Scala analysis: xen09-wilson-marwa-07-15
Marwa permutation 15 from Figure 7, 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: 3/2 701.955001 perfect fifth 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: 9/8 203.9100 major whole tone 5: 256/243 90.2250 limma, Pythagorean minor second 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: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 4 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 3 32/27 294.135 cents Pythagorean minor third 2: 2 81/64 407.820 cents Pythagorean major third 2: 1 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: 1 14/9 764.916 cents septimal minor sixth 5: 2 128/81 792.180 cents Pythagorean minor sixth 5: 3 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 4 16/9 996.090 cents Pythagorean minor seventh 6: 1 243/128 1109.775 cents Pythagorean major seventh 6: 1 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: 3.66667 = 11/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 63.0 294.1 498.0 702.0 792.2 996.1 1200.0 63.0 : 231.2 435.1 639.0 729.2 933.1 1137.0 1200.0 294.1 : 203.9 407.8 498.0 702.0 905.9 968.8 1200.0 498.0 : 203.9 294.1 498.0 702.0 764.9 996.1 1200.0 702.0 : 90.2 294.1 498.0 561.0 792.2 996.1 1200.0 792.2 : 203.9 407.8 470.8 702.0 905.9 1109.8 1200.0 996.1 : 203.9 266.9 498.0 702.0 905.9 996.1 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: 4 Most common interval of one step : 9/8, 203.9100 cents, amount: 4 Least squares average step : 166.36161 cents, oct.: 1164.53129 cents Scale is not proper Step pattern alph. order: ABCCDCC Step pattern size order : ADCCBCC Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.447201 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 Rothenberg efficiency : 0.496599 redundancy: 0.503401 Efficiency x scale size : 3.476190 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.66667 = 11/3 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: 4 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 168.2132 cents: 5 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.031627 Average absolute harmonicity : 0.253854 Specific harmonicity : 0.198757 Fundamental : 1/162, -7.3399 octaves, 1.6150 Hz. Guide tone : 2688, 11.3923 octaves, 703249.520 Hz. Exponens Consonantiae : 4.354560E+05, 18.73217 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 181.5, average 25.92857 Mersenne's string divisions : 6473775 Sum of van Prooijen's expressibility: 6.67970, average 0.95424 Sum of Tenney's harmonic distance : 14.14746, average 2.02107 Vogel's harmonic complexity : 11.71429 Wille's k value : 121 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 112.69384, average 4.02478 Lattice compactness (without 2's) : 62.51216, average 2.23258 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 7 2.85714 22 1 3: -4 .. 1 -1.71429 14 5 7: 0 .. 1 0.14286 1 1 Average exponent except 2's :-11 / 7 =-1.57143 Average absolute exponent except 2's: 15 / 7 = 2.14286 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 1 1 1 1 N T3 SD: 41.6459 c. M:-64.9629 c. 11: 0 2 2 2 1 2 2 N T3 SD: 48.9951 c. M: 75.9532 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 14.5915 c. M:-37.0391 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 14: 1 2 3 2 1 3 2 P T3 SD: 23.6018 c. M: 36.9921 c. 15: 1 3 2 3 1 2 3 N T3 SD: 20.6128 c. M: 36.0900 c. 16: 1 3 3 2 2 2 3 P T3 SD: 21.2281 c. M:-32.8200 c. 17: 1 3 3 3 1 3 3 N M DE S SD: 8.7531 c. M: 15.7094 c. 24: 1 5 4 4 2 4 4 N SD: 6.3972 c. M: 12.9609 c. 36: 2 7 6 6 3 6 6 N SD: 4.3460 c. M:-7.8200 c. 41: 2 8 7 7 3 7 7 N SD: 1.9580 c. M: 4.4243 c. 53: 3 10 9 9 4 9 9 N SD: 1.8816 c. M:-4.9636 c. 77: 4 15 13 13 6 13 13 N SD: 1.4011 c. M:-2.6252 c. 94: 5 18 16 16 7 16 16 N SD: 0.4898 c. M:-0.8689 c. 171: 9 33 29 29 13 29 29 N SD: 0.4287 c. M:-0.8025 c. 212: 11 41 36 36 16 36 36 N SD: 0.2999 c. M: 0.6968 c. 265: 14 51 45 45 20 45 45 N SD: 0.2183 c. M:-0.4353 c. 306: 16 59 52 52 23 52 52 N SD: 0.0825 c. M: 0.2158 c. 400: 21 77 68 68 30 68 68 N SD: 0.0958 c. M: 0.1800 c. 571: 30 110 97 97 43 97 97 N SD: 0.0684 c. M:-0.1142 c. 706: 37 136 120 120 53 120 120 N SD: 0.0648 c. M: 0.1120 c. 877: 46 169 149 149 66 149 149 N SD: 0.0356 c. M:-0.0663 c. 971: 51 187 165 165 73 165 165 N SD: 0.0256 c. M:-0.0669 c. 1277: 67 246 217 217 96 217 217 N SD: 0.0057 c. M: 0.0109 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 30.7262 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 18.4632 cents 6 x 7:8:9 x 11:12 SD: 11.9689 cents 7 x 8:9 x 11:12:14 SD: 21.8962 cents 8 x 9:11:12:13:14:16 SD: 19.7620 cents 9 x 11:12 x 14:16:18 SD: 11.9689 cents 11:12:13:15 x 17:20:22 SD: 18.4272 cents 12:13:14:16:18:19:21:24 SD: 12.1346 cents 14:15:17:19:21:22:25:28 SD: 11.1080 cents 15:16:18:20:23:24:27:30 SD: 10.3154 cents 16:17:19:21:24:25:28:32 SD: 8.6235 cents 17:18:20:23:26:27:30:34 SD: 8.4118 cents 18:19:21:24:27:28:32:36 SD: 7.0358 cents 20:21:24:27:30:32:36:40 S SD: 6.8699 cents 21:22:25:28:32:33:37:42 SD: 5.4336 cents 22:23:26:29:33:35:39:44 SD: 3.9677 cents 26:27:31:35:39:41:46:52 SD: 3.0991 cents 36:37:43:48:54:57:64:72 SD: 2.9761 cents 48:50:57:64:72:76:85:96 SD: 1.6175 cents 54:56:64:72:81:85:96:108 SD: 0.9680 cents 86:89:102:115:129:136:153:172 SD: 0.9362 cents 102:106:121:136:153:161:181:204 SD: 0.7803 cents 108:112:128:144:162:171:192:216 SD: 0.4826 cents 162:168:192:216:243:256:288:324 SD: 0.0000 cents