Scala analysis: 260_C17
Chromatic tetrachord 23/22 * 99/92 * 32/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/22 76.956405 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: 23/22 76.9564 2: 99/92 126.9536 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 23/22 76.956 cents 1: 1 99/92 126.954 cents 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 368/297 371.091 cents 2: 1 88/69 421.089 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 : 77.0 203.9 498.0 77.0 : 127.0 421.1 498.0 203.9: 294.1 371.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.9564 .. 294.1350 cents 704/621, 217.1786 cents 23/22, 76.9564 cents 2: 203.9100 .. 421.0886 cents 704/621, 217.1786 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 23/22, 76.9564 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 2.157260 Largest / Average step : 1.771737 Largest / Smallest step : 3.822099 Median interval of one step : 99/92, 126.9536 cents, amount: 1 Least squares average step : 141.35081 cents, oct.: 424.05244 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1275-tone equal temperament with octave 4/3 degrees: 197 522 1275 Least number of segments generator : 638 of 249.218 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 676 of 264.062 cents and inv. generated superset size: 29 = 26 more = 966.667% 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 76.95640 cents Scale diversity : 1.066400 Lumma stability : 0.309034 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 : 1089/1058, 49.9972 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 : 297 (O: 99 U: 297) Highest odd numerator or denominator: 23 Scale harmonicity : 0.013648 Average absolute harmonicity : 0.116869 Specific harmonicity : 0.072461 Fundamental : 1/264, -8.0444 octaves, 0.9910 Hz. Guide tone : 828, 9.6935 octaves, 216625.968 Hz. Exponens Consonantiae : 2.185920E+05, 17.73788 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 34.5, average 11.50000 Mersenne's string divisions : 5355 Sum of van Prooijen's expressibility: 2.79309, average 0.93103 Sum of Tenney's harmonic distance : 5.64066, average 1.88022 Vogel's harmonic complexity : 21.33333 Wille's k value : 148 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 20.03100, average 3.33850 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 -0.66667 6 3: -1 .. 2 0.33333 3 2 11: -1 .. 0 -0.33333 1 23: 0 .. 1 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 23 33| Scale is weakly epimorphic with val: <7 10 24 34| Scale is weakly epimorphic with val: <7 10 25 35| Scale is weakly epimorphic with val: <7 10 26 36| Scale is weakly epimorphic with val: <7 11 23 32| Scale is weakly epimorphic with val: <7 11 23 35| Scale is weakly epimorphic with val: <7 11 24 30| Scale is weakly epimorphic with val: <7 11 24 33| Scale is weakly epimorphic with val: <7 11 24 36| Scale is weakly epimorphic with val: <7 11 25 31| Scale is weakly epimorphic with val: <7 11 25 34| Scale is weakly epimorphic with val: <7 11 26 32| Scale is weakly epimorphic with val: <7 11 26 35| Scale is weakly epimorphic with val: <7 11 27 30| Scale is weakly epimorphic with val: <7 11 27 33| Scale is weakly epimorphic with val: <7 11 27 36| Scale is weakly epimorphic with val: <7 12 23 31| Scale is weakly epimorphic with val: <7 12 23 34| Scale is weakly epimorphic with val: <7 12 24 32| Scale is weakly epimorphic with val: <7 12 24 35| Scale is weakly epimorphic with val: <7 12 25 30| Scale is weakly epimorphic with val: <7 12 25 33| Scale is weakly epimorphic with val: <7 12 25 36| Scale is weakly epimorphic with val: <7 12 26 31| Scale is weakly epimorphic with val: <7 12 26 34| Scale is weakly epimorphic with val: <7 12 27 32| Scale is weakly epimorphic with val: <7 12 27 35| Scale is weakly epimorphic with val: <8 11 23 34| Scale is weakly epimorphic with val: <8 11 24 35| Scale is weakly epimorphic with val: <8 11 25 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 49.5255 c. M: 76.9564 c. 5: 1 1 3 N M DE S SD: 13.3561 c. M:-22.6526 c. 7: 1 2 4 N T3 SD: 6.4470 c. M:-9.5379 c. 12: 2 3 7 N T3 SD: 4.0677 c. M:-6.0511 c. 19: 3 5 11 N T3 SD: 3.4828 c. M:-5.7932 c. 20: 3 5 12 N T3 SD: 3.0042 c. M: 4.6920 c. 27: 4 7 16 N T3 SD: 1.9207 c. M: 3.1720 c. 32: 5 8 19 N T3 SD: 1.0391 c. M: 1.5792 c. 39: 6 10 23 N T3 SD: 0.3081 c. M:-0.4162 c. 71: 11 18 42 N T3 SD: 0.3031 c. M: 0.4832 c. 110: 17 28 65 N T3 SD: 0.0952 c. M: 0.1643 c. 149: 23 38 88 N T3 SD: 0.0450 c. M: 0.0770 c. 259: 40 66 153 N T3 SD: 0.0496 c. M: 0.0769 c. 408: 63 104 241 N T3 SD: 0.0432 c. M: 0.0533 c. 557: 86 142 329 N T3 SD: 0.0419 c. M: 0.0590 c. 679: 105 173 401 N T3 SD: 0.0352 c. M:-0.0609 c. 718: 111 183 424 N T3 SD: 0.0269 c. M:-0.0394 c. 828: 128 211 489 N T3 SD: 0.0208 c. M:-0.0361 c. 867: 134 221 512 N T3 SD: 0.0155 c. M:-0.0194 c. 977: 151 249 577 N T3 SD: 0.0109 c. M:-0.0188 c. 1016: 157 259 600 N T3 SD: 0.0086 c. M:-0.0139 c. 1126: 174 287 665 N T3 SD: 0.0041 c. M:-0.0061 c. 1275: 197 325 753 N T3 SD: 0.0033 c. M: 0.0045 c. 2291: 354 584 1353 N T3 SD: 0.0021 c. M:-0.0037 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: 29.3648 cents 13:14:15:17 SD: 25.1380 cents 14:15:16:19 SD: 19.6846 cents 15:16:17:20 SD: 12.3493 cents 17:18:19:23 SD: 11.7925 cents 18:19:20:24 S SD: 9.0654 cents 22:23:25:29 SD: 8.7827 cents 23:24:26:31 SD: 6.9173 cents 24:25:27:32 SD: 2.0947 cents 63:66:71:84 SD: 1.5680 cents 87:91:98:116 SD: 0.7910 cents 111:116:125:148 SD: 0.6201 cents 153:160:172:204 SD: 0.4502 cents 177:185:199:236 SD: 0.3891 cents 240:251:270:320 SD: 0.2090 cents 264:276:297:352 SD: 0.0000 cents