Scala analysis: xen09-wilson-marwa-11a-08
Marwa permutation 8 from Figure 11a, Hawkins 16/15 135/128 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/27 294.134997 Pythagorean minor third 2: 512/405 405.866283 narrow diminished fourth 3: 4/3 498.044999 perfect fourth 4: 128/81 792.179997 Pythagorean minor sixth 5: 2048/1215 903.911282 narrow 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: 32/27 294.1350 Pythagorean minor third 2: 16/15 111.7313 minor diatonic semitone 3: 135/128 92.1787 major chroma, major limma 4: 32/27 294.1350 Pythagorean minor third 5: 16/15 111.7313 minor diatonic semitone 6: 135/128 92.1787 major chroma, major limma 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 135/128 92.179 cents major chroma, major limma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 32/27 294.135 cents Pythagorean minor third 2: 2 9/8 203.910 cents major whole tone 2: 1 1215/1024 296.089 cents wide augmented second 2: 1 5/4 386.314 cents major third 2: 2 512/405 405.866 cents narrow diminished fourth 2: 1 4/3 498.045 cents perfect fourth 3: 1 81/64 407.820 cents Pythagorean major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 64/45 609.776 cents 2nd tritone 4: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 3/2 701.955 cents perfect fifth 5: 2 405/256 794.134 cents wide augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 2048/1215 903.911 cents narrow diminished seventh 5: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 2 256/135 1107.821 cents octave - major chroma 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 : 294.1 405.9 498.0 792.2 903.9 996.1 1200.0 294.1 : 111.7 203.9 498.0 609.8 702.0 905.9 1200.0 405.9 : 92.2 386.3 498.0 590.2 794.1 1088.3 1200.0 498.0 : 294.1 405.9 498.0 702.0 996.1 1107.8 1200.0 792.2 : 111.7 203.9 407.8 702.0 813.7 905.9 1200.0 903.9 : 92.2 296.1 590.2 702.0 794.1 1088.3 1200.0 996.1 : 203.9 498.0 609.8 702.0 996.1 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 294.1350 cents 4096/3645, 201.9563 cents 135/128, 92.1787 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 3: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 4: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 2025/2048,-19.5526 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 6: 905.8650 .. 1107.8213 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.859741 Largest / Average step : 1.715787 Largest / Smallest step : 3.190921 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 176.17728 cents, oct.: 1233.24095 cents Scale is not proper Step pattern alph. order: ABCABCD Step pattern size order : DBADBAC Scale is not a Constant Structure Scale diversity : 1.361761 Lumma stability : 0.153631 Lumma impropriety factor : 0.317044 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / 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 : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 1215 (O: 1215 U: 1215) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.032538 Average absolute harmonicity : 0.217979 Specific harmonicity : 0.167043 Fundamental : 1/1215, -10.2467 octaves, 0.2153 Hz. Guide tone : 2048, 11.0000 octaves, 535809.158 Hz. Exponens Consonantiae : 2.488320E+06, 21.24674 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 2241.5, average 320.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.46324, average 1.49475 Sum of Tenney's harmonic distance : 22.20341, average 3.17192 Vogel's harmonic complexity : 16.00000 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 150.10906, average 5.36104 Lattice compactness (without 2's) : 68.19247, average 2.43545 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 11 5.57143 39 1 3: -5 .. 0 -2.71429 19 4 5: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-21 / 7 =-3.00000 Average absolute exponent except 2's: 21 / 7 = 3.00000 Scale is weakly epimorphic with val: <7 10 17| Scale is weakly epimorphic with val: <7 11 18|
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 44.8334 c. M:-64.9629 c. 8: 2 1 0 2 1 1 1 N D3 SD: 35.8394 c. M:-53.9100 c. 9: 2 1 1 2 1 0 2 N SD: 31.3947 c. M: 62.7567 c. 12: 3 1 1 3 1 1 2 N SD: 4.8458 c. M:-7.8200 c. Chromatic Hypodorian inverse 41: 10 4 3 10 4 3 7 N SD: 2.1960 c. M:-3.8898 c. 53: 13 5 4 13 5 4 9 N SD: 0.9277 c. M:-1.7491 c. 65: 16 6 5 16 6 5 11 N SD: 0.9090 c. M:-1.6662 c. 118: 29 11 9 29 11 9 20 N SD: 0.7783 c. M:-1.1735 c. 301: 74 28 23 74 28 23 51 N SD: 0.7879 c. M:-1.1755 c. 311: 76 29 24 76 29 24 53 N SD: 0.7728 c. M: 1.1832 c. 323: 79 30 25 79 30 25 55 N SD: 0.7019 c. M: 1.1249 c. 335: 82 31 26 82 31 26 57 N SD: 0.6794 c. M: 1.2247 c. 364: 89 34 28 89 34 28 62 N SD: 0.5713 c. M: 0.9712 c. 376: 92 35 29 92 35 29 64 N SD: 0.4945 c. M: 0.7198 c. 388: 95 36 30 95 36 30 66 N SD: 0.4658 c. M: 0.8185 c. 417: 102 39 32 102 39 32 71 N SD: 0.4392 c. M: 0.8131 c. 429: 105 40 33 105 40 33 73 N SD: 0.3502 c. M: 0.5716 c. 441: 108 41 34 108 41 34 75 N SD: 0.3072 c. M: 0.5099 c. 482: 118 45 37 118 45 37 82 N SD: 0.2575 c. M: 0.4788 c. 494: 121 46 38 121 46 38 84 N SD: 0.1908 c. M: 0.2772 c. 506: 124 47 39 124 47 39 86 N SD: 0.1888 c. M: 0.3540 c. 547: 134 51 42 134 51 42 93 N SD: 0.1192 c. M: 0.2239 c. 559: 137 52 43 137 52 43 95 N SD: 0.0836 c. M: 0.1546 c. 612: 150 57 47 150 57 47 104 N SD: 0.0140 c. M: 0.0231 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: 45.1125 cents 3 x x 4 x 5 x 6 S SD: 6.5175 cents 4 x 5 x 6 x 7:8 S SD: 24.0653 cents 5:6 x 7:8 x 9:10 S SD: 18.4632 cents 6:7 x 8:9:10:11:12 S SD: 18.3365 cents 7:8:9 x 11:12 x 14 SD: 15.1859 cents 8:9:10:11:13 x 14:16 SD: 20.0289 cents 9:11 x 12:14:15:16:18 SD: 10.4929 cents 10:12 x 13:16:17:18:20 SD: 9.8963 cents 12:14:15:16:19:20:21:24 SD: 6.7954 cents 15:18:19:20:24:25:27:30 SD: 6.0293 cents 21:25:27:28:33:35:37:42 SD: 5.7683 cents 22:26:28:29:35:37:39:44 SD: 3.8496 cents 26:31:33:35:41:44:46:52 SD: 3.3794 cents 31:37:39:41:49:52:55:62 SD: 3.1908 cents 33:39:42:44:52:56:59:66 SD: 2.9130 cents 38:45:48:51:60:64:68:76 SD: 2.3294 cents 42:50:53:56:66:71:75:84 SD: 2.2484 cents 45:53:57:60:71:76:80:90 SD: 1.7377 cents 54:64:68:72:85:91:96:108 SD: 1.3703 cents 60:71:76:80:95:101:107:120 SD: 1.1494 cents 76:90:96:101:120:128:135:152 SD: 0.9333 cents 98:116:124:131:155:165:174:196 SD: 0.8775 cents 102:121:129:136:161:172:181:204 SD: 0.5994 cents 114:135:144:152:180:192:203:228 SD: 0.5751 cents 140:166:177:187:221:236:249:280 SD: 0.5371 cents 162:192:205:216:256:273:288:324 SD: 0.2488 cents 276:327:349:368:436:465:491:552 SD: 0.2448 cents 303:359:383:404:479:511:539:606 SD: 0.2364 cents 360:427:455:480:569:607:640:720 SD: 0.2213 cents 372:441:470:496:588:627:661:744 SD: 0.2133 cents 378:448:478:504:597:637:672:756 SD: 0.1657 cents 405:480:512:540:640:683:720:810 SD: 0.1207 cents 534:633:675:712:844:900:949:1068 SD: 0.1144 cents 567:672:717:756:896:956:1008:1134 SD: 0.0976 cents