents 19:20:22:25 x 29:37:38 SD: 8.7555 cents 20:21:23:27:30:31:39:40 SD: 6.8237 cents 21:22:24:28 x 32:41:42 SD: 8.1401 cents 22:23:25:29:33:34:42:44 SD: 7.1249 cents 23:24:27:31 x 35:44:46 SD: 8.0907 cents 24:25:28:32:36:37:46:48 SD: 4.0350 cents 26:27:30:35:39:40:50:52 SD: 3.5632 cents 30:31:35:40:45:46:58:60 SD: 2.8516 cents 38:39:44:51:57:59:73:76 SD: 2.5147 cents 42:43:49:56:63:65:81:84 SD: 2.4510 cents 44:45:51:59:66:68:85:88 SD: 2.1139 cents 62:64:72:83:93:96:120:124 SD: 2.0304 cents 63:65:73:84:95:97:122:126 SD: 1.9210 cents 64:66:74:85:96:99:123:128 SD: 1.5940 cents 66:68:76:88:99:102:127:132 SD: 1.4522 cents 68:70:79:91:102:105:131:136 SD: 1.3964 cents 70:72:81:93:105:108:135:140 SD: 0.8849 cents 96:99:111:128:144:148:185:192 SD: 0.7232 cents 102:105:118:136:153:157:197:204 SD: 0.7175 cents 108:111:125:144:162:167:208:216 SD: 0.6769 cents 114:117:132:152:171:176:220:228 SD: 0.6101 cents 138:142:160:184:207:213:266:276 SD: 0.5234 cents 140:144:162:187:210:216:270:280 SD: 0.4412 cents 204:210:236:272:306:315:393:408 SD: 0.3973 cents 210:216:243:280:315:324:405:420 SD: 0.0000 cents