Scala analysis: 094_E11
Enharmonic tetrachord 360/353 * 353/339 * 113/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 360/353 33.994468 2: 120/113 104.053960 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 113/90 393.9910 1: 360/353 33.9945 2: 353/339 70.0595 3: 113/90 393.9910
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 360/353 33.994 cents 1: 1 353/339 70.059 cents 1: 1 113/90 393.991 cents 2: 1 120/113 104.054 cents 2: 1 452/353 427.986 cents 2: 1 353/270 464.051 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 : 34.0 104.1 498.0 34.0 : 70.1 464.1 498.0 104.1: 394.0 428.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.9945 .. 393.9910 cents 39889/32400, 359.9966 cents 360/353, 33.9945 cents 2: 104.0540 .. 464.0505 cents 39889/32400, 359.9966 cents 10800/12769,-289.9371 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 360/353, 33.9945 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 113/90, 393.9910 cents Average / Smallest step : 4.883589 Largest / Average step : 2.373226 Largest / Smallest step : 11.589858 Median interval of one step : 353/339, 70.0595 cents, amount: 1 Least squares average step : 124.01696 cents, oct.: 372.05087 cents Scale is not proper Scale has trivalence property Scale is a mode of a 718-tone equal temperament with octave 4/3 degrees: 49 150 718 Least number of segments generator : 361 of 250.410 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 421 of 292.029 cents and inv. generated superset size: 20 = 17 more = 666.667% 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 33.99447 cents Scale diversity : 0.420059 Lumma stability : 0.136512 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 : 360/353, 33.9945 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 353 Odd number limit : 353 (O: 353 U: 353) Highest odd numerator or denominator: 353 Scale harmonicity : 0.057471 Fundamental : 1/119667, -16.8687 octaves, 0.0022 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 4.308012E+07, 25.36052 octaves Euler's gradus suavitatis : 478 Sum of Mann's harmonic distance : 476.5, average 158.83333 Mersenne's string divisions : 1162903 Sum of van Prooijen's expressibility: 5.07797, average 1.69266 Sum of Tenney's harmonic distance : 10.31552, average 3.43851 Vogel's harmonic complexity : 321.66667 Wille's k value : 19944 Wilson's harmonic complexity : 480 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 16.06046, average 2.67674 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 2.66667 8 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 113: -1 .. 0 -0.33333 1 1 353: -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 60| Scale is weakly epimorphic with val: <7 11 15 49 62| Scale is weakly epimorphic with val: <7 11 16 49 61| Scale is weakly epimorphic with val: <7 11 16 50 60| Scale is weakly epimorphic with val: <7 11 17 48 61| Scale is weakly epimorphic with val: <7 11 17 50 62| Scale is JI-epimorphic with val: <7 11 18 48 60| Scale is weakly epimorphic with val: <7 11 18 49 62| Scale is JI-epimorphic with val: <7 11 19 49 61| Scale is weakly epimorphic with val: <7 11 19 50 60| Scale is weakly epimorphic with val: <7 12 18 48 62| Scale is weakly epimorphic with val: <7 12 18 50 60| Scale is weakly epimorphic with val: <7 12 19 48 61| Scale is weakly epimorphic with val: <7 12 19 49 60| Scale is weakly epimorphic with val: <8 11 16 48 61| Scale is weakly epimorphic with val: <8 11 17 48 60| Scale is weakly epimorphic with val: <8 11 17 49 62| Scale is weakly epimorphic with val: <8 11 18 49 61| Scale is weakly epimorphic with val: <8 11 18 50 60| Scale is weakly epimorphic with val: <8 11 19 50 62| Scale is weakly epimorphic with val: <8 12 15 48 61| Scale is weakly epimorphic with val: <8 12 15 49 60| Scale is weakly epimorphic with val: <8 12 16 49 62| Scale is weakly epimorphic with val: <8 12 16 50 61| Scale is weakly epimorphic with val: <8 12 17 48 62| Scale is weakly epimorphic with val: <8 12 17 50 60|
FIT/MODE
3: 0 1 2 N G T3 SD: 40.8036 c. M:-61.9610 c. 4: 0 1 3 N G T3 SD: 22.9065 c. M: 33.9945 c. 5: 0 1 4 N G T3 SD: 19.7938 c. M: 33.9945 c. 6: 0 1 5 N G T3 SD: 23.0837 c. M: 33.9945 c. 9: 1 1 7 N M DE S SD: 12.9025 c. M:-21.3439 c. 10: 1 1 8 N M DE S SD: 9.4818 c. M:-15.8100 c. 11: 1 1 9 N M DE S SD: 10.1579 c. M: 13.5003 c. 13: 1 2 10 N T3 SD: 6.7576 c. M:-10.8795 c. 14: 1 2 11 N T3 SD: 1.7912 c. M:-2.6700 c. 29: 2 4 23 N T3 SD: 0.6179 c. M: 1.0102 c. 43: 3 6 34 N T3 SD: 0.4480 c. M:-0.7529 c. 72: 5 10 57 N T3 SD: 0.3818 c. M:-0.5920 c. 101: 7 14 80 N T3 SD: 0.4180 c. M:-0.5235 c. 115: 8 16 91 N T3 SD: 0.3822 c. M:-0.6521 c. 134: 9 19 106 N T3 SD: 0.3140 c. M: 0.5437 c. 148: 10 21 117 N T3 SD: 0.2506 c. M: 0.3428 c. 163: 11 23 129 N T3 SD: 0.2419 c. M: 0.3841 c. 177: 12 25 140 N T3 SD: 0.1361 c. M: 0.2287 c. 206: 14 29 163 N T3 SD: 0.1003 c. M: 0.1467 c. 220: 15 31 174 N T3 SD: 0.0523 c. M:-0.0827 c. 249: 17 35 197 N T3 SD: 0.0262 c. M: 0.0446 c. 469: 32 66 371 N T3 SD: 0.0114 c. M:-0.0151 c. 718: 49 101 568 N T3 SD: 0.0044 c. M: 0.0056 c. 1905: 130 268 1507 N T3 SD: 0.0041 c. M: 0.0071 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 x 21:27 SD: 14.5444 cents 21 x 22:28 SD: 11.7585 cents 22 x 23:29 SD: 16.7761 cents 23 x 24:31 SD: 17.8384 cents 24 x 25:32 SD: 16.6908 cents 25:26:27:33 SD: 16.0001 cents 26:27:28:35 S SD: 14.3164 cents 27:28:29:36 SD: 11.6690 cents 28:29:30:37 SD: 11.5173 cents 29:30:31:39 SD: 10.3325 cents 30:31:32:40 S SD: 8.0106 cents 32:33:34:43 SD: 7.8456 cents 33:34:35:44 SD: 5.9409 cents 36:37:38:48 SD: 5.6749 cents 42:43:45:56 SD: 5.6004 cents 44:45:47:59 SD: 4.9782 cents 45:46:48:60 S SD: 2.8943 cents 48:49:51:64 SD: 0.6421 cents 147:150:156:196 SD: 0.5111 cents 195:199:207:260 SD: 0.4455 cents 210:214:223:280 SD: 0.4435 cents 243:248:258:324 SD: 0.4384 cents 258:263:274:344 SD: 0.2575 cents 306:312:325:408 SD: 0.1483 cents 354:361:376:472 SD: 0.1132 cents 453:462:481:604 SD: 0.0773 cents