Scala analysis: 272_C19
Chromatic tetrachord 132/127 * 127/117 * 13/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 132/127 66.851319 2: 44/39 208.835280 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/11 289.2097 tridecimal minor third 1: 132/127 66.8513 2: 127/117 141.9840 3: 13/11 289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 132/127 66.851 cents 1: 1 127/117 141.984 cents 1: 1 13/11 289.210 cents tridecimal minor third 2: 1 44/39 208.835 cents 2: 1 156/127 356.061 cents 2: 1 127/99 431.194 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 : 66.9 208.8 498.0 66.9 : 142.0 431.2 498.0 208.8: 289.2 356.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.8513 .. 289.2097 cents 1651/1452, 222.3584 cents 132/127, 66.8513 cents 2: 208.8353 .. 431.1937 cents 1651/1452, 222.3584 cents 484/507,-80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 132/127, 66.8513 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/11, 289.2097 cents Average / Smallest step : 2.483347 Largest / Average step : 1.742070 Largest / Smallest step : 4.326163 Median interval of one step : 127/117, 141.9840 cents, amount: 1 Least squares average step : 141.33263 cents, oct.: 423.99790 cents Scale is not proper Scale has trivalence property Scale is a mode of a 663-tone equal temperament with octave 4/3 degrees: 89 278 663 Least number of segments generator : 332 of 249.398 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 376 of 282.451 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 66.85132 cents Scale diversity : 1.012544 Lumma stability : 0.268455 Lumma impropriety factor : 0.161380 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 : 132/127, 66.8513 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% -- Rational properties -- Prime limit : 127 Odd number limit : 127 (O: 127 U: 127) Highest odd numerator or denominator: 127 Scale harmonicity : 0.020978 Fundamental : 1/4953, -12.2741 octaves, 0.0528 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 6.537960E+05, 19.31848 octaves Euler's gradus suavitatis : 155 Sum of Mann's harmonic distance : 174.5, average 58.16667 Mersenne's string divisions : 21497 Sum of van Prooijen's expressibility: 4.17199, average 1.39066 Sum of Tenney's harmonic distance : 8.53808, average 2.84603 Vogel's harmonic complexity : 104.66667 Wille's k value : 825 Wilson's harmonic complexity : 157 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.21766, average 2.20294 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 1 -0.33333 3 1 11: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 127: -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: <7 10 24 25 52| Scale is weakly epimorphic with val: <7 10 25 26 50| Scale is weakly epimorphic with val: <7 10 26 27 51| Scale is weakly epimorphic with val: <7 10 27 28 52| Scale is weakly epimorphic with val: <7 11 23 25 52| Scale is weakly epimorphic with val: <7 11 23 27 50| Scale is weakly epimorphic with val: <7 11 23 28 52| Scale is weakly epimorphic with val: <7 11 23 30 50| Scale is weakly epimorphic with val: <7 11 24 25 51| Scale is weakly epimorphic with val: <7 11 24 26 50| Scale is weakly epimorphic with val: <7 11 24 28 51| Scale is weakly epimorphic with val: <7 11 24 29 50| Scale is weakly epimorphic with val: <7 11 25 26 52| Scale is weakly epimorphic with val: <7 11 25 27 51| = patent Scale is weakly epimorphic with val: <7 11 25 29 52| Scale is weakly epimorphic with val: <7 11 25 30 51| Scale is JI-epimorphic with val: <7 11 26 27 50| Scale is weakly epimorphic with val: <7 11 26 28 52| Scale is weakly epimorphic with val: <7 11 26 30 50| Scale is JI-epimorphic with val: <7 11 27 28 51| Scale is weakly epimorphic with val: <7 11 27 29 50| Scale is weakly epimorphic with val: <7 12 27 28 50| Scale is weakly epimorphic with val: <8 11 23 25 52| Scale is weakly epimorphic with val: <8 11 24 26 50| Scale is weakly epimorphic with val: <8 11 25 27 51| Scale is weakly epimorphic with val: <8 11 26 27 50| Scale is weakly epimorphic with val: <8 11 26 28 52| Scale is weakly epimorphic with val: <8 11 26 30 50| Scale is weakly epimorphic with val: <8 11 27 28 51| Scale is weakly epimorphic with val: <8 11 27 29 50| Scale is weakly epimorphic with val: <8 12 24 25 50| Scale is weakly epimorphic with val: <8 12 25 26 51| Scale is weakly epimorphic with val: <8 12 25 27 50| Scale is weakly epimorphic with val: <8 12 25 30 50| Scale is weakly epimorphic with val: <8 12 26 27 52| Scale is weakly epimorphic with val: <8 12 26 28 51| Scale is weakly epimorphic with val: <8 12 27 28 50| Scale is weakly epimorphic with val: <8 12 27 29 52|
FIT/MODE
3: 0 1 2 N G T3 SD: 45.8355 c. M: 66.8513 c. 5: 1 1 3 N M DE S SD: 19.7109 c. M:-32.7577 c. 7: 1 2 4 N T3 SD: 3.6400 c. M:-4.6126 c. 22: 3 6 13 N T3 SD: 3.0020 c. M: 5.0896 c. 24: 3 7 14 N T3 SD: 2.7601 c. M: 4.5957 c. 29: 4 8 17 N T3 SD: 1.9107 c. M: 2.7477 c. 31: 4 9 18 N T3 SD: 1.4939 c. M: 2.5874 c. 36: 5 10 21 N T3 SD: 1.5409 c. M:-2.3216 c. 38: 5 11 22 N T3 SD: 0.9116 c. M: 1.3191 c. 45: 6 13 26 N T3 SD: 0.8760 c. M:-1.4504 c. 60: 8 17 35 N T3 SD: 0.8024 c. M: 1.3165 c. 67: 9 19 39 N T3 SD: 0.4035 c. M: 0.6971 c. 74: 10 21 43 N T3 SD: 0.2842 c. M:-0.4521 c. 105: 14 30 61 N T3 SD: 0.2680 c. M: 0.4453 c. 112: 15 32 65 N T3 SD: 0.1286 c. M:-0.1657 c. 179: 24 51 104 N T3 SD: 0.1004 c. M: 0.1572 c. 186: 25 53 108 N T3 SD: 0.0537 c. M:-0.0902 c. 298: 40 85 173 N T3 SD: 0.0440 c. M:-0.0762 c. 365: 49 104 212 N T3 SD: 0.0383 c. M: 0.0657 c. 477: 64 136 277 N T3 SD: 0.0173 c. M: 0.0277 c. 663: 89 189 385 N T3 SD: 0.0033 c. M:-0.0054 c. 1803: 242 514 1047 N T3 SD: 0.0032 c. M: 0.0044 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: 68.0849 cents 6 x 7:8 S SD: 29.0178 cents 7 x 8:9 S SD: 33.4032 cents 8 x 9:11 SD: 26.7501 cents 9 x 10:12 S SD: 13.2158 cents 10 x 11:13 SD: 30.9932 cents 11 x 12:15 S SD: 35.0025 cents 12 x 14:16 S SD: 29.0178 cents 13:14:15:17 SD: 26.7073 cents 14:15:16:19 SD: 21.6123 cents 15:16:17:20 SD: 15.1872 cents 17:18:19:23 SD: 14.6604 cents 18:19:20:24 S SD: 12.5356 cents 21:22:24:28 S SD: 8.7326 cents 22:23:25:29 SD: 8.4931 cents 23:24:26:31 SD: 6.7381 cents 24:25:27:32 SD: 2.0779 cents 54:56:61:72 SD: 1.4873 cents 78:81:88:104 SD: 0.5047 cents 102:106:115:136 SD: 0.3953 cents 180:187:203:240 SD: 0.3453 cents 282:293:318:376 SD: 0.3443 cents 303:315:342:404 SD: 0.2903 cents 327:340:369:436 SD: 0.2454 cents 381:396:430:508 SD: 0.2065 cents 405:421:457:540 SD: 0.1231 cents 483:502:545:644 SD: 0.0834 cents 507:527:572:676 SD: 0.0431 cents 585:608:660:780 SD: 0.0299 cents