Scala analysis: xen18-ayers-table-55
First Unnamed Mean scale from window in Table 55
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 7/6 266.870906 septimal minor 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: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 13/12 138.5727 tridecimal 2/3-tone 2: 14/13 128.2982 2/3-tone 3: 8/7 231.1741 septimal whole tone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 11/10 165.0042 Ptolemy's second, 4/5-tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 14/13 128.298 cents 2/3-tone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 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 13/11 289.210 cents tridecimal minor third 2: 1 6/5 315.641 cents minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 5/4 386.314 cents major third 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 13/10 454.214 cents tridecimal semi-diminished fourth 3: 2 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 18/13 563.382 cents tridecimal augmented 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 13/9 636.618 cents tridecimal diminished fifth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 2 3/2 701.955 cents perfect fifth 4: 1 20/13 745.786 cents tridecimal semi-augmented fifth 4: 1 11/7 782.492 cents undecimal augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 22/13 910.790 cents tridecimal major sixth 5: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 20/11 1034.996 cents large minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 24/13 1061.427 cents tridecimal neutral seventh 6: 1 13/7 1071.702 cents 16/3-tone Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.66667 = 20/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 138.6 266.9 498.0 702.0 884.4 1049.4 1200.0 138.6 : 128.3 359.5 563.4 745.8 910.8 1061.4 1200.0 266.9 : 231.2 435.1 617.5 782.5 933.1 1071.7 1200.0 498.0 : 203.9 386.3 551.3 702.0 840.5 968.8 1200.0 702.0 : 182.4 347.4 498.0 636.6 764.9 996.1 1200.0 884.4 : 165.0 315.6 454.2 582.5 813.7 1017.6 1200.0 1049.4: 150.6 289.2 417.5 648.7 852.6 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 231.1741 cents 52/49, 102.8758 cents 14/13, 128.2982 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 417.5080 .. 617.4878 cents 55/49, 199.9798 cents 98/99,-17.5761 cents 4: 582.5122 .. 782.4920 cents 55/49, 199.9798 cents 49/50,-34.9756 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 98/99,-17.5761 cents 6: 968.8259 .. 1071.7018 cents 52/49, 102.8758 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.336172 Largest / Average step : 1.348516 Largest / Smallest step : 1.801849 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 172.08743 cents, oct.: 1204.61203 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : BAGFEDC Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.628017 Lumma stability : 0.273325 Lumma impropriety factor : 0.058440 Rothenberg efficiency : 0.299320 redundancy: 0.700680 Efficiency x scale size : 2.095238 Number of different interval sizes : 40 = 6.66667 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.66667 = 20/3 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 169/168, 10.2744 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 2 Most common triad is 0.0 498.045 701.955 cents, amount: 1 Number of recognisable fifths : 2, average 701.9550 cents Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Scale is harmonic, base degree is : 2 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent -- Rational properties -- Prime limit : 13 Odd number limit : 13 (O: 13 U: 13) Highest odd numerator or denominator: 13 Scale harmonicity : 0.015071 Average absolute harmonicity : 0.250290 Specific harmonicity : 0.128047 Fundamental : 1/12, -3.5850 octaves, 21.8021 Hz. Guide tone : 60060, 15.8741 octaves, 15713231.452 Hz. Exponens Consonantiae : 7.207200E+05, 19.45908 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 39.0, average 5.57143 Mersenne's string divisions : 928200 Sum of van Prooijen's expressibility: 4.65365, average 0.66481 Sum of Tenney's harmonic distance : 8.97037, average 1.28148 Vogel's harmonic complexity : 8.14286 Wille's k value : 6 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 62.02833, average 2.21530 Lattice compactness (without 2's) : 38.74326, average 1.38369 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.28571 8 1 3: -1 .. 1 -0.57143 6 2 5: 0 .. 1 0.14286 1 1 7: 0 .. 1 0.14286 1 1 11: 0 .. 1 0.14286 1 1 13: 0 .. 1 0.14286 1 1 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 11 16 19 24 27| Scale is JI-epimorphic with val: <7 11 16 20 24 26| = patent Scale is weakly epimorphic with val: <7 11 17 19 23 27| Scale is weakly epimorphic with val: <7 11 17 20 23 26| Scale is weakly epimorphic with val: <7 12 15 20 23 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 34.9570 c. M:-75.9862 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 29.4953 c. M:-48.0450 c. 9: 1 1 2 1 2 1 1 N D3 I SD: 27.2972 c. M:-48.9746 c. 10: 1 1 2 2 1 2 1 N D3 SD: 25.7031 c. M: 44.3587 c. 14: 2 1 3 2 2 2 2 P T3 SD: 20.2649 c. M:-32.8559 c. 15: 2 1 3 3 2 2 2 N SD: 16.6437 c. M: 26.8709 c. 17: 2 2 3 3 3 2 2 N I SD: 14.5157 c. M:-33.2883 c. 19: 2 2 4 3 3 3 2 N SD: 12.2401 c. M:-24.3213 c. 23: 3 2 5 3 4 3 3 N SD: 14.7473 c. M:-23.6941 c. 24: 3 2 5 4 4 3 3 N SD: 9.7681 c. M: 16.8709 c. 26: 3 3 5 4 4 4 3 P SD: 8.3728 c. M:-12.1755 c. 31: 4 3 6 5 5 4 4 N SD: 7.4476 c. M:-16.2660 c. 34: 4 4 6 6 5 5 4 P SD: 7.2786 c. M:-15.4820 c. 41: 5 4 8 7 6 6 5 N SD: 4.3266 c. M:-7.7688 c. 46: 5 5 9 8 7 6 6 N SD: 4.7067 c. M: 8.1379 c. 50: 6 5 10 8 8 7 6 N SD: 4.8687 c. M:-6.6371 c. 53: 6 6 10 9 8 7 7 N SD: 3.6684 c. M: 7.8535 c. 58: 7 6 11 10 9 8 7 N SD: 3.9600 c. M:-6.2549 c. 62: 7 7 12 10 10 8 8 N SD: 4.3626 c. M:-5.9639 c. 63: 7 7 12 11 9 9 8 N SD: 4.0180 c. M: 8.1682 c. 72: 8 8 14 12 11 10 9 N SD: 2.2864 c. M: 5.2393 c. 77: 9 8 15 13 12 10 10 N SD: 2.6778 c. M: 5.2071 c. 80: 9 9 15 14 12 11 10 N SD: 2.4470 c. M: 3.5727 c. 87: 10 9 17 15 13 12 11 N SD: 2.1271 c. M: 4.8019 c. 94: 11 10 18 16 14 13 12 N SD: 1.8437 c. M: 3.5076 c. 103: 12 11 20 17 16 14 13 N SD: 1.7592 c. M:-2.9259 c. 111: 13 12 21 19 17 15 14 N SD: 1.7560 c. M:-3.3994 c. 113: 13 12 22 19 17 16 14 N SD: 1.5582 c. M: 2.9428 c. 121: 14 13 23 21 18 17 15 N SD: 1.5501 c. M:-2.1772 c. 130: 15 14 25 22 20 18 16 N SD: 1.3590 c. M:-2.9448 c. 145: 17 15 28 25 22 20 18 N SD: 1.5699 c. M:-2.1170 c. 149: 17 16 29 25 23 20 19 N SD: 1.4800 c. M: 2.3831 c. 157: 18 17 30 27 24 21 20 N SD: 1.4406 c. M:-2.2655 c. 166: 19 18 32 28 25 23 21 N SD: 1.2107 c. M: 2.4310 c. 174: 20 19 33 30 26 24 22 N SD: 1.3628 c. M:-2.0946 c. 176: 20 19 34 30 27 24 22 N SD: 1.2208 c. M: 2.2090 c. 183: 21 20 35 31 28 25 23 N SD: 0.9023 c. M:-1.9816 c. 190: 22 20 37 32 29 26 24 N SD: 0.8671 c. M: 1.6077 c. 198: 23 21 38 34 30 27 25 N SD: 0.7597 c. M:-1.0753 c. 224: 26 24 43 38 34 31 28 N SD: 0.5515 c. M:-0.9862 c. 270: 31 29 52 46 41 37 34 N SD: 0.3870 c. M: 0.7949 c. 296: 34 32 57 50 45 41 37 N SD: 0.5965 c. M: 0.7348 c. 301: 35 32 58 51 46 41 38 N SD: 0.5818 c. M:-0.9622 c. 311: 36 33 60 53 47 43 39 N SD: 0.4284 c. M: 0.7574 c. 320: 37 34 62 54 49 44 40 N SD: 0.5642 c. M:-0.7050 c. 328: 38 35 63 56 50 45 41 N SD: 0.5521 c. M:-1.0071 c. 364: 42 39 70 62 55 50 46 N SD: 0.5194 c. M: 1.0113 c. 373: 43 40 72 63 57 51 47 N SD: 0.4289 c. M:-0.6145 c. 400: 46 43 77 68 61 55 50 N SD: 0.4081 c. M:-0.6413 c. 414: 48 44 80 70 63 57 52 N SD: 0.3708 c. M:-0.5578 c. 494: 57 53 95 84 75 68 62 N SD: 0.1500 c. M:-0.3356 c. 684: 79 73 132 116 104 94 86 N SD: 0.1700 c. M: 0.2401 c. 908: 105 97 175 154 138 125 114 N SD: 0.1549 c. M: 0.2177 c. 954: 110 102 184 162 145 131 120 N SD: 0.1668 c. M: 0.3063 c. 1012: 117 108 195 172 154 139 127 N SD: 0.1107 c. M:-0.2263 c. 1084: 125 116 209 184 165 149 136 N SD: 0.1176 c. M: 0.1963 c. 1178: 136 126 227 200 179 162 148 N SD: 0.0886 c. M: 0.1482 c. 1506: 174 161 290 256 229 207 189 N SD: 0.0586 c. M:-0.1034 c. 1776: 205 190 342 302 270 244 223 N SD: 0.0609 c. M:-0.1007 c. 1889: 218 202 364 321 287 260 237 N SD: 0.0594 c. M: 0.0867 c. 2000: 231 214 385 340 304 275 251 N SD: 0.0592 c. M:-0.1291 c. 2190: 253 234 422 372 333 301 275 N SD: 0.0367 c. M:-0.0575 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 x 5:6 x 7:8 S SD: 34.4330 cents 5 x 6:7 x 8:9:10 S SD: 24.9134 cents 6 x 7:8:9:10:11:12 S SD: 0.0000 cents 7 x 8:9:11:12:13:14 SD: 20.1399 cents 8 x 9:11:12:13:15:16 SD: 16.8629 cents 10:11:12:13:15:17:18:20 SD: 12.1073 cents 11:12:13:15:17:18:20:22 SD: 11.1069 cents 12:13:14:16:18:20:22:24 S SD: 0.0000 cents