Scala analysis: xen09-wilson-marwa-14a-10
Marwa permutation 10 from Figure 14a, Didymus 16/15 25/24 6/5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/225 223.462571 Neapolitan diminished third 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 8/5 813.686286 minor sixth 5: 128/75 925.417571 diminished seventh 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: 256/225 223.4626 Neapolitan diminished third 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 9/8 203.9100 major whole tone 4: 6/5 315.6413 minor third 5: 16/15 111.7313 minor diatonic semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 9/8 203.9100 major whole tone
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 : 223.5 294.1 498.0 813.7 925.4 996.1 1200.0 223.5 : 70.7 274.6 590.2 702.0 772.6 976.5 1200.0 294.1 : 203.9 519.6 631.3 702.0 905.9 1129.3 1200.0 498.0 : 315.6 427.4 498.0 702.0 925.4 996.1 1200.0 813.7 : 111.7 182.4 386.3 609.8 680.4 884.4 1200.0 925.4 : 70.7 274.6 498.0 568.7 772.6 1088.3 1200.0 996.1 : 203.9 427.4 498.0 702.0 1017.6 1129.3 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 : 175.45886 cents, oct.: 1228.21203 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : DACEBAC Scale is sum-free (all different intervals) 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 Formal octave complements present : 1 = 14.2857% 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: 225 Scale harmonicity : 0.034722 Average absolute harmonicity : 0.226787 Specific harmonicity : 0.174165 Fundamental : 1/675, -9.3987 octaves, 0.3876 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 1.728000E+05, 17.39874 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 395.5, average 56.50000 Mersenne's string divisions : 432070275 Sum of van Prooijen's expressibility: 7.78894, average 1.11271 Sum of Tenney's harmonic distance : 16.81984, average 2.40283 Vogel's harmonic complexity : 15.85714 Wille's k value : 337 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 112.26493, average 4.00946 Lattice compactness (without 2's) : 53.12846, average 1.89745 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 8 4.28571 30 1 3: -3 .. 0 -1.28571 9 3 5: -2 .. 0 -0.71429 5 3 Average exponent except 2's :-14 / 7 =-2.00000 Average absolute exponent except 2's: 14 / 7 = 2.00000
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 43.0118 c. M: 68.2747 c. 9: 2 0 2 2 1 0 2 N SD: 33.9216 c. M: 62.7567 c. 10: 2 0 2 3 1 0 2 N SD: 30.9851 c. M: 54.1350 c. 11: 2 1 2 2 1 1 2 P D3 S SD: 35.5741 c. M: 52.6903 c. 12: 2 1 2 3 1 1 2 N SD: 14.3296 c. M: 25.4176 c. 17: 3 1 3 4 2 1 3 N SD: 16.0275 c. M: 37.2157 c. 19: 4 1 3 5 2 1 3 N SD: 17.3878 c. M:-29.1690 c. 21: 4 1 4 5 2 1 4 N SD: 13.5235 c. M: 24.6614 c. 22: 4 1 4 6 2 1 4 N SD: 10.4501 c. M: 21.4077 c. 25: 5 1 4 7 2 2 4 N SD: 11.7350 c. M: 18.0450 c. 28: 5 2 5 7 3 1 5 N SD: 10.6538 c. M:-17.4396 c. 29: 5 2 5 8 2 2 5 N SD: 10.1843 c. M: 16.5660 c. 31: 6 2 5 8 3 2 5 N SD: 8.1662 c. M:-15.5424 c. 34: 6 2 6 9 3 2 6 N SD: 7.7169 c. M: 11.7821 c. 36: 7 2 6 9 4 2 6 N SD: 7.5679 c. M: 13.6863 c. 41: 8 2 7 11 4 2 7 N SD: 6.2802 c. M:-11.1678 c. 48: 9 3 8 13 4 3 8 N SD: 5.1276 c. M:-11.3137 c. 49: 9 3 8 13 5 3 8 N SD: 5.3291 c. M: 8.2491 c. 53: 10 3 9 14 5 3 9 N SD: 1.6512 c. M:-2.9525 c. 65: 12 4 11 17 6 4 11 N SD: 1.3893 c. M: 2.3406 c. 118: 22 7 20 31 11 7 20 N SD: 0.3843 c. M:-0.7803 c. 289: 54 17 49 76 27 17 49 N SD: 0.4770 c. M:-0.7589 c. 323: 60 19 55 85 30 19 55 N SD: 0.3883 c. M: 0.6365 c. 376: 70 22 64 99 35 22 64 N SD: 0.2548 c. M: 0.5180 c. 429: 80 25 73 113 40 25 73 N SD: 0.3123 c. M:-0.4566 c. 441: 82 26 75 116 41 26 75 N SD: 0.2007 c. M: 0.3333 c. 494: 92 29 84 130 46 29 84 N SD: 0.1080 c. M: 0.2079 c. 559: 104 33 95 147 52 33 95 N SD: 0.1139 c. M: 0.2068 c. 612: 114 36 104 161 57 36 104 N SD: 0.0410 c. M:-0.0726 c. 1171: 218 69 199 308 109 69 199 N SD: 0.0353 c. M: 0.0638 c. 1289: 240 76 219 339 120 76 219 N SD: 0.0337 c. M: 0.0491 c. 1783: 332 105 303 469 166 105 303 N SD: 0.0140 c. M: 0.0239 c. 1901: 354 112 323 500 177 112 323 N SD: 0.0133 c. M:-0.0260 c. 2395: 446 141 407 630 223 141 407 N SD: 0.0118 c. M: 0.0223 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: 55.8656 cents 3 x x 4 x 5 x 6 S SD: 13.6863 cents 4 x 5 x 6 x 7:8 S SD: 36.8478 cents 5 x 6:7:8 x 9:10 S SD: 17.9552 cents 6 x 7:8 x 10:11:12 S SD: 14.5151 cents 7:8 x 9:11:12 x 14 SD: 14.2212 cents 8:9 x 11:13 x 14:16 SD: 13.6881 cents 9:10:11:12:14:15:16:18 S SD: 13.2389 cents 10:11:12:13:16:17:18:20 SD: 11.3475 cents 11 x 13:15:18:19:20:22 SD: 11.7815 cents 12 x 14:16:19:20:21:24 SD: 9.8617 cents 13:15 x 17:21:22:23:26 SD: 7.9540 cents 15:17:18:20:24:26:27:30 SD: 5.8753 cents 21:24:25:28:34:36:37:42 SD: 4.1386 cents 27:31:32:36:43:46:48:54 SD: 2.5568 cents 37:42:44:49:59:63:66:74 SD: 2.3590 cents 42:48:50:56:67:72:75:84 SD: 2.3233 cents 44:50:52:59:70:75:78:88 SD: 2.2647 cents 45:51:53:60:72:77:80:90 SD: 1.9378 cents 58:66:69:77:93:99:103:116 SD: 1.5378 cents 65:74:77:87:104:111:116:130 SD: 1.3642 cents 72:82:85:96:115:123:128:144 SD: 1.1128 cents 81:92:96:108:130:138:144:162 SD: 0.9748 cents 102:116:121:136:163:174:181:204 SD: 0.6136 cents 108:123:128:144:173:184:192:216 SD: 0.5699 cents 130:148:154:173:208:222:231:260 SD: 0.5469 cents 153:174:181:204:245:261:272:306 SD: 0.5232 cents 167:190:198:223:267:285:297:334 SD: 0.4342 cents 195:222:231:260:312:333:347:390 SD: 0.3388 cents 225:256:267:300:360:384:400:450 SD: 0.3090 cents 255:290:302:340:408:435:453:510 SD: 0.3034 cents 270:307:320:360:432:461:480:540 SD: 0.1935 cents 297:338:352:396:475:507:528:594 SD: 0.1330 cents 378:430:448:504:605:645:672:756 SD: 0.1045 cents