Scala analysis: xen10-wilson-purvi-11a-07
Purvi modulation 7 from Figure 11a, Archytas (28/27 36/35 5/4), (5/4 28/27 36/35)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 3: 4/3 498.044999 perfect fourth 4: 5/3 884.358713 major sixth, BP sixth 5: 15/8 1088.268715 classic major seventh 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 5/4 386.3137 major third 2: 28/27 62.9609 Archytas' 1/3-tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 5/4 386.3137 major third 5: 9/8 203.9100 major whole tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 5/4 386.314 cents major third 2: 2 16/15 111.731 cents minor diatonic semitone 2: 1 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 45/32 590.224 cents diatonic tritone 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: 1 64/45 609.776 cents 2nd tritone 5: 1 54/35 750.725 cents septimal semi-augmented fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 2 15/8 1088.269 cents classic major seventh 6: 2 8/5 813.686 cents minor sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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 : 386.3 449.3 498.0 884.4 1088.3 1151.2 1200.0 386.3 : 63.0 111.7 498.0 702.0 764.9 813.7 1200.0 449.3 : 48.8 435.1 639.0 702.0 750.7 1137.0 1200.0 498.0 : 386.3 590.2 653.2 702.0 1088.3 1151.2 1200.0 884.4 : 203.9 266.9 315.6 702.0 764.9 813.7 1200.0 1088.3: 63.0 111.7 498.0 561.0 609.8 996.1 1200.0 1151.2: 48.8 435.1 498.0 546.8 933.1 1137.0 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 .. 590.2237 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 64/75,-274.5824 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 : 28/27, 62.9609 cents, amount: 2 Least squares average step : 193.32253 cents, oct.: 1353.25770 cents Scale is not proper Step pattern alph. order: ABCADBC Step pattern size order : DBADCBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.578397 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 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 : 245/243, 14.1905 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Phrygian octave species of abstract tetrachord 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 : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 35 Scale harmonicity : 0.030910 Average absolute harmonicity : 0.230064 Specific harmonicity : 0.166480 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 420, 8.7142 octaves, 109882.737 Hz. Exponens Consonantiae : 9.072000E+04, 16.46913 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 82.5, average 11.78571 Mersenne's string divisions : 19045656 Sum of van Prooijen's expressibility: 6.13929, average 0.87704 Sum of Tenney's harmonic distance : 11.71129, average 1.67304 Vogel's harmonic complexity : 14.57143 Wille's k value : 202 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 79.59522, average 2.84269 Lattice compactness (without 2's) : 51.35492, average 1.83410 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.42857 9 1 3: -3 .. 1 -0.85714 8 1 5: 0 .. 1 0.71429 5 3 7: 0 .. 1 0.28571 2 2 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 2 1 0 2 1 1 0 N T3 SD: 43.1967 c. M:-65.0111 c. 8: 3 0 0 3 1 1 0 N SD: 38.6421 c. M:-63.6863 c. 9: 3 0 1 3 1 1 0 N SD: 36.0640 c. M: 49.2746 c. 10: 3 1 0 3 2 1 0 N SD: 30.1821 c. M:-48.7704 c. 12: 4 1 0 4 2 1 0 N SD: 28.0943 c. M:-50.7254 c. 13: 4 1 0 5 2 0 1 N SD: 28.1497 c. M: 43.5373 c. 14: 5 0 1 4 3 0 1 N SD: 27.4136 c. M:-42.2577 c. 15: 5 1 0 5 3 0 1 N SD: 22.2266 c. M:-31.7313 c. 16: 5 1 1 5 3 0 1 N SD: 21.1691 c. M:-36.7313 c. 18: 6 1 0 6 3 1 1 N SD: 19.1771 c. M: 31.3783 c. 19: 6 1 1 6 3 1 1 N SD: 9.0829 c. M: 14.5845 c. 22: 7 1 1 7 4 1 1 N SD: 7.6852 c. M: 12.9110 c. 34: 11 2 1 11 6 2 1 N SD: 6.8675 c. M:-13.4763 c. 41: 13 2 2 13 7 2 2 N SD: 6.5789 c. M: 10.2502 c. 43: 14 2 2 14 7 2 2 N SD: 4.9262 c. M:-8.6645 c. 46: 15 2 2 15 8 2 2 N SD: 4.4252 c. M:-7.3835 c. 53: 17 3 2 17 9 3 2 N SD: 2.0964 c. M:-3.5556 c. 75: 24 4 3 24 13 4 3 N SD: 2.0984 c. M: 4.3587 c. 94: 30 5 4 30 16 5 4 N SD: 2.5298 c. M: 3.5076 c. 96: 31 5 4 31 16 5 4 N SD: 1.5913 c. M:-3.1413 c. 99: 32 5 4 32 17 5 4 N SD: 1.2830 c. M:-2.6404 c. 118: 38 6 5 38 20 6 5 N SD: 1.0601 c. M: 2.0771 c. 149: 48 8 6 48 25 8 6 N SD: 1.0925 c. M:-1.7321 c. 152: 49 8 6 49 26 8 6 N SD: 0.8196 c. M:-1.4020 c. 171: 55 9 7 55 29 9 7 N SD: 0.3007 c. M: 0.5494 c. 323: 104 17 13 104 55 17 13 N SD: 0.2505 c. M:-0.4732 c. 441: 142 23 18 142 75 23 18 N SD: 0.1570 c. M: 0.2950 c. 494: 159 26 20 159 84 26 20 N SD: 0.1083 c. M:-0.1874 c. 665: 214 35 27 214 113 35 27 N SD: 0.1005 c. M: 0.1484 c. 935: 301 49 38 301 159 49 38 N SD: 0.0583 c. M: 0.0806 c. 1106: 356 58 45 356 188 58 45 N SD: 0.0585 c. M: 0.0911 c. 1429: 460 75 58 460 243 75 58 N SD: 0.0580 c. M: 0.1040 c. 1525: 491 80 62 491 259 80 62 N SD: 0.0490 c. M:-0.1003 c. 1696: 546 89 69 546 288 89 69 N SD: 0.0492 c. M:-0.0752 c. 1848: 595 97 75 595 314 97 75 N SD: 0.0510 c. M:-0.0760 c. 1966: 633 103 80 633 334 103 80 N SD: 0.0469 c. M:-0.0767 c. 2019: 650 106 82 650 343 106 82 N SD: 0.0311 c. M:-0.0567 c. 2190: 705 115 89 705 372 115 89 N SD: 0.0299 c. M: 0.0495 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: 91.2019 cents 3 x x 4:5 x x 6 S SD: 0.0000 cents 4:5 x x 7 x x 8 SD: 28.1557 cents 5:6 x 7:8:9 x 10 S SD: 29.7446 cents 6 x x 8:10:11 x 12 S SD: 9.7264 cents 7 x 9 x 12:13 x 14 SD: 13.3566 cents 8:10 x 11:13:15 x 16 SD: 13.7973 cents 9:11 x 12:15:17 x 18 SD: 8.1900 cents 10 x 13 x 17:19 x 20 SD: 10.3849 cents 11:14 x 15:18:21 x 22 SD: 13.3700 cents 12:15 x 16:20 x 23:24 SD: 4.9821 cents 13:16:17 x 22:24:25:26 SD: 8.7164 cents 14 x 18:19:23:26:27:28 SD: 7.8822 cents 15:19 x 20:25:28:29:30 SD: 4.3580 cents 16:20:21 x 27:30:31:32 SD: 5.1731 cents 18 x 23:24:30:34:35:36 SD: 4.6660 cents 19:24 x 25:32:36:37:38 SD: 6.4946 cents 20:25:26:27:33:38:39:40 SD: 5.2292 cents 21:26:27:28:35:39:41:42 SD: 4.0407 cents 22:28 x 29:37:41:43:44 SD: 7.0735 cents 23:29:30:31:38:43:45:46 SD: 4.6482 cents 24:30:31:32:40:45:47:48 SD: 1.9702 cents 48:60:62:64:80:90:93:96 S SD: 1.2514 cents 57:71:74:76:95:107:111:114 SD: 1.0562 cents 72:90:93:96:120:135:140:144 S SD: 0.8849 cents 87:109:113:116:145:163:169:174 SD: 0.8093 cents 105:131:136:140:175:197:204:210 SD: 0.5732 cents 111:139:144:148:185:208:216:222 SD: 0.5415 cents 144:180:187:192:240:270:280:288 SD: 0.4412 cents 159:199:206:212:265:298:309:318 SD: 0.3781 cents 168:210:218:224:280:315:327:336 SD: 0.3567 cents 192:240:249:256:320:360:373:384 SD: 0.2470 cents 216:270:280:288:360:405:420:432 S SD: 0.0000 cents