Scala analysis: 106_E13
Enharmonic tetrachord 28/27 * 36/35 * 5/4, Archytas
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 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: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 63.0 111.7 498.0 63.0 : 48.8 435.1 498.0 111.7: 386.3 449.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 449.2746 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.404013 Largest / Average step : 2.326981 Largest / Smallest step : 7.921072 Median interval of one step : 28/27, 62.9609 cents, amount: 1 Least squares average step : 127.18275 cents, oct.: 381.54824 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1052-tone equal temperament with octave 4/3 degrees: 133 236 1052 Least number of segments generator : 527 of 249.496 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 585 of 276.955 cents and inv. generated superset size: 30 = 27 more = 1000.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 48.77038 cents Scale diversity : 0.509188 Lumma stability : 0.195847 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 : 245/243, 14.1905 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) 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 Limited inverse transpositions with margin 337.5433 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 35 (O: 35 U: 35) Highest odd numerator or denominator: 27 Scale harmonicity : 0.034861 Average absolute harmonicity : 0.113370 Specific harmonicity : 0.185923 Fundamental : 1/135, -7.0768 octaves, 1.9380 Hz. Guide tone : 112, 6.8074 octaves, 29302.063 Hz. Exponens Consonantiae : 1.512000E+04, 13.88417 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 46.5, average 15.50000 Mersenne's string divisions : 11935 Sum of van Prooijen's expressibility: 3.08458, average 1.02819 Sum of Tenney's harmonic distance : 6.33791, average 2.11264 Vogel's harmonic complexity : 12.33333 Wille's k value : 22 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 17.85478, average 2.97580 Lattice compactness (without 2's) : 11.26205, average 1.87701 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 2.66667 8 3: -3 ..-1 -1.66667 5 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 16 21| Scale is weakly epimorphic with val: <6 10 19 21| Scale is weakly epimorphic with val: <7 10 15 18| Scale is weakly epimorphic with val: <7 10 15 21| Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 19 19| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <8 11 17 20| Scale is weakly epimorphic with val: <8 11 18 18| Scale is weakly epimorphic with val: <8 11 18 21| Scale is weakly epimorphic with val: <8 12 17 19| Scale is weakly epimorphic with val: <8 12 17 22|
FIT/MODE
3: 0 0 3 N M DE S SD: 74.0449 c. M: 111.7313 c. 4: 1 0 3 N G T3 SD: 36.2940 c. M:-61.5503 c. 5: 1 0 4 N G T3 SD: 22.2863 c. M:-36.6481 c. 6: 1 0 5 N G T3 SD: 20.2231 c. M: 28.7238 c. 7: 1 1 5 N M DE S SD: 18.2703 c. M:-30.5673 c. 8: 1 1 6 N M DE S SD: 7.3897 c. M:-12.7800 c. 9: 1 1 7 N M DE S SD: 4.4428 c. M: 7.6226 c. 17: 2 2 13 N M DE S SD: 4.0348 c. M:-5.4558 c. 22: 3 2 17 N T3 SD: 2.9821 c. M:-4.9543 c. 23: 3 2 18 N T3 SD: 2.3081 c. M: 3.4606 c. 31: 4 3 24 N T3 SD: 0.8624 c. M:-1.3030 c. 40: 5 4 31 N T3 SD: 0.4493 c. M: 0.7053 c. 71: 9 7 55 N T3 SD: 0.3075 c. M:-0.5042 c. 103: 13 10 80 N T3 SD: 0.3043 c. M: 0.5174 c. 111: 14 11 86 N T3 SD: 0.2679 c. M:-0.4410 c. 134: 17 13 104 N T3 SD: 0.1848 c. M: 0.2287 c. 174: 22 17 135 N T3 SD: 0.0583 c. M: 0.1005 c. 245: 31 24 190 N T3 SD: 0.0543 c. M:-0.0747 c. 388: 49 38 301 N T3 SD: 0.0490 c. M: 0.0635 c. 419: 53 41 325 N T3 SD: 0.0218 c. M:-0.0376 c. 459: 58 45 356 N T3 SD: 0.0235 c. M:-0.0304 c. 593: 75 58 460 N T3 SD: 0.0236 c. M:-0.0296 c. 633: 80 62 491 N T3 SD: 0.0102 c. M: 0.0168 c. 878: 111 86 681 N T3 SD: 0.0100 c. M:-0.0169 c. 1052: 133 103 816 N T3 SD: 0.0032 c. M:-0.0049 c. 1685: 213 165 1307 N T3 SD: 0.0029 c. M: 0.0037 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 20:21 x 27 SD: 15.2072 cents 21:22 x 28 SD: 8.7881 cents 22:23 x 29 SD: 12.1177 cents 24:25:26:32 SD: 9.3091 cents 26:27:28:35 S SD: 7.8498 cents 27:28:29:36 SD: 3.9936 cents 30:31:32:40 S SD: 2.0647 cents 75:78:80:100 S SD: 1.6464 cents 78:81:83:104 SD: 1.5989 cents 105:109:112:140 SD: 0.5886 cents 135:140:144:180 S SD: 0.0000 cents