Scala analysis: 330_C25
Chromatic tetrachord 117/112 * 56/51 * 136/117
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 117/112 75.611757 2: 39/34 237.527253 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 136/117 260.5177 1: 117/112 75.6118 2: 56/51 161.9155 3: 136/117 260.5177
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 117/112 75.612 cents 1: 1 56/51 161.915 cents 1: 1 136/117 260.518 cents 2: 1 39/34 237.527 cents 2: 1 17/14 336.130 cents supraminor third 2: 1 448/351 422.433 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 : 75.6 237.5 498.0 75.6 : 161.9 422.4 498.0 237.5: 260.5 336.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.6118 .. 260.5177 cents 15232/13689, 184.9060 cents 117/112, 75.6118 cents 2: 237.5273 .. 422.4332 cents 15232/13689, 184.9060 cents 4563/4624,-22.9905 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 117/112, 75.6118 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 136/117, 260.5177 cents Average / Smallest step : 2.195624 Largest / Average step : 1.569242 Largest / Smallest step : 3.445466 Median interval of one step : 56/51, 161.9155 cents, amount: 1 Least squares average step : 146.05723 cents, oct.: 438.17170 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2187-tone equal temperament with octave 4/3 degrees: 332 1043 2187 Least number of segments generator : 1094 of 249.136 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1136 of 258.701 cents and inv. generated superset size: 86 = 83 more = 2866.667% 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 22.99049 cents Scale diversity : 1.040159 Lumma stability : 0.303634 Lumma impropriety factor : 0.046161 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 : 4624/4563, 22.9905 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 : 17 Odd number limit : 351 (O: 117 U: 351) Highest odd numerator or denominator: 117 Scale harmonicity : 0.013062 Average absolute harmonicity : 0.085367 Specific harmonicity : 0.062624 Fundamental : 1/5712, -12.4798 octaves, 0.0458 Hz. Guide tone : 468, 8.8704 octaves, 122440.765 Hz. Exponens Consonantiae : 2.673216E+06, 21.35014 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 154.5, average 51.50000 Mersenne's string divisions : 117019 Sum of van Prooijen's expressibility: 4.13637, average 1.37879 Sum of Tenney's harmonic distance : 8.31913, average 2.77304 Vogel's harmonic complexity : 32.66667 Wille's k value : 2983 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 23.11922, average 3.85320 Lattice compactness (without 2's) : 12.67971, average 2.11328 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.00000 7 3: -1 .. 2 0.66667 4 1 7: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 1 17: -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 18 25 28| Scale is weakly epimorphic with val: <6 10 18 25 31| Scale is weakly epimorphic with val: <6 10 18 26 27| Scale is weakly epimorphic with val: <6 10 18 29 30| Scale is weakly epimorphic with val: <6 10 19 26 29| Scale is weakly epimorphic with val: <6 10 19 26 32| Scale is weakly epimorphic with val: <6 10 19 27 28| Scale is weakly epimorphic with val: <6 10 19 30 31| Scale is weakly epimorphic with val: <6 10 20 27 27| Scale is weakly epimorphic with val: <6 10 20 27 30| Scale is weakly epimorphic with val: <6 10 20 27 33| Scale is weakly epimorphic with val: <6 10 20 28 29| Scale is weakly epimorphic with val: <6 10 21 26 27| Scale is weakly epimorphic with val: <6 10 21 28 28| Scale is weakly epimorphic with val: <6 10 21 28 31| Scale is weakly epimorphic with val: <6 10 21 29 30| Scale is weakly epimorphic with val: <6 10 22 27 28| Scale is weakly epimorphic with val: <6 10 22 29 29| Scale is weakly epimorphic with val: <6 10 22 29 32| Scale is weakly epimorphic with val: <6 10 22 30 31| Scale is weakly epimorphic with val: <6 11 18 25 27| Scale is weakly epimorphic with val: <6 11 18 28 30| Scale is weakly epimorphic with val: <6 11 19 26 28| Scale is weakly epimorphic with val: <6 11 19 29 31| Scale is weakly epimorphic with val: <6 11 20 25 28| Scale is weakly epimorphic with val: <6 11 20 25 31| Scale is weakly epimorphic with val: <6 11 20 27 29| Scale is weakly epimorphic with val: <6 11 20 30 32| Scale is weakly epimorphic with val: <6 11 21 25 27| Scale is weakly epimorphic with val: <6 11 21 26 29| Scale is weakly epimorphic with val: <6 11 21 26 32| Scale is weakly epimorphic with val: <6 11 21 28 30| Scale is weakly epimorphic with val: <6 11 22 26 28| Scale is weakly epimorphic with val: <6 11 22 27 27| Scale is weakly epimorphic with val: <6 11 22 27 30| Scale is weakly epimorphic with val: <6 11 22 27 33| Scale is weakly epimorphic with val: <6 11 22 29 31| Scale is weakly epimorphic with val: <7 10 18 28 28| Scale is weakly epimorphic with val: <7 10 18 29 30| Scale is weakly epimorphic with val: <7 10 18 29 33| Scale is weakly epimorphic with val: <7 10 19 29 29| Scale is weakly epimorphic with val: <7 10 19 30 31| Scale is weakly epimorphic with val: <7 10 20 27 27| Scale is weakly epimorphic with val: <7 10 20 30 30| Scale is weakly epimorphic with val: <7 10 21 28 28| Scale is weakly epimorphic with val: <7 10 22 29 29| Scale is JI-epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 25 33| Scale is weakly epimorphic with val: <7 11 18 26 29| Scale is weakly epimorphic with val: <7 11 18 26 32| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is weakly epimorphic with val: <7 11 18 29 29| Scale is weakly epimorphic with val: <7 11 18 29 32| Scale is JI-epimorphic with val: <7 11 19 26 28| Scale is weakly epimorphic with val: <7 11 19 26 31| Scale is weakly epimorphic with val: <7 11 19 27 27| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 11 19 29 31| Scale is weakly epimorphic with val: <7 11 19 30 30| Scale is weakly epimorphic with val: <7 11 19 30 33| Scale is weakly epimorphic with val: <7 11 20 25 28| Scale is weakly epimorphic with val: <7 11 20 25 31| Scale is JI-epimorphic with val: <7 11 20 27 29| Scale is weakly epimorphic with val: <7 11 20 27 32| Scale is weakly epimorphic with val: <7 11 20 28 28| Scale is weakly epimorphic with val: <7 11 20 28 31| Scale is weakly epimorphic with val: <7 11 20 30 32| Scale is weakly epimorphic with val: <7 11 21 25 27| Scale is weakly epimorphic with val: <7 11 21 25 30| Scale is weakly epimorphic with val: <7 11 21 25 33| Scale is weakly epimorphic with val: <7 11 21 26 29| Scale is weakly epimorphic with val: <7 11 21 26 32| Scale is JI-epimorphic with val: <7 11 21 28 30| Scale is weakly epimorphic with val: <7 11 21 28 33| Scale is weakly epimorphic with val: <7 11 21 29 29| Scale is weakly epimorphic with val: <7 11 21 29 32| Scale is weakly epimorphic with val: <7 11 22 26 28| Scale is weakly epimorphic with val: <7 11 22 26 31| Scale is weakly epimorphic with val: <7 11 22 27 27| Scale is weakly epimorphic with val: <7 11 22 27 30| Scale is weakly epimorphic with val: <7 11 22 27 33| Scale is JI-epimorphic with val: <7 11 22 29 31| Scale is weakly epimorphic with val: <7 11 22 30 30| Scale is weakly epimorphic with val: <7 11 22 30 33| Scale is weakly epimorphic with val: <7 12 18 25 29| Scale is weakly epimorphic with val: <7 12 18 25 32| Scale is weakly epimorphic with val: <7 12 18 26 28| Scale is weakly epimorphic with val: <7 12 18 29 31| Scale is weakly epimorphic with val: <7 12 19 26 27| Scale is weakly epimorphic with val: <7 12 19 26 30| Scale is weakly epimorphic with val: <7 12 19 26 33| Scale is weakly epimorphic with val: <7 12 19 27 29| Scale is weakly epimorphic with val: <7 12 19 30 32| Scale is weakly epimorphic with val: <7 12 20 25 27| Scale is weakly epimorphic with val: <7 12 20 27 28| Scale is weakly epimorphic with val: <7 12 20 27 31| Scale is weakly epimorphic with val: <7 12 20 28 30| Scale is weakly epimorphic with val: <7 12 21 26 28| Scale is weakly epimorphic with val: <7 12 21 28 29| Scale is weakly epimorphic with val: <7 12 21 28 32| Scale is weakly epimorphic with val: <7 12 21 29 31| Scale is weakly epimorphic with val: <7 12 22 27 29| Scale is weakly epimorphic with val: <7 12 22 29 30| Scale is weakly epimorphic with val: <7 12 22 29 33| Scale is weakly epimorphic with val: <7 12 22 30 32| Scale is weakly epimorphic with val: <8 11 18 29 29| Scale is weakly epimorphic with val: <8 11 19 27 27| Scale is weakly epimorphic with val: <8 11 19 30 30| Scale is weakly epimorphic with val: <8 11 20 28 28| Scale is weakly epimorphic with val: <8 11 21 29 29| Scale is weakly epimorphic with val: <8 11 22 27 27| Scale is weakly epimorphic with val: <8 11 22 30 30| Scale is weakly epimorphic with val: <8 12 18 28 29| Scale is weakly epimorphic with val: <8 12 18 29 31| Scale is weakly epimorphic with val: <8 12 19 26 27| Scale is weakly epimorphic with val: <8 12 19 29 30| Scale is weakly epimorphic with val: <8 12 19 30 32| Scale is weakly epimorphic with val: <8 12 20 27 28| Scale is weakly epimorphic with val: <8 12 20 30 31| Scale is weakly epimorphic with val: <8 12 21 28 29| Scale is weakly epimorphic with val: <8 12 22 26 27| Scale is weakly epimorphic with val: <8 12 22 29 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 60.0864 c. M: 75.6118 c. 4: 1 1 2 P M ME S SD: 29.0017 c. M:-48.8995 c. 5: 1 1 3 N M DE S SD: 26.0990 c. M: 38.3093 c. 6: 1 2 3 P T3 SD: 7.8917 c. M:-11.4952 c. 13: 2 4 7 N T3 SD: 4.4610 c. M: 7.6603 c. 19: 3 6 10 N T3 SD: 1.9798 c. M:-3.0269 c. 27: 4 9 14 N T3 SD: 1.6834 c. M:-2.2722 c. 40: 6 13 21 N T3 SD: 0.7600 c. M: 0.9559 c. 46: 7 15 24 N T3 SD: 0.3992 c. M:-0.6682 c. 86: 13 28 45 N T3 SD: 0.1948 c. M: 0.3259 c. 132: 20 43 69 N T3 SD: 0.1337 c. M:-0.1760 c. 151: 23 49 79 N T3 SD: 0.1467 c. M:-0.2494 c. 191: 29 62 100 N T3 SD: 0.1379 c. M: 0.2388 c. 197: 30 64 103 N T3 SD: 0.1508 c. M:-0.2327 c. 218: 33 71 114 N T3 SD: 0.1335 c. M: 0.2196 c. 237: 36 77 124 N T3 SD: 0.0432 c. M: 0.0628 c. 283: 43 92 148 N T3 SD: 0.0487 c. M:-0.0629 c. 369: 56 120 193 N T3 SD: 0.0207 c. M: 0.0277 c. 606: 92 197 317 N T3 SD: 0.0062 c. M: 0.0107 c. 1581: 240 514 827 N T3 SD: 0.0045 c. M: 0.0072 c. 1864: 283 606 975 N T3 SD: 0.0040 c. M:-0.0060 c. 2187: 332 711 1144 N T3 SD: 0.0043 c. M: 0.0055 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: 57.5250 cents 6 x 7:8 S SD: 14.6718 cents 7 x 8:9 S SD: 31.6403 cents 8 x 9:11 SD: 31.4965 cents 9 x 10:12 S SD: 27.5618 cents 10 x 11:13 SD: 42.3697 cents 11:12:13:15 SD: 33.0211 cents 12:13:14:16 S SD: 23.1544 cents 13:14:15:17 SD: 21.1090 cents 14:15:16:19 SD: 17.9520 cents 15:16:17:20 SD: 13.9002 cents 18:19:21:24 SD: 11.4733 cents 19:20:22:25 SD: 10.3533 cents 20:21:23:27 SD: 7.8923 cents 21:22:24:28 S SD: 2.6796 cents 48:50:55:64 SD: 1.7582 cents 69:72:79:92 SD: 1.2515 cents 108:113:124:144 SD: 1.0644 cents 129:135:148:172 SD: 1.0378 cents 135:141:155:180 SD: 0.5586 cents 156:163:179:208 SD: 0.2280 cents 225:235:258:300 SD: 0.2257 cents 360:376:413:480 SD: 0.1370 cents 381:398:437:508 SD: 0.0409 cents 537:561:616:716 SD: 0.0390 cents