Scala analysis: 143_C3
Chromatic tetrachord 34/33 * 22/21 * 21/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 68/63 132.219501 supraminor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 21/17 365.8255 submajor third 1: 34/33 51.6825 2: 22/21 80.5370 undecimal minor semitone 3: 21/17 365.8255 submajor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 34/33 51.682 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 21/17 365.825 cents submajor third 2: 1 68/63 132.220 cents supraminor second 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 22/17 446.363 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 : 51.7 132.2 498.0 51.7 : 80.5 446.4 498.0 132.2: 365.8 417.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 365.8255 cents 693/578, 314.1430 cents 34/33, 51.6825 cents 2: 132.2195 .. 446.3625 cents 693/578, 314.1430 cents 1156/1323,-233.6060 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 21/17, 365.8255 cents Average / Smallest step : 3.212211 Largest / Average step : 2.203569 Largest / Smallest step : 7.078329 Median interval of one step : 22/21, 80.5370 cents, amount: 1 Least squares average step : 129.30403 cents, oct.: 387.91210 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1243-tone equal temperament with octave 4/3 degrees: 129 330 1243 Least number of segments generator : 622 of 249.223 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1047 of 419.512 cents and inv. generated superset size: 19 = 16 more = 633.333% 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 51.68247 cents Scale diversity : 0.648265 Lumma stability : 0.207541 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 : 121/119, 28.8546 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 : 0.015170 Average absolute harmonicity : 0.084825 Specific harmonicity : 0.069907 Fundamental : 1/693, -9.4367 octaves, 0.3775 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 4.712400E+04, 15.52417 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 102.5, average 34.16667 Mersenne's string divisions : 61439 Sum of van Prooijen's expressibility: 3.79498, average 1.26499 Sum of Tenney's harmonic distance : 7.76102, average 2.58701 Vogel's harmonic complexity : 27.00000 Wille's k value : 178 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 12.86245, average 2.14374 Lattice compactness (without 2's) : 10.05986, average 1.67664 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -2 ..-1 -1.33333 4 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 2 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 18 23 30| Scale is weakly epimorphic with val: <6 10 18 24 29| Scale is weakly epimorphic with val: <6 10 18 26 33| Scale is weakly epimorphic with val: <6 10 18 27 29| Scale is weakly epimorphic with val: <6 10 19 24 31| Scale is weakly epimorphic with val: <6 10 19 25 30| Scale is weakly epimorphic with val: <6 10 20 23 31| Scale is weakly epimorphic with val: <6 10 20 25 32| Scale is weakly epimorphic with val: <6 10 20 26 31| Scale is weakly epimorphic with val: <6 10 21 23 30| Scale is weakly epimorphic with val: <6 10 21 24 32| Scale is weakly epimorphic with val: <6 10 21 26 33| Scale is weakly epimorphic with val: <6 10 21 27 32| Scale is weakly epimorphic with val: <6 10 22 24 31| Scale is weakly epimorphic with val: <6 10 22 25 33| Scale is weakly epimorphic with val: <6 11 18 24 31| Scale is weakly epimorphic with val: <6 11 18 25 33| Scale is weakly epimorphic with val: <6 11 18 27 31| Scale is weakly epimorphic with val: <6 11 19 23 31| Scale is weakly epimorphic with val: <6 11 19 25 32| Scale is weakly epimorphic with val: <6 11 20 23 33| Scale is weakly epimorphic with val: <6 11 20 24 32| Scale is weakly epimorphic with val: <6 11 20 26 33| Scale is weakly epimorphic with val: <6 11 21 25 33| Scale is weakly epimorphic with val: <6 11 22 23 31| Scale is weakly epimorphic with val: <7 10 18 23 29| Scale is weakly epimorphic with val: <7 10 18 25 27| Scale is weakly epimorphic with val: <7 10 18 26 32| Scale is weakly epimorphic with val: <7 10 19 23 28| Scale is weakly epimorphic with val: <7 10 19 24 30| Scale is weakly epimorphic with val: <7 10 19 26 28| Scale is weakly epimorphic with val: <7 10 19 27 33| Scale is weakly epimorphic with val: <7 10 20 24 29| Scale is weakly epimorphic with val: <7 10 20 25 31| Scale is weakly epimorphic with val: <7 10 20 27 29| Scale is weakly epimorphic with val: <7 10 21 23 29| Scale is weakly epimorphic with val: <7 10 21 25 30| Scale is weakly epimorphic with val: <7 10 21 26 32| Scale is weakly epimorphic with val: <7 10 22 23 31| Scale is weakly epimorphic with val: <7 10 22 24 30| Scale is weakly epimorphic with val: <7 10 22 26 31| Scale is weakly epimorphic with val: <7 10 22 27 33| Scale is JI-epimorphic with val: <7 11 18 23 28| Scale is weakly epimorphic with val: <7 11 18 23 31| Scale is weakly epimorphic with val: <7 11 18 24 27| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 24 33| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 27| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is JI-epimorphic with val: <7 11 19 24 29| Scale is weakly epimorphic with val: <7 11 19 24 32| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 27 29| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 20 23 29| Scale is weakly epimorphic with val: <7 11 20 23 32| Scale is weakly epimorphic with val: <7 11 20 25 27| Scale is JI-epimorphic with val: <7 11 20 25 30| = patent Scale is weakly epimorphic with val: <7 11 20 25 33| Scale is weakly epimorphic with val: <7 11 20 26 29| Scale is weakly epimorphic with val: <7 11 20 26 32| Scale is weakly epimorphic with val: <7 11 21 23 28| Scale is weakly epimorphic with val: <7 11 21 23 31| Scale is weakly epimorphic with val: <7 11 21 24 27| Scale is weakly epimorphic with val: <7 11 21 24 30| Scale is weakly epimorphic with val: <7 11 21 24 33| Scale is weakly epimorphic with val: <7 11 21 26 28| Scale is JI-epimorphic with val: <7 11 21 26 31| Scale is weakly epimorphic with val: <7 11 21 27 27| Scale is weakly epimorphic with val: <7 11 21 27 30| Scale is weakly epimorphic with val: <7 11 21 27 33| Scale is weakly epimorphic with val: <7 11 22 24 29| Scale is weakly epimorphic with val: <7 11 22 24 32| Scale is weakly epimorphic with val: <7 11 22 25 28| Scale is weakly epimorphic with val: <7 11 22 25 31| Scale is weakly epimorphic with val: <7 11 22 27 29| Scale is JI-epimorphic with val: <7 11 22 27 32| Scale is weakly epimorphic with val: <7 12 18 24 32| Scale is weakly epimorphic with val: <7 12 18 25 31| Scale is weakly epimorphic with val: <7 12 19 23 32| Scale is weakly epimorphic with val: <7 12 19 25 33| Scale is weakly epimorphic with val: <7 12 19 26 32| Scale is weakly epimorphic with val: <7 12 20 23 31| Scale is weakly epimorphic with val: <7 12 20 24 33| Scale is weakly epimorphic with val: <7 12 20 27 33| Scale is weakly epimorphic with val: <7 12 21 24 32| Scale is weakly epimorphic with val: <7 12 22 25 33| Scale is weakly epimorphic with val: <8 11 18 23 27| Scale is weakly epimorphic with val: <8 11 18 25 31| Scale is weakly epimorphic with val: <8 11 18 26 27| Scale is weakly epimorphic with val: <8 11 19 23 29| Scale is weakly epimorphic with val: <8 11 19 24 28| Scale is weakly epimorphic with val: <8 11 19 26 32| Scale is weakly epimorphic with val: <8 11 19 27 28| Scale is weakly epimorphic with val: <8 11 20 24 30| Scale is weakly epimorphic with val: <8 11 20 25 29| Scale is weakly epimorphic with val: <8 11 20 27 33| Scale is weakly epimorphic with val: <8 11 21 23 30| Scale is weakly epimorphic with val: <8 11 21 25 31| Scale is weakly epimorphic with val: <8 11 21 26 30| Scale is weakly epimorphic with val: <8 11 22 23 29| Scale is weakly epimorphic with val: <8 11 22 24 31| Scale is weakly epimorphic with val: <8 11 22 26 32| Scale is weakly epimorphic with val: <8 11 22 27 31| Scale is weakly epimorphic with val: <8 12 18 23 29| Scale is weakly epimorphic with val: <8 12 18 24 31| Scale is weakly epimorphic with val: <8 12 18 26 29| Scale is weakly epimorphic with val: <8 12 19 24 30| Scale is weakly epimorphic with val: <8 12 19 25 32| Scale is weakly epimorphic with val: <8 12 19 27 30| Scale is weakly epimorphic with val: <8 12 20 23 30| Scale is weakly epimorphic with val: <8 12 20 25 31| Scale is weakly epimorphic with val: <8 12 20 26 33| Scale is weakly epimorphic with val: <8 12 21 23 32| Scale is weakly epimorphic with val: <8 12 21 24 31| Scale is weakly epimorphic with val: <8 12 21 26 32| Scale is weakly epimorphic with val: <8 12 22 24 33| Scale is weakly epimorphic with val: <8 12 22 25 32| Scale is weakly epimorphic with val: <8 12 22 27 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 35.6521 c. M: 51.6825 c. 4: 0 1 3 N G T3 SD: 30.1689 c. M: 51.6825 c. 5: 0 1 4 N G T3 SD: 35.2823 c. M: 51.6825 c. 7: 1 1 5 N M DE S SD: 12.6563 c. M:-19.4668 c. 8: 1 1 6 N M DE S SD: 7.5544 c. M:-10.5732 c. 11: 1 2 8 N T3 SD: 4.2454 c. M: 6.4056 c. 18: 2 3 13 N T3 SD: 4.1190 c. M:-6.1263 c. 19: 2 3 14 N T3 SD: 0.7930 c. M: 1.1550 c. 49: 5 8 36 N T3 SD: 0.4998 c. M: 0.8615 c. 68: 7 11 50 N T3 SD: 0.3257 c. M: 0.4131 c. 154: 16 25 113 N T3 SD: 0.2206 c. M:-0.3769 c. 173: 18 28 127 N T3 SD: 0.1442 c. M:-0.2086 c. 192: 20 31 141 N T3 SD: 0.1216 c. M:-0.1972 c. 222: 23 36 163 N T3 SD: 0.0959 c. M:-0.1438 c. 241: 25 39 177 N T3 SD: 0.0261 c. M:-0.0414 c. 501: 52 81 368 N T3 SD: 0.0067 c. M:-0.0108 c. 742: 77 120 545 N T3 SD: 0.0063 c. M:-0.0108 c. 1243: 129 201 913 N T3 SD: 0.0041 c. M:-0.0052 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 20:21:22:27 SD: 17.0366 cents 21:22:23:28 SD: 12.7861 cents 22:23:24:29 SD: 12.3354 cents 23:24:25:31 SD: 10.4427 cents 24:25:26:32 SD: 6.6748 cents 27:28:29:36 SD: 4.7091 cents 36:37:39:48 SD: 2.5476 cents 63:65:68:84 SD: 0.8077 cents 99:102:107:132 SD: 0.7710 cents 102:105:110:136 SD: 0.7063 cents 162:167:175:216 SD: 0.5664 cents 165:170:178:220 SD: 0.3087 cents 201:207:217:268 SD: 0.2833 cents 264:272:285:352 SD: 0.0964 cents 429:442:463:572 SD: 0.0593 cents