Scala analysis: 142_C3
Chromatic tetrachord 64/63 * 17/16 * 21/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/63 27.264092 septimal comma, Archytas' comma 2: 68/63 132.219501 supraminor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 21/17 365.8255 submajor third 1: 64/63 27.2641 septimal comma, Archytas' comma 2: 17/16 104.9554 17th harmonic 3: 21/17 365.8255 submajor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 17/16 104.955 cents 17th harmonic 1: 1 21/17 365.825 cents submajor third 2: 1 68/63 132.220 cents supraminor second 2: 1 64/51 393.090 cents 2: 1 21/16 470.781 cents narrow fourth 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 : 27.3 132.2 498.0 27.3 : 105.0 470.8 498.0 132.2: 365.8 393.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 365.8255 cents 1323/1088, 338.5614 cents 64/63, 27.2641 cents 2: 132.2195 .. 470.7809 cents 1323/1088, 338.5614 cents 1156/1323,-233.6060 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 21/17, 365.8255 cents Average / Smallest step : 6.089145 Largest / Average step : 2.203569 Largest / Smallest step : 13.417850 Median interval of one step : 17/16, 104.9554 cents, amount: 1 Least squares average step : 127.55986 cents, oct.: 382.67959 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1955-tone equal temperament with octave 4/3 degrees: 107 519 1955 Least number of segments generator : 978 of 249.150 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1852 of 471.805 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 27.26409 cents Scale diversity : 0.529734 Lumma stability : 0.109484 Lumma impropriety factor : 0.469046 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 : 64/63, 27.2641 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 63 (O: 21 U: 63) Highest odd numerator or denominator: 63 Scale harmonicity : 0.019329 Average absolute harmonicity : 0.093829 Specific harmonicity : 0.095146 Fundamental : 1/63, -5.9773 octaves, 4.1528 Hz. Guide tone : 1088, 10.0875 octaves, 284648.615 Hz. Exponens Consonantiae : 6.854400E+04, 16.06474 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 132.5, average 44.16667 Mersenne's string divisions : 116459 Sum of van Prooijen's expressibility: 4.07580, average 1.35860 Sum of Tenney's harmonic distance : 8.31655, average 2.77218 Vogel's harmonic complexity : 12.33333 Wille's k value : 10 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 21.89927, average 3.64988 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 3.33333 10 3: -2 ..-1 -1.66667 5 1 7: -1 .. 0 -0.66667 2 1 17: 0 .. 1 0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 18 29| Scale is weakly epimorphic with val: <6 10 21 32| Scale is weakly epimorphic with val: <6 11 18 31| Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 10 19 33| Scale is weakly epimorphic with val: <7 10 20 29| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 33| Scale is JI-epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 21 33| Scale is weakly epimorphic with val: <7 11 22 29| Scale is weakly epimorphic with val: <7 11 22 32| Scale is weakly epimorphic with val: <7 12 20 33| Scale is weakly epimorphic with val: <8 11 19 28| Scale is weakly epimorphic with val: <8 11 22 31| Scale is weakly epimorphic with val: <8 12 19 30| Scale is weakly epimorphic with val: <8 12 21 28| Scale is weakly epimorphic with val: <8 12 21 31| Scale is weakly epimorphic with val: <8 12 22 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 25.0697 c. M:-33.7955 c. 4: 0 1 3 N G T3 SD: 16.3580 c. M: 27.2641 c. 11: 1 2 8 N T3 SD: 10.6066 c. M:-18.0127 c. 12: 1 2 9 N T3 SD: 9.3485 c. M:-14.2397 c. 14: 1 3 10 N T3 SD: 7.5422 c. M:-10.0791 c. 15: 1 3 11 N T3 SD: 3.4459 c. M:-5.9389 c. 19: 1 4 14 N T3 SD: 0.9017 c. M: 1.1550 c. 53: 3 11 39 N T3 SD: 0.6572 c. M:-0.9271 c. 71: 4 15 52 N T3 SD: 0.7650 c. M:-1.0601 c. 72: 4 15 53 N T3 SD: 0.5131 c. M: 0.7910 c. 75: 4 16 55 N T3 SD: 0.5302 c. M: 0.7017 c. 90: 5 19 66 N T3 SD: 0.4144 c. M:-0.5925 c. 109: 6 23 80 N T3 SD: 0.1877 c. M:-0.2879 c. 128: 7 27 94 N T3 SD: 0.0454 c. M:-0.0737 c. 403: 22 85 296 N T3 SD: 0.0445 c. M: 0.0755 c. 456: 25 96 335 N T3 SD: 0.0433 c. M: 0.0628 c. 531: 29 112 390 N T3 SD: 0.0407 c. M: 0.0639 c. 565: 31 119 415 N T3 SD: 0.0361 c. M:-0.0623 c. 584: 32 123 429 N T3 SD: 0.0242 c. M: 0.0329 c. 693: 38 146 509 N T3 SD: 0.0283 c. M:-0.0457 c. 712: 39 150 523 N T3 SD: 0.0124 c. M:-0.0165 c. 840: 46 177 617 N T3 SD: 0.0057 c. M:-0.0098 c. 968: 53 204 711 N T3 SD: 0.0061 c. M:-0.0094 c. 1808: 99 381 1328 N T3 SD: 0.0050 c. M:-0.0072 c. 1827: 100 385 1342 N T3 SD: 0.0047 c. M: 0.0072 c. 1955: 107 412 1436 N T3 SD: 0.0033 c. M: 0.0054 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 67.3257 cents 7 x 8:9 S SD: 58.6432 cents 8 x 9:11 SD: 44.6585 cents 9 x 10:12 S SD: 25.0921 cents 10 x 11:13 SD: 27.3679 cents 11 x 12:15 S SD: 21.5225 cents 12 x 13:16 SD: 3.1766 cents 13 x 14:17 SD: 16.9226 cents 14 x 15:19 SD: 16.5996 cents 15 x 16:20 S SD: 10.2441 cents 16 x 17:21 SD: 19.2786 cents 17 x 18:23 SD: 20.8886 cents 18 x 19:24 SD: 19.3082 cents 19 x 21:25 SD: 23.5095 cents 20 x 22:27 SD: 19.6046 cents 21 x 23:28 SD: 12.6370 cents 27:28:29:36 SD: 12.2322 cents 30:31:32:40 S SD: 11.9730 cents 33:34:36:44 SD: 10.1951 cents 34:35:37:45 SD: 9.9406 cents 35:36:38:47 SD: 8.9284 cents 36:37:39:48 SD: 7.0490 cents 38:39:41:51 SD: 7.0144 cents 39:40:42:52 SD: 5.6749 cents 47:48:51:63 SD: 5.3026 cents 48:49:52:64 SD: 3.5194 cents 51:52:55:68 SD: 2.1758 cents 60:61:65:80 SD: 2.1651 cents 63:64:68:84 SD: 0.0000 cents