Scala analysis: xen10-wilson-purvi-07b-05
Purvi modulation 5 from Figure 7b, Kathleen Schlesinger (15/13 16/15 13/12), (16/15 13/12 15/13)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 64/39 857.517337 39th subharmonic 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: 16/15 111.7313 minor diatonic semitone 2: 15/13 247.7411 tridecimal 5/4-tone 3: 13/12 138.5727 tridecimal 2/3-tone 4: 9/8 203.9100 major whole tone 5: 128/117 155.5623 6: 13/12 138.5727 tridecimal 2/3-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 128/117 155.562 cents 1: 2 9/8 203.910 cents major whole tone 1: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 16/13 359.472 cents tridecimal neutral third 2: 1 5/4 386.314 cents major third 3: 1 13/10 454.214 cents tridecimal semi-diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 20/13 745.786 cents tridecimal semi-augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 1 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 117/64 1044.438 cents 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 1 15/8 1088.269 cents classic 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 : 111.7 359.5 498.0 702.0 857.5 996.1 1200.0 111.7 : 247.7 386.3 590.2 745.8 884.4 1088.3 1200.0 359.5 : 138.6 342.5 498.0 636.6 840.5 952.3 1200.0 498.0 : 203.9 359.5 498.0 702.0 813.7 1061.4 1200.0 702.0 : 155.6 294.1 498.0 609.8 857.5 996.1 1200.0 857.5 : 138.6 342.5 454.2 702.0 840.5 1044.4 1200.0 996.1 : 203.9 315.6 563.4 702.0 905.9 1061.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 247.7411 cents 225/208, 136.0098 cents 16/15, 111.7313 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 416/405, 46.3939 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 26/25, 67.9002 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 26/25, 67.9002 cents 6: 952.2589 .. 1088.2687 cents 225/208, 136.0098 cents 416/405, 46.3939 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 1.534293 Largest / Average step : 1.445156 Largest / Smallest step : 2.217294 Median interval of one step : 128/117, 155.5623 cents, amount: 1 Least squares average step : 169.97684 cents, oct.: 1189.83788 cents Scale is strictly proper Step pattern alph. order: ABCDECD Step pattern size order : AEBDCBD Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.571781 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.393003 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 : 512/507, 16.9897 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 classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 136.0098 cents: 3 -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 117 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.022960 Average absolute harmonicity : 0.248766 Specific harmonicity : 0.135983 Fundamental : 1/1170, -10.1923 octaves, 0.2236 Hz. Guide tone : 192, 7.5850 octaves, 50232.109 Hz. Exponens Consonantiae : 2.246400E+05, 17.77726 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 101.5, average 14.50000 Mersenne's string divisions : 48613425 Sum of van Prooijen's expressibility: 5.78958, average 0.82708 Sum of Tenney's harmonic distance : 12.41224, average 1.77318 Vogel's harmonic complexity : 21.71429 Wille's k value : 877 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 93.60393, average 3.34300 Lattice compactness (without 2's) : 40.16818, average 1.43458 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 6 2.85714 22 1 3: -2 .. 1 -0.57143 6 3 5: -1 .. 0 -0.14286 1 1 13: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 17 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 27.8325 c. M:-59.6973 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 18.2414 c. M: 36.0900 c. 14: 1 3 2 2 2 2 2 P T3 SD: 19.0325 c. M:-32.4814 c. 17: 2 3 2 3 2 2 3 SP M ME S SD: 12.6016 c. M:-29.4452 c. 19: 2 4 2 3 3 2 3 SP D3 SD: 15.1993 c. M:-26.6932 c. 20: 2 4 2 4 2 3 3 P D3 S SD: 15.1112 c. M:-23.9100 c. 21: 2 4 3 3 3 2 4 SP T3 SD: 14.2350 c. M: 24.6614 c. 22: 2 5 2 4 3 2 4 P SD: 12.2076 c. M:-22.3458 c. 24: 2 5 3 4 3 3 4 P SD: 6.6202 c. M: 11.7313 c. 31: 3 6 4 5 4 4 5 SP SD: 6.9501 c. M: 11.0852 c. 34: 3 7 4 6 4 4 6 P SD: 6.3109 c. M: 10.4585 c. 41: 4 8 5 7 5 5 7 SP SD: 4.9912 c. M: 8.7368 c. 43: 4 9 5 7 6 5 7 SP SD: 5.0527 c. M:-8.5612 c. 46: 4 10 5 8 6 5 8 P SD: 4.3607 c. M: 7.3835 c. 53: 5 11 6 9 7 6 9 SP SD: 1.6116 c. M:-2.8600 c. 77: 7 16 9 13 10 9 13 SP SD: 1.2397 c. M: 2.6404 c. 130: 12 27 15 22 17 15 22 SP SD: 0.6694 c. M: 0.9621 c. 217: 20 45 25 37 28 25 37 SP SD: 0.5547 c. M: 1.1322 c. 224: 21 46 26 38 29 26 38 SP SD: 0.4138 c. M:-0.7687 c. 270: 25 56 31 46 35 31 46 SP SD: 0.4070 c. M: 0.6202 c. 277: 26 57 32 47 36 32 47 SP SD: 0.3819 c. M:-0.9041 c. 354: 33 73 41 60 46 41 60 SP SD: 0.2559 c. M:-0.5202 c. 364: 34 75 42 62 47 42 62 SP SD: 0.3020 c. M: 0.4856 c. 407: 38 84 47 69 53 47 69 SP SD: 0.3162 c. M:-0.4702 c. 417: 39 86 48 71 54 48 71 SP SD: 0.2818 c. M:-0.4989 c. 441: 41 91 51 75 57 51 75 SP SD: 0.2055 c. M: 0.3745 c. 494: 46 102 57 84 64 57 84 SP SD: 0.0670 c. M: 0.1386 c. 848: 79 175 98 144 110 98 144 SP SD: 0.0697 c. M:-0.1364 c. 1065: 99 220 123 181 138 123 181 SP SD: 0.0745 c. M: 0.1820 c. 1118: 104 231 129 190 145 129 190 SP SD: 0.0640 c. M: 0.1034 c. 1289: 120 266 149 219 167 149 219 SP SD: 0.0642 c. M: 0.1240 c. 1342: 125 277 155 228 174 155 228 SP SD: 0.0233 c. M:-0.0422 c. 1836: 171 379 212 312 238 212 312 SP SD: 0.0138 c. M:-0.0334 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: 8.9471 cents 4 x 5 x 6 x 7:8 S SD: 9.5649 cents 5 x 6:7 x 8:9:10 S SD: 21.3912 cents 6 x 7:8:9:10:11:12 S SD: 18.3587 cents 7:8 x 9 x 11:12:14 SD: 33.3608 cents 8:9:10:11:12:13:14:16 S SD: 16.3429 cents 9:10:11:12:14:15:16:18 S SD: 14.1599 cents 10:11:12:13:15:16:18:20 SD: 13.6007 cents 12:13:15:16:18:20:21:24 SD: 7.6993 cents 14:15:17:19:21:23:25:28 SD: 5.7259 cents 18:19:22:24:27:30:32:36 SD: 4.9377 cents 26:28:32:35:39:43:46:52 SD: 4.0407 cents 30:32:37:40:45:49:53:60 SD: 2.0049 cents 44:47:54:59:66:72:78:88 SD: 1.8900 cents 48:51:59:64:72:79:85:96 SD: 1.5815 cents 60:64:74:80:90:98:107:120 SD: 1.4868 cents 72:77:89:96:108:118:128:144 SD: 1.2903 cents 78:83:96:104:117:128:139:156 SD: 0.8408 cents 90:96:111:120:135:148:160:180 SD: 0.7279 cents 108:115:133:144:162:177:192:216 SD: 0.5559 cents 134:143:165:179:201:220:238:268 SD: 0.5529 cents 148:158:182:197:222:243:263:296 SD: 0.5386 cents 178:190:219:237:267:292:316:356 SD: 0.5356 cents 192:205:236:256:288:315:341:384 SD: 0.4734 cents 198:211:244:264:297:325:352:396 SD: 0.3946 cents 212:226:261:283:318:348:377:424 SD: 0.3495 cents 242:258:298:323:363:397:430:484 SD: 0.3472 cents 256:273:315:341:384:420:455:512 SD: 0.2701 cents 270:288:332:360:405:443:480:540 SD: 0.2331 cents 312:333:384:416:468:512:555:624 SD: 0.2101 cents 342:365:421:456:513:561:608:684 SD: 0.1754 cents 360:384:443:480:540:591:640:720 SD: 0.1057 cents 468:499:576:624:702:768:832:936 SD: 0.0991 cents