Scala analysis: 255_C17
Chromatic tetrachord 36/35 * 35/32 * 32/27, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 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: 36/35 48.7704 septimal diesis, 1/4-tone 2: 35/32 155.1396 septimal neutral second 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 35/32 155.140 cents septimal neutral second 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 128/105 342.905 cents septimal neutral third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 48.8 203.9 498.0 48.8 : 155.1 449.3 498.0 203.9: 294.1 342.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 294.1350 cents 280/243, 245.3646 cents 36/35, 48.7704 cents 2: 203.9100 .. 449.2746 cents 280/243, 245.3646 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 3.404013 Largest / Average step : 1.771737 Largest / Smallest step : 6.031017 Median interval of one step : 35/32, 155.1396 cents, amount: 1 Least squares average step : 139.33753 cents, oct.: 418.01258 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1634-tone equal temperament with octave 4/3 degrees: 160 669 1634 Least number of segments generator : 819 of 249.632 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 897 of 273.407 cents and inv. generated superset size: 40 = 37 more = 1333.333% 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 48.77038 cents Scale diversity : 0.857043 Lumma stability : 0.195847 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 : 36/35, 48.7704 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 : 7 Odd number limit : 105 (O: 35 U: 105) Highest odd numerator or denominator: 35 Scale harmonicity : 0.033686 Average absolute harmonicity : 0.125306 Specific harmonicity : 0.165991 Fundamental : 1/840, -9.7142 octaves, 0.3115 Hz. Guide tone : 36, 5.1699 octaves, 9418.520 Hz. Exponens Consonantiae : 3.024000E+04, 14.88417 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 47.5, average 15.83333 Mersenne's string divisions : 8449 Sum of van Prooijen's expressibility: 2.97543, average 0.99181 Sum of Tenney's harmonic distance : 6.03688, average 2.01229 Vogel's harmonic complexity : 17.33333 Wille's k value : 472 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 23.34763, average 3.89127 Lattice compactness (without 2's) : 13.18033, average 2.19672 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.33333 7 3: -1 .. 2 1.00000 5 2 5: -1 .. 0 -0.33333 1 7: -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 11 15 19| Scale is weakly epimorphic with val: <7 11 15 22| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 18 19| Scale is weakly epimorphic with val: <7 11 18 22| Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <7 12 15 19| Scale is weakly epimorphic with val: <7 12 15 22| Scale is weakly epimorphic with val: <7 12 16 18| Scale is weakly epimorphic with val: <7 12 16 21| Scale is weakly epimorphic with val: <7 12 17 20| Scale is weakly epimorphic with val: <7 12 18 19| Scale is weakly epimorphic with val: <7 12 18 22| Scale is weakly epimorphic with val: <7 12 19 21| Scale is weakly epimorphic with val: <8 11 15 20| Scale is weakly epimorphic with val: <8 11 16 19| Scale is weakly epimorphic with val: <8 11 17 18|
FIT/MODE
3: 0 1 2 N G T3 SD: 35.6585 c. M: 48.7704 c. 5: 0 2 3 N G T3 SD: 28.2876 c. M: 48.7704 c. 7: 1 2 4 N T3 SD: 14.0450 c. M:-22.3789 c. 8: 1 2 5 N T3 SD: 12.5928 c. M: 17.1431 c. 9: 1 3 5 N T3 SD: 10.7612 c. M:-17.4433 c. 10: 1 3 6 N T3 SD: 2.7739 c. M: 4.6920 c. 22: 2 7 13 N T3 SD: 2.0192 c. M: 3.4936 c. 29: 3 9 17 N T3 SD: 2.0259 c. M:-2.7515 c. 32: 3 10 19 N T3 SD: 1.5072 c. M: 2.0787 c. 39: 4 12 23 N T3 SD: 1.3558 c. M:-2.3112 c. 49: 5 15 29 N T3 SD: 1.2379 c. M:-2.0505 c. 51: 5 16 30 N T3 SD: 0.6748 c. M:-1.1674 c. 61: 6 19 36 N T3 SD: 0.1733 c. M:-0.2177 c. 193: 19 60 114 N T3 SD: 0.1525 c. M:-0.2600 c. 205: 20 64 121 N T3 SD: 0.1420 c. M: 0.1806 c. 215: 21 67 127 N T3 SD: 0.0794 c. M: 0.1241 c. 276: 27 86 163 N T3 SD: 0.0281 c. M: 0.0486 c. 337: 33 105 199 N T3 SD: 0.0215 c. M:-0.0372 c. 613: 60 191 362 N T3 SD: 0.0173 c. M: 0.0221 c. 950: 93 296 561 N T3 SD: 0.0173 c. M:-0.0263 c. 960: 94 299 567 N T3 SD: 0.0133 c. M: 0.0228 c. 1021: 100 318 603 N T3 SD: 0.0077 c. M:-0.0097 c. 1297: 127 404 766 N T3 SD: 0.0045 c. M: 0.0072 c. 1358: 133 423 802 N T3 SD: 0.0044 c. M:-0.0072 c. 1634: 160 509 965 N T3 SD: 0.0017 c. M: 0.0022 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 14:15:16:19 SD: 27.2374 cents 15:16:17:20 SD: 21.4147 cents 16:17:18:21 S SD: 20.8169 cents 17:18:19:23 SD: 19.1082 cents 18:19:20:24 S SD: 16.5747 cents 21:22:24:28 S SD: 13.9541 cents 22:23:25:29 SD: 12.8611 cents 23:24:26:31 SD: 10.7519 cents 24:25:27:32 SD: 7.3007 cents 30:31:34:40 SD: 5.0242 cents 32:33:36:43 SD: 4.7351 cents 33:34:37:44 SD: 2.1749 cents 63:65:71:84 SD: 2.0486 cents 72:74:81:96 SD: 0.4454 cents 177:182:199:236 SD: 0.4051 cents 207:213:233:276 SD: 0.3871 cents 240:247:270:320 SD: 0.3339 cents 279:287:314:372 SD: 0.2368 cents 312:321:351:416 SD: 0.1541 cents 384:395:432:512 SD: 0.0417 cents 456:469:513:608 SD: 0.0352 cents