Scala analysis: xen09-wilson-marwa-07-01
Marwa permutation 1 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: 243/128 1109.775004 Pythagorean major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 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: 9/8 203.9100 major whole tone 7: 256/243 90.2250 limma, Pythagorean minor second
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 : 203.9 407.8 470.8 702.0 905.9 1109.8 1200.0 203.9 : 203.9 266.9 498.0 702.0 905.9 996.1 1200.0 407.8 : 63.0 294.1 498.0 702.0 792.2 996.1 1200.0 470.8 : 231.2 435.1 639.0 729.2 933.1 1137.0 1200.0 702.0 : 203.9 407.8 498.0 702.0 905.9 968.8 1200.0 905.9 : 203.9 294.1 498.0 702.0 764.9 996.1 1200.0 1109.8: 90.2 294.1 498.0 561.0 792.2 996.1 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 : 177.34063 cents, oct.: 1241.38439 cents Scale is not proper Step pattern alph. order: AABCAAD Step pattern size order : CCADCCB 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 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 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: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.031627 Average absolute harmonicity : 0.234890 Specific harmonicity : 0.192000 Fundamental : 1/128, -7.0000 octaves, 2.0439 Hz. Guide tone : 3402, 11.7322 octaves, 890050.173 Hz. Exponens Consonantiae : 4.354560E+05, 18.73217 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 310.5, average 44.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.47904, average 1.21129 Sum of Tenney's harmonic distance : 16.30582, average 2.32940 Vogel's harmonic complexity : 11.42857 Wille's k value : 121 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 118.43773, average 4.22992 Lattice compactness (without 2's) : 64.76409, average 2.31300 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 1 -3.42857 26 1 3: 0 .. 5 2.28571 16 5 7: 0 .. 1 0.14286 1 1 Average exponent except 2's : 17 / 7 = 2.42857 Average absolute exponent except 2's: 17 / 7 = 2.42857 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 0 2 1 1 1 N T3 SD: 66.4093 c. M: 127.9238 c. 8: 1 2 0 2 1 1 1 P D3 S SD: 39.7008 c. M: 59.7750 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 33.4173 c. M:-54.1350 c. Pseudo Rast 11: 2 2 0 2 2 2 1 N T3 SD: 29.0435 c. M: 47.4095 c. 12: 2 2 1 2 2 2 1 P M ME S SD: 12.3286 c. M:-29.2191 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 17: 3 3 1 3 3 3 1 N M DE S SD: 14.1064 c. M:-23.3367 c. Seventeen-tone Major 23: 4 4 1 4 4 4 2 N T3 SD: 13.2793 c. M: 23.6941 c. 24: 4 4 1 5 4 4 2 N SD: 9.5772 c. M: 20.7809 c. 26: 4 5 1 5 5 4 2 N SD: 11.3929 c. M: 19.2946 c. 27: 5 4 2 5 4 5 2 N T3 SD: 12.5254 c. M:-18.3122 c. Twenty-seven tone "Major" 28: 5 5 1 5 5 5 2 N T3 SD: 11.0660 c. M:-20.7514 c. 29: 5 5 1 6 5 5 2 N SD: 7.2335 c. M: 15.6085 c. 36: 6 6 2 7 6 6 3 N SD: 5.6963 c. M: 9.7750 c. 41: 7 7 2 8 7 7 3 N SD: 1.6508 c. M: 2.4882 c. 94: 16 16 5 18 16 16 7 N SD: 0.7627 c. M:-1.5595 c. 135: 23 23 7 26 23 23 10 N SD: 0.7594 c. M:-1.3361 c. 171: 29 29 9 33 29 29 13 N SD: 0.6071 c. M: 1.0031 c. 212: 36 36 11 41 36 36 16 N SD: 0.4133 c. M: 0.9696 c. 224: 38 38 12 43 38 38 17 N SD: 0.5339 c. M: 0.8464 c. 253: 43 43 13 49 43 43 19 N SD: 0.4633 c. M: 1.2157 c. 265: 45 45 14 51 45 45 20 N SD: 0.2008 c. M: 0.3410 c. 306: 52 52 16 59 52 52 23 N SD: 0.0746 c. M: 0.1927 c. 571: 97 97 30 110 97 97 43 N SD: 0.0807 c. M: 0.1428 c. 665: 113 113 35 128 113 113 50 N SD: 0.0743 c. M:-0.1965 c. 706: 120 120 37 136 120 120 53 N SD: 0.0800 c. M:-0.1400 c. 877: 149 149 46 169 149 149 66 N SD: 0.0566 c. M: 0.0854 c. 971: 165 165 51 187 165 165 73 N SD: 0.0283 c. M:-0.0739 c. 1277: 217 217 67 246 217 217 96 N SD: 0.0085 c. M:-0.0136 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 6:7 x 8 S SD: 16.6332 cents 5 x 6:7 x 8 x 10 S SD: 42.9227 cents 6:7 x 8:9:10:11:12 S SD: 15.6521 cents 7:8:9 x 11:12:13:14 SD: 16.8042 cents 8:9:10:11:12:14:15:16 S SD: 15.2365 cents 9:10:11:12:14:15:17:18 SD: 13.8197 cents 10:11 x 13:15:17:19:20 SD: 7.3662 cents 11:12:14 x 17:19:21:22 SD: 14.2627 cents 12:14:15:16:18:20:23:24 SD: 10.9788 cents 14:16:18 x 21:24:27:28 S SD: 9.0880 cents 15:17:19:20:23:25:28:30 SD: 8.6575 cents 16:18:20:21:24:27:30:32 S SD: 4.3449 cents 17:19 x 22:26:29:32:34 SD: 8.2058 cents 18:20:23:24:27:30:34:36 SD: 6.4179 cents 19:21:24:25:29:32:36:38 SD: 6.2246 cents 22:25:28:29:33:37:42:44 SD: 3.4419 cents 26:29:33:34:39:44:49:52 SD: 3.0963 cents 38:43:48:50:57:64:72:76 SD: 1.7781 cents 48:54:61:63:72:81:91:96 SD: 1.0709 cents 64:72:81:84:96:108:122:128 SD: 1.0157 cents 80:90:101:105:120:135:152:160 SD: 0.6444 cents 112:126:142:147:168:189:213:224 SD: 0.6163 cents 128:144:162:168:192:216:243:256 SD: 0.0000 cents