Scala analysis: xen09-wilson-marwa-08-05
Marwa permutation 5 from Figure 8, Archytas 28/27 8/7 9/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 112/81 561.005903 5: 128/81 792.179997 Pythagorean minor 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: 28/27 62.9609 Archytas' 1/3-tone 2: 8/7 231.1741 septimal whole tone 3: 9/8 203.9100 major whole tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 8/7 231.1741 septimal whole tone 6: 9/8 203.9100 major whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 3 9/8 203.910 cents major whole tone 1: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 81/64 407.820 cents Pythagorean major third 2: 2 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 5 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 4: 1 112/81 561.006 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 2 12/7 933.129 cents septimal major sixth 6: 2 7/4 968.826 cents harmonic seventh 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 294.1 498.0 561.0 792.2 996.1 1200.0 63.0 : 231.2 435.1 498.0 729.2 933.1 1137.0 1200.0 294.1 : 203.9 266.9 498.0 702.0 905.9 968.8 1200.0 498.0 : 63.0 294.1 498.0 702.0 764.9 996.1 1200.0 561.0 : 231.2 435.1 639.0 702.0 933.1 1137.0 1200.0 792.2 : 203.9 407.8 470.8 702.0 905.9 968.8 1200.0 996.1 : 203.9 266.9 498.0 702.0 764.9 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 231.1741 cents 54/49, 168.2132 cents 28/27, 62.9609 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 470.7809 .. 638.9941 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 4: 561.0059 .. 729.2191 cents 54/49, 168.2132 cents 6272/6561,-77.9882 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 6: 968.8259 .. 1137.0391 cents 54/49, 168.2132 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.722778 Largest / Average step : 1.348516 Largest / Smallest step : 3.671709 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 162.33450 cents, oct.: 1136.34147 cents Scale is not proper Step pattern alph. order: ABCABCC Step pattern size order : SLMSLMM Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.378117 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 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 : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 64/63, 27.2641 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 is Lydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 1 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 Limited inverse transpositions with margin 168.2132 cents: 4 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.035775 Average absolute harmonicity : 0.220618 Specific harmonicity : 0.184387 Fundamental : 1/81, -6.3399 octaves, 3.2299 Hz. Guide tone : 896, 9.8074 octaves, 234416.507 Hz. Exponens Consonantiae : 7.257600E+04, 16.14720 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 275.5, average 39.35714 Mersenne's string divisions : 1249438575 Sum of van Prooijen's expressibility: 8.11106, average 1.15872 Sum of Tenney's harmonic distance : 17.32701, average 2.47529 Vogel's harmonic complexity : 10.28571 Wille's k value : 40 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 101.81466, average 3.63624 Lattice compactness (without 2's) : 59.44782, average 2.12314 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 7 3.57143 25 1 3: -4 .. 0 -2.42857 17 4 7: 0 .. 1 0.28571 2 2 Average exponent except 2's :-15 / 7 =-2.14286 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 10 22| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 12 18|
FIT/MODE
7: 0 2 1 0 2 1 1 N T3 SD: 44.8166 c. M:-64.9629 c. 9: 0 2 1 1 2 1 2 N D3 SD: 52.2313 c. M: 98.0450 c. 10: 0 2 2 0 2 2 2 N M DE S SD: 53.8446 c. M: 81.0059 c. 11: 0 2 2 1 2 2 2 N T3 SD: 45.9780 c. M: 75.9532 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 20.7264 c. M:-38.9941 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 13: 1 2 2 1 3 2 2 N T3 SD: 25.0795 c. M:-38.5892 c. 15: 1 3 2 1 3 2 3 N T3 SD: 19.4555 c. M: 36.0900 c. 17: 1 3 3 1 3 3 3 N M DE S SD: 8.7390 c. M: 15.7094 c. Safi al-Din's maqam Abu Salik 24: 1 5 4 1 5 4 4 N SD: 7.5949 c. M: 12.9609 c. Diatonic + Enharmonic Diesis Mixolydian 36: 2 7 6 2 7 6 6 N SD: 4.7875 c. M:-7.8200 c. Diatonic + Soft Chromatic Diesis Mixolydian 41: 2 8 7 2 8 7 7 N SD: 2.6911 c. M: 4.9083 c. 53: 3 10 9 3 10 9 9 N SD: 2.6752 c. M:-5.0318 c. 77: 4 15 13 4 15 13 13 N SD: 1.3790 c. M:-2.6252 c. 94: 5 18 16 5 18 16 16 N SD: 0.5521 c. M:-0.8689 c. 171: 9 33 29 9 33 29 29 N SD: 0.4479 c. M:-0.8025 c. 212: 11 41 36 11 41 36 36 N SD: 0.3817 c. M: 0.6968 c. 265: 14 51 45 14 51 45 45 N SD: 0.2885 c. M:-0.5035 c. 306: 16 59 52 16 59 52 52 N SD: 0.1175 c. M: 0.2216 c. 400: 21 77 68 21 77 68 68 N SD: 0.0943 c. M: 0.1800 c. 571: 30 110 97 30 110 97 97 N SD: 0.0803 c. M:-0.1149 c. 706: 37 136 120 37 136 120 120 N SD: 0.0742 c. M: 0.1120 c. 877: 46 169 149 46 169 149 149 N SD: 0.0351 c. M:-0.0663 c. 1277: 67 246 217 67 246 217 217 N SD: 0.0058 c. M: 0.0109 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 45.1125 cents 3 x x 4 x 5 x 6 S SD: 30.7262 cents 4 x 5 x x 6:7:8 S SD: 32.9591 cents 5 x 6 x 7:8:9:10 S SD: 8.6025 cents 6 x 7:8 x 9:11:12 SD: 21.6535 cents 7 x 8:9:10:11:12:14 S SD: 20.5320 cents 8 x 9 x 11:13:14:16 SD: 21.2746 cents 9 x 11:12 x 14:16:18 SD: 11.9689 cents 11:12:13 x 15:17:20:22 SD: 17.7084 cents 12:13:14:16:17:19:21:24 SD: 13.5366 cents 14:15:17:19 x 22:25:28 SD: 12.9593 cents 15:16:18:20:21:24:27:30 S SD: 9.2897 cents 16:17:19:21:22:25:28:32 SD: 8.7339 cents 17:18:20:23:24:27:30:34 SD: 8.6101 cents 18:19:21:24:25:28:32:36 SD: 7.1215 cents 21:22:25:28:29:33:37:42 SD: 3.8017 cents 26:27:31:35:36:41:46:52 SD: 3.1176 cents 27:28:32:36:37:43:48:54 SD: 2.9367 cents 45:47:53:60:62:71:80:90 SD: 2.5368 cents 48:50:57:64:66:76:85:96 SD: 2.1288 cents 50:52:59:67:69:79:89:100 SD: 1.8785 cents 54:56:64:72:75:85:96:108 SD: 1.4665 cents 60:62:71:80:83:95:107:120 SD: 1.3316 cents 76:79:90:101:105:120:135:152 SD: 1.0801 cents 81:84:96:108:112:128:144:162 S SD: 0.0000 cents