Scala analysis: 146_C3
Chromatic tetrachord 28/27 * 51/49 * 21/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 68/63 132.219501 supraminor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 21/17 365.8255 submajor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 51/49 69.2586 3: 21/17 365.8255 submajor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 51/49 69.259 cents 1: 1 21/17 365.825 cents submajor third 2: 1 68/63 132.220 cents supraminor second 2: 1 196/153 428.786 cents 2: 1 9/7 435.084 cents septimal major third, BP third 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 : 63.0 132.2 498.0 63.0 : 69.3 435.1 498.0 132.2: 365.8 428.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 365.8255 cents 81/68, 302.8646 cents 28/27, 62.9609 cents 2: 132.2195 .. 435.0841 cents 81/68, 302.8646 cents 1156/1323,-233.6060 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 21/17, 365.8255 cents Average / Smallest step : 2.636795 Largest / Average step : 2.203569 Largest / Smallest step : 5.810360 Median interval of one step : 51/49, 69.2586 cents, amount: 1 Least squares average step : 130.10964 cents, oct.: 390.32891 cents Scale is not proper Scale has trivalence property Scale is a mode of a 791-tone equal temperament with octave 4/3 degrees: 100 210 791 Least number of segments generator : 396 of 249.337 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 781 of 491.749 cents and inv. generated superset size: 22 = 19 more = 733.333% 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 62.96090 cents Scale diversity : 0.670876 Lumma stability : 0.252832 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 : 1377/1372, 6.2977 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% Limited inverse transpositions with margin 296.5669 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 153 (O: 51 U: 153) Highest odd numerator or denominator: 63 Scale harmonicity : 0.016477 Average absolute harmonicity : 0.094843 Specific harmonicity : 0.086611 Fundamental : 1/189, -7.5622 octaves, 1.3843 Hz. Guide tone : 476, 8.8948 octaves, 124533.769 Hz. Exponens Consonantiae : 8.996400E+04, 16.45706 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 96.5, average 32.16667 Mersenne's string divisions : 50435 Sum of van Prooijen's expressibility: 3.70783, average 1.23594 Sum of Tenney's harmonic distance : 7.58955, average 2.52985 Vogel's harmonic complexity : 17.66667 Wille's k value : 31 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 6 Triangular lattice diameter : 2 Lattice compactness : 15.55761, average 2.59294 Lattice compactness (without 2's) : 13.02938, average 2.17156 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -3 ..-1 -2.00000 6 1 7: -1 .. 1 0.00000 2 1 17: 0 .. 1 0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 19 30| Scale is weakly epimorphic with val: <6 10 21 27| Scale is weakly epimorphic with val: <6 10 21 30| Scale is weakly epimorphic with val: <6 10 21 33| Scale is weakly epimorphic with val: <6 10 22 33| Scale is weakly epimorphic with val: <6 11 20 33| Scale is weakly epimorphic with val: <7 10 18 27| 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 21 30| 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 weakly epimorphic with val: <7 11 20 27| Scale is JI-epimorphic with val: <7 11 20 30| = patent Scale is weakly epimorphic with val: <7 11 20 33| 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 12 20 33| Scale is weakly epimorphic with val: <8 11 18 27| Scale is weakly epimorphic with val: <8 11 20 27| Scale is weakly epimorphic with val: <8 11 20 30| Scale is weakly epimorphic with val: <8 11 20 33| Scale is weakly epimorphic with val: <8 11 21 30| Scale is weakly epimorphic with val: <8 12 19 30| Scale is weakly epimorphic with val: <8 12 22 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 41.2562 c. M: 62.9609 c. 4: 0 1 3 N G T3 SD: 36.6219 c. M: 62.9609 c. 5: 0 1 4 N G T3 SD: 40.9370 c. M: 62.9609 c. 6: 1 1 4 N M DE S SD: 22.6863 c. M:-33.7955 c. 7: 1 1 5 N M DE S SD: 7.4975 c. M:-10.0791 c. 8: 1 1 6 N M DE S SD: 4.4690 c. M: 7.7083 c. 15: 2 2 11 N M DE S SD: 2.0182 c. M:-3.4451 c. 23: 3 3 17 N M DE S SD: 1.7580 c. M: 2.2947 c. 38: 5 5 28 N M DE S SD: 1.6275 c. M:-2.5713 c. 41: 5 6 30 N T3 SD: 1.5178 c. M: 2.2237 c. 48: 6 7 35 N T3 SD: 1.5931 c. M:-2.6677 c. 49: 6 7 36 N T3 SD: 1.1418 c. M: 1.9758 c. 56: 7 8 41 N T3 SD: 0.7964 c. M:-1.1854 c. 64: 8 9 47 N T3 SD: 0.4094 c. M: 0.7053 c. 79: 10 11 58 N T3 SD: 0.1103 c. M:-0.1722 c. 222: 28 31 163 N T3 SD: 0.1177 c. M: 0.1444 c. 245: 31 34 180 N T3 SD: 0.0592 c. M: 0.0851 c. 309: 39 43 227 N T3 SD: 0.0656 c. M: 0.1009 c. 324: 41 45 238 N T3 SD: 0.0388 c. M:-0.0633 c. 388: 49 54 285 N T3 SD: 0.0368 c. M: 0.0635 c. 467: 59 65 343 N T3 SD: 0.0262 c. M: 0.0387 c. 633: 80 88 465 N T3 SD: 0.0234 c. M: 0.0369 c. 712: 90 99 523 N T3 SD: 0.0086 c. M: 0.0137 c. 791: 100 110 581 N T3 SD: 0.0033 c. M:-0.0048 c. 1503: 190 209 1104 N T3 SD: 0.0024 c. M: 0.0040 c. 2294: 290 319 1685 N T3 SD: 0.0006 c. M: 0.0009 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 18:19 x 24 SD: 15.3211 cents 20:21:22:27 SD: 14.9067 cents 21:22:23:28 SD: 10.2615 cents 22:23:24:29 SD: 10.1465 cents 23:24:25:31 SD: 8.2491 cents 24:25:26:32 SD: 3.3305 cents 27:28:29:36 SD: 2.8358 cents 51:53:55:68 SD: 1.3100 cents 111:115:120:148 SD: 1.0728 cents 138:143:149:184 SD: 0.4847 cents 162:168:175:216 SD: 0.4713 cents 189:196:204:252 SD: 0.0000 cents