Scala analysis: 252_C17
Chromatic tetrachord 45/44 * 11/10 * 32/27, Barbour?
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 45/44 38.905773 1/5-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: 45/44 38.9058 1/5-tone 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 45/44 38.906 cents 1/5-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 40/33 333.041 cents 2: 1 176/135 459.139 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 : 38.9 203.9 498.0 38.9 : 165.0 459.1 498.0 203.9: 294.1 333.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9058 .. 294.1350 cents 1408/1215, 255.2292 cents 45/44, 38.9058 cents 2: 203.9100 .. 459.1392 cents 1408/1215, 255.2292 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 45/44, 38.9058 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 4.267104 Largest / Average step : 1.771737 Largest / Smallest step : 7.560189 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 138.63291 cents, oct.: 415.89874 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1485-tone equal temperament with octave 4/3 degrees: 116 608 1485 Least number of segments generator : 743 of 249.190 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1154 of 387.033 cents and inv. generated superset size: 53 = 50 more = 1766.667% 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 38.90577 cents Scale diversity : 0.755132 Lumma stability : 0.156234 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 : 45/44, 38.9058 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.026609 Average absolute harmonicity : 0.121872 Specific harmonicity : 0.133245 Fundamental : 1/264, -8.0444 octaves, 0.9910 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 4.752000E+04, 15.53625 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 56.5, average 18.83333 Mersenne's string divisions : 10591 Sum of van Prooijen's expressibility: 3.08458, average 1.02819 Sum of Tenney's harmonic distance : 6.23318, average 2.07773 Vogel's harmonic complexity : 17.00000 Wille's k value : 148 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 21.76305, average 3.62718 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 -1.00000 7 3: -1 .. 2 1.00000 5 2 5: 0 .. 1 0.33333 1 11: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 11 15 24| Scale is weakly epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 11 17 23| Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 18 24| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 12 15 24| Scale is weakly epimorphic with val: <7 12 15 27| Scale is weakly epimorphic with val: <7 12 16 25| Scale is weakly epimorphic with val: <7 12 17 23| Scale is weakly epimorphic with val: <7 12 17 26| Scale is weakly epimorphic with val: <7 12 18 24| Scale is weakly epimorphic with val: <7 12 18 27| Scale is weakly epimorphic with val: <7 12 19 25|
FIT/MODE
3: 0 1 2 N G T3 SD: 31.3565 c. M: 38.9058 c. 5: 0 2 3 N G T3 SD: 22.6250 c. M: 38.9058 c. 7: 1 2 4 N T3 SD: 19.4132 c. M:-32.2435 c. 9: 1 3 5 N T3 SD: 13.8359 c. M:-17.4433 c. 10: 1 3 6 N T3 SD: 6.8507 c. M:-10.8987 c. 12: 1 4 7 N T3 SD: 2.5673 c. M:-3.6087 c. 27: 2 9 16 N T3 SD: 1.2987 c. M: 2.0136 c. 37: 3 12 22 N T3 SD: 1.4351 c. M: 1.9999 c. 39: 3 13 23 N T3 SD: 0.4190 c. M: 0.5946 c. 88: 7 29 52 N T3 SD: 0.4216 c. M:-0.7114 c. 103: 8 34 61 N T3 SD: 0.4926 c. M: 0.8237 c. 115: 9 38 68 N T3 SD: 0.2126 c. M: 0.3612 c. 127: 10 42 75 N T3 SD: 0.1794 c. M:-0.3104 c. 154: 12 51 91 N T3 SD: 0.1102 c. M: 0.1643 c. 166: 13 55 98 N T3 SD: 0.0843 c. M:-0.1084 c. 281: 22 93 166 N T3 SD: 0.0698 c. M:-0.0871 c. 320: 25 106 189 N T3 SD: 0.0134 c. M: 0.0228 c. 806: 63 267 476 N T3 SD: 0.0137 c. M:-0.0233 c. 999: 78 331 590 N T3 SD: 0.0117 c. M: 0.0194 c. 1126: 88 373 665 N T3 SD: 0.0105 c. M:-0.0178 c. 1165: 91 386 688 N T3 SD: 0.0063 c. M:-0.0106 c. 1485: 116 492 877 N T3 SD: 0.0021 c. M:-0.0034 c. 1805: 141 598 1066 N T3 SD: 0.0008 c. M: 0.0013 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: 24.6459 cents 16:17:18:21 S SD: 23.8185 cents 17:18:19:23 SD: 22.0442 cents 18:19:20:24 S SD: 19.5911 cents 21:22:24:28 S SD: 16.5881 cents 22:23:25:29 SD: 15.4275 cents 23:24:26:31 SD: 13.4545 cents 24:25:27:32 SD: 10.5889 cents 29:30:33:39 SD: 10.5609 cents 30:31:34:40 SD: 7.3202 cents 32:33:36:43 SD: 6.5653 cents 33:34:37:44 SD: 4.6826 cents 39:40:44:52 SD: 2.3218 cents 48:49:54:64 SD: 1.0697 cents 87:89:98:116 SD: 0.7511 cents 129:132:145:172 SD: 0.5798 cents 135:138:152:180 SD: 0.5538 cents 177:181:199:236 SD: 0.3695 cents 216:221:243:288 SD: 0.2374 cents 264:270:297:352 SD: 0.0000 cents