Scala analysis: xen15-leedy-mixolydian
Just mixolydian
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: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP 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: 10/9 182.4037 minor whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 21/20 84.4672 minor semitone 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 2 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: 1 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 10/7 617.488 cents Euler's tritone 4: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 40/27 680.449 cents grave fifth 4: 4 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 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 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: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 1 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 386.3 498.0 702.0 884.4 968.8 1200.0 203.9 : 182.4 294.1 498.0 680.4 764.9 996.1 1200.0 386.3 : 111.7 315.6 498.0 582.5 813.7 1017.6 1200.0 498.0 : 203.9 386.3 470.8 702.0 905.9 1088.3 1200.0 702.0 : 182.4 266.9 498.0 702.0 884.4 996.1 1200.0 884.4 : 84.5 315.6 519.6 702.0 813.7 1017.6 1200.0 968.8 : 231.2 435.1 617.5 729.2 933.1 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 231.1741 cents 160/147, 146.7069 cents 21/20, 84.4672 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 470.7809 .. 617.4878 cents 160/147, 146.7069 cents 49/48, 35.6968 cents 4: 582.5122 .. 729.2191 cents 160/147, 146.7069 cents 49/50,-34.9756 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 6: 968.8259 .. 1115.5328 cents 160/147, 146.7069 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.029528 Largest / Average step : 1.348516 Largest / Smallest step : 2.736851 Median interval of one step : 10/9, 182.4037 cents, amount: 2 Least squares average step : 170.80887 cents, oct.: 1195.66207 cents Scale is not proper Step pattern alph. order: ABCABDE Step pattern size order : DCBDCAE Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.616552 Lumma stability : 0.259768 Lumma impropriety factor : 0.029146 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 81/80, 21.5063 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 3 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 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 Scale is differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval class 5 -- Rational properties -- Prime limit : 7 Odd number limit : 27 (O: 27 U: 27) Highest odd numerator or denominator: 9 Scale harmonicity : 0.033686 Average absolute harmonicity : 0.273964 Specific harmonicity : 0.221862 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 1260, 10.2992 octaves, 329648.212 Hz. Exponens Consonantiae : 3.024000E+04, 14.88417 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 30.0, average 4.28571 Mersenne's string divisions : 471240 Sum of van Prooijen's expressibility: 4.15152, average 0.59307 Sum of Tenney's harmonic distance : 7.93997, average 1.13428 Vogel's harmonic complexity : 8.14286 Wille's k value : 13 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 74.18263, average 2.64938 Lattice compactness (without 2's) : 41.50203, average 1.48222 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.71429 11 1 3: -1 .. 2 0.14286 5 3 5: 0 .. 1 0.28571 2 2 7: 0 .. 1 0.14286 1 1 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is JI-epimorphic with val: <7 11 16 20| = patent Scale is weakly epimorphic with val: <7 12 18 22|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.3408 c. M:-59.7455 c. Lebeng 10: 2 1 1 2 1 1 2 P D3 I SD: 25.8891 c. M: 44.3587 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 14.2765 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 16: 3 2 2 2 3 1 3 P T3 SD: 18.1608 c. M:-26.9550 c. 19: 3 3 2 3 3 1 4 N SD: 10.8715 c. M: 21.4575 c. 22: 4 3 2 4 3 2 4 P SD: 9.4855 c. M:-14.2718 c. Murchhana Suddhasadja, Raga Harikambhoji, Palaiyazh 27: 5 4 2 5 4 2 5 N SD: 10.6300 c. M:-18.3122 c. 29: 5 4 3 5 4 2 6 N SD: 10.2540 c. M: 17.1018 c. 31: 5 5 3 5 5 2 6 N SD: 5.3238 c. M: 10.3616 c. 41: 7 6 4 7 6 3 8 N SD: 3.4640 c. M: 6.3099 c. 46: 8 7 4 8 7 3 9 N SD: 3.3601 c. M:-4.9906 c. 53: 9 8 5 9 8 4 10 N SD: 1.9440 c. M:-4.7590 c. 72: 12 11 7 12 11 5 14 N SD: 2.3154 c. M: 3.9100 c. 77: 13 12 7 13 12 5 15 N SD: 2.2614 c. M:-3.9530 c. 84: 14 13 8 14 13 6 16 N SD: 2.1348 c. M: 3.9100 c. 87: 15 13 8 15 13 6 17 N SD: 1.9603 c. M: 3.3087 c. 94: 16 14 9 16 14 7 18 N SD: 1.9097 c. M: 3.5076 c. 99: 17 15 9 17 15 7 19 N SD: 1.2181 c. M:-2.1506 c. 118: 20 18 11 20 18 8 23 N SD: 1.0686 c. M: 2.7242 c. 130: 22 20 12 22 20 9 25 N SD: 0.9508 c. M:-1.7951 c. 171: 29 26 16 29 26 12 33 N SD: 0.2801 c. M: 0.4049 c. 441: 75 67 41 75 67 31 85 N SD: 0.0962 c. M:-0.1716 c. 612: 104 93 57 104 93 43 118 N SD: 0.0785 c. M: 0.1985 c. 935: 159 142 87 159 142 66 180 N SD: 0.0979 c. M:-0.1581 c. 1053: 179 160 98 179 160 74 203 N SD: 0.0731 c. M: 0.1649 c. 1106: 188 168 103 188 168 78 213 N SD: 0.0580 c. M: 0.0911 c. 1236: 210 188 115 210 188 87 238 N SD: 0.0683 c. M:-0.1073 c. 1277: 217 194 119 217 194 90 246 N SD: 0.0522 c. M: 0.0987 c. 1407: 239 214 131 239 214 99 271 N SD: 0.0495 c. M:-0.0763 c. 1677: 285 255 156 285 255 118 323 N SD: 0.0499 c. M:-0.0906 c. 1718: 292 261 160 292 261 121 331 N SD: 0.0418 c. M: 0.0747 c. 1848: 314 281 172 314 281 130 356 N SD: 0.0294 c. M:-0.0569 c. 2019: 343 307 188 343 307 142 389 N SD: 0.0292 c. M: 0.0467 c. 2289: 389 348 213 389 348 161 441 N SD: 0.0298 c. M:-0.0559 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 0.0000 cents 5 x 6:7 x 8:9:10 S SD: 27.9302 cents 6:7 x 8:9:10:11:12 S SD: 17.0378 cents 7:8:9 x 11 x 12:14 SD: 20.8637 cents 8:9:10:11:12:13:14:16 S SD: 9.8552 cents 10:11 x 13:15:17:18:20 SD: 13.9331 cents 12:14:15:16:18:20:21:24 S SD: 8.9944 cents 15:17:19:20:23:25:26:30 SD: 7.0151 cents 16:18:20:21:24:27:28:32 S SD: 4.9608 cents 24:27:30:32:36:40:42:48 S SD: 0.0000 cents