Scala analysis: 377_D3
Diatonic tetrachord 240/229 * 229/207 * 23/20
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 240/229 81.224169 2: 80/69 256.084366 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/20 241.9606 1: 240/229 81.2242 2: 229/207 174.8602 3: 23/20 241.9606
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 240/229 81.224 cents 1: 1 229/207 174.860 cents 1: 1 23/20 241.961 cents 2: 1 80/69 256.084 cents 2: 1 276/229 323.185 cents 2: 1 229/180 416.821 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 : 81.2 256.1 498.0 81.2 : 174.9 416.8 498.0 256.1: 242.0 323.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 81.2242 .. 241.9606 cents 5267/4800, 160.7365 cents 240/229, 81.2242 cents 2: 256.0844 .. 416.8208 cents 5267/4800, 160.7365 cents 1600/1587, 14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 240/229, 81.2242 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/20, 241.9606 cents Average / Smallest step : 2.043911 Largest / Average step : 1.457462 Largest / Smallest step : 2.978924 Median interval of one step : 229/207, 174.8602 cents, amount: 1 Least squares average step : 149.10914 cents, oct.: 447.32741 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1447-tone equal temperament with octave 4/3 degrees: 236 744 1447 Least number of segments generator : 724 of 249.195 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1134 of 390.313 cents and inv. generated superset size: 11 = 8 more = 366.667% 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 14.12373 cents Scale diversity : 1.059102 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.354530 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 : 1600/1587, 14.1237 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 : 229 Odd number limit : 229 (O: 229 U: 229) Highest odd numerator or denominator: 229 Scale harmonicity : 0.017295 Fundamental : 1/15801, -13.9477 octaves, 0.0166 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 3.792240E+06, 21.85462 octaves Euler's gradus suavitatis : 263 Sum of Mann's harmonic distance : 312.5, average 104.16667 Mersenne's string divisions : 69881 Sum of van Prooijen's expressibility: 4.67581, average 1.55860 Sum of Tenney's harmonic distance : 9.56117, average 3.18706 Vogel's harmonic complexity : 176.66667 Wille's k value : 2633 Wilson's harmonic complexity : 263 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 18.52317, average 3.08719 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.33333 10 3: -1 .. 1 -0.33333 3 1 5: 0 .. 1 0.66667 2 23: -1 .. 0 -0.33333 1 1 229: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 19 30 58| Scale is weakly epimorphic with val: <7 10 15 30 57| Scale is weakly epimorphic with val: <7 10 16 31 58| Scale is weakly epimorphic with val: <7 10 17 32 56| Scale is weakly epimorphic with val: <7 10 18 33 57| Scale is weakly epimorphic with val: <7 10 19 34 58| Scale is weakly epimorphic with val: <7 11 15 30 56| Scale is weakly epimorphic with val: <7 11 15 31 58| Scale is weakly epimorphic with val: <7 11 15 33 56| Scale is weakly epimorphic with val: <7 11 15 34 58| Scale is weakly epimorphic with val: <7 11 15 36 56| Scale is weakly epimorphic with val: <7 11 16 31 57| Scale is weakly epimorphic with val: <7 11 16 32 56| Scale is weakly epimorphic with val: <7 11 16 34 57| Scale is weakly epimorphic with val: <7 11 16 35 56| Scale is weakly epimorphic with val: <7 11 17 30 57| Scale is weakly epimorphic with val: <7 11 17 32 58| Scale is weakly epimorphic with val: <7 11 17 33 57| = patent Scale is weakly epimorphic with val: <7 11 17 35 58| Scale is weakly epimorphic with val: <7 11 17 36 57| Scale is weakly epimorphic with val: <7 11 18 30 56| Scale is weakly epimorphic with val: <7 11 18 31 58| Scale is JI-epimorphic with val: <7 11 18 33 56| Scale is weakly epimorphic with val: <7 11 18 34 58| Scale is weakly epimorphic with val: <7 11 18 36 56| Scale is weakly epimorphic with val: <7 11 19 31 57| Scale is weakly epimorphic with val: <7 11 19 32 56| Scale is JI-epimorphic with val: <7 11 19 34 57| Scale is weakly epimorphic with val: <7 11 19 35 56| Scale is weakly epimorphic with val: <7 12 17 30 56| Scale is weakly epimorphic with val: <7 12 18 31 57| Scale is weakly epimorphic with val: <7 12 19 31 56| Scale is weakly epimorphic with val: <7 12 19 32 58| Scale is weakly epimorphic with val: <7 12 19 34 56| Scale is weakly epimorphic with val: <8 11 15 33 57| Scale is weakly epimorphic with val: <8 11 16 30 56| Scale is weakly epimorphic with val: <8 11 16 33 56| Scale is weakly epimorphic with val: <8 11 16 34 58| Scale is weakly epimorphic with val: <8 11 16 36 56| Scale is weakly epimorphic with val: <8 11 17 31 57| Scale is weakly epimorphic with val: <8 11 17 34 57| Scale is weakly epimorphic with val: <8 11 17 35 56| Scale is weakly epimorphic with val: <8 11 18 32 58| Scale is weakly epimorphic with val: <8 11 18 35 58| Scale is weakly epimorphic with val: <8 11 18 36 57| Scale is weakly epimorphic with val: <8 12 15 30 56| Scale is weakly epimorphic with val: <8 12 15 32 57| Scale is weakly epimorphic with val: <8 12 15 33 56| Scale is weakly epimorphic with val: <8 12 15 36 56| Scale is weakly epimorphic with val: <8 12 16 31 57| Scale is weakly epimorphic with val: <8 12 16 33 58| Scale is weakly epimorphic with val: <8 12 16 34 57| Scale is weakly epimorphic with val: <8 12 17 32 58| Scale is weakly epimorphic with val: <8 12 17 34 56| Scale is weakly epimorphic with val: <8 12 17 35 58| Scale is weakly epimorphic with val: <8 12 18 35 57| Scale is weakly epimorphic with val: <8 12 19 36 58|
FIT/MODE
3: 0 1 2 N G T3 SD: 70.0235 c. M: 90.0694 c. 4: 1 1 2 P M ME S SD: 25.3222 c. M:-43.2871 c. 5: 1 2 2 SP M ME S SD: 26.8634 c. M:-42.7426 c. 6: 1 2 3 P T3 SD: 4.2052 c. M: 7.0619 c. 19: 3 7 9 SP T3 SD: 3.7957 c. M:-6.0446 c. 23: 4 8 11 SP T3 SD: 3.7971 c. M:-5.3924 c. 25: 4 9 12 SP T3 SD: 1.8944 c. M:-2.8990 c. 31: 5 11 15 SP T3 SD: 0.7622 c. M:-0.9711 c. 37: 6 13 18 SP T3 SD: 0.3274 c. M: 0.4601 c. 142: 23 50 69 SP T3 SD: 0.3215 c. M: 0.5549 c. 165: 27 58 80 SP T3 SD: 0.3213 c. M:-0.4843 c. 171: 28 60 83 SP T3 SD: 0.2274 c. M:-0.3271 c. 177: 29 62 86 SP T3 SD: 0.2179 c. M:-0.3764 c. 202: 33 71 98 SP T3 SD: 0.2095 c. M:-0.3348 c. 208: 34 73 101 SP T3 SD: 0.1288 c. M:-0.1870 c. 245: 40 86 119 SP T3 SD: 0.0600 c. M:-0.0893 c. 282: 46 99 137 SP T3 SD: 0.0101 c. M:-0.0172 c. 883: 144 310 429 SP T3 SD: 0.0068 c. M: 0.0114 c. 1165: 190 409 566 SP T3 SD: 0.0048 c. M: 0.0080 c. 1447: 236 508 703 SP T3 SD: 0.0045 c. M: 0.0059 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: 51.6762 cents 6 x 7:8 S SD: 5.3933 cents 7 x 8:9 S SD: 33.8548 cents 8 x 9:11 SD: 37.2833 cents 9 x 10:12 S SD: 36.8403 cents 11:12:13:15 SD: 28.7307 cents 12:13:14:16 S SD: 19.4514 cents 14:15:16:19 SD: 18.3186 cents 15:16:17:20 SD: 16.6094 cents 17:18:20:23 SD: 13.2996 cents 18:19:21:24 SD: 5.4730 cents 24:25:28:32 SD: 5.0298 cents 38:40:44:51 SD: 4.6125 cents 39:41:45:52 SD: 3.3048 cents 45:47:52:60 SD: 2.7631 cents 57:60:66:76 SD: 2.6373 cents 62:65:72:83 SD: 2.5091 cents 63:66:73:84 SD: 0.4129 cents 144:151:167:192 SD: 0.3510 cents 207:217:240:276 SD: 0.1510 cents 270:283:313:360 SD: 0.1015 cents