Scala analysis: xen10-wilson-purvi-10a-05
Purvi modulation 5 from Figure 10a, Didymus (16/15 25/24 6/5), (6/5 16/15 25/24)
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: 32/25 427.372572 classic diminished fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 48/25 1129.327573 classic diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 9/8 203.9100 major whole tone 2: 256/225 223.4626 Neapolitan diminished third 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 9/8 203.9100 major whole tone 5: 6/5 315.6413 minor third 6: 16/15 111.7313 minor diatonic semitone 7: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 9/8 203.910 cents major whole tone 1: 1 256/225 223.463 cents Neapolitan diminished third 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 2 75/64 274.582 cents classic augmented second 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 32/25 427.373 cents classic diminished fourth 2: 1 27/20 519.551 cents acute fourth 3: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 36/25 631.283 cents classic diminished fifth 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 8/5 813.686 cents minor sixth 5: 1 40/27 680.449 cents grave fifth 5: 2 25/16 772.627 cents classic augmented fifth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 128/75 925.418 cents diminished seventh 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 225/128 976.537 cents augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 2 48/25 1129.328 cents classic diminished octave 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 : 203.9 427.4 498.0 702.0 1017.6 1129.3 1200.0 203.9 : 223.5 294.1 498.0 813.7 925.4 996.1 1200.0 427.4 : 70.7 274.6 590.2 702.0 772.6 976.5 1200.0 498.0 : 203.9 519.6 631.3 702.0 905.9 1129.3 1200.0 702.0 : 315.6 427.4 498.0 702.0 925.4 996.1 1200.0 1017.6: 111.7 182.4 386.3 609.8 680.4 884.4 1200.0 1129.3: 70.7 274.6 498.0 568.7 772.6 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 315.6413 cents 144/125, 244.9689 cents 25/24, 70.6724 cents 2: 182.4037 .. 519.5513 cents 243/200, 337.1476 cents 25/27,-133.2376 cents 3: 386.3137 .. 631.2826 cents 144/125, 244.9689 cents 25/27,-133.2376 cents 4: 568.7174 .. 813.6863 cents 144/125, 244.9689 cents 625/648,-62.5651 cents 5: 680.4487 .. 1017.5963 cents 243/200, 337.1476 cents 25/27,-133.2376 cents 6: 884.3587 .. 1129.3276 cents 144/125, 244.9689 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.425678 Largest / Average step : 1.841241 Largest / Smallest step : 4.466258 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 183.03255 cents, oct.: 1281.22785 cents Scale is not proper Step pattern alph. order: ABCADEC Step pattern size order : CDACEBA Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.613265 Lumma stability : 0.117787 Lumma impropriety factor : 0.496263 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 : 2048/2025, 19.5526 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 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 : 5 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 25 Scale harmonicity : 0.034722 Average absolute harmonicity : 0.257112 Specific harmonicity : 0.180722 Fundamental : 1/600, -9.2288 octaves, 0.4360 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 1.728000E+05, 17.39874 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 88.0, average 12.57143 Mersenne's string divisions : 4951590 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 11.65118, average 1.66445 Vogel's harmonic complexity : 15.71429 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 105.51578, average 3.76842 Lattice compactness (without 2's) : 51.53610, average 1.84058 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 1.14286 16 1 3: -1 .. 2 0.71429 7 3 5: -2 .. 0 -0.71429 5 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429
FIT/MODE
7: 1 1 1 1 2 0 1 N T3 SD: 52.0956 c. M: 100.7561 c. 9: 1 2 0 2 2 1 1 N T3 SD: 62.8093 c. M: 98.0450 c. 10: 1 2 1 2 2 1 1 N D3 SD: 50.6835 c. M: 83.9100 c. 11: 2 2 0 2 3 1 1 N G SD: 36.0413 c. M: 61.6814 c. 12: 2 2 1 2 3 1 1 N SD: 16.6559 c. M: 29.3276 c. Mela Naganandini, Raga Nagabharanam, Nupur, Samanta 14: 2 3 1 2 4 1 1 N SD: 16.6077 c. M: 32.4814 c. 17: 3 3 1 3 4 2 1 N SD: 11.7679 c. M: 29.3610 c. 19: 3 4 1 3 5 2 1 N SD: 9.5328 c. M:-14.7327 c. 29: 5 5 2 5 8 2 2 N SD: 9.4794 c. M:-16.8865 c. 31: 5 6 2 5 8 3 2 N SD: 6.8995 c. M: 11.1447 c. 34: 6 6 2 6 9 3 2 N SD: 4.5123 c. M:-7.8547 c. 48: 8 9 3 8 13 4 3 N SD: 3.8192 c. M:-7.4037 c. 53: 9 10 3 9 14 5 3 N SD: 1.5642 c. M:-2.8161 c. 118: 20 22 7 20 31 11 7 N SD: 0.4059 c. M: 0.6471 c. 171: 29 32 10 29 45 16 10 N SD: 0.3738 c. M:-0.6976 c. 289: 49 54 17 49 76 27 17 N SD: 0.2655 c. M: 0.4498 c. 323: 55 60 19 55 85 30 19 N SD: 0.2460 c. M:-0.4244 c. 441: 75 82 26 75 116 41 26 N SD: 0.1098 c. M:-0.1716 c. 559: 95 104 33 95 147 52 33 N SD: 0.0974 c. M: 0.1812 c. 612: 104 114 36 104 161 57 36 N SD: 0.0478 c. M:-0.0842 c. 730: 124 136 43 124 192 68 43 N SD: 0.0430 c. M: 0.0744 c. 1171: 199 218 69 199 308 109 69 N SD: 0.0236 c. M: 0.0455 c. 1783: 303 332 105 303 469 166 105 N SD: 0.0095 c. M:-0.0160 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: 44.4125 cents 4 x 5 x 6:7 x 8 S SD: 15.9381 cents 5:6 x 7:8:9 x 10 S SD: 35.8343 cents 6:7 x 8:9:11 x 12 SD: 14.1042 cents 7:8:9 x 11:13 x 14 SD: 20.2153 cents 8:9:10:11:12:14:15:16 S SD: 13.2389 cents 9:10 x 12:14:16:17:18 S SD: 12.5709 cents 10:11:13 x 15:18:19:20 SD: 8.4373 cents 13:15 x 17:20:23:25:26 SD: 12.7705 cents 14:16:18:19:21:25:27:28 SD: 6.3752 cents 18:20:23:24:27:32:35:36 SD: 5.3715 cents 22:25:28:29:33:40:42:44 SD: 4.9313 cents 24:27:31:32:36:43:46:48 SD: 2.5568 cents 39:44:50:52:59:70:75:78 SD: 2.3952 cents 40:45:51:53:60:72:77:80 SD: 1.9378 cents 50:56:64:67:75:90:96:100 SD: 1.6538 cents 54:61:69:72:81:97:104:108 SD: 1.4341 cents 64:72:82:85:96:115:123:128 SD: 1.1128 cents 72:81:92:96:108:130:138:144 SD: 0.9748 cents 90:101:115:120:135:162:173:180 SD: 0.8002 cents 96:108:123:128:144:173:184:192 SD: 0.5699 cents 136:153:174:181:204:245:261:272 SD: 0.5232 cents 150:169:192:200:225:270:288:300 SD: 0.3661 cents 186:209:238:248:279:335:357:372 SD: 0.3508 cents 200:225:256:267:300:360:384:400 SD: 0.3090 cents 240:270:307:320:360:432:461:480 SD: 0.1935 cents 264:297:338:352:396:475:507:528 SD: 0.1330 cents 336:378:430:448:504:605:645:672 SD: 0.1045 cents 600:675:768:800:900:1080:1152:1200 SD: 0.0000 cents