Scala analysis: 111_E13
Enharmonic tetrachord 256/243 * 81/80 * 5/4, Fox-Strangways?
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 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: 256/243 90.2250 limma, Pythagorean minor second 2: 81/80 21.5063 syntonic comma, Didymus comma 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 81/64 407.820 cents Pythagorean major third 2: 1 320/243 476.539 cents grave fourth 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 : 90.2 111.7 498.0 90.2 : 21.5 407.8 498.0 111.7: 386.3 476.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 386.3137 cents 100/81, 364.8074 cents 81/80, 21.5063 cents 2: 111.7313 .. 476.5387 cents 100/81, 364.8074 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 7.719370 Largest / Average step : 2.326981 Largest / Smallest step : 17.962825 Median interval of one step : 256/243, 90.2250 cents, amount: 1 Least squares average step : 129.13018 cents, oct.: 387.39055 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1529-tone equal temperament with octave 4/3 degrees: 277 343 1529 Least number of segments generator : 765 of 249.185 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1384 of 450.814 cents and inv. generated superset size: 35 = 32 more = 1166.667% 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 21.50629 cents Scale diversity : 0.404594 Lumma stability : 0.086363 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 : 81/80, 21.5063 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.036058 Average absolute harmonicity : 0.112563 Specific harmonicity : 0.187793 Fundamental : 1/1215, -10.2467 octaves, 0.2153 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 268.5, average 89.50000 Mersenne's string divisions : 108283 Sum of van Prooijen's expressibility: 4.03882, average 1.34627 Sum of Tenney's harmonic distance : 8.25324, average 2.75108 Vogel's harmonic complexity : 16.00000 Wille's k value : 202 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 31.10442, average 5.18407 Lattice compactness (without 2's) : 16.53732, average 2.75622 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 4.66667 14 3: -5 ..-1 -2.33333 7 2 5: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-8 / 3 =-2.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 11 18|
FIT/MODE
3: 0 0 3 N M DE S SD: 82.9145 c. M: 111.7313 c. 4: 1 0 3 N G T3 SD: 21.1256 c. M:-34.2863 c. 5: 1 0 4 N G T3 SD: 8.8508 c. M: 12.1223 c. 12: 2 1 9 N T3 SD: 8.4739 c. M:-12.7800 c. 13: 2 1 10 N T3 SD: 8.0682 c. M: 13.6027 c. 16: 3 1 12 N T3 SD: 7.6005 c. M:-12.7800 c. 17: 3 1 13 N T3 SD: 3.4262 c. M:-5.4558 c. 22: 4 1 17 N T3 SD: 0.8645 c. M:-1.4608 c. 49: 9 2 38 N T3 SD: 0.7245 c. M:-1.2527 c. 67: 12 3 52 N T3 SD: 0.6052 c. M: 1.0229 c. 71: 13 3 55 N T3 SD: 0.6293 c. M:-0.9663 c. 89: 16 4 69 N T3 SD: 0.4124 c. M: 0.6888 c. 94: 17 4 73 N T3 SD: 0.2831 c. M: 0.4659 c. 116: 21 5 90 N T3 SD: 0.0681 c. M: 0.1005 c. 254: 46 11 197 N T3 SD: 0.0257 c. M:-0.0347 c. 370: 67 16 287 N T3 SD: 0.0226 c. M: 0.0385 c. 624: 113 27 484 N T3 SD: 0.0205 c. M: 0.0342 c. 878: 159 38 681 N T3 SD: 0.0211 c. M: 0.0323 c. 905: 164 39 702 N T3 SD: 0.0186 c. M:-0.0285 c. 1021: 185 44 792 N T3 SD: 0.0178 c. M: 0.0248 c. 1043: 189 45 809 N T3 SD: 0.0148 c. M:-0.0248 c. 1159: 210 50 899 N T3 SD: 0.0096 c. M:-0.0161 c. 1275: 231 55 989 N T3 SD: 0.0091 c. M: 0.0130 c. 1297: 235 56 1006 N T3 SD: 0.0109 c. M:-0.0145 c. 1413: 256 61 1096 N T3 SD: 0.0050 c. M:-0.0082 c. 1529: 277 66 1186 N T3 SD: 0.0034 c. M: 0.0050 c. 1783: 323 77 1383 N T3 SD: 0.0009 c. M: 0.0015 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 17:18 x 23 SD: 13.3695 cents 18:19 x 24 SD: 1.6890 cents 19:20 x 25 S SD: 11.4874 cents 20:21 x 27 SD: 11.1319 cents 21:22 x 28 SD: 4.8440 cents 22:23 x 29 SD: 11.9115 cents 24:25:26:32 SD: 11.0693 cents 27:28:29:36 SD: 9.9268 cents 28 x 30:37 SD: 8.6682 cents 29 x 31:39 SD: 7.6604 cents 30 x 32:40 S SD: 0.0000 cents 31 x 33:41 SD: 7.2235 cents 32 x 34:43 SD: 7.5403 cents 33 x 35:44 SD: 4.9323 cents 34:36 x 45 S SD: 7.7371 cents 35:37 x 47 SD: 6.8481 cents 36:38 x 48 SD: 1.6890 cents 37:39 x 49 SD: 5.8864 cents 39:41:42:52 SD: 5.6544 cents 41:43:44:55 SD: 5.5965 cents 42:44:45:56 SD: 4.1275 cents 47 x 50:63 SD: 5.1383 cents 48 x 51:64 SD: 3.3879 cents 49 x 52:65 SD: 6.2617 cents 50:53 x 67 SD: 6.8561 cents 51:54 x 68 SD: 4.3648 cents 52:55 x 69 SD: 5.4067 cents 54:57:58:72 SD: 4.1493 cents 56:59:60:75 SD: 3.6355 cents 57:60:61:76 SD: 1.9537 cents 60:63:64:80 S SD: 1.9193 cents 66 x 70:88 SD: 4.9323 cents 67:71 x 89 SD: 6.0250 cents 68:72:73:91 SD: 5.1623 cents 69:73:74:92 SD: 3.9701 cents 70:74:75:93 SD: 3.8527 cents 71:75:76:95 SD: 3.2623 cents 72:76:77:96 SD: 1.8763 cents 75:79:80:100 SD: 0.0902 cents