Scala analysis: 261_C17
Chromatic tetrachord 24/23 * 69/64 * 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 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: 24/23 73.6807 vicesimotertial minor semitone 2: 69/64 130.2293 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 69/64 130.229 cents 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 256/207 367.816 cents 2: 1 23/18 424.364 cents vicesimotertial major 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 : 73.7 203.9 498.0 73.7 : 130.2 424.4 498.0 203.9: 294.1 367.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 294.1350 cents 92/81, 220.4543 cents 24/23, 73.6807 cents 2: 203.9100 .. 424.3643 cents 92/81, 220.4543 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 2.253169 Largest / Average step : 1.771737 Largest / Smallest step : 3.992025 Median interval of one step : 69/64, 130.2293 cents, amount: 1 Least squares average step : 141.11683 cents, oct.: 423.35050 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1656-tone equal temperament with octave 4/3 degrees: 245 678 1656 Least number of segments generator : 829 of 249.323 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1267 of 381.053 cents and inv. generated superset size: 74 = 71 more = 2466.667% 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 73.68065 cents Scale diversity : 1.050773 Lumma stability : 0.295880 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 : 529/512, 56.5487 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 : 23 Odd number limit : 207 (O: 69 U: 207) Highest odd numerator or denominator: 23 Scale harmonicity : 0.017829 Average absolute harmonicity : 0.118408 Specific harmonicity : 0.092524 Fundamental : 1/552, -9.1085 octaves, 0.4740 Hz. Guide tone : 72, 6.1699 octaves, 18837.041 Hz. Exponens Consonantiae : 3.974400E+04, 15.27845 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 35.5, average 11.83333 Mersenne's string divisions : 5593 Sum of van Prooijen's expressibility: 2.79309, average 0.93103 Sum of Tenney's harmonic distance : 5.67845, average 1.89282 Vogel's harmonic complexity : 24.00000 Wille's k value : 310 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 23.60310, average 3.93385 Lattice compactness (without 2's) : 11.06450, average 1.84408 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.66667 8 3: -1 .. 2 0.66667 4 2 23: -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 11 30| Scale is weakly epimorphic with val: <7 11 33| = patent Scale is weakly epimorphic with val: <7 11 36| Scale is weakly epimorphic with val: <7 12 32| Scale is weakly epimorphic with val: <7 12 35| Scale is weakly epimorphic with val: <8 11 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 47.8361 c. M: 73.6807 c. 5: 1 1 3 N M DE S SD: 15.2129 c. M:-25.9283 c. 7: 1 2 4 N T3 SD: 5.6973 c. M:-9.5379 c. 12: 2 3 7 N T3 SD: 5.7739 c. M:-9.3268 c. 15: 2 4 9 N T3 SD: 4.9978 c. M: 7.2747 c. 19: 3 5 11 N T3 SD: 4.4024 c. M:-5.7932 c. 20: 3 5 12 N T3 SD: 2.7730 c. M: 4.6920 c. 27: 4 7 16 N T3 SD: 0.5820 c. M: 1.0028 c. 61: 9 16 36 N T3 SD: 0.1655 c. M:-0.2068 c. 88: 13 23 52 N T3 SD: 0.1128 c. M: 0.1643 c. 149: 22 39 88 N T3 SD: 0.0833 c. M: 0.1438 c. 237: 35 62 140 N T3 SD: 0.0848 c. M: 0.1297 c. 325: 48 85 192 N T3 SD: 0.0897 c. M: 0.1232 c. 359: 53 94 212 N T3 SD: 0.0896 c. M: 0.1531 c. 386: 57 101 228 N T3 SD: 0.0826 c. M: 0.1351 c. 413: 61 108 244 N T3 SD: 0.0936 c. M: 0.1195 c. 425: 63 111 251 N T3 SD: 0.0850 c. M:-0.1472 c. 459: 68 120 271 N T3 SD: 0.0765 c. M:-0.1038 c. 486: 72 127 287 N T3 SD: 0.0613 c. M:-0.1038 c. 520: 77 136 307 N T3 SD: 0.0684 c. M:-0.0969 c. 547: 81 143 323 N T3 SD: 0.0473 c. M:-0.0701 c. 574: 85 150 339 N T3 SD: 0.0415 c. M:-0.0717 c. 608: 90 159 359 N T3 SD: 0.0422 c. M:-0.0591 c. 635: 94 166 375 N T3 SD: 0.0276 c. M:-0.0457 c. 696: 103 182 411 N T3 SD: 0.0227 c. M:-0.0308 c. 723: 107 189 427 N T3 SD: 0.0164 c. M:-0.0273 c. 784: 116 205 463 N T3 SD: 0.0076 c. M:-0.0097 c. 872: 129 228 515 N T3 SD: 0.0051 c. M: 0.0086 c. 1656: 245 433 978 N T3 SD: 0.0020 c. M:-0.0035 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 12:13:14:16 S SD: 30.1387 cents 13:14:15:17 SD: 25.8937 cents 14:15:16:19 SD: 20.4843 cents 15:16:17:20 SD: 13.3795 cents 17:18:19:23 SD: 12.5008 cents 18:19:20:24 S SD: 9.7720 cents 21:22:24:28 S SD: 9.3710 cents 22:23:25:29 SD: 8.8503 cents 23:24:26:31 SD: 6.8306 cents 24:25:27:32 SD: 1.0027 cents 135:141:152:180 SD: 0.7146 cents 159:166:179:212 SD: 0.5039 cents 183:191:206:244 SD: 0.3741 cents 207:216:233:276 SD: 0.3097 cents 231:241:260:308 SD: 0.2964 cents 297:310:334:396 SD: 0.2699 cents 321:335:361:428 SD: 0.2134 cents 345:360:388:460 SD: 0.1859 cents 369:385:415:492 SD: 0.1856 cents 480:501:540:640 SD: 0.1503 cents 504:526:567:672 SD: 0.0954 cents 528:551:594:704 SD: 0.0455 cents 552:576:621:736 SD: 0.0000 cents