Scala analysis: 257_C17
Chromatic tetrachord 243/230 * 115/108 * 32/27, Ps.-Philolaus?
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 243/230 95.186943 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 243/230 95.1869 2: 115/108 108.7231 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 243/230 95.187 cents 1: 1 115/108 108.723 cents 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 144/115 389.322 cents 2: 1 920/729 402.858 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 : 95.2 203.9 498.0 95.2 : 108.7 402.9 498.0 203.9: 294.1 389.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 95.1869 .. 294.1350 cents 7360/6561, 198.9481 cents 243/230, 95.1869 cents 2: 203.9100 .. 402.8581 cents 7360/6561, 198.9481 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 243/230, 95.1869 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.744094 Largest / Average step : 1.771737 Largest / Smallest step : 3.090077 Median interval of one step : 115/108, 108.7231 cents, amount: 1 Least squares average step : 142.65300 cents, oct.: 427.95899 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1104-tone equal temperament with octave 4/3 degrees: 211 452 1104 Least number of segments generator : 553 of 249.474 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 715 of 322.556 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 90.22500 cents Scale diversity : 1.098977 Lumma stability : 0.382242 Lumma impropriety factor : 0.181158 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 : 13225/13122, 13.5361 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% Limited inverse transpositions with margin 185.4119 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 729 (O: 243 U: 729) Highest odd numerator or denominator: 243 Scale harmonicity : 0.014391 Average absolute harmonicity : 0.116734 Specific harmonicity : 0.074489 Fundamental : 1/2760, -11.4305 octaves, 0.0948 Hz. Guide tone : 972, 9.9248 octaves, 254300.049 Hz. Exponens Consonantiae : 2.682720E+06, 21.35527 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 248.5, average 82.83333 Mersenne's string divisions : 56287 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.68385, average 2.56128 Vogel's harmonic complexity : 30.00000 Wille's k value : 1552 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 27.69271, average 4.61545 Lattice compactness (without 2's) : 20.67719, average 3.44620 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.66667 6 3: -1 .. 5 2.00000 8 2 5: -1 .. 0 -0.33333 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 4 / 3 = 1.33333 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <7 11 15 31| Scale is weakly epimorphic with val: <7 11 15 34| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 16 36| Scale is weakly epimorphic with val: <7 11 17 32| Scale is weakly epimorphic with val: <7 11 17 35| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 11 19 36| Scale is weakly epimorphic with val: <7 12 15 31| Scale is weakly epimorphic with val: <7 12 15 34| Scale is weakly epimorphic with val: <7 12 16 30| Scale is weakly epimorphic with val: <7 12 16 33| Scale is weakly epimorphic with val: <7 12 16 36| Scale is weakly epimorphic with val: <7 12 17 32| Scale is weakly epimorphic with val: <7 12 17 35| Scale is weakly epimorphic with val: <7 12 18 31| Scale is weakly epimorphic with val: <7 12 18 34| Scale is weakly epimorphic with val: <7 12 19 30| Scale is weakly epimorphic with val: <7 12 19 33| Scale is weakly epimorphic with val: <7 12 19 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 59.1512 c. M: 95.1869 c. 4: 1 1 2 P M ME S SD: 31.0647 c. M:-45.1125 c. 5: 1 1 3 N M DE S SD: 3.7224 c. M: 4.6920 c. 22: 4 5 13 N T3 SD: 2.6767 c. M: 4.6333 c. 27: 5 6 16 N T3 SD: 1.8024 c. M: 2.9564 c. 32: 6 7 19 N T3 SD: 1.3840 c. M: 1.8035 c. 37: 7 8 22 N T3 SD: 1.2813 c. M: 1.9999 c. 63: 12 14 37 N T3 SD: 0.9605 c. M:-1.6324 c. 68: 13 15 40 N T3 SD: 0.6742 c. M:-1.1674 c. 73: 14 16 43 N T3 SD: 0.4812 c. M:-0.7660 c. 78: 15 17 46 N T3 SD: 0.4173 c. M:-0.5909 c. 100: 19 22 59 N T3 SD: 0.3629 c. M: 0.5584 c. 105: 20 23 62 N T3 SD: 0.1878 c. M: 0.3212 c. 110: 21 24 65 N T3 SD: 0.1128 c. M: 0.1643 c. 288: 55 63 170 N T3 SD: 0.0967 c. M:-0.1501 c. 293: 56 64 173 N T3 SD: 0.0390 c. M:-0.0675 c. 403: 77 88 238 N T3 SD: 0.0158 c. M: 0.0270 c. 701: 134 153 414 N T3 SD: 0.0100 c. M:-0.0171 c. 1104: 211 241 652 N T3 SD: 0.0006 c. M:-0.0010 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: 70.0332 cents 6 x 7:8 S SD: 31.4805 cents 7 x 8:9 S SD: 34.3053 cents 8 x 9:11 SD: 26.6365 cents 9 x 10:12 S SD: 10.7531 cents 10 x 11:13 SD: 29.3037 cents 11 x 12:15 S SD: 32.9836 cents 12:13:14:16 S SD: 25.4872 cents 13:14:15:17 SD: 21.4674 cents 14:15:16:19 SD: 15.8837 cents 15:16:17:20 SD: 6.9679 cents 31:33:35:41 SD: 6.7098 cents 32:34:36:43 SD: 5.5471 cents 33:35:37:44 SD: 2.9573 cents 54:57:61:72 SD: 2.4280 cents 57:60:64:76 SD: 2.4082 cents 71:75:80:95 SD: 2.2223 cents 72:76:81:96 SD: 0.5280 cents 159:168:179:212 SD: 0.4056 cents 177:187:199:236 SD: 0.3626 cents 231:244:260:308 SD: 0.3080 cents 249:263:280:332 SD: 0.3044 cents 264:279:297:352 SD: 0.1619 cents 336:355:378:448 SD: 0.0141 cents