Scala analysis: 300_C22
Chromatic tetrachord 28/27 * 23/21 * 27/23
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: 92/81 220.454344 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/23 277.5907 vicesimotertial minor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 23/21 157.4934 3: 27/23 277.5907 vicesimotertial minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 23/21 157.493 cents 1: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 92/81 220.454 cents 2: 1 28/23 340.552 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 : 63.0 220.5 498.0 63.0 : 157.5 435.1 498.0 220.5: 277.6 340.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 277.5907 cents 729/644, 214.6298 cents 28/27, 62.9609 cents 2: 220.4543 .. 435.0841 cents 729/644, 214.6298 cents 2116/2187,-57.1363 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 : 27/23, 277.5907 cents Average / Smallest step : 2.636795 Largest / Average step : 1.672082 Largest / Smallest step : 4.408937 Median interval of one step : 23/21, 157.4934 cents, amount: 1 Least squares average step : 142.71461 cents, oct.: 428.14384 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2223-tone equal temperament with octave 4/3 degrees: 281 984 2223 Least number of segments generator : 1112 of 249.135 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1441 of 322.844 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 57.13631 cents Scale diversity : 0.972858 Lumma stability : 0.252832 Lumma impropriety factor : 0.114721 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 : 2187/2116, 57.1363 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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 : 23 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.015375 Average absolute harmonicity : 0.093948 Specific harmonicity : 0.079819 Fundamental : 1/81, -6.3399 octaves, 3.2299 Hz. Guide tone : 644, 9.3309 octaves, 168486.864 Hz. Exponens Consonantiae : 5.216400E+04, 15.67077 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 117.5, average 39.16667 Mersenne's string divisions : 66605 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.82998, average 2.60999 Vogel's harmonic complexity : 16.00000 Wille's k value : 13 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.69070, average 2.94845 Lattice compactness (without 2's) : 15.41578, average 2.56930 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -4 ..-1 -2.66667 8 1 7: 0 .. 1 0.33333 1 1 23: 0 .. 1 0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 19 31| Scale is weakly epimorphic with val: <6 10 21 32| Scale is weakly epimorphic with val: <6 10 21 35| Scale is weakly epimorphic with val: <6 10 22 31| Scale is weakly epimorphic with val: <6 11 20 35| Scale is weakly epimorphic with val: <7 10 19 31| Scale is weakly epimorphic with val: <7 10 19 34| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 18 34| Scale is JI-epimorphic with val: <7 11 20 32| Scale is weakly epimorphic with val: <7 11 20 35| Scale is weakly epimorphic with val: <7 11 21 31| Scale is weakly epimorphic with val: <7 11 21 34| Scale is weakly epimorphic with val: <8 11 18 31| Scale is weakly epimorphic with val: <8 11 20 32| Scale is weakly epimorphic with val: <8 11 20 35| Scale is weakly epimorphic with val: <8 11 21 31| Scale is weakly epimorphic with val: <8 12 19 35| Scale is weakly epimorphic with val: <8 12 22 35|
FIT/MODE
3: 0 1 2 N G T3 SD: 48.0545 c. M: 62.9609 c. 4: 1 1 2 P M ME S SD: 39.1773 c. M:-61.5503 c. 5: 1 1 3 N M DE S SD: 24.4545 c. M:-36.6481 c. 6: 1 2 3 P T3 SD: 20.1495 c. M:-28.5682 c. 7: 1 2 4 N T3 SD: 6.2220 c. M:-8.1884 c. 9: 1 3 5 N T3 SD: 4.4314 c. M: 7.6226 c. 16: 2 5 9 N T3 SD: 1.5329 c. M: 2.5597 c. 41: 5 13 23 N T3 SD: 1.6519 c. M: 2.2237 c. 47: 6 15 26 N T3 SD: 1.2510 c. M:-2.0764 c. 54: 7 17 30 N T3 SD: 1.0598 c. M:-1.6005 c. 63: 8 20 35 N T3 SD: 0.5441 c. M:-0.8990 c. 79: 10 25 44 N T3 SD: 0.1242 c. M:-0.1985 c. 174: 22 55 97 N T3 SD: 0.0324 c. M: 0.0551 c. 253: 32 80 141 N T3 SD: 0.0236 c. M:-0.0329 c. 427: 54 135 238 N T3 SD: 0.0145 c. M:-0.0237 c. 601: 76 190 335 N T3 SD: 0.0170 c. M: 0.0218 c. 680: 86 215 379 N T3 SD: 0.0158 c. M:-0.0271 c. 933: 118 295 520 N T3 SD: 0.0174 c. M:-0.0287 c. 1028: 130 325 573 N T3 SD: 0.0155 c. M:-0.0214 c. 1107: 140 350 617 N T3 SD: 0.0149 c. M:-0.0258 c. 1369: 173 433 763 N T3 SD: 0.0145 c. M: 0.0232 c. 1448: 183 458 807 N T3 SD: 0.0153 c. M:-0.0200 c. 1455: 184 460 811 N T3 SD: 0.0150 c. M:-0.0221 c. 1464: 185 463 816 N T3 SD: 0.0151 c. M: 0.0249 c. 1534: 194 485 855 N T3 SD: 0.0147 c. M:-0.0252 c. 1543: 195 488 860 N T3 SD: 0.0113 c. M: 0.0194 c. 1622: 205 513 904 N T3 SD: 0.0108 c. M: 0.0144 c. 1717: 217 543 957 N T3 SD: 0.0097 c. M: 0.0164 c. 1796: 227 568 1001 N T3 SD: 0.0076 c. M: 0.0120 c. 1970: 249 623 1098 N T3 SD: 0.0058 c. M: 0.0100 c. 2049: 259 648 1142 N T3 SD: 0.0058 c. M:-0.0077 c. 2144: 271 678 1195 N T3 SD: 0.0055 c. M: 0.0084 c. 2223: 281 703 1239 N T3 SD: 0.0034 c. M: 0.0051 c. 2397: 303 758 1336 N T3 SD: 0.0025 c. M: 0.0040 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: 63.6303 cents 6 x 7:8 S SD: 23.2083 cents 7 x 8:9 S SD: 31.9335 cents 8 x 9:11 SD: 27.8914 cents 9 x 10:12 S SD: 19.0253 cents 10 x 11:13 SD: 35.3408 cents 11 x 13:15 SD: 39.4999 cents 12:13:14:16 S SD: 29.5741 cents 13:14:15:17 SD: 26.1272 cents 14:15:16:19 SD: 21.7155 cents 15:16:17:20 SD: 16.3052 cents 18:19:20:24 S SD: 16.2849 cents 19:20:22:25 SD: 16.0061 cents 20:21:23:27 SD: 12.4167 cents 21:22:24:28 S SD: 6.8624 cents 24:25:27:32 SD: 6.0844 cents 29:30:33:39 SD: 5.2659 cents 30:31:34:40 SD: 2.4166 cents 51:53:58:68 SD: 1.4180 cents 81:84:92:108 SD: 0.0000 cents