Scala analysis: xen18-ayers-table-65
7 Iterated Mediants between 1/1 and 2/1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 4/3 498.044999 perfect fourth 3: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 5/3 884.358713 major sixth, BP sixth 7: 7/4 968.825906 harmonic seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 5/4 386.3137 major third 2: 16/15 111.7313 minor diatonic semitone 3: 21/20 84.4672 minor semitone 4: 15/14 119.4428 major diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 21/20 84.4672 minor semitone 8: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 5/4 386.314 cents major third 2: 1 35/32 155.140 cents septimal neutral second 2: 1 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 1 9/8 203.910 cents major whole tone 2: 1 8/7 231.174 cents septimal whole tone 2: 1 6/5 315.641 cents minor third 2: 1 4/3 498.045 cents perfect fourth 2: 1 10/7 617.488 cents Euler's tritone 3: 1 7/6 266.871 cents septimal minor third 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 2 6/5 315.641 cents minor third 3: 1 5/4 386.314 cents major third 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 3/2 701.955 cents perfect fifth 3: 1 32/21 729.219 cents wide fifth 4: 2 5/4 386.314 cents major third 4: 1 32/25 427.373 cents classic diminished fourth 4: 1 4/3 498.045 cents perfect fourth 4: 1 3/2 701.955 cents perfect fifth 4: 1 25/16 772.627 cents classic augmented fifth 4: 2 8/5 813.686 cents minor sixth 5: 1 21/16 470.781 cents narrow fourth 5: 1 4/3 498.045 cents perfect fourth 5: 1 10/7 617.488 cents Euler's tritone 5: 1 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 1 42/25 898.153 cents quasi-equal major sixth 5: 1 12/7 933.129 cents septimal major sixth 6: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 3/2 701.955 cents perfect fifth 6: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 25/14 1003.802 cents middle minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 64/35 1044.860 cents septimal neutral seventh 7: 1 8/5 813.686 cents minor sixth 7: 1 7/4 968.826 cents harmonic seventh 7: 1 28/15 1080.557 cents grave major seventh 7: 2 15/8 1088.269 cents classic major seventh 7: 2 40/21 1115.533 cents acute major seventh 7: 1 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.85714 = 48/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 386.3 498.0 582.5 702.0 813.7 884.4 968.8 1200.0 386.3 : 111.7 196.2 315.6 427.4 498.0 582.5 813.7 1200.0 498.0 : 84.5 203.9 315.6 386.3 470.8 702.0 1088.3 1200.0 582.5 : 119.4 231.2 301.8 386.3 617.5 1003.8 1115.5 1200.0 702.0 : 111.7 182.4 266.9 498.0 884.4 996.1 1080.6 1200.0 813.7 : 70.7 155.1 386.3 772.6 884.4 968.8 1088.3 1200.0 884.4 : 84.5 315.6 702.0 813.7 898.2 1017.6 1129.3 1200.0 968.8 : 231.2 617.5 729.2 813.7 933.1 1044.9 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 386.3137 cents 6/5, 315.6413 cents 25/24, 70.6724 cents 2: 155.1396 .. 617.4878 cents 64/49, 462.3482 cents 7/8,-231.1741 cents 3: 266.8709 .. 729.2191 cents 64/49, 462.3482 cents 49/60,-350.6169 cents 4: 386.3137 .. 813.6863 cents 32/25, 427.3726 cents 105/128,-342.9054 cents 5: 470.7809 .. 933.1291 cents 64/49, 462.3482 cents 105/128,-342.9054 cents 6: 582.5122 .. 1044.8604 cents 64/49, 462.3482 cents 49/60,-350.6169 cents 7: 813.6863 .. 1129.3276 cents 6/5, 315.6413 cents 7/8,-231.1741 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 2.122469 Largest / Average step : 2.575425 Largest / Smallest step : 5.466258 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 155.36336 cents, oct.: 1242.90688 cents Scale is not proper Step pattern alph. order: ABCDBECF Step pattern size order : FCBDCABE Scale is not a Constant Structure Scale diversity : 1.548945 Lumma stability : 0.117787 Lumma impropriety factor : 0.741434 Rothenberg efficiency : 0.360714 redundancy: 0.639286 Efficiency x scale size : 2.885714 Number of different interval sizes : 34 = 4.85714 / class Number of one step interval sizes : 6 Highest interval variety : 8 Mean interval variety : 6.85714 = 48/7 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 4 Number of recognisable fifths : 3, average 701.9550 cents Scale contains a complete diamond : 1 3 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 : 5 = 62.5000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 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 : 35 (O: 35 U: 35) Highest odd numerator or denominator: 7 Scale harmonicity : 0.029923 Average absolute harmonicity : 0.245508 Specific harmonicity : 0.178466 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 840, 9.7142 octaves, 219765.475 Hz. Exponens Consonantiae : 5.040000E+04, 15.62114 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 34.0, average 4.25000 Mersenne's string divisions : 360360 Sum of van Prooijen's expressibility: 4.74135, average 0.59267 Sum of Tenney's harmonic distance : 9.22877, average 1.15360 Vogel's harmonic complexity : 11.50000 Wille's k value : 52 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 93.11591, average 2.58655 Lattice compactness (without 2's) : 49.32441, average 1.37012 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.12500 11 1 3: -1 .. 1 -0.12500 3 2 5: -1 .. 1 0.00000 4 3 7: 0 .. 1 0.25000 2 2 Average exponent except 2's : 1 / 8 = 0.12500 Average absolute exponent except 2's: 9 / 8 = 1.12500 Scale is weakly epimorphic with val: <8 14 17 21|
FIT/MODE
8: 3 0 1 1 0 1 0 2 N SD: 47.4553 c. M: 68.8259 c. 9: 3 1 0 1 1 1 0 2 N SD: 33.4327 c. M: 49.1789 c. 10: 3 1 1 1 1 0 1 2 N SD: 23.4187 c. M: 44.3587 c. 12: 4 1 1 1 1 1 1 2 N SD: 15.4296 c. M:-31.1741 c. 15: 5 1 1 2 1 1 1 3 N SD: 14.2722 c. M: 22.5122 c. 19: 6 2 1 2 2 1 1 4 N SD: 10.4387 c. M: 21.4575 c. 22: 7 2 2 2 2 1 2 4 N SD: 9.6965 c. M:-17.4878 c. 27: 9 2 2 3 2 2 2 5 N SD: 9.1198 c. M: 13.6863 c. 31: 10 3 2 3 3 2 2 6 N SD: 3.4485 c. M:-5.9639 c. 53: 17 5 4 5 5 3 4 10 N SD: 2.8821 c. M:-6.1671 c. 56: 18 5 4 6 5 3 4 11 N SD: 3.9399 c. M: 5.7873 c. 68: 22 6 5 7 6 4 5 13 N SD: 2.3819 c. M:-3.9274 c. 72: 23 7 5 7 7 4 5 14 N SD: 1.9937 c. M: 2.9804 c. 84: 27 8 6 8 8 5 6 16 N SD: 1.8448 c. M:-3.2021 c. 87: 28 8 6 9 8 5 6 17 N SD: 1.8789 c. M: 3.3087 c. 99: 32 9 7 10 9 6 7 19 N SD: 1.0423 c. M:-1.5651 c. 130: 42 12 9 13 12 8 9 25 N SD: 1.0297 c. M:-1.7951 c. 140: 45 13 10 14 13 8 10 27 N SD: 0.7734 c. M: 1.5016 c. 171: 55 16 12 17 16 10 12 33 N SD: 0.2532 c. M: 0.4049 c. 270: 87 25 19 27 25 16 19 52 N SD: 0.2468 c. M:-0.3530 c. 441: 142 41 31 44 41 26 31 85 N SD: 0.1010 c. M: 0.1993 c. 612: 197 57 43 61 57 36 43 118 N SD: 0.0935 c. M: 0.1985 c. 935: 301 87 66 93 87 55 66 180 N SD: 0.0932 c. M:-0.1616 c. 966: 311 90 68 96 90 57 68 186 N SD: 0.0821 c. M:-0.1182 c. 1106: 356 103 78 110 103 65 78 213 N SD: 0.0694 c. M:-0.1280 c. 1137: 366 106 80 113 106 67 80 219 N SD: 0.0690 c. M:-0.1080 c. 1236: 398 115 87 123 115 73 87 238 N SD: 0.0716 c. M:-0.1073 c. 1277: 411 119 90 127 119 75 90 246 N SD: 0.0698 c. M:-0.1033 c. 1376: 443 128 97 137 128 81 97 265 N SD: 0.0547 c. M:-0.0799 c. 1407: 453 131 99 140 131 83 99 271 N SD: 0.0412 c. M:-0.0763 c. 1547: 498 144 109 154 144 91 109 298 N SD: 0.0376 c. M: 0.0665 c. 1578: 508 147 111 157 147 93 111 304 N SD: 0.0327 c. M:-0.0539 c. 2019: 650 188 142 201 188 119 142 389 N SD: 0.0277 c. M: 0.0456 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 0.0000 cents 3 x 4 x x x 5 x 6 S SD: 0.0000 cents 4:5 x x 6 x x 7:8 S SD: 0.0000 cents 5:6 x 7 x 8 x 9:10 S SD: 17.1734 cents 6 x 8 x 9 x 10:11:12 S SD: 16.1074 cents 7:9 x 10 x 11 x 12:14 SD: 15.2960 cents 8:10 x 11:12:13 x 14:16 S SD: 6.8588 cents 9:11:12:13 x 14:15:16:18 SD: 12.4236 cents 10 x 13:14:15:16:17:18:20 SD: 10.5705 cents 11:14:15 x 17 x 18:19:22 SD: 13.6210 cents 12:15:16:17:18:19:20:21:24 S SD: 3.4196 cents 28:35:37:39:42:45:47:49:56 SD: 2.8799 cents 32:40:43:45:48:51:53:56:64 SD: 2.5147 cents 36:45:48:50:54:58:60:63:72 SD: 2.2839 cents 40:50:53:56:60:64:67:70:80 SD: 1.7337 cents 48:60:64:67:72:77:80:84:96 SD: 0.8560 cents 60:75:80:84:90:96:100:105:120 S SD: 0.0000 cents