Scala analysis: xen09-wilson-marwa-17b-05
Marwa permutation 5 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: 5/4 386.313714 major third 2: 9/7 435.084095 septimal major third, BP third 3: 4/3 498.044999 perfect fourth 4: 5/3 884.358713 major sixth, BP sixth 5: 15/8 1088.268715 classic major seventh 6: 27/14 1137.039096 septimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 5/4 386.3137 major third 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 5/4 386.3137 major third 5: 9/8 203.9100 major whole tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 5/4 386.314 cents major third 2: 2 16/15 111.731 cents minor diatonic semitone 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 9/7 435.084 cents septimal major third, BP third 2: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 54/35 750.725 cents septimal semi-augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 140/81 947.320 cents 5: 2 15/8 1088.269 cents classic major seventh 6: 2 8/5 813.686 cents minor sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 2 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 386.3 435.1 498.0 884.4 1088.3 1137.0 1200.0 386.3 : 48.8 111.7 498.0 702.0 750.7 813.7 1200.0 435.1 : 63.0 449.3 653.2 702.0 764.9 1151.2 1200.0 498.0 : 386.3 590.2 639.0 702.0 1088.3 1137.0 1200.0 884.4 : 203.9 252.7 315.6 702.0 750.7 813.7 1200.0 1088.3: 48.8 111.7 498.0 546.8 609.8 996.1 1200.0 1137.0: 63.0 449.3 498.0 561.0 947.3 1151.2 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 : 28/27, 62.9609 cents, amount: 2 Least squares average step : 192.51164 cents, oct.: 1347.58150 cents Scale is not proper Step pattern alph. order: ABCADBC Step pattern size order : DABDCAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.578397 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / 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 : 245/243, 14.1905 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Phrygian octave species of abstract tetrachord All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 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 : 0.234625 Specific harmonicity : 0.161986 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 9.072000E+04, 16.46913 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 53.5, average 7.64286 Mersenne's string divisions : 950544 Sum of van Prooijen's expressibility: 5.43676, average 0.77668 Sum of Tenney's harmonic distance : 10.31335, average 1.47334 Vogel's harmonic complexity : 14.42857 Wille's k value : 157 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 82.89294, average 2.96046 Lattice compactness (without 2's) : 54.89613, average 1.96058 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.42857 9 1 3: -1 .. 3 0.57143 8 1 5: 0 .. 1 0.42857 3 3 7: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 2 0 1 2 1 0 1 N T3 SD: 61.7920 c. M: 108.4677 c. 8: 3 0 0 3 1 1 0 N SD: 41.8500 c. M:-63.6863 c. 9: 3 0 1 3 1 1 0 N SD: 36.8253 c. M:-62.9609 c. 10: 3 0 1 3 2 0 1 N SD: 41.3093 c. M: 75.0841 c. 11: 4 0 1 3 2 0 1 N SD: 31.6782 c. M:-50.0499 c. 12: 4 0 1 4 2 0 1 N SD: 21.3012 c. M: 37.0391 c. 15: 5 0 1 5 2 1 1 N SD: 25.0229 c. M: 48.2687 c. 16: 5 1 1 5 3 0 1 N SD: 20.0565 c. M:-36.7313 c. 17: 5 1 1 5 3 1 1 N SD: 22.6121 c. M: 37.2999 c. 18: 6 0 1 6 3 1 1 N SD: 21.3682 c. M: 35.0841 c. 19: 6 1 1 6 3 1 1 N SD: 7.2549 c. M: 14.5845 c. 22: 7 1 1 7 4 1 1 N SD: 6.3903 c. M: 11.6314 c. 34: 11 1 2 11 6 1 2 N SD: 5.9646 c. M: 11.5547 c. 41: 13 2 2 13 7 2 2 N SD: 4.4341 c. M: 6.3099 c. 53: 17 2 3 17 9 2 3 N SD: 2.7919 c. M: 4.9636 c. 72: 23 3 4 23 12 3 4 N SD: 2.8008 c. M: 4.9354 c. 75: 24 3 4 24 13 3 4 N SD: 2.3663 c. M: 4.3587 c. 77: 25 3 4 25 13 3 4 N SD: 2.2653 c. M:-3.9530 c. 94: 30 4 5 30 16 4 5 N SD: 2.2455 c. M: 3.5076 c. 96: 31 4 5 31 16 4 5 N SD: 1.7622 c. M:-3.1413 c. 99: 32 4 5 32 17 4 5 N SD: 1.6036 c. M:-2.6404 c. 118: 38 5 6 38 20 5 6 N SD: 1.1268 c. M:-2.2040 c. 130: 42 5 7 42 22 5 7 N SD: 1.2243 c. M:-1.7951 c. 149: 48 6 8 48 25 6 8 N SD: 1.0243 c. M:-1.5473 c. 152: 49 6 8 49 26 6 8 N SD: 0.6560 c. M:-1.2050 c. 171: 55 7 9 55 29 7 9 N SD: 0.2737 c. M: 0.5494 c. 323: 104 13 17 104 55 13 17 N SD: 0.2247 c. M: 0.4092 c. 441: 142 18 23 142 75 18 23 N SD: 0.1953 c. M:-0.3759 c. 494: 159 20 26 159 84 20 26 N SD: 0.1428 c. M: 0.2663 c. 612: 197 25 32 197 104 25 32 N SD: 0.1167 c. M:-0.2158 c. 665: 214 27 35 214 113 27 35 N SD: 0.1432 c. M: 0.1970 c. 764: 246 31 40 246 130 31 40 N SD: 0.1149 c. M:-0.2130 c. 783: 252 32 41 252 133 32 41 N SD: 0.1081 c. M:-0.1649 c. 913: 294 37 48 294 155 37 48 N SD: 0.1045 c. M:-0.1977 c. 935: 301 38 49 301 159 38 49 N SD: 0.0576 c. M: 0.0806 c. 1106: 356 45 58 356 188 45 58 N SD: 0.0451 c. M: 0.0911 c. 1525: 491 62 80 491 259 62 80 N SD: 0.0525 c. M:-0.1003 c. 1600: 515 65 84 515 272 65 84 N SD: 0.0619 c. M: 0.1087 c. 1677: 540 68 88 540 285 68 88 N SD: 0.0605 c. M:-0.1034 c. 1696: 546 69 89 546 288 69 89 N SD: 0.0500 c. M:-0.0752 c. 1848: 595 75 97 595 314 75 97 N SD: 0.0352 c. M:-0.0569 c. 2019: 650 82 106 650 343 82 106 N SD: 0.0250 c. M: 0.0406 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 4:5 x x 7 x x 8 SD: 28.1557 cents 5:6 x 7:8:9 x 10 S SD: 29.7446 cents 6 x x 8:10:11 x 12 S SD: 9.7264 cents 7 x 9 x 12:13 x 14 SD: 12.8769 cents 8:10 x 11:13:15 x 16 SD: 13.7973 cents 9:11 x 12:15:17 x 18 SD: 8.1900 cents 10 x 13 x 17:19 x 20 SD: 11.3663 cents 11 x 14:15:18 x 21:22 SD: 11.2082 cents 12:15 x 16:20 x 23:24 SD: 2.1439 cents 13:16:17 x 22:24:25:26 SD: 9.1667 cents 14 x 18:19:23:26:27:28 SD: 7.1374 cents 15:19 x 20:25:28:29:30 SD: 4.0944 cents 16:20 x 21:27:30:31:32 SD: 5.9390 cents 18 x 23:24:30:34:35:36 SD: 3.6497 cents 19:24 x 25:32:36:37:38 SD: 7.0586 cents 20:25:26:27:33:38:39:40 SD: 6.4254 cents 21:26:27:28:35:39:41:42 SD: 4.5179 cents 22 x 28:29:37:41:42:44 SD: 6.1589 cents 23:29:30:31:38:43:44:46 SD: 5.7945 cents 24:30:31:32:40:45:46:48 S SD: 1.9105 cents 26 x 33:35:43:49:50:52 SD: 5.4135 cents 27:34:35:36:45:51:52:54 SD: 3.2997 cents 32:40:41:43:53:60:62:64 SD: 2.8555 cents 36:45:46:48:60:68:69:72 SD: 2.8323 cents 39:49:50:52:65:73:75:78 SD: 1.6659 cents 48:60:62:64:80:90:93:96 S SD: 1.6155 cents 56:70:72:75:93:105:108:112 SD: 1.4130 cents 57:71:73:76:95:107:110:114 SD: 1.3411 cents 60:75:77:80:100:113:116:120 SD: 1.3360 cents 63:79:81:84:105:118:122:126 SD: 1.3095 cents 69:86:89:92:115:129:133:138 SD: 1.2965 cents 72:90:93:96:120:135:139:144 SD: 1.1703 cents 80:100:103:107:133:150:154:160 SD: 1.1431 cents 81:101:104:108:135:152:156:162 SD: 0.8036 cents 84:105:108:112:140:158:162:168 SD: 0.7839 cents 87:109:112:116:145:163:168:174 SD: 0.7468 cents 108:135:139:144:180:203:208:216 SD: 0.7429 cents 111:139:143:148:185:208:214:222 SD: 0.6869 cents 120:150:154:160:200:225:231:240 SD: 0.6483 cents 129:161:166:172:215:242:249:258 SD: 0.5042 cents 144:180:185:192:240:270:278:288 SD: 0.3180 cents 168:210:216:224:280:315:324:336 S SD: 0.0000 cents