Scala analysis: xen18-ayers-table-44
Transposing 3 Fibonacci-Type Means to Lower Tetrachord Between 1/1 and 4/3
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: 13/12 138.572661 tridecimal 2/3-tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 8/5 813.686286 minor sixth 6: 13/8 840.527662 tridecimal neutral sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/13 359.4723 tridecimal neutral third 1: 16/15 111.7313 minor diatonic semitone 2: 65/64 26.8414 13th-partial chroma 3: 16/13 359.4723 tridecimal neutral third 4: 9/8 203.9100 major whole tone 5: 16/15 111.7313 minor diatonic semitone 6: 65/64 26.8414 13th-partial chroma 7: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 65/64 26.841 cents 13th-partial chroma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 16/13 359.472 cents tridecimal neutral third 2: 2 13/12 138.573 cents tridecimal 2/3-tone 2: 1 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 256/195 471.204 cents 2: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 3: 4 4/3 498.045 cents perfect fourth 3: 1 45/32 590.224 cents diatonic tritone 3: 1 96/65 675.114 cents 4: 1 65/48 524.886 cents 4: 1 64/45 609.776 cents 2nd tritone 4: 4 3/2 701.955 cents perfect fifth 4: 1 64/39 857.517 cents 39th subharmonic 5: 1 13/9 636.618 cents tridecimal diminished fifth 5: 1 195/128 728.796 cents 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 2 13/8 840.528 cents tridecimal neutral sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 2 128/65 1173.159 cents 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 : 111.7 138.6 498.0 702.0 813.7 840.5 1200.0 111.7 : 26.8 386.3 590.2 702.0 728.8 1088.3 1200.0 138.6 : 359.5 563.4 675.1 702.0 1061.4 1173.2 1200.0 498.0 : 203.9 315.6 342.5 702.0 813.7 840.5 1200.0 702.0 : 111.7 138.6 498.0 609.8 636.6 996.1 1200.0 813.7 : 26.8 386.3 498.0 524.9 884.4 1088.3 1200.0 840.5 : 359.5 471.2 498.0 857.5 1061.4 1173.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.8414 .. 359.4723 cents 1024/845, 332.6310 cents 65/64, 26.8414 cents 2: 138.5727 .. 563.3823 cents 216/169, 424.8097 cents 169/192,-220.8997 cents 3: 342.4827 .. 675.1136 cents 1024/845, 332.6310 cents 169/192,-220.8997 cents 4: 524.8864 .. 857.5173 cents 1024/845, 332.6310 cents 4225/4608,-150.2273 cents 5: 636.6177 .. 1061.4273 cents 216/169, 424.8097 cents 169/192,-220.8997 cents 6: 840.5277 .. 1173.1586 cents 1024/845, 332.6310 cents 169/192,-220.8997 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 65/64, 26.8414 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 6.386728 Largest / Average step : 2.096922 Largest / Smallest step : 13.392471 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Least squares average step : 158.58878 cents, oct.: 1110.12145 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : BADCBAD Scale is a Constant Structure, by a margin of 16.98968 cents Scale diversity : 1.509418 Lumma stability : 0.044736 Lumma impropriety factor : 0.769046 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 : 512/507, 16.9897 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 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 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 : 13 Odd number limit : 195 (O: 195 U: 195) Highest odd numerator or denominator: 15 Scale harmonicity : 0.024458 Average absolute harmonicity : 0.249566 Specific harmonicity : 0.131873 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 624, 9.2854 octaves, 163254.353 Hz. Exponens Consonantiae : 7.488000E+04, 16.19229 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 52.5, average 7.50000 Mersenne's string divisions : 211575 Sum of van Prooijen's expressibility: 5.05719, average 0.72246 Sum of Tenney's harmonic distance : 10.35079, average 1.47868 Vogel's harmonic complexity : 13.00000 Wille's k value : 97 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 93.48131, average 3.33862 Lattice compactness (without 2's) : 36.07837, average 1.28851 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.57143 16 1 3: -1 .. 1 -0.28571 4 2 5: -1 .. 0 -0.28571 2 2 13: 0 .. 1 0.28571 2 2 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 11 15 26| Scale is JI-epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 12 17 29|
FIT/MODE
7: 1 0 2 1 1 0 2 N T3 SD: 32.3714 c. M:-59.6973 c. 9: 1 0 3 1 1 0 3 N SD: 26.2255 c. M: 40.5277 c. 10: 1 0 3 2 1 0 3 N SD: 15.8441 c. M:-26.3137 c. 17: 2 0 5 3 2 0 5 N G SD: 17.1590 c. M:-33.3725 c. 19: 2 0 6 3 2 0 6 N SD: 11.3432 c. M: 19.4750 c. 24: 2 1 7 4 2 1 7 N SD: 8.8873 c. M: 13.6863 c. 31: 3 1 9 5 3 1 9 N SD: 8.1161 c. M:-16.2660 c. 33: 3 1 10 5 3 1 10 N SD: 8.4769 c. M: 13.6863 c. 34: 3 1 10 6 3 1 10 N SD: 4.1090 c. M:-6.5312 c. 43: 4 1 13 7 4 1 13 N SD: 3.1125 c. M: 4.3840 c. 53: 5 1 16 9 5 1 16 N SD: 1.6641 c. M: 2.7918 c. 87: 8 2 26 15 8 2 26 N SD: 1.0372 c. M: 1.4933 c. 130: 12 3 39 22 12 3 39 N SD: 0.7034 c. M: 1.3786 c. 183: 17 4 55 31 17 4 55 N SD: 0.6262 c. M: 1.1834 c. 217: 20 5 65 37 20 5 65 N SD: 0.5662 c. M: 1.1322 c. 224: 21 5 67 38 21 5 67 N SD: 0.5087 c. M:-0.7687 c. 270: 25 6 81 46 25 6 81 N SD: 0.4724 c. M: 0.7949 c. 277: 26 6 83 47 26 6 83 N SD: 0.4540 c. M:-0.9041 c. 311: 29 7 93 53 29 7 93 N SD: 0.3633 c. M:-0.6299 c. 354: 33 8 106 60 33 8 106 N SD: 0.2268 c. M:-0.4104 c. 407: 38 9 122 69 38 9 122 N SD: 0.1946 c. M:-0.3080 c. 441: 41 10 132 75 41 10 132 N SD: 0.1574 c. M:-0.2887 c. 494: 46 11 148 84 46 11 148 N SD: 0.0655 c. M: 0.1111 c. 848: 79 19 254 144 79 19 254 N SD: 0.0609 c. M:-0.1066 c. 1342: 125 30 402 228 125 30 402 N SD: 0.0232 c. M:-0.0422 c. 1836: 171 41 550 312 171 41 550 N SD: 0.0202 c. M:-0.0392 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 x 5:6 S SD: 14.6104 cents 4 x x 5:6 x 7:8 S SD: 42.5326 cents 5 x 6:7 x 8 x 10 S SD: 49.0459 cents 6 x 7:8:9 x 10:12 S SD: 27.1158 cents 7 x 8:9 x 11 x 14 SD: 29.0605 cents 8 x 9:11:12 x 13:16 SD: 16.8606 cents 9 x 10:12 x 14:15:18 S SD: 15.7745 cents 10 x 11:13:15:16 x 20 SD: 10.2368 cents 11 x 12:15:17 x 18:22 SD: 13.3803 cents 12 x 13:16:18:19:20:24 SD: 7.9053 cents 13 x 14:17:20 x 21:26 SD: 11.4235 cents 14:15 x 19:21:22:23:28 SD: 8.0441 cents 15:16 x 20:23:24 x 30 SD: 7.6101 cents 16:17 x 21:24 x 26:32 SD: 5.6187 cents 17:18 x 23:26:27:28:34 SD: 8.5639 cents 18:19:20:24:27:29 x 36 SD: 8.1536 cents 20:21:22:27:30:32:33:40 SD: 7.2887 cents 21:22:23:28:32 x 34:42 SD: 7.6644 cents 22:23:24:29:33:35:36:44 SD: 6.3715 cents 23 x 25:31:35:37 x 46 SD: 6.6099 cents 24 x 26:32:36:38:39:48 SD: 3.0214 cents 25 x 27:33:38:40:41:50 SD: 5.5529 cents 26 x 28:35:39 x 42:52 SD: 4.4072 cents 27:29 x 36:41:43:44:54 SD: 4.3576 cents 28:30 x 37:42:45:46:56 SD: 4.4660 cents 29:31 x 39:44:46:47:58 SD: 4.9217 cents 30:32:33:40:45:48:49:60 SD: 3.9822 cents 31:33:34:41:47 x 50:62 SD: 5.7121 cents 32:34:35:43:48:51:52:64 SD: 3.3436 cents 38 x 41:51:57:61:62:76 SD: 2.6846 cents 39 x 42:52:59:62:63:78 SD: 3.9164 cents 40 x 43:53:60:64:65:80 SD: 2.8700 cents 41:44 x 55:62:66:67:82 SD: 4.1607 cents 42:45:46:56:63:67:68:84 SD: 3.1443 cents 45:48:49:60:68:72:73:90 SD: 2.2607 cents 46:49:50:61:69:74:75:92 SD: 2.2562 cents 48:51:52:64:72:77:78:96 SD: 1.1622 cents 53 x 57:71:80:85:86:106 SD: 3.1891 cents 54:58:59:72:81:86:88:108 SD: 3.0285 cents 56:60:61:75:84:90:91:112 SD: 2.3404 cents 57:61:62:76:86:91:93:114 SD: 2.2430 cents 58:62:63:77:87:93:94:116 SD: 1.6028 cents 60:64:65:80:90:96:98:120 SD: 1.2651 cents 72:77:78:96:108:115:117:144 SD: 0.7736 cents 120:128:130:160:180:192:195:240 SD: 0.0000 cents