Scala analysis: 093_E11
Enharmonic tetrachord 180/173 * 346/339 * 113/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 180/173 68.669842 2: 120/113 104.053960 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 113/90 393.9910 1: 180/173 68.6698 2: 346/339 35.3841 3: 113/90 393.9910
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 346/339 35.384 cents 1: 1 180/173 68.670 cents 1: 1 113/90 393.991 cents 2: 1 120/113 104.054 cents 2: 1 173/135 429.375 cents 2: 1 226/173 462.661 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 : 68.7 104.1 498.0 68.7 : 35.4 429.4 498.0 104.1: 394.0 462.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.3841 .. 393.9910 cents 12769/10380, 358.6069 cents 346/339, 35.3841 cents 2: 104.0540 .. 462.6609 cents 12769/10380, 358.6069 cents 10800/12769,-289.9371 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 346/339, 35.3841 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 113/90, 393.9910 cents Average / Smallest step : 4.691794 Largest / Average step : 2.373226 Largest / Smallest step : 11.134686 Median interval of one step : 180/173, 68.6698 cents, amount: 1 Least squares average step : 126.49377 cents, oct.: 379.48131 cents Scale is not proper Scale has trivalence property Scale is a mode of a 718-tone equal temperament with octave 4/3 degrees: 99 150 718 Least number of segments generator : 361 of 250.410 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 501 of 347.522 cents and inv. generated superset size: 18 = 15 more = 600.000% 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 35.38412 cents Scale diversity : 0.424784 Lumma stability : 0.142092 Lumma impropriety factor : 0.582150 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 : 30510/29929, 33.2857 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% -- Rational properties -- Prime limit : 173 Odd number limit : 339 (O: 173 U: 339) Highest odd numerator or denominator: 173 Scale harmonicity : 0.057471 Fundamental : 1/58647, -15.8398 octaves, 0.0045 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 2.111292E+07, 24.33162 octaves Euler's gradus suavitatis : 298 Sum of Mann's harmonic distance : 296.5, average 98.83333 Mersenne's string divisions : 575743 Sum of van Prooijen's expressibility: 4.76825, average 1.58942 Sum of Tenney's harmonic distance : 9.70476, average 3.23492 Vogel's harmonic complexity : 201.33333 Wille's k value : 9774 Wilson's harmonic complexity : 300 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 15.57867, average 2.59645 Lattice compactness (without 2's) : 11.04863, average 1.84144 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 113: -1 .. 0 -0.33333 1 1 173: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 15 48 53| Scale is weakly epimorphic with val: <7 11 15 49 55| Scale is weakly epimorphic with val: <7 11 16 49 54| Scale is weakly epimorphic with val: <7 11 16 50 53| Scale is weakly epimorphic with val: <7 11 17 48 54| Scale is weakly epimorphic with val: <7 11 17 50 55| Scale is JI-epimorphic with val: <7 11 18 48 53| Scale is weakly epimorphic with val: <7 11 18 49 55| Scale is JI-epimorphic with val: <7 11 19 49 54| Scale is weakly epimorphic with val: <7 11 19 50 53| Scale is weakly epimorphic with val: <7 12 18 48 55| Scale is weakly epimorphic with val: <7 12 18 50 53| Scale is weakly epimorphic with val: <7 12 19 48 54| Scale is weakly epimorphic with val: <7 12 19 49 53| Scale is weakly epimorphic with val: <8 11 16 48 53| Scale is weakly epimorphic with val: <8 11 17 49 54| Scale is weakly epimorphic with val: <8 11 18 49 53| Scale is weakly epimorphic with val: <8 11 18 50 55| Scale is weakly epimorphic with val: <8 11 19 50 54| Scale is weakly epimorphic with val: <8 12 15 48 53| Scale is weakly epimorphic with val: <8 12 16 49 54| Scale is weakly epimorphic with val: <8 12 16 50 53| Scale is weakly epimorphic with val: <8 12 17 48 54| Scale is weakly epimorphic with val: <8 12 17 50 55| Scale is weakly epimorphic with val: <8 12 18 49 55|
FIT/MODE
3: 0 1 2 N G T3 SD: 53.4001 c. M: 68.6698 c. 4: 1 0 3 N G T3 SD: 34.3354 c. M:-55.8414 c. 5: 1 0 4 N G T3 SD: 18.0461 c. M:-30.9392 c. 6: 1 0 5 N G T3 SD: 14.7029 c. M: 21.0465 c. 8: 1 1 6 N M DE S SD: 12.3780 c. M:-20.4573 c. 9: 1 1 7 N M DE S SD: 8.5944 c. M: 13.3315 c. 13: 2 1 10 N T3 SD: 7.7804 c. M:-10.8795 c. 14: 2 1 11 N T3 SD: 2.1037 c. M:-2.6700 c. 29: 4 2 23 N T3 SD: 0.5834 c. M: 1.0102 c. 43: 6 3 34 N T3 SD: 0.4884 c. M:-0.8248 c. 72: 10 5 57 N T3 SD: 0.3366 c. M:-0.5031 c. 101: 14 7 80 N T3 SD: 0.3578 c. M: 0.5000 c. 115: 16 8 91 N T3 SD: 0.3659 c. M:-0.6234 c. 124: 17 9 98 N T3 SD: 0.3121 c. M: 0.3895 c. 139: 19 10 110 N T3 SD: 0.3518 c. M: 0.5917 c. 153: 21 11 121 N T3 SD: 0.1908 c. M: 0.3107 c. 167: 23 12 132 N T3 SD: 0.1938 c. M:-0.3267 c. 182: 25 13 144 N T3 SD: 0.1533 c. M: 0.2571 c. 196: 27 14 155 N T3 SD: 0.0825 c. M:-0.1289 c. 225: 31 16 178 N T3 SD: 0.0308 c. M: 0.0503 c. 493: 68 35 390 N T3 SD: 0.0150 c. M:-0.0260 c. 718: 99 51 568 N T3 SD: 0.0034 c. M: 0.0056 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: 81.4085 cents 7 x 8:9 S SD: 70.9288 cents 8 x 9:11 SD: 56.5889 cents 9 x 10:12 S SD: 39.1749 cents 10 x 11:13 SD: 37.5370 cents 11 x 12:15 S SD: 30.3465 cents 12 x 13:16 SD: 17.2594 cents 13 x 14:17 SD: 20.7238 cents 14 x 15:19 SD: 17.1446 cents 15 x 16:20 S SD: 3.8387 cents 16 x 17:21 SD: 13.6395 cents 17 x 18:23 SD: 12.8916 cents 18 x 19:24 SD: 5.2255 cents 19 x 20:25 S SD: 13.7702 cents 20:21 x 27 SD: 13.3424 cents 21:22 x 28 SD: 5.9336 cents 22:23 x 29 SD: 10.7255 cents 23:24 x 31 SD: 9.6877 cents 24:25 x 32 SD: 1.0013 cents 37 x 39:49 SD: 8.7259 cents 38 x 40:51 SD: 9.5071 cents 39 x 41:52 SD: 8.7371 cents 40:42 x 53 SD: 9.5834 cents 41:43:44:55 SD: 8.3805 cents 42:44:45:56 SD: 6.4777 cents 43:45:46:57 SD: 6.3595 cents 44:46:47:59 SD: 5.4527 cents 45:47:48:60 SD: 3.3776 cents 48:50:51:64 SD: 0.7320 cents 99:103:105:132 SD: 0.7298 cents 147:153:156:196 SD: 0.4390 cents 195:203:207:260 SD: 0.3832 cents 225:234:239:300 SD: 0.2970 cents 273:284:290:364 SD: 0.1996 cents 321:334:341:428 SD: 0.1957 cents 372:387:395:496 SD: 0.1010 cents 420:437:446:560 SD: 0.0241 cents