Scala analysis: 107_E13
Enharmonic tetrachord 56/55 * 22/21 * 5/4, Ptolemy?
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 56/55 31.194250 undecimal diesis, konbini comma 2: 16/15 111.731285 minor diatonic semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 56/55 31.1943 undecimal diesis, konbini comma 2: 22/21 80.5370 undecimal minor semitone 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 55/42 466.851 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 31.2 111.7 498.0 31.2 : 80.5 466.9 498.0 111.7: 386.3 417.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 386.3137 cents 275/224, 355.1195 cents 56/55, 31.1943 cents 2: 111.7313 .. 466.8507 cents 275/224, 355.1195 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 5.321974 Largest / Average step : 2.326981 Largest / Smallest step : 12.384132 Median interval of one step : 22/21, 80.5370 cents, amount: 1 Least squares average step : 124.91370 cents, oct.: 374.74110 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1948-tone equal temperament with octave 4/3 degrees: 122 437 1948 Least number of segments generator : 975 of 249.278 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1057 of 270.243 cents and inv. generated superset size: 40 = 37 more = 1333.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 31.19425 cents Scale diversity : 0.452645 Lumma stability : 0.125267 Lumma impropriety factor : 0.551321 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 56/55, 31.1943 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 55 Scale harmonicity : 0.024077 Average absolute harmonicity : 0.105741 Specific harmonicity : 0.118809 Fundamental : 1/165, -7.3663 octaves, 1.5856 Hz. Guide tone : 112, 6.8074 octaves, 29302.063 Hz. Exponens Consonantiae : 1.848000E+04, 14.17368 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 74.5, average 24.83333 Mersenne's string divisions : 24087 Sum of van Prooijen's expressibility: 3.39358, average 1.13119 Sum of Tenney's harmonic distance : 6.94794, average 2.31598 Vogel's harmonic complexity : 15.33333 Wille's k value : 27 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 16.41495, average 2.73582 Lattice compactness (without 2's) : 8.87832, average 1.47972 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.66667 2 1 7: 0 .. 1 0.33333 1 11: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 15 18 25| Scale is weakly epimorphic with val: <7 10 15 19 23| Scale is weakly epimorphic with val: <7 10 15 19 26| Scale is weakly epimorphic with val: <7 10 15 20 24| Scale is weakly epimorphic with val: <7 10 15 20 27| Scale is weakly epimorphic with val: <7 10 15 21 25| Scale is weakly epimorphic with val: <7 10 15 22 23| Scale is weakly epimorphic with val: <7 10 15 22 26| Scale is weakly epimorphic with val: <7 10 16 21 23| Scale is weakly epimorphic with val: <7 10 16 22 24| Scale is JI-epimorphic with val: <7 11 15 18 23| Scale is weakly epimorphic with val: <7 11 15 18 26| Scale is JI-epimorphic with val: <7 11 15 19 24| Scale is weakly epimorphic with val: <7 11 15 19 27| Scale is JI-epimorphic with val: <7 11 15 20 25| Scale is weakly epimorphic with val: <7 11 15 21 23| Scale is JI-epimorphic with val: <7 11 15 21 26| Scale is weakly epimorphic with val: <7 11 15 22 24| Scale is JI-epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 16 18 24| Scale is weakly epimorphic with val: <7 11 16 18 27| Scale is weakly epimorphic with val: <7 11 16 19 25| Scale is weakly epimorphic with val: <7 11 16 20 23| Scale is weakly epimorphic with val: <7 11 16 20 26| Scale is weakly epimorphic with val: <7 11 16 21 24| Scale is weakly epimorphic with val: <7 11 16 21 27| Scale is weakly epimorphic with val: <7 11 16 22 25| Scale is weakly epimorphic with val: <7 11 18 18 23| Scale is weakly epimorphic with val: <7 11 18 18 26| Scale is weakly epimorphic with val: <7 11 18 19 24| Scale is weakly epimorphic with val: <7 11 18 19 27| Scale is weakly epimorphic with val: <7 11 18 20 25| Scale is weakly epimorphic with val: <7 11 18 21 23| Scale is weakly epimorphic with val: <7 11 18 21 26| Scale is weakly epimorphic with val: <7 11 18 22 24| Scale is weakly epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 11 19 19 25| Scale is weakly epimorphic with val: <7 11 19 20 23| Scale is weakly epimorphic with val: <7 11 19 20 26| Scale is weakly epimorphic with val: <7 11 19 21 24| Scale is weakly epimorphic with val: <7 11 19 21 27| Scale is weakly epimorphic with val: <7 11 19 22 25| Scale is weakly epimorphic with val: <7 12 15 20 23| Scale is weakly epimorphic with val: <7 12 15 21 24| Scale is weakly epimorphic with val: <7 12 15 22 25| Scale is weakly epimorphic with val: <8 11 17 19 23| Scale is weakly epimorphic with val: <8 11 17 20 24| Scale is weakly epimorphic with val: <8 11 17 21 25| Scale is weakly epimorphic with val: <8 11 17 22 26| Scale is weakly epimorphic with val: <8 11 18 18 23| Scale is weakly epimorphic with val: <8 11 18 18 26| Scale is weakly epimorphic with val: <8 11 18 19 24| Scale is weakly epimorphic with val: <8 11 18 19 27| Scale is weakly epimorphic with val: <8 11 18 20 25| Scale is weakly epimorphic with val: <8 11 18 21 23| Scale is weakly epimorphic with val: <8 11 18 21 26| Scale is weakly epimorphic with val: <8 11 18 22 24| Scale is weakly epimorphic with val: <8 11 18 22 27| Scale is weakly epimorphic with val: <8 12 15 18 24| Scale is weakly epimorphic with val: <8 12 15 19 25| Scale is weakly epimorphic with val: <8 12 15 20 26| Scale is weakly epimorphic with val: <8 12 15 21 27| Scale is weakly epimorphic with val: <8 12 17 18 23| Scale is weakly epimorphic with val: <8 12 17 18 26| Scale is weakly epimorphic with val: <8 12 17 19 24| Scale is weakly epimorphic with val: <8 12 17 19 27| Scale is weakly epimorphic with val: <8 12 17 20 25| Scale is weakly epimorphic with val: <8 12 17 21 23| Scale is weakly epimorphic with val: <8 12 17 21 26| Scale is weakly epimorphic with val: <8 12 17 22 24| Scale is weakly epimorphic with val: <8 12 17 22 27| Scale is weakly epimorphic with val: <8 12 18 20 23| Scale is weakly epimorphic with val: <8 12 18 21 24| Scale is weakly epimorphic with val: <8 12 18 22 25|
FIT/MODE
3: 0 1 2 N G T3 SD: 36.1469 c. M:-54.2837 c. 4: 0 1 3 N G T3 SD: 19.4629 c. M: 31.1943 c. 5: 0 1 4 N G T3 SD: 19.3221 c. M: 31.1943 c. 8: 1 1 6 N M DE S SD: 19.3919 c. M:-31.0614 c. 9: 1 1 7 N M DE S SD: 13.9529 c. M:-24.1441 c. 10: 1 1 8 N M DE S SD: 12.8230 c. M:-18.6102 c. 12: 1 2 9 N T3 SD: 9.4800 c. M:-12.7800 c. 13: 1 2 10 N T3 SD: 4.5057 c. M:-7.1169 c. 14: 1 2 11 N T3 SD: 3.8411 c. M: 5.0074 c. 17: 1 3 13 N T3 SD: 3.3350 c. M:-5.4558 c. 18: 1 3 14 N T3 SD: 2.1243 c. M: 3.5251 c. 31: 2 5 24 N T3 SD: 0.6863 c. M:-0.9377 c. 49: 3 8 38 N T3 SD: 0.4074 c. M: 0.7017 c. 80: 5 13 62 N T3 SD: 0.1937 c. M:-0.3288 c. 129: 8 21 100 N T3 SD: 0.2226 c. M: 0.3077 c. 143: 9 23 111 N T3 SD: 0.1841 c. M: 0.2807 c. 174: 11 28 135 N T3 SD: 0.1779 c. M:-0.2914 c. 192: 12 31 149 N T3 SD: 0.1162 c. M: 0.1900 c. 223: 14 36 173 N T3 SD: 0.0554 c. M:-0.0731 c. 272: 17 44 211 N T3 SD: 0.0440 c. M: 0.0664 c. 303: 19 49 235 N T3 SD: 0.0317 c. M:-0.0412 c. 495: 31 80 384 N T3 SD: 0.0281 c. M: 0.0485 c. 575: 36 93 446 N T3 SD: 0.0075 c. M: 0.0123 c. 1373: 86 222 1065 N T3 SD: 0.0040 c. M: 0.0067 c. 1676: 105 271 1300 N T3 SD: 0.0047 c. M:-0.0079 c. 1948: 122 315 1511 N T3 SD: 0.0025 c. M: 0.0035 c. 2251: 141 364 1746 N T3 SD: 0.0021 c. M:-0.0027 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x x 7 SD: 84.4672 cents 6 x 7:8 S SD: 77.5698 cents 7 x 8:9 S SD: 67.5105 cents 8 x 9:11 SD: 53.2328 cents 9 x 10:12 S SD: 35.3362 cents 10 x 11:13 SD: 34.4934 cents 11 x 12:15 S SD: 27.5105 cents 12 x 13:16 SD: 13.4207 cents 13 x 14:17 SD: 18.7389 cents 14 x 15:19 SD: 15.7988 cents 15 x 16:20 S SD: 0.0000 cents 16 x 17:21 SD: 14.0467 cents 17 x 18:23 SD: 14.1599 cents 18 x 19:24 SD: 9.0641 cents 19 x 20:25 S SD: 16.2144 cents 20 x 21:27 SD: 17.3627 cents 21 x 22:28 SD: 15.5971 cents 22 x 23:29 SD: 20.0048 cents 23 x 25:31 SD: 18.8048 cents 24:25:26:32 SD: 15.9129 cents 25:26:27:33 SD: 15.3210 cents 26:27:28:35 S SD: 13.8029 cents 27:28:29:36 SD: 11.3170 cents 29:30:31:39 SD: 10.4925 cents 30:31:32:40 S SD: 8.5242 cents 33:34:35:44 SD: 7.5798 cents 39:40:42:52 SD: 6.9454 cents 40:41:43:53 SD: 6.9349 cents 41:42:44:55 S SD: 6.0762 cents 42:43:45:56 SD: 4.0897 cents 45:46:48:60 S SD: 2.2855 cents 57:58:61:76 SD: 1.9294 cents 60:61:64:80 SD: 0.8594 cents 105:107:112:140 SD: 0.4905 cents 165:168:176:220 S SD: 0.0000 cents