Scala analysis: xen09-wilson-marwa-07-02
Marwa permutation 2 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: 9/8 203.910002 major whole tone 2: 81/64 407.820003 Pythagorean major third 3: 21/16 470.780907 narrow fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 9/8 203.9100 major whole tone 2: 9/8 203.9100 major whole tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 8/7 231.1741 septimal whole tone 5: 9/8 203.9100 major whole tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 8/7 231.1741 septimal 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 : 203.9 407.8 470.8 702.0 905.9 968.8 1200.0 203.9 : 203.9 266.9 498.0 702.0 764.9 996.1 1200.0 407.8 : 63.0 294.1 498.0 561.0 792.2 996.1 1200.0 470.8 : 231.2 435.1 498.0 729.2 933.1 1137.0 1200.0 702.0 : 203.9 266.9 498.0 702.0 905.9 968.8 1200.0 905.9 : 63.0 294.1 498.0 702.0 764.9 996.1 1200.0 968.8 : 231.2 435.1 639.0 702.0 933.1 1137.0 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 : 171.29995 cents, oct.: 1199.09966 cents Scale is not proper Step pattern alph. order: AABCABC Step pattern size order : MMSLMSL Scale is sum-free (all different intervals) 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 Hypophrygian octave species of abstract tetrachord Scale is Hypodorian octave species of abstract tetrachord All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 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: 1 -- 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 : 0.239492 Specific harmonicity : 0.192137 Fundamental : 1/64, -6.0000 octaves, 4.0879 Hz. Guide tone : 1134, 10.1472 octaves, 296683.391 Hz. Exponens Consonantiae : 7.257600E+04, 16.14720 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 130.5, average 18.64286 Mersenne's string divisions : 129419895 Sum of van Prooijen's expressibility: 6.93853, average 0.99122 Sum of Tenney's harmonic distance : 13.26016, average 1.89431 Vogel's harmonic complexity : 10.00000 Wille's k value : 40 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 99.37371, average 3.54906 Lattice compactness (without 2's) : 54.57665, average 1.94917 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -2.71429 21 1 3: 0 .. 4 1.57143 11 4 7: 0 .. 1 0.28571 2 2 Average exponent except 2's : 13 / 7 = 1.85714 Average absolute exponent except 2's: 13 / 7 = 1.85714 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: 1 1 1 1 1 1 1 SP B ME I SD: 43.7118 c. M: 64.9629 c. Lebeng 10: 2 1 1 2 2 0 2 P D3 S SD: 31.6416 c. M:-54.1350 c. 11: 2 2 0 2 2 1 2 N T3 SD: 28.5796 c. M: 47.4095 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 16.6486 c. M:-31.1741 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 17: 3 3 1 3 3 1 3 N M DE S SD: 14.0613 c. M:-23.3367 c. Safi al-Din's maqam `Ussaq 20: 3 4 1 4 3 1 4 N T3 SD: 13.3253 c. M: 23.9100 c. 21: 4 3 1 4 4 1 4 N SD: 13.0755 c. M:-24.6614 c. 24: 4 4 1 5 4 1 5 N SD: 11.3447 c. M: 20.7809 c. Diatonic + Enharmonic Diesis Hypophrygian 26: 4 5 1 5 5 1 5 N T3 S SD: 11.3667 c. M: 19.2946 c. 29: 5 5 1 6 5 1 6 N SD: 9.2813 c. M: 17.1018 c. 31: 5 5 2 6 5 2 6 N SD: 10.9912 c. M: 20.7232 c. 32: 5 6 2 6 5 2 6 N T3 SD: 10.3815 c. M:-16.7191 c. 33: 6 5 2 6 6 2 6 N SD: 9.0225 c. M:-14.2718 c. 36: 6 6 2 7 6 2 7 N SD: 4.4118 c. M: 7.8200 c. Diatonic + Soft Chromatic Diesis Hypophrygian 41: 7 7 2 8 7 2 8 N SD: 1.7750 c. M: 2.9722 c. 77: 13 13 4 15 13 4 15 N SD: 2.0769 c. M: 3.2484 c. 89: 15 15 5 17 15 5 17 N SD: 1.9219 c. M: 3.3256 c. 94: 16 16 5 18 16 5 18 N SD: 0.8660 c. M:-1.5595 c. 135: 23 23 7 26 23 7 26 N SD: 0.5676 c. M:-1.0689 c. 171: 29 29 9 33 29 9 33 N SD: 0.4983 c. M: 0.8025 c. 265: 45 45 14 51 45 14 51 N SD: 0.1770 c. M: 0.2728 c. 306: 52 52 16 59 52 16 59 N SD: 0.1052 c. M: 0.1985 c. 571: 97 97 30 110 97 30 110 N SD: 0.0600 c. M: 0.1142 c. 706: 120 120 37 136 120 37 136 N SD: 0.0602 c. M:-0.1120 c. 877: 149 149 46 169 149 46 169 N SD: 0.0538 c. M: 0.0854 c. 971: 165 165 51 187 165 51 187 N SD: 0.0392 c. M:-0.0739 c. 1277: 217 217 67 246 217 67 246 N SD: 0.0073 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: 11.5751 cents 4 x 5 x 6 x 7:8 S SD: 5.3766 cents 5 x 6:7 x 8:9:10 S SD: 35.6966 cents 6:7 x 8:9:10:11:12 S SD: 17.9939 cents 7:8:9 x 11:12 x 14 SD: 18.6721 cents 8:9:10:11:12 x 14:16 S SD: 13.8932 cents 10:11 x 13:15:17:18:20 SD: 10.9670 cents 11:12:14 x 17 x 19:22 SD: 15.6398 cents 12:14:15:16:18:20:21:24 S SD: 10.7214 cents 14:16:18 x 21:24:25:28 SD: 9.7941 cents 15:17:19:20:23:25:26:30 SD: 7.9455 cents 16:18:20:21:24:27:28:32 S SD: 3.0723 cents 17:19 x 22:26:29:30:34 SD: 8.1938 cents 18:20:23:24:27:30:32:36 SD: 7.4030 cents 19:21:24:25:29:32:33:38 SD: 6.4805 cents 22:25:28:29:33:37:39:44 SD: 4.4850 cents 26:29:33:34:39:44:46:52 SD: 3.6914 cents 32:36:41:42:48:54:56:64 SD: 3.0346 cents 38:43:48:50:57:64:67:76 SD: 2.5220 cents 42:47:53:55:63:71:74:84 SD: 2.3597 cents 48:54:61:63:72:81:84:96 SD: 1.0157 cents 64:72:81:84:96:108:112:128 S SD: 0.0000 cents