Scala analysis: 263_C17
Chromatic tetrachord 14/13 * 117/112 * 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-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: 14/13 128.2982 2/3-tone 2: 117/112 75.6118 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 117/112 75.612 cents 1: 1 14/13 128.298 cents 2/3-tone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 26/21 369.747 cents 2: 1 448/351 422.433 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 : 128.3 203.9 498.0 128.3: 75.6 369.7 498.0 203.9: 294.1 422.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.6118 .. 294.1350 cents 3584/3159, 218.5232 cents 117/112, 75.6118 cents 2: 203.9100 .. 422.4332 cents 3584/3159, 218.5232 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 117/112, 75.6118 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 2.195624 Largest / Average step : 1.771737 Largest / Smallest step : 3.890070 Median interval of one step : 14/13, 128.2982 cents, amount: 1 Least squares average step : 145.01809 cents, oct.: 435.05427 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 75.61176 cents Scale diversity : 1.060319 Lumma stability : 0.303634 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 : 1568/1521, 52.6865 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 351 (O: 117 U: 351) Highest odd numerator or denominator: 13 Scale harmonicity : 0.022007 Average absolute harmonicity : 0.121396 Specific harmonicity : 0.116517 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 7.862400E+04, 16.26268 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 25.5, average 8.50000 Mersenne's string divisions : 3213 Sum of van Prooijen's expressibility: 2.54531, average 0.84844 Sum of Tenney's harmonic distance : 5.19659, average 1.73220 Vogel's harmonic complexity : 18.00000 Wille's k value : 175 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 20.09504, average 3.34917 Lattice compactness (without 2's) : 11.59575, average 1.93263 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.00000 6 3: -1 .. 2 0.33333 3 2 7: 0 .. 1 0.33333 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 21 25| Scale is weakly epimorphic with val: <7 10 22 26| 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 11 20 25| Scale is weakly epimorphic with val: <7 11 20 28| Scale is weakly epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 11 21 29| Scale is weakly epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <7 11 22 30| Scale is weakly epimorphic with val: <7 12 18 27| Scale is weakly epimorphic with val: <7 12 18 30| Scale is weakly epimorphic with val: <7 12 19 25| Scale is weakly epimorphic with val: <7 12 19 28| Scale is weakly epimorphic with val: <7 12 20 26| Scale is weakly epimorphic with val: <7 12 20 29| Scale is weakly epimorphic with val: <7 12 21 27| Scale is weakly epimorphic with val: <7 12 21 30| Scale is weakly epimorphic with val: <7 12 22 25| Scale is weakly epimorphic with val: <7 12 22 28| Scale is weakly epimorphic with val: <8 11 20 25| Scale is weakly epimorphic with val: <8 11 21 26| Scale is weakly epimorphic with val: <8 11 22 27|
FIT/MODE
3: 1 0 2 N G T3 SD: 30.8685 c. M: 37.8950 c. 4: 1 1 2 P M ME S SD: 26.1373 c. M:-45.1125 c. 5: 1 1 3 N M DE S SD: 16.7838 c. M: 28.6892 c. 7: 2 1 4 N T3 SD: 9.7806 c. M:-14.0003 c. 12: 3 2 7 N T3 SD: 3.0202 c. M: 3.7870 c. Vietnamese tritonic 20: 5 3 12 N T3 SD: 3.4812 c. M: 4.6920 c. 27: 7 4 16 N T3 SD: 0.7495 c. M: 1.0028 c. 39: 10 6 23 N T3 SD: 0.4189 c. M: 0.5944 c. 66: 17 10 39 N T3 SD: 0.0952 c. M: 0.1643 c. 171: 44 26 101 N T3 SD: 0.0865 c. M: 0.1463 c. 237: 61 36 140 N T3 SD: 0.0746 c. M: 0.1094 c. 303: 78 46 179 N T3 SD: 0.0728 c. M: 0.0896 c. 481: 124 73 284 N T3 SD: 0.0689 c. M:-0.0959 c. 520: 134 79 307 N T3 SD: 0.0615 c. M:-0.0969 c. 547: 141 83 323 N T3 SD: 0.0537 c. M:-0.0826 c. 586: 151 89 346 N T3 SD: 0.0446 c. M:-0.0675 c. 613: 158 93 362 N T3 SD: 0.0433 c. M:-0.0722 c. 652: 168 99 385 N T3 SD: 0.0315 c. M:-0.0440 c. 718: 185 109 424 N T3 SD: 0.0217 c. M:-0.0281 c. 784: 202 119 463 N T3 SD: 0.0151 c. M:-0.0246 c. 850: 219 129 502 N T3 SD: 0.0127 c. M:-0.0216 c. 889: 229 135 525 N T3 SD: 0.0086 c. M:-0.0139 c. 955: 246 145 564 N T3 SD: 0.0036 c. M: 0.0060 c. 1976: 509 300 1167 N T3 SD: 0.0043 c. M: 0.0063 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 10:11 x 13 SD: 28.5854 cents 11:12 x 15 S SD: 22.4315 cents 12:13:14:16 S SD: 21.2646 cents 13:14:15:17 SD: 18.4128 cents 14:15:16:19 SD: 13.9869 cents 15:16:17:20 SD: 6.9738 cents 24:26:27:32 SD: 3.4248 cents 39:42:44:52 SD: 1.6418 cents 90:97:101:120 SD: 1.4983 cents 102:110:115:136 SD: 1.4932 cents 104:112:117:139 SD: 1.3855 cents 105:113:118:140 SD: 0.7263 cents 129:139:145:172 SD: 0.5910 cents 144:155:162:192 SD: 0.2863 cents 168:181:189:224 SD: 0.2453 cents 273:294:307:364 SD: 0.2349 cents 312:336:351:416 SD: 0.0000 cents