Scala analysis: 334_C26
Chromatic tetrachord 93/89 * 89/81 * 36/31
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93/89 76.110456 2: 31/27 239.170570 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 36/31 258.8744 1: 93/89 76.1105 2: 89/81 163.0601 3: 36/31 258.8744
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 93/89 76.110 cents 1: 1 89/81 163.060 cents 1: 1 36/31 258.874 cents 2: 1 31/27 239.171 cents 2: 1 108/89 334.985 cents 2: 1 356/279 421.935 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 : 76.1 239.2 498.0 76.1 : 163.1 421.9 498.0 239.2: 258.9 335.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.1105 .. 258.8744 cents 1068/961, 182.7640 cents 93/89, 76.1105 cents 2: 239.1706 .. 421.9345 cents 1068/961, 182.7640 cents 961/972,-19.7039 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 93/89, 76.1105 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 36/31, 258.8744 cents Average / Smallest step : 2.181238 Largest / Average step : 1.559344 Largest / Smallest step : 3.401299 Median interval of one step : 89/81, 163.0601 cents, amount: 1 Least squares average step : 146.32761 cents, oct.: 438.98284 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2022-tone equal temperament with octave 4/3 degrees: 309 971 2022 Least number of segments generator : 1013 of 249.515 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1051 of 258.875 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 : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.70386 cents Scale diversity : 1.039060 Lumma stability : 0.305637 Lumma impropriety factor : 0.039562 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 : 972/961, 19.7039 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 89 Odd number limit : 279 (O: 93 U: 279) Highest odd numerator or denominator: 93 Scale harmonicity : 0.078947 Fundamental : 1/2403, -11.2306 octaves, 0.1089 Hz. Guide tone : 372, 8.5392 octaves, 97324.710 Hz. Exponens Consonantiae : 8.939160E+05, 19.76978 octaves Euler's gradus suavitatis : 129 Sum of Mann's harmonic distance : 123.5, average 41.16667 Mersenne's string divisions : 5278 Sum of van Prooijen's expressibility: 3.93697, average 1.31232 Sum of Tenney's harmonic distance : 7.91978, average 2.63993 Vogel's harmonic complexity : 86.66667 Wille's k value : 1379 Wilson's harmonic complexity : 132 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 15.89292, average 2.64882 Lattice compactness (without 2's) : 13.00000, average 2.16667 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -3 .. 1 -1.00000 5 1 31: 0 .. 1 0.66667 2 1 89: -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: <6 10 33 48| Scale is weakly epimorphic with val: <6 11 36 48| Scale is weakly epimorphic with val: <6 11 38 46| Scale is weakly epimorphic with val: <7 10 33 47| Scale is weakly epimorphic with val: <7 11 34 46| Scale is weakly epimorphic with val: <7 11 35 48| Scale is weakly epimorphic with val: <7 11 37 46| Scale is weakly epimorphic with val: <7 11 38 48| Scale is weakly epimorphic with val: <7 12 37 46| Scale is weakly epimorphic with val: <7 12 39 47| Scale is weakly epimorphic with val: <8 11 36 46| Scale is weakly epimorphic with val: <8 12 38 47| Scale is weakly epimorphic with val: <8 12 39 46|
FIT/MODE
3: 0 1 2 N G T3 SD: 60.9495 c. M: 76.1105 c. 4: 1 1 2 P M ME S SD: 28.5172 c. M:-48.4008 c. 5: 1 1 3 N M DE S SD: 26.7606 c. M: 39.9526 c. 6: 1 2 3 P T3 SD: 6.9433 c. M:-9.8519 c. 13: 2 4 7 N T3 SD: 5.3796 c. M: 9.3036 c. 19: 3 6 10 N T3 SD: 2.3793 c. M: 3.2545 c. 25: 4 8 13 N T3 SD: 2.0660 c. M:-3.5767 c. 27: 4 9 14 N T3 SD: 1.3911 c. M: 2.3260 c. 33: 5 11 17 N T3 SD: 1.3830 c. M:-2.3058 c. 46: 7 15 24 N T3 SD: 0.5927 c. M: 0.9751 c. 52: 8 17 27 N T3 SD: 0.3352 c. M:-0.5119 c. 79: 12 26 41 N T3 SD: 0.3493 c. M: 0.4581 c. 98: 15 32 51 N T3 SD: 0.1933 c. M: 0.3123 c. 150: 23 49 78 N T3 SD: 0.1609 c. M:-0.2564 c. 177: 27 58 92 N T3 SD: 0.0794 c. M: 0.1375 c. 229: 35 75 119 N T3 SD: 0.0380 c. M:-0.0650 c. 327: 50 107 170 N T3 SD: 0.0373 c. M: 0.0480 c. 504: 77 165 262 N T3 SD: 0.0209 c. M: 0.0299 c. 556: 85 182 289 N T3 SD: 0.0171 c. M:-0.0295 c. 733: 112 240 381 N T3 SD: 0.0062 c. M: 0.0108 c. 1289: 197 422 670 N T3 SD: 0.0038 c. M:-0.0066 c. 2022: 309 662 1051 N T3 SD: 0.0004 c. M: 0.0006 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 6:7 S SD: 56.9703 cents 6 x 7:8 S SD: 13.8502 cents 7 x 8:9 S SD: 31.7333 cents 8 x 9:11 SD: 31.9426 cents 9 x 10:12 S SD: 28.3834 cents 10 x 11:13 SD: 43.0750 cents 11:12:13:15 SD: 32.6118 cents 12:13:14:16 S SD: 22.7763 cents 13:14:15:17 SD: 20.8890 cents 14:15:16:19 SD: 17.8903 cents 15:16:17:20 SD: 14.0411 cents 18:19:21:24 SD: 10.9204 cents 19:20:22:25 SD: 10.0057 cents 20:21:23:27 SD: 7.7470 cents 21:22:24:28 S SD: 3.0466 cents 48:50:55:64 SD: 2.1546 cents 66:69:76:88 SD: 1.7132 cents 87:91:100:116 SD: 0.8584 cents 108:113:124:144 SD: 0.7464 cents 135:141:155:180 SD: 0.2758 cents 222:232:255:296 SD: 0.2576 cents 243:254:279:324 SD: 0.1787 cents 357:373:410:476 SD: 0.1712 cents 378:395:434:504 SD: 0.0164 cents