Scala analysis: 262_C17
Chromatic tetrachord 40/39 * 351/320 * 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 40/39 43.8311 tridecimal minor diesis 2: 351/320 160.0790 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 351/320 160.079 cents 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 1280/1053 337.966 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished 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 : 43.8 203.9 498.0 43.8 : 160.1 454.2 498.0 203.9: 294.1 338.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 294.1350 cents 52/45, 250.3039 cents 40/39, 43.8311 cents 2: 203.9100 .. 454.2139 cents 52/45, 250.3039 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 3.787612 Largest / Average step : 1.771737 Largest / Smallest step : 6.710654 Median interval of one step : 351/320, 160.0790 cents, amount: 1 Least squares average step : 138.98472 cents, oct.: 416.95415 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1761-tone equal temperament with octave 4/3 degrees: 155 721 1761 Least number of segments generator : 881 of 249.164 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1615 of 456.753 cents and inv. generated superset size: 29 = 26 more = 966.667% 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 43.83105 cents Scale diversity : 0.807186 Lumma stability : 0.176012 Lumma impropriety factor : 0.181158 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 : 40/39, 43.8311 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% -- Rational properties -- Prime limit : 13 Odd number limit : 1053 (O: 351 U: 1053) Highest odd numerator or denominator: 39 Scale harmonicity : 0.023500 Average absolute harmonicity : 0.121169 Specific harmonicity : 0.120911 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 1.123200E+05, 16.77726 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 51.5, average 17.16667 Mersenne's string divisions : 9401 Sum of van Prooijen's expressibility: 3.02243, average 1.00748 Sum of Tenney's harmonic distance : 6.12964, average 2.04321 Vogel's harmonic complexity : 17.00000 Wille's k value : 175 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 23.72438, average 3.95406 Lattice compactness (without 2's) : 12.46289, average 2.07715 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.66667 8 3: -1 .. 2 0.00000 4 2 5: 0 .. 1 0.33333 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 17 25| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 11 15 26| Scale is weakly epimorphic with val: <7 11 15 29| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 17 25| Scale is weakly epimorphic with val: <7 11 17 28| Scale is weakly epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 18 29| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 12 15 26| Scale is weakly epimorphic with val: <7 12 15 29| Scale is weakly epimorphic with val: <7 12 16 27| Scale is weakly epimorphic with val: <7 12 16 30| Scale is weakly epimorphic with val: <7 12 17 25| Scale is weakly epimorphic with val: <7 12 17 28| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <7 12 19 27| Scale is weakly epimorphic with val: <7 12 19 30| Scale is weakly epimorphic with val: <8 11 15 25| Scale is weakly epimorphic with val: <8 11 16 26| Scale is weakly epimorphic with val: <8 11 17 27| Scale is weakly epimorphic with val: <8 11 18 28| Scale is weakly epimorphic with val: <8 11 19 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 33.4524 c. M: 43.8311 c. 5: 0 2 3 N G T3 SD: 25.4504 c. M: 43.8311 c. 7: 1 2 4 N T3 SD: 16.7059 c. M:-27.3182 c. 8: 1 2 5 N T3 SD: 14.5299 c. M:-18.4246 c. 9: 1 3 5 N T3 SD: 12.0649 c. M:-17.4433 c. 10: 1 3 6 N T3 SD: 4.3855 c. M:-5.9734 c. 12: 1 4 7 N T3 SD: 2.4792 c. M:-3.6087 c. 22: 2 7 13 N T3 SD: 0.8401 c. M:-1.4458 c. 34: 3 11 20 N T3 SD: 0.6772 c. M:-1.1674 c. 56: 5 18 33 N T3 SD: 0.5232 c. M:-0.6442 c. 103: 9 33 61 N T3 SD: 0.5086 c. M: 0.8237 c. 115: 10 37 68 N T3 SD: 0.3669 c. M: 0.5228 c. 137: 12 44 81 N T3 SD: 0.2246 c. M: 0.3296 c. 149: 13 48 88 N T3 SD: 0.2180 c. M: 0.3775 c. 159: 14 51 94 N T3 SD: 0.1775 c. M: 0.3067 c. 171: 15 55 101 N T3 SD: 0.0845 c. M: 0.1429 c. 193: 17 62 114 N T3 SD: 0.0350 c. M: 0.0470 c. 364: 32 117 215 N T3 SD: 0.0356 c. M: 0.0469 c. 557: 49 179 329 N T3 SD: 0.0265 c. M: 0.0424 c. 591: 52 190 349 N T3 SD: 0.0167 c. M:-0.0272 c. 784: 69 252 463 N T3 SD: 0.0053 c. M:-0.0089 c. 1761: 155 566 1040 N T3 SD: 0.0038 c. M:-0.0060 c. 2125: 187 683 1255 N T3 SD: 0.0032 c. M: 0.0045 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: 70.0332 cents 6 x 7:8 S SD: 31.4805 cents 7 x 8:9 S SD: 34.3053 cents 8 x 9:11 SD: 26.6365 cents 9 x 10:12 S SD: 10.7531 cents 10 x 11:13 SD: 29.3037 cents 11 x 12:15 S SD: 32.9836 cents 12 x 14:16 S SD: 31.4805 cents 13 x 15:17 SD: 27.6192 cents 15:16:17:20 SD: 23.0306 cents 16:17:18:21 S SD: 22.3097 cents 17:18:19:23 SD: 20.5649 cents 18:19:20:24 S SD: 18.0732 cents 21:22:24:28 S SD: 15.2412 cents 22:23:25:29 SD: 14.1087 cents 23:24:26:31 SD: 12.0688 cents 24:25:27:32 SD: 8.9471 cents 30:31:34:40 SD: 6.0606 cents 32:33:36:43 SD: 5.4839 cents 33:34:37:44 SD: 3.2615 cents 39:40:44:52 SD: 1.6418 cents 72:74:81:96 SD: 1.2010 cents 81:83:91:108 SD: 0.9557 cents 120:123:135:160 SD: 0.3608 cents 192:197:216:256 SD: 0.2254 cents 312:320:351:416 SD: 0.0000 cents