Scala analysis: xen09-wilson-marwa-17b-07
Marwa permutation 7 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: 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: 12/7 933.129094 septimal major sixth 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: 8/7 231.1741 septimal whole tone 2: 9/8 203.9100 major whole tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 5/4 386.3137 major third 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 9/8 203.9100 major whole tone 7: 28/27 62.9609 Archytas' 1/3-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 81/70 252.680 cents Al-Hwarizmi's lute middle finger 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 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 54/35 750.725 cents septimal semi-augmented fifth 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: 1 140/81 947.320 cents 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 : 231.2 435.1 498.0 884.4 933.1 1137.0 1200.0 231.2 : 203.9 266.9 653.2 702.0 905.9 968.8 1200.0 435.1 : 63.0 449.3 498.0 702.0 764.9 996.1 1200.0 498.0 : 386.3 435.1 639.0 702.0 933.1 1137.0 1200.0 884.4 : 48.8 252.7 315.6 546.8 750.7 813.7 1200.0 933.1 : 203.9 266.9 498.0 702.0 764.9 1151.2 1200.0 1137.0: 63.0 294.1 498.0 561.0 947.3 996.1 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: 252.6804 .. 449.2746 cents 2450/2187, 196.5942 cents 162/175,-133.6333 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 750.7254 .. 947.3196 cents 2450/2187, 196.5942 cents 162/175,-133.6333 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 162/175,-133.6333 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 : 185.86280 cents, oct.: 1301.03961 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : DCBEACB Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.477280 Lumma stability : 0.081284 Lumma impropriety factor : 0.416298 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 : 2 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 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 : 0.031896 Average absolute harmonicity : 0.226086 Specific harmonicity : 0.169744 Fundamental : 1/42, -5.3923 octaves, 6.2292 Hz. Guide tone : 1080, 10.0768 octaves, 282555.611 Hz. Exponens Consonantiae : 4.536000E+04, 15.46913 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 54.5, average 7.78571 Mersenne's string divisions : 1308720 Sum of van Prooijen's expressibility: 5.25189, average 0.75027 Sum of Tenney's harmonic distance : 10.60560, average 1.51509 Vogel's harmonic complexity : 10.42857 Wille's k value : 40 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 75.74264, average 2.70509 Lattice compactness (without 2's) : 54.13002, average 1.93321 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.00000 9 1 3: -1 .. 3 0.57143 8 1 5: 0 .. 1 0.14286 1 1 7: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 18 18| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 2 0 2 0 2 0 N T3 SD: 54.2282 c. M:-79.2016 c. 8: 2 1 0 3 0 2 0 N SD: 42.3827 c. M:-68.8259 c. 9: 2 1 1 3 0 2 0 N SD: 37.9822 c. M:-62.9609 c. 10: 2 2 0 3 1 1 1 N SD: 34.5670 c. M: 57.0391 c. 11: 2 2 0 4 0 2 1 N G SD: 37.5817 c. M: 61.6814 c. 12: 2 2 1 4 0 2 1 N SD: 26.5131 c. M: 37.0391 c. 14: 3 2 1 4 1 2 1 N SD: 18.2585 c. M: 27.2159 c. 17: 3 3 1 5 1 3 1 N D3 SD: 17.7877 c. M: 37.2999 c. 19: 4 3 1 6 1 3 1 N SD: 10.4515 c. M:-21.4575 c. 22: 4 4 1 7 1 4 1 N D3 SD: 8.1220 c. M: 12.9923 c. 31: 6 5 2 10 1 5 2 N SD: 7.3240 c. M: 14.4585 c. 36: 7 6 2 12 1 6 2 N SD: 6.2103 c. M:-15.6413 c. 41: 8 7 2 13 2 7 2 N SD: 3.7019 c. M: 6.3099 c. 53: 10 9 3 17 2 9 3 N SD: 3.7101 c. M: 4.9636 c. 58: 11 10 3 19 2 10 3 N SD: 2.6376 c. M:-5.2965 c. 72: 14 12 4 23 3 12 4 N SD: 1.9411 c. M: 3.7058 c. 77: 15 13 4 25 3 13 4 N SD: 2.0195 c. M:-3.9530 c. 94: 18 16 5 30 4 16 5 N SD: 1.5843 c. M: 3.5076 c. 99: 19 17 5 32 4 17 5 N SD: 1.1575 c. M:-2.3548 c. 130: 25 22 7 42 5 22 7 N SD: 1.1022 c. M:-1.7951 c. 152: 29 26 8 49 6 26 8 N SD: 1.1112 c. M: 2.2267 c. 171: 33 29 9 55 7 29 9 N SD: 0.2093 c. M:-0.4049 c. 441: 85 75 23 142 18 75 23 N SD: 0.2030 c. M:-0.3759 c. 494: 95 84 26 159 20 84 26 N SD: 0.2429 c. M: 0.4049 c. 571: 110 97 30 184 23 97 30 N SD: 0.1587 c. M:-0.4049 c. 612: 118 104 32 197 25 104 32 N SD: 0.1576 c. M:-0.2158 c. 665: 128 113 35 214 27 113 35 N SD: 0.1590 c. M: 0.1970 c. 742: 143 126 39 239 30 126 39 N SD: 0.1226 c. M:-0.2774 c. 836: 161 142 44 269 34 142 44 N SD: 0.1227 c. M: 0.1970 c. 913: 176 155 48 294 37 155 48 N SD: 0.1144 c. M:-0.1977 c. 935: 180 159 49 301 38 159 49 N SD: 0.0840 c. M: 0.1581 c. 1106: 213 188 58 356 45 188 58 N SD: 0.0491 c. M: 0.0911 c. 1277: 246 217 67 411 52 217 67 N SD: 0.0375 c. M: 0.0987 c. 1677: 323 285 88 540 68 285 88 N SD: 0.0381 c. M:-0.0778 c. 1848: 356 314 97 595 75 314 97 N SD: 0.0254 c. M:-0.0569 c. 2019: 389 343 106 650 82 343 106 N SD: 0.0266 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 x 5 x x 7 x 8 SD: 20.1462 cents 5:6 x 7:8:9 x 10 S SD: 32.4954 cents 6:7 x 8:10 x x 12 S SD: 8.9242 cents 7:8:9 x x 12 x 14 S SD: 0.0000 cents 9:10 x 12:15 x 17:18 SD: 12.1229 cents 10:11:13 x x 17:19:20 SD: 14.9960 cents 11:13:14:15:18:19:21:22 SD: 11.6754 cents 12:14:15:16:20:21:23:24 SD: 10.1439 cents 13:15:17 x x 22:25:26 SD: 8.1460 cents 14:16:18:19:23:24:27:28 SD: 5.6414 cents 15:17:19:20:25:26:29:30 SD: 5.0745 cents 16:18 x 21:27 x 31:32 SD: 8.9736 cents 17:19:22:23:28:29:33:34 SD: 7.6619 cents 18:21:23:24:30:31:35:36 SD: 5.8108 cents 21:24:27:28:35:36:41:42 SD: 3.0346 cents 27:31:35:36:45:46:52:54 SD: 2.8062 cents 36:41:46:48:60:62:69:72 SD: 2.5952 cents 42:48:54:56:70:72:81:84 S SD: 0.0000 cents