Scala analysis: 250_C17
Chromatic tetrachord 81/80 * 10/9 * 32/27, Barbour?
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/80 21.506290 syntonic comma, Didymus comma 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: 81/80 21.5063 syntonic comma, Didymus comma 2: 10/9 182.4037 minor whole tone 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 10/9 182.404 cents minor whole tone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 6/5 315.641 cents minor third 2: 1 320/243 476.539 cents grave fourth 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 : 21.5 203.9 498.0 21.5 : 182.4 476.5 498.0 203.9: 294.1 315.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 294.1350 cents 2560/2187, 272.6287 cents 81/80, 21.5063 cents 2: 203.9100 .. 476.5387 cents 2560/2187, 272.6287 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 7.719370 Largest / Average step : 1.771737 Largest / Smallest step : 13.676697 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 137.39009 cents, oct.: 412.17028 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1783-tone equal temperament with octave 4/3 degrees: 77 730 1783 Least number of segments generator : 892 of 249.162 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1185 of 331.006 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 21.50629 cents Scale diversity : 0.559745 Lumma stability : 0.086363 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 : 81/80, 21.5063 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% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.038860 Average absolute harmonicity : 0.127251 Specific harmonicity : 0.187061 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 7.776000E+04, 16.24674 octaves Euler's gradus suavitatis : 21 Sum of Mann's harmonic distance : 92.5, average 30.83333 Mersenne's string divisions : 2737 Sum of van Prooijen's expressibility: 3.33985, average 1.11328 Sum of Tenney's harmonic distance : 6.74809, average 2.24936 Vogel's harmonic complexity : 13.66667 Wille's k value : 121 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 27.74063, average 4.62344 Lattice compactness (without 2's) : 17.45819, average 2.90970 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.66667 9 3: -1 .. 4 1.66667 7 2 5: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 4 / 3 = 1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 17| = patent Scale is weakly epimorphic with val: <7 12 16| Scale is weakly epimorphic with val: <7 12 19|
FIT/MODE
3: 0 1 2 N G T3 SD: 25.1565 c. M: 37.8950 c. 5: 0 2 3 N G T3 SD: 12.7087 c. M: 21.5063 c. 12: 1 4 7 N T3 SD: 11.7320 c. M:-19.9975 c. 14: 1 5 8 N T3 SD: 9.8131 c. M:-14.0684 c. 15: 1 5 9 N T3 SD: 7.2762 c. M:-11.6967 c. 17: 1 6 10 N T3 SD: 4.5480 c. M:-7.7905 c. 19: 1 7 11 N T3 SD: 4.3094 c. M:-5.7932 c. 20: 1 7 12 N T3 SD: 3.3440 c. M: 4.6920 c. 22: 1 8 13 N T3 SD: 0.6605 c. M:-1.1321 c. 49: 2 18 29 N T3 SD: 0.7702 c. M: 1.1779 c. 68: 3 25 40 N T3 SD: 0.7257 c. M:-1.1674 c. 71: 3 26 42 N T3 SD: 0.3860 c. M: 0.4832 c. 93: 4 34 55 N T3 SD: 0.2405 c. M: 0.4077 c. 115: 5 42 68 N T3 SD: 0.2253 c. M: 0.3612 c. 137: 6 50 81 N T3 SD: 0.2596 c. M: 0.3296 c. 139: 6 51 82 N T3 SD: 0.1873 c. M:-0.3243 c. 161: 7 59 95 N T3 SD: 0.1714 c. M:-0.2575 c. 210: 9 77 124 N T3 SD: 0.0978 c. M: 0.1615 c. 232: 10 85 137 N T3 SD: 0.0286 c. M: 0.0388 c. 486: 21 178 287 N T3 SD: 0.0151 c. M:-0.0220 c. 718: 31 263 424 N T3 SD: 0.0145 c. M:-0.0249 c. 1043: 45 382 616 N T3 SD: 0.0127 c. M: 0.0183 c. 1065: 46 390 629 N T3 SD: 0.0095 c. M: 0.0155 c. 1297: 56 475 766 N T3 SD: 0.0044 c. M: 0.0072 c. 1783: 77 653 1053 N T3 SD: 0.0013 c. M:-0.0021 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 14 x 16:19 SD: 20.5077 cents 22:23:25:29 SD: 20.4639 cents 23:24:26:31 SD: 18.6847 cents 24:25:27:32 SD: 16.3887 cents 26:27:29:35 SD: 16.3858 cents 27:28:30:36 S SD: 15.5671 cents 29:30:33:39 SD: 14.8887 cents 30:31:34:40 SD: 12.5013 cents 31:32:35:41 SD: 12.2670 cents 32:33:36:43 SD: 11.5019 cents 33:34:37:44 SD: 10.2453 cents 38:39:43:51 SD: 9.3173 cents 39:40:44:52 SD: 7.6205 cents 42:43:47:56 SD: 7.1037 cents 45:46:51:60 SD: 6.9679 cents 46:47:52:61 SD: 6.7159 cents 47:48:53:63 SD: 6.0030 cents 48:49:54:64 SD: 4.7302 cents 54:55:61:72 SD: 4.1610 cents 56:57:63:75 SD: 3.9851 cents 57:58:64:76 SD: 3.0808 cents 63:64:71:84 SD: 2.1720 cents 72:73:81:96 SD: 0.7911 cents 153:155:172:204 SD: 0.5310 cents 159:161:179:212 SD: 0.4056 cents 168:170:189:224 SD: 0.3394 cents 240:243:270:320 SD: 0.0000 cents