Scala analysis: 329_C25
Chromatic tetrachord 78/73 * 73/68 * 136/117
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78/73 114.693192 2: 39/34 237.527253 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 136/117 260.5177 1: 78/73 114.6932 2: 73/68 122.8341 3: 136/117 260.5177
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 78/73 114.693 cents 1: 1 73/68 122.834 cents 1: 1 136/117 260.518 cents 2: 1 39/34 237.527 cents 2: 1 272/219 375.211 cents 2: 1 146/117 383.352 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 : 114.7 237.5 498.0 114.7: 122.8 383.4 498.0 237.5: 260.5 375.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 114.6932 .. 260.5177 cents 4964/4563, 145.8246 cents 78/73, 114.6932 cents 2: 237.5273 .. 383.3518 cents 4964/4563, 145.8246 cents 4563/4624,-22.9905 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 78/73, 114.6932 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 136/117, 260.5177 cents Average / Smallest step : 1.447470 Largest / Average step : 1.569242 Largest / Smallest step : 2.271432 Median interval of one step : 73/68, 122.8341 cents, amount: 1 Least squares average step : 148.84876 cents, oct.: 446.54629 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1776-tone equal temperament with octave 4/3 degrees: 409 847 1776 Least number of segments generator : 889 of 249.303 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 929 of 260.520 cents and inv. generated superset size: 56 = 53 more = 1866.667% 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 : 1.134465 Lumma stability : 0.460574 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 : 5329/5304, 8.1409 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 137.6837 cents: 2 -- Rational properties -- Prime limit : 73 Odd number limit : 219 (O: 73 U: 219) Highest odd numerator or denominator: 73 Scale harmonicity : 0.016500 Fundamental : 1/7446, -12.8622 octaves, 0.0351 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 1.161576E+06, 20.14765 octaves Euler's gradus suavitatis : 108 Sum of Mann's harmonic distance : 115.5, average 38.50000 Mersenne's string divisions : 77161 Sum of van Prooijen's expressibility: 3.93151, average 1.31050 Sum of Tenney's harmonic distance : 7.95714, average 2.65238 Vogel's harmonic complexity : 74.33333 Wille's k value : 4270 Wilson's harmonic complexity : 109 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.52666, average 2.42111 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 1 0.33333 3 1 13: 0 .. 1 0.66667 2 17: -1 .. 0 -0.33333 1 1 73: -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 26 27 44| Scale is weakly epimorphic with val: <6 10 27 28 45| Scale is weakly epimorphic with val: <6 10 28 29 46| Scale is weakly epimorphic with val: <6 10 29 30 44| Scale is weakly epimorphic with val: <6 10 30 31 45| Scale is weakly epimorphic with val: <6 11 25 27 46| Scale is weakly epimorphic with val: <6 11 26 28 44| Scale is weakly epimorphic with val: <6 11 27 29 45| Scale is weakly epimorphic with val: <6 11 28 30 46| Scale is weakly epimorphic with val: <6 11 29 31 44| Scale is weakly epimorphic with val: <6 11 30 30 44| Scale is weakly epimorphic with val: <6 11 30 32 45| Scale is weakly epimorphic with val: <6 11 30 33 44| Scale is weakly epimorphic with val: <7 10 27 27 45| Scale is weakly epimorphic with val: <7 10 28 28 46| Scale is weakly epimorphic with val: <7 10 29 29 44| Scale is weakly epimorphic with val: <7 10 30 30 45| Scale is weakly epimorphic with val: <7 10 30 31 44| Scale is weakly epimorphic with val: <7 11 25 27 45| Scale is weakly epimorphic with val: <7 11 25 28 44| Scale is weakly epimorphic with val: <7 11 25 30 45| Scale is weakly epimorphic with val: <7 11 25 31 44| Scale is weakly epimorphic with val: <7 11 25 33 45| Scale is weakly epimorphic with val: <7 11 26 28 46| Scale is weakly epimorphic with val: <7 11 26 29 45| Scale is weakly epimorphic with val: <7 11 26 31 46| Scale is weakly epimorphic with val: <7 11 26 32 45| Scale is weakly epimorphic with val: <7 11 27 27 46| Scale is JI-epimorphic with val: <7 11 27 29 44| Scale is weakly epimorphic with val: <7 11 27 30 46| Scale is weakly epimorphic with val: <7 11 27 32 44| Scale is weakly epimorphic with val: <7 11 27 33 46| Scale is weakly epimorphic with val: <7 11 28 28 44| Scale is JI-epimorphic with val: <7 11 28 30 45| Scale is weakly epimorphic with val: <7 11 28 31 44| Scale is weakly epimorphic with val: <7 11 28 33 45| Scale is weakly epimorphic with val: <7 11 29 29 45| Scale is JI-epimorphic with val: <7 11 29 31 46| Scale is weakly epimorphic with val: <7 11 29 32 45| Scale is weakly epimorphic with val: <7 11 30 30 46| Scale is weakly epimorphic with val: <7 11 30 32 44| Scale is weakly epimorphic with val: <7 11 30 33 46| Scale is weakly epimorphic with val: <7 12 25 27 46| Scale is weakly epimorphic with val: <7 12 26 28 44| Scale is weakly epimorphic with val: <7 12 27 29 45| Scale is weakly epimorphic with val: <7 12 28 29 44| Scale is weakly epimorphic with val: <7 12 28 30 46| Scale is weakly epimorphic with val: <7 12 28 32 44| Scale is weakly epimorphic with val: <7 12 29 30 45| Scale is weakly epimorphic with val: <7 12 29 31 44| Scale is weakly epimorphic with val: <7 12 29 33 45| Scale is weakly epimorphic with val: <7 12 30 31 46| Scale is weakly epimorphic with val: <7 12 30 32 45| Scale is weakly epimorphic with val: <8 11 27 27 45| Scale is weakly epimorphic with val: <8 11 28 28 46| Scale is weakly epimorphic with val: <8 11 28 30 44| Scale is weakly epimorphic with val: <8 11 28 33 44| Scale is weakly epimorphic with val: <8 11 29 29 44| Scale is weakly epimorphic with val: <8 11 29 31 45| Scale is weakly epimorphic with val: <8 11 30 30 45| Scale is weakly epimorphic with val: <8 11 30 32 46| Scale is weakly epimorphic with val: <8 12 26 27 44| Scale is weakly epimorphic with val: <8 12 27 28 45| Scale is weakly epimorphic with val: <8 12 27 29 44| Scale is weakly epimorphic with val: <8 12 27 32 44| Scale is weakly epimorphic with val: <8 12 28 29 46| Scale is weakly epimorphic with val: <8 12 28 30 45| Scale is weakly epimorphic with val: <8 12 28 33 45| Scale is weakly epimorphic with val: <8 12 29 30 44| Scale is weakly epimorphic with val: <8 12 29 31 46| Scale is weakly epimorphic with val: <8 12 30 31 45|
FIT/MODE
3: 1 0 2 N G T3 SD: 50.8197 c. M: 71.5123 c. 4: 1 1 2 P M ME S SD: 8.7280 c. M:-11.4952 c. 13: 3 3 7 N M DE S SD: 4.4249 c. M: 7.6603 c. 17: 4 4 9 N M DE S SD: 2.3210 c. M: 3.1531 c. 21: 5 5 11 N M DE S SD: 2.2550 c. M:-3.8890 c. 36: 8 9 19 N T3 SD: 2.6836 c. M: 4.0165 c. 38: 9 9 20 N M DE S SD: 2.1020 c. M:-3.2648 c. 40: 9 10 21 N T3 SD: 1.6173 c. M: 2.6331 c. 44: 10 11 23 N T3 SD: 0.8726 c. M: 1.5011 c. 48: 11 12 25 N T3 SD: 0.7221 c. M:-1.1193 c. 61: 14 15 32 N T3 SD: 0.4884 c. M: 0.7518 c. 65: 15 16 34 N T3 SD: 0.1387 c. M:-0.2403 c. 174: 40 43 91 N T3 SD: 0.1185 c. M: 0.2001 c. 239: 55 59 125 N T3 SD: 0.0504 c. M: 0.0803 c. 304: 70 75 159 N T3 SD: 0.0171 c. M:-0.0271 c. 673: 155 166 352 N T3 SD: 0.0160 c. M:-0.0247 c. 977: 225 241 511 N T3 SD: 0.0150 c. M:-0.0254 c. 1038: 239 256 543 N T3 SD: 0.0157 c. M: 0.0202 c. 1103: 254 272 577 N T3 SD: 0.0111 c. M: 0.0189 c. 1168: 269 288 611 N T3 SD: 0.0120 c. M: 0.0178 c. 1342: 309 331 702 N T3 SD: 0.0111 c. M: 0.0167 c. 1407: 324 347 736 N T3 SD: 0.0059 c. M: 0.0090 c. 1472: 339 363 770 N T3 SD: 0.0060 c. M: 0.0085 c. 1711: 394 422 895 N T3 SD: 0.0038 c. M: 0.0060 c. 1776: 409 438 929 N T3 SD: 0.0022 c. M:-0.0030 c. 2080: 479 513 1088 N T3 SD: 0.0012 c. M:-0.0019 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 10:11 x 13 SD: 33.3630 cents 11:12:13:15 SD: 24.6682 cents 12:13:14:16 S SD: 12.6107 cents 13:14:15:17 SD: 12.5589 cents 14:15:16:19 SD: 10.5507 cents 15:16:17:20 SD: 7.0167 cents 27:29:31:36 SD: 3.0558 cents 42:45:48:56 S SD: 2.6441 cents 60:64:69:80 SD: 1.7773 cents 75:80:86:100 SD: 1.0068 cents 102:109:117:136 SD: 0.0725 cents 585:625:671:780 SD: 0.0681 cents