Scala analysis: xen09-wilson-marwa-17b-10
Marwa permutation 10 from Figure 17b, Archytas 36/35 28/27 5/4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 5/3 884.358713 major sixth, BP sixth 5: 12/7 933.129094 septimal major sixth 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: 8/7 231.1741 septimal whole tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 9/8 203.9100 major whole tone 4: 5/4 386.3137 major third 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 2 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 9/7 435.084 cents septimal major third, BP third 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: 2 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 1 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 231.2 294.1 498.0 884.4 933.1 996.1 1200.0 231.2 : 63.0 266.9 653.2 702.0 764.9 968.8 1200.0 294.1 : 203.9 590.2 639.0 702.0 905.9 1137.0 1200.0 498.0 : 386.3 435.1 498.0 702.0 933.1 996.1 1200.0 884.4 : 48.8 111.7 315.6 546.8 609.8 813.7 1200.0 933.1 : 63.0 266.9 498.0 561.0 764.9 1151.2 1200.0 996.1 : 203.9 435.1 498.0 702.0 1088.3 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 : 9/8, 203.9100 cents, amount: 2 Least squares average step : 177.80857 cents, oct.: 1244.65997 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : DBCEABC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.605831 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 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 : 245/243, 14.1905 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 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 6 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 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 : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.030910 Average absolute harmonicity : 0.235827 Specific harmonicity : 0.187557 Fundamental : 1/189, -7.5622 octaves, 1.3843 Hz. Guide tone : 480, 8.9069 octaves, 125580.271 Hz. Exponens Consonantiae : 9.072000E+04, 16.46913 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 68.0, average 9.71429 Mersenne's string divisions : 4708200 Sum of van Prooijen's expressibility: 5.25189, average 0.75027 Sum of Tenney's harmonic distance : 11.32365, average 1.61766 Vogel's harmonic complexity : 14.57143 Wille's k value : 157 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 82.53737, average 2.94776 Lattice compactness (without 2's) : 49.82269, average 1.77938 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 5 2.42857 17 1 3: -3 .. 1 -0.85714 8 3 5: 0 .. 1 0.14286 1 1 7: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 44.3634 c. M: 75.9862 c. 8: 2 0 1 3 0 1 1 N SD: 40.2283 c. M:-68.8259 c. 9: 2 0 2 3 0 1 1 N SD: 38.9856 c. M:-70.5767 c. 10: 2 0 2 3 1 0 2 N SD: 32.3515 c. M: 54.1350 c. 11: 2 1 2 3 1 0 2 N SD: 29.8189 c. M:-48.6891 c. 12: 2 1 2 4 0 1 2 N SD: 18.3907 c. M: 33.1291 c. 17: 3 1 3 5 1 1 3 N SD: 17.8231 c. M: 37.2999 c. 18: 3 1 3 6 1 1 3 N SD: 20.8370 c. M: 31.3783 c. 19: 4 1 3 6 1 1 3 N SD: 14.1049 c. M:-21.6545 c. 22: 4 1 4 7 1 1 4 N SD: 12.2549 c. M: 21.4077 c. 24: 5 1 4 8 1 1 4 N SD: 11.5709 c. M:-18.8259 c. 26: 5 1 5 8 1 2 4 N SD: 11.4524 c. M:-19.2946 c. 28: 5 2 5 9 1 1 5 N SD: 12.1321 c. M: 16.8884 c. 30: 6 1 5 10 1 2 5 N SD: 10.7569 c. M: 18.0450 c. 31: 6 2 5 10 1 2 5 N SD: 7.8312 c. M:-15.5424 c. 36: 7 2 6 12 1 2 6 N SD: 6.5777 c. M:-15.6413 c. 37: 7 2 6 12 2 2 6 N SD: 7.2990 c. M: 11.5585 c. 41: 8 2 7 13 2 2 7 N SD: 3.0208 c. M: 6.3099 c. 53: 10 3 9 17 2 3 9 N SD: 2.6134 c. M: 4.8272 c. 77: 15 4 13 25 3 4 13 N SD: 2.1422 c. M:-3.9530 c. 94: 18 5 16 30 4 5 16 N SD: 1.5175 c. M: 3.5076 c. 99: 19 5 17 32 4 5 17 N SD: 1.5688 c. M: 3.2259 c. 113: 22 6 19 36 5 6 19 N SD: 2.1590 c. M:-3.2101 c. 118: 23 6 20 38 5 6 20 N SD: 1.4437 c. M:-2.7242 c. 130: 25 7 22 42 5 7 22 N SD: 0.9629 c. M:-1.7951 c. 171: 33 9 29 55 7 9 29 N SD: 0.3362 c. M:-0.6018 c. 395: 76 21 67 127 16 21 67 N SD: 0.3521 c. M:-0.5485 c. 400: 77 21 68 129 16 21 68 N SD: 0.2636 c. M:-0.6413 c. 441: 85 23 75 142 18 23 75 N SD: 0.1506 c. M: 0.2574 c. 612: 118 32 104 197 25 32 104 N SD: 0.1093 c. M:-0.2042 c. 665: 128 35 113 214 27 35 113 N SD: 0.1191 c. M: 0.1968 c. 836: 161 44 142 269 34 44 142 N SD: 0.0958 c. M: 0.1482 c. 1106: 213 58 188 356 45 58 188 N SD: 0.0666 c. M: 0.1024 c. 1277: 246 67 217 411 52 67 217 N SD: 0.0377 c. M: 0.0987 c. 1677: 323 88 285 540 68 88 285 N SD: 0.0409 c. M:-0.0778 c. 1718: 331 90 292 553 70 90 292 N SD: 0.0488 c. M: 0.0747 c. 1848: 356 97 314 595 75 97 314 N SD: 0.0242 c. M:-0.0569 c. 2289: 441 120 389 737 93 120 389 N SD: 0.0265 c. M:-0.0450 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 x 5 x x x 7:8 SD: 32.0421 cents 5 x 6:7:8 x 9:10 S SD: 22.8511 cents 6 x 7:8:10 x 11:12 S SD: 11.9689 cents 7:8 x 9 x 12 x 14 S SD: 15.7402 cents 8:9 x 11:13 x 14:16 SD: 15.8061 cents 9:10:11:12:15 x 16:18 S SD: 12.0376 cents 10:11:12:13 x 17:18:20 SD: 14.3706 cents 11 x 13:15:18:19:20:22 SD: 10.8416 cents 12 x 14:16:20 x 21:24 S SD: 7.7114 cents 13:15 x 17 x 22:23:26 SD: 8.8842 cents 14:16:17:19:23:24:25:28 SD: 8.3084 cents 15:17:18:20:25:26:27:30 SD: 5.5345 cents 16:18:19:21:27 x 28:32 SD: 8.6665 cents 17:19:20:23:28:29:30:34 SD: 7.7573 cents 18 x 21:24:30:31:32:36 S SD: 4.7354 cents 21:24:25:28:35:36:37:42 SD: 2.4766 cents 27:31:32:36:45:46:48:54 SD: 1.9105 cents 42:48:50:56:70:72:75:84 SD: 1.5580 cents 48:55:57:64:80:82:85:96 SD: 1.5243 cents 63:72:75:84:105:108:112:126 SD: 1.1016 cents 90:103:107:120:150:154:160:180 SD: 0.9610 cents 98:112:116:131:163:168:174:196 SD: 0.9228 cents 99:113:117:132:165:170:176:198 SD: 0.8751 cents 112:128:133:149:187:192:199:224 SD: 0.8672 cents 113:129:134:151:188:194:201:226 SD: 0.8578 cents 119:136:141:159:198:204:212:238 SD: 0.8462 cents 120:137:142:160:200:206:213:240 SD: 0.6953 cents 126:144:149:168:210:216:224:252 SD: 0.5527 cents 141:161:167:188:235:242:251:282 SD: 0.5182 cents 147:168:174:196:245:252:261:294 SD: 0.4464 cents 162:185:192:216:270:278:288:324 SD: 0.3180 cents 168:192:199:224:280:288:299:336 SD: 0.3085 cents 189:216:224:252:315:324:336:378 S SD: 0.0000 cents