Scala analysis: 114_E13
Enharmonic tetrachord 136/135 * 18/17 * 5/4, Hofmann
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 136/135 12.776693 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: 136/135 12.7767 2: 18/17 98.9546 Arabic lute index finger 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 136/135 12.777 cents 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 34/27 399.090 cents septendecimal major third 2: 1 45/34 485.268 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 : 12.8 111.7 498.0 12.8 : 99.0 485.3 498.0 111.7: 386.3 399.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 12.7767 .. 386.3137 cents 675/544, 373.5370 cents 136/135, 12.7767 cents 2: 111.7313 .. 485.2683 cents 675/544, 373.5370 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 136/135, 12.7767 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 12.993581 Largest / Average step : 2.326981 Largest / Smallest step : 30.235814 Median interval of one step : 18/17, 98.9546 cents, amount: 1 Least squares average step : 123.59816 cents, oct.: 370.79448 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1052-tone equal temperament with octave 4/3 degrees: 27 236 1052 Least number of segments generator : 527 of 249.496 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 843 of 399.099 cents and inv. generated superset size: 133 = 130 more = 4433.333% 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 12.77669 cents Scale diversity : 0.352874 Lumma stability : 0.051307 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 : 136/135, 12.7767 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 485.2683 cents Number of appreciable 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 : 17 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 135 Scale harmonicity : 0.020611 Average absolute harmonicity : 0.103953 Specific harmonicity : 0.104607 Fundamental : 1/135, -7.0768 octaves, 1.9380 Hz. Guide tone : 272, 8.0875 octaves, 71162.154 Hz. Exponens Consonantiae : 3.672000E+04, 15.16428 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 154.5, average 51.50000 Mersenne's string divisions : 58807 Sum of van Prooijen's expressibility: 3.78355, average 1.26118 Sum of Tenney's harmonic distance : 7.72327, average 2.57442 Vogel's harmonic complexity : 14.33333 Wille's k value : 22 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 18.28215, average 3.04703 Lattice compactness (without 2's) : 11.41640, average 1.90273 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -3 ..-1 -1.66667 5 1 5: -1 .. 0 -0.66667 2 1 17: 0 .. 1 0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 16 31| Scale is weakly epimorphic with val: <7 10 15 29| Scale is weakly epimorphic with val: <7 10 15 32| Scale is weakly epimorphic with val: <7 10 16 28| Scale is weakly epimorphic with val: <7 10 19 31| Scale is JI-epimorphic with val: <7 11 15 28| Scale is weakly epimorphic with val: <7 11 15 31| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 18 28| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 12 15 33| Scale is weakly epimorphic with val: <8 11 17 29| Scale is weakly epimorphic with val: <8 11 18 28| Scale is weakly epimorphic with val: <8 11 18 31| Scale is weakly epimorphic with val: <8 12 15 30| Scale is weakly epimorphic with val: <8 12 17 28| Scale is weakly epimorphic with val: <8 12 17 31| Scale is weakly epimorphic with val: <8 12 18 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 32.1971 c. M:-54.2837 c. 4: 0 1 3 N G T3 SD: 10.4335 c. M:-12.7800 c. 5: 0 1 4 N G T3 SD: 10.1685 c. M: 12.7767 c. 9: 0 2 7 N G T3 SD: 7.4017 c. M: 12.7767 c. 14: 0 3 11 N G T3 SD: 7.9229 c. M: 12.7767 c. 18: 0 4 14 N G T3 SD: 7.4017 c. M: 12.7767 c. 19: 0 4 15 N G T3 SD: 8.3780 c. M: 12.7767 c. 22: 1 4 17 N T3 SD: 5.7558 c. M:-9.8617 c. 26: 1 5 20 N T3 SD: 4.1208 c. M:-6.3789 c. 27: 1 5 21 N T3 SD: 3.3294 c. M:-5.6694 c. 28: 1 5 22 N T3 SD: 4.0898 c. M:-5.0106 c. 30: 1 6 23 N T3 SD: 3.4006 c. M:-4.4792 c. 31: 1 6 24 N T3 SD: 1.9453 c. M:-3.2893 c. 32: 1 6 25 N T3 SD: 2.2744 c. M:-2.7872 c. 35: 1 7 27 N T3 SD: 1.4780 c. M:-2.1076 c. 36: 1 7 28 N T3 SD: 0.8624 c. M:-1.0579 c. 40: 1 8 31 N T3 SD: 0.2672 c. M:-0.3288 c. 116: 3 23 90 N T3 SD: 0.0834 c. M:-0.1038 c. 156: 4 31 121 N T3 SD: 0.0066 c. M:-0.0096 c. 896: 23 178 695 N T3 SD: 0.0053 c. M:-0.0079 c. 1052: 27 209 816 N T3 SD: 0.0037 c. M:-0.0058 c. 1208: 31 240 937 N T3 SD: 0.0025 c. M:-0.0043 c. 1364: 35 271 1058 N T3 SD: 0.0018 c. M:-0.0031 c. 1520: 39 302 1179 N T3 SD: 0.0014 c. M:-0.0021 c. 1676: 43 333 1300 N T3 SD: 0.0014 c. M:-0.0020 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 x 26:32 SD: 13.4207 cents 25 x 27:33 SD: 13.8317 cents 26 x 28:35 S SD: 11.7146 cents 27 x 29:36 SD: 5.9905 cents 60:61:64:80 SD: 5.2798 cents 63:64:67:84 SD: 5.1263 cents 69:70:74:92 SD: 5.1129 cents 71:72:76:95 S SD: 4.7710 cents 72:73:77:96 SD: 3.9937 cents 75:76:80:100 S SD: 3.3846 cents 86:87:92:115 SD: 3.3812 cents 87:88:93:116 SD: 2.6461 cents 90:91:96:120 SD: 2.1177 cents 102:103:109:136 SD: 1.7330 cents 105:106:112:140 SD: 1.2111 cents 117:118:125:156 SD: 1.1312 cents 120:121:128:160 SD: 0.5302 cents 135:136:144:180 S SD: 0.0000 cents