Scala analysis: 381_D3
Diatonic tetrachord 28/27 * 180/161 * 23/20
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 80/69 256.084366 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/20 241.9606 1: 28/27 62.9609 Archytas' 1/3-tone 2: 180/161 193.1235 3: 23/20 241.9606
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 180/161 193.123 cents 1: 1 23/20 241.961 cents 2: 1 80/69 256.084 cents 2: 1 161/135 304.922 cents 2: 1 9/7 435.084 cents septimal major third, BP third 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 : 63.0 256.1 498.0 63.0 : 193.1 435.1 498.0 256.1: 242.0 304.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 241.9606 cents 621/560, 178.9997 cents 28/27, 62.9609 cents 2: 256.0844 .. 435.0841 cents 621/560, 178.9997 cents 1600/1587, 14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/20, 241.9606 cents Average / Smallest step : 2.636795 Largest / Average step : 1.457462 Largest / Smallest step : 3.843030 Median interval of one step : 180/161, 193.1235 cents, amount: 1 Least squares average step : 147.80462 cents, oct.: 443.41385 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1764-tone equal temperament with octave 4/3 degrees: 223 907 1764 Least number of segments generator : 883 of 249.305 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 995 of 280.927 cents and inv. generated superset size: 73 = 70 more = 2433.333% 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 : 0.873848 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.281191 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 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 23 Odd number limit : 161 (O: 161 U: 161) Highest odd numerator or denominator: 69 Scale harmonicity : 0.014130 Average absolute harmonicity : 0.093904 Specific harmonicity : 0.075358 Fundamental : 1/621, -9.2784 octaves, 0.4213 Hz. Guide tone : 560, 9.1293 octaves, 146510.317 Hz. Exponens Consonantiae : 3.477600E+05, 18.40773 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 105.5, average 35.16667 Mersenne's string divisions : 57365 Sum of van Prooijen's expressibility: 3.74733, average 1.24911 Sum of Tenney's harmonic distance : 7.69964, average 2.56655 Vogel's harmonic complexity : 26.00000 Wille's k value : 103 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 18.33881, average 3.05647 Lattice compactness (without 2's) : 12.19036, average 2.03173 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 2.66667 8 3: -3 ..-1 -1.66667 5 1 5: 0 .. 1 0.33333 1 7: 0 .. 1 0.33333 1 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 21 31| Scale is weakly epimorphic with val: <6 10 15 21 34| Scale is weakly epimorphic with val: <6 10 16 21 32| Scale is weakly epimorphic with val: <6 10 16 21 35| Scale is weakly epimorphic with val: <6 10 17 21 30| Scale is weakly epimorphic with val: <6 10 17 21 33| Scale is weakly epimorphic with val: <6 10 17 21 36| Scale is weakly epimorphic with val: <6 10 18 21 31| Scale is weakly epimorphic with val: <6 10 18 21 34| Scale is weakly epimorphic with val: <6 10 19 19 30| Scale is weakly epimorphic with val: <6 10 19 21 32| Scale is weakly epimorphic with val: <6 10 19 21 35| Scale is weakly epimorphic with val: <6 10 19 22 30| Scale is weakly epimorphic with val: <7 10 15 18 30| Scale is weakly epimorphic with val: <7 10 15 19 31| Scale is weakly epimorphic with val: <7 10 15 19 34| Scale is weakly epimorphic with val: <7 10 15 21 30| Scale is weakly epimorphic with val: <7 10 16 18 31| Scale is weakly epimorphic with val: <7 10 16 19 32| Scale is weakly epimorphic with val: <7 10 16 19 35| Scale is weakly epimorphic with val: <7 10 16 21 31| Scale is weakly epimorphic with val: <7 10 17 18 32| Scale is weakly epimorphic with val: <7 10 17 19 30| Scale is weakly epimorphic with val: <7 10 17 19 33| Scale is weakly epimorphic with val: <7 10 17 19 36| Scale is weakly epimorphic with val: <7 10 17 21 32| Scale is weakly epimorphic with val: <7 10 18 18 33| Scale is weakly epimorphic with val: <7 10 18 19 31| Scale is weakly epimorphic with val: <7 10 18 19 34| Scale is weakly epimorphic with val: <7 10 18 21 33| Scale is weakly epimorphic with val: <7 10 19 19 32| Scale is weakly epimorphic with val: <7 10 19 19 35| Scale is weakly epimorphic with val: <7 10 19 21 34| Scale is weakly epimorphic with val: <7 11 15 18 31| Scale is weakly epimorphic with val: <7 11 15 18 34| Scale is JI-epimorphic with val: <7 11 15 20 30| Scale is weakly epimorphic with val: <7 11 15 20 33| Scale is weakly epimorphic with val: <7 11 15 20 36| Scale is weakly epimorphic with val: <7 11 15 21 31| Scale is weakly epimorphic with val: <7 11 15 21 34| Scale is weakly epimorphic with val: <7 11 16 18 32| Scale is weakly epimorphic with val: <7 11 16 18 35| Scale is JI-epimorphic with val: <7 11 16 20 31| Scale is weakly epimorphic with val: <7 11 16 20 34| Scale is weakly epimorphic with val: <7 11 16 21 32| Scale is weakly epimorphic with val: <7 11 16 21 35| Scale is weakly epimorphic with val: <7 11 17 18 30| Scale is weakly epimorphic with val: <7 11 17 18 33| Scale is weakly epimorphic with val: <7 11 17 18 36| Scale is JI-epimorphic with val: <7 11 17 20 32| Scale is weakly epimorphic with val: <7 11 17 20 35| Scale is weakly epimorphic with val: <7 11 17 21 30| Scale is weakly epimorphic with val: <7 11 17 21 33| Scale is weakly epimorphic with val: <7 11 17 21 36| Scale is weakly epimorphic with val: <7 11 18 18 31| Scale is weakly epimorphic with val: <7 11 18 18 34| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is JI-epimorphic with val: <7 11 18 20 33| Scale is weakly epimorphic with val: <7 11 18 20 36| Scale is weakly epimorphic with val: <7 11 18 21 31| Scale is weakly epimorphic with val: <7 11 18 21 34| Scale is weakly epimorphic with val: <7 11 19 20 31| Scale is JI-epimorphic with val: <7 11 19 20 34| Scale is weakly epimorphic with val: <7 11 19 21 32| Scale is weakly epimorphic with val: <7 11 19 21 35| Scale is weakly epimorphic with val: <7 12 17 20 30| Scale is weakly epimorphic with val: <7 12 18 20 31| Scale is weakly epimorphic with val: <7 12 19 20 32| Scale is weakly epimorphic with val: <8 11 15 18 33| Scale is weakly epimorphic with val: <8 11 15 20 32| Scale is weakly epimorphic with val: <8 11 15 20 35| Scale is weakly epimorphic with val: <8 11 15 21 33| Scale is weakly epimorphic with val: <8 11 16 18 34| Scale is weakly epimorphic with val: <8 11 16 20 30| Scale is weakly epimorphic with val: <8 11 16 20 33| Scale is weakly epimorphic with val: <8 11 16 20 36| Scale is weakly epimorphic with val: <8 11 16 21 34| Scale is weakly epimorphic with val: <8 11 17 18 35| Scale is weakly epimorphic with val: <8 11 17 20 31| Scale is weakly epimorphic with val: <8 11 17 20 34| Scale is weakly epimorphic with val: <8 11 17 21 35| Scale is weakly epimorphic with val: <8 11 18 18 36| Scale is weakly epimorphic with val: <8 11 18 20 32| Scale is weakly epimorphic with val: <8 11 18 20 35| Scale is weakly epimorphic with val: <8 11 18 21 36| Scale is weakly epimorphic with val: <8 11 19 20 30| Scale is weakly epimorphic with val: <8 11 19 20 33| Scale is weakly epimorphic with val: <8 11 19 20 36| Scale is weakly epimorphic with val: <8 12 15 19 32| Scale is weakly epimorphic with val: <8 12 15 22 32| Scale is weakly epimorphic with val: <8 12 16 19 33| Scale is weakly epimorphic with val: <8 12 16 22 33| Scale is weakly epimorphic with val: <8 12 17 19 34| Scale is weakly epimorphic with val: <8 12 17 22 34| Scale is weakly epimorphic with val: <8 12 18 19 35| Scale is weakly epimorphic with val: <8 12 18 22 35| Scale is weakly epimorphic with val: <8 12 19 19 36| Scale is weakly epimorphic with val: <8 12 19 22 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 63.4470 c. M: 90.0694 c. 4: 0 2 2 P M DE S SD: 36.5784 c. M: 62.9609 c. 6: 1 2 3 P T3 SD: 12.2710 c. M:-20.0466 c. 8: 1 3 4 P T3 SD: 4.0975 c. M: 7.0619 c. 23: 3 9 11 SP T3 SD: 2.4619 c. M:-3.7652 c. 25: 3 10 12 SP T3 SD: 2.4910 c. M: 3.1955 c. 31: 4 12 15 SP T3 SD: 0.9382 c. M:-1.3030 c. 39: 5 15 19 SP T3 SD: 0.6460 c. M:-0.8910 c. 64: 8 25 31 SP T3 SD: 0.5819 c. M:-0.7201 c. 70: 9 27 34 SP T3 SD: 0.6205 c. M:-1.0735 c. 72: 9 28 35 SP T3 SD: 0.4157 c. M: 0.7053 c. 103: 13 40 50 SP T3 SD: 0.1248 c. M:-0.1912 c. 142: 18 55 69 SP T3 SD: 0.1027 c. M:-0.1716 c. 214: 27 83 104 SP T3 SD: 0.0849 c. M: 0.1235 c. 245: 31 95 119 SP T3 SD: 0.0450 c. M:-0.0570 c. 356: 45 138 173 SP T3 SD: 0.0387 c. M: 0.0669 c. 459: 58 178 223 SP T3 SD: 0.0165 c. M: 0.0271 c. 601: 76 233 292 SP T3 SD: 0.0154 c. M:-0.0198 c. 704: 89 273 342 SP T3 SD: 0.0074 c. M:-0.0126 c. 1163: 147 451 565 SP T3 SD: 0.0059 c. M: 0.0094 c. 1305: 165 506 634 SP T3 SD: 0.0060 c. M:-0.0103 c. 1764: 223 684 857 SP T3 SD: 0.0020 c. M: 0.0034 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 10 x 12:13 S SD: 36.9736 cents 11:12:13:15 SD: 33.8264 cents 12:13:14:16 S SD: 25.4591 cents 13:14:15:17 SD: 24.6502 cents 14:15:16:19 SD: 22.9726 cents 15:16:17:20 SD: 20.8985 cents 17:18:20:23 SD: 16.9085 cents 18:19:21:24 SD: 10.8284 cents 21:22:24:28 S SD: 10.1623 cents 23:24:27:31 SD: 10.1529 cents 24:25:28:32 SD: 4.4199 cents 30:31:35:40 SD: 4.1462 cents 49:51:57:65 SD: 4.0952 cents 50:52:58:67 SD: 3.3284 cents 51:53:59:68 SD: 1.7580 cents 57:59:66:76 SD: 1.3252 cents 81:84:94:108 SD: 0.5341 cents 132:137:153:176 SD: 0.4961 cents 138:143:160:184 SD: 0.4482 cents 189:196:219:252 SD: 0.3436 cents 213:221:247:284 SD: 0.3075 cents 270:280:313:360 SD: 0.0802 cents 351:364:407:468 SD: 0.0617 cents