Scala analysis: al-farabi_chrom2
Al-Farabi's Chromatic permuted
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 56/45 378.602191 septimal narrow major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 28/15 1080.557192 grave major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 7/6 266.8709 septimal minor third 3: 15/14 119.4428 major diatonic semitone 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 7/6 266.8709 septimal minor third 7: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 6/5 315.641 cents minor third 2: 1 135/112 323.353 cents septimal wide minor third 2: 2 56/45 378.602 cents septimal narrow major third 2: 2 5/4 386.314 cents major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 10/7 617.488 cents Euler's tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 2 8/5 813.686 cents minor sixth 5: 2 45/28 821.398 cents septimale wide minor sixth 5: 1 224/135 876.647 cents narrow septimal major sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 7/4 968.826 cents harmonic seventh 6: 2 12/7 933.129 cents septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 28/15 1080.557 cents grave major seventh 6: 2 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 111.7 378.6 498.0 702.0 813.7 1080.6 1200.0 111.7 : 266.9 386.3 590.2 702.0 968.8 1088.3 1200.0 378.6 : 119.4 323.4 435.1 702.0 821.4 933.1 1200.0 498.0 : 203.9 315.6 582.5 702.0 813.7 1080.6 1200.0 702.0 : 111.7 378.6 498.0 609.8 876.6 996.1 1200.0 813.7 : 266.9 386.3 498.0 764.9 884.4 1088.3 1200.0 1080.6: 119.4 231.2 498.0 617.5 821.4 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 266.8709 cents 35/32, 155.1396 cents 16/15, 111.7313 cents 2: 231.1741 .. 386.3137 cents 35/32, 155.1396 cents 48/49,-35.6968 cents 3: 435.0841 .. 590.2237 cents 35/32, 155.1396 cents 36/35, 48.7704 cents 4: 609.7763 .. 764.9159 cents 35/32, 155.1396 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 968.8259 cents 35/32, 155.1396 cents 36/35, 48.7704 cents 6: 933.1291 .. 1088.2687 cents 35/32, 155.1396 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.534293 Largest / Average step : 1.556747 Largest / Smallest step : 2.388507 Median interval of one step : 15/14, 119.4428 cents, amount: 2 Least squares average step : 172.30475 cents, oct.: 1206.13326 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : ADBCADB Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.472999 Lumma stability : 0.283797 Lumma impropriety factor : 0.059495 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% 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 Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 7 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.033686 Average absolute harmonicity : 0.250961 Specific harmonicity : 0.176879 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 336, 8.3923 octaves, 87906.190 Hz. Exponens Consonantiae : 3.024000E+04, 14.88417 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 101.5, average 14.50000 Mersenne's string divisions : 183774045 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 12.16528, average 1.73790 Vogel's harmonic complexity : 11.42857 Wille's k value : 67 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 73.48074, average 2.62431 Lattice compactness (without 2's) : 42.23288, average 1.50832 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 2.00000 16 1 3: -2 .. 1 -0.57143 6 2 5: -1 .. 0 -0.57143 4 2 7: 0 .. 1 0.28571 2 2 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is JI-epimorphic with val: <7 11 16 19|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 37.7208 c. M:-59.6973 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 23.2849 c. M:-35.2883 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 15.8492 c. M:-26.3137 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 12.9199 c. M:-21.3978 c. Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil 19: 2 4 2 3 2 4 2 P T3 I SD: 7.7324 c. M:-14.5845 c. 22: 2 5 2 4 2 5 2 N T3 I SD: 5.9345 c. M:-10.3519 c. Double Harmonic Major 31: 3 7 3 5 3 7 3 N T3 I SD: 4.7325 c. M:-8.4946 c. Double Harmonic Major, Major Gipsy 41: 4 9 4 7 4 9 4 N T3 I SD: 3.2097 c. M:-5.8259 c. 63: 6 14 6 11 6 14 6 N T3 I SD: 3.4464 c. M:-5.3613 c. 72: 7 16 7 12 7 16 7 N T3 I SD: 3.1842 c. M:-4.9354 c. Xenakis Byzantine Liturgical Soft Chromatic, Quasi-Miracle-7 77: 7 17 8 13 7 17 8 N SD: 3.0943 c. M: 5.2325 c. 87: 8 19 9 15 8 19 9 N SD: 3.0876 c. M: 6.1884 c. 89: 8 20 9 15 8 20 9 N SD: 2.4837 c. M: 4.6975 c. 94: 9 21 9 16 9 21 9 N T3 I SD: 2.9528 c. M:-4.5492 c. 96: 9 21 10 16 9 21 10 N SD: 2.7646 c. M: 5.5572 c. 99: 9 22 10 17 9 22 10 N SD: 1.8109 c. M: 2.8446 c. 108: 10 24 11 18 10 24 11 N SD: 1.8152 c. M: 2.7794 c. 111: 10 25 11 19 10 25 11 N SD: 1.8063 c. M: 3.6232 c. 118: 11 26 12 20 11 26 12 N SD: 1.3265 c. M: 2.5911 c. 130: 12 29 13 22 12 29 13 N SD: 0.7074 c. M: 1.3786 c. 149: 14 33 15 25 14 33 15 N SD: 0.9464 c. M: 1.3626 c. 152: 14 34 15 26 14 34 15 N SD: 0.7377 c. M: 1.2050 c. 171: 16 38 17 29 16 38 17 N SD: 0.3033 c. M:-0.5494 c. 301: 28 67 30 51 28 67 30 N SD: 0.2344 c. M: 0.3972 c. 441: 41 98 44 75 41 98 44 N SD: 0.1956 c. M: 0.3709 c. 472: 44 105 47 80 44 105 47 N SD: 0.1757 c. M:-0.2601 c. 612: 57 136 61 104 57 136 61 N SD: 0.0919 c. M: 0.1708 c. 783: 73 174 78 133 73 174 78 N SD: 0.0834 c. M:-0.1461 c. 913: 85 203 91 155 85 203 91 N SD: 0.0924 c. M: 0.1629 c. 935: 87 208 93 159 87 208 93 N SD: 0.0592 c. M:-0.0845 c. 1106: 103 246 110 188 103 246 110 N SD: 0.0513 c. M:-0.0938 c. 1236: 115 275 123 210 115 275 123 N SD: 0.0505 c. M: 0.0941 c. 1407: 131 313 140 239 131 313 140 N SD: 0.0407 c. M:-0.0758 c. 1547: 144 344 154 263 144 344 154 N SD: 0.0383 c. M: 0.0631 c. 1718: 160 382 171 292 160 382 171 N SD: 0.0265 c. M:-0.0506 c. 1848: 172 411 184 314 172 411 184 N SD: 0.0312 c. M: 0.0499 c. 2019: 188 449 201 343 188 449 201 N SD: 0.0165 c. M: 0.0234 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: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 27.9993 cents 5 x 6:7 x 8:9:10 S SD: 24.5462 cents 6 x 7:8:9:10:11:12 S SD: 22.6394 cents 7:8:9 x x 11:13:14 SD: 27.2090 cents 8:9:10:11:12:13:15:16 SD: 15.7625 cents 9:10:11:12 x 14:17:18 SD: 15.6045 cents 10:11:12:13:15:16:19:20 SD: 14.0423 cents 12:13:15:16:18:19:22:24 SD: 6.5179 cents 16:17:20:21:24:26:30:32 SD: 5.7652 cents 20:21:25:27:30:32:37:40 SD: 5.5446 cents 24:26:30:32:36:38:45:48 SD: 4.8823 cents 28:30:35:37:42:45:52:56 SD: 3.1877 cents 30:32:37:40:45:48:56:60 SD: 2.2181 cents 45:48:56:60:68:72:84:90 SD: 1.8252 cents 58:62:72:77:87:93:108:116 SD: 1.5660 cents 60:64:75:80:90:96:112:120 SD: 1.1016 cents 78:83:97:104:117:125:146:156 SD: 1.0002 cents 90:96:112:120:135:144:168:180 S SD: 0.0000 cents