Scala analysis: 175_C7
Chromatic tetrachord 40/39 * 143/135 * 27/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 88/81 143.497939 2nd undecimal neutral second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/22 354.5471 neutral third, Zalzal wosta of al-Farabi 1: 40/39 43.8311 tridecimal minor diesis 2: 143/135 99.6669 3: 27/22 354.5471 neutral third, Zalzal wosta of al-Farabi
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 143/135 99.667 cents 1: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 88/81 143.498 cents 2nd undecimal neutral second 2: 1 180/143 398.378 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished 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 : 43.8 143.5 498.0 43.8 : 99.7 454.2 498.0 143.5: 354.5 398.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 354.5471 cents 1053/880, 310.7160 cents 40/39, 43.8311 cents 2: 143.4979 .. 454.2139 cents 1053/880, 310.7160 cents 1936/2187,-211.0491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 27/22, 354.5471 cents Average / Smallest step : 3.787612 Largest / Average step : 2.135633 Largest / Smallest step : 8.088947 Median interval of one step : 143/135, 99.6669 cents, amount: 1 Least squares average step : 130.35442 cents, oct.: 391.06327 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1659-tone equal temperament with octave 4/3 degrees: 146 478 1659 Least number of segments generator : 830 of 249.173 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1513 of 454.215 cents and inv. generated superset size: 27 = 24 more = 900.000% 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 43.83105 cents Scale diversity : 0.677798 Lumma stability : 0.176012 Lumma impropriety factor : 0.423755 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 : 40/39, 43.8311 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 : 13 Odd number limit : 143 (O: 143 U: 143) Highest odd numerator or denominator: 81 Scale harmonicity : 0.016556 Average absolute harmonicity : 0.091635 Specific harmonicity : 0.087812 Fundamental : 1/1053, -10.0403 octaves, 0.2485 Hz. Guide tone : 440, 8.7814 octaves, 115115.249 Hz. Exponens Consonantiae : 4.633200E+05, 18.82165 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 127.5, average 42.50000 Mersenne's string divisions : 93457 Sum of van Prooijen's expressibility: 3.97667, average 1.32556 Sum of Tenney's harmonic distance : 8.12527, average 2.70842 Vogel's harmonic complexity : 22.66667 Wille's k value : 175 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 19.31197, average 3.21866 Lattice compactness (without 2's) : 14.89575, average 2.48262 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -4 ..-1 -2.00000 6 1 5: 0 .. 1 0.33333 1 11: 0 .. 1 0.33333 1 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 25 25| Scale is weakly epimorphic with val: <6 10 15 25 28| Scale is weakly epimorphic with val: <6 10 16 25 26| Scale is weakly epimorphic with val: <6 10 16 25 29| Scale is weakly epimorphic with val: <6 10 17 25 27| Scale is weakly epimorphic with val: <6 10 17 25 30| Scale is weakly epimorphic with val: <6 10 18 25 25| Scale is weakly epimorphic with val: <6 10 18 25 28| Scale is weakly epimorphic with val: <6 10 19 25 26| Scale is weakly epimorphic with val: <6 10 19 25 29| Scale is weakly epimorphic with val: <7 10 17 24 25| Scale is weakly epimorphic with val: <7 10 18 24 26| Scale is weakly epimorphic with val: <7 10 19 24 27| Scale is weakly epimorphic with val: <7 10 19 27 27| Scale is weakly epimorphic with val: <7 11 15 24 26| Scale is weakly epimorphic with val: <7 11 15 24 29| Scale is weakly epimorphic with val: <7 11 15 25 27| Scale is weakly epimorphic with val: <7 11 15 25 30| Scale is weakly epimorphic with val: <7 11 15 27 29| Scale is weakly epimorphic with val: <7 11 16 24 27| Scale is weakly epimorphic with val: <7 11 16 24 30| Scale is JI-epimorphic with val: <7 11 16 25 25| Scale is weakly epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 27 27| Scale is weakly epimorphic with val: <7 11 16 27 30| Scale is weakly epimorphic with val: <7 11 17 24 25| Scale is weakly epimorphic with val: <7 11 17 24 28| Scale is JI-epimorphic with val: <7 11 17 25 26| Scale is weakly epimorphic with val: <7 11 17 25 29| Scale is weakly epimorphic with val: <7 11 17 27 28| Scale is weakly epimorphic with val: <7 11 18 24 26| Scale is weakly epimorphic with val: <7 11 18 24 29| Scale is JI-epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 19 24 27| Scale is weakly epimorphic with val: <7 11 19 24 30| Scale is weakly epimorphic with val: <7 11 19 25 25| Scale is JI-epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 27 27| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 12 19 25 25| Scale is weakly epimorphic with val: <8 11 15 23 27| Scale is weakly epimorphic with val: <8 11 15 23 30| Scale is weakly epimorphic with val: <8 11 15 24 25| Scale is weakly epimorphic with val: <8 11 16 23 25| Scale is weakly epimorphic with val: <8 11 16 23 28| Scale is weakly epimorphic with val: <8 11 16 24 26| Scale is weakly epimorphic with val: <8 11 17 23 26| Scale is weakly epimorphic with val: <8 11 17 23 29| Scale is weakly epimorphic with val: <8 11 17 24 27| Scale is weakly epimorphic with val: <8 11 17 27 27| Scale is weakly epimorphic with val: <8 11 18 23 27| Scale is weakly epimorphic with val: <8 11 18 23 30| Scale is weakly epimorphic with val: <8 11 18 24 28| Scale is weakly epimorphic with val: <8 11 18 27 28| Scale is weakly epimorphic with val: <8 11 19 23 25| Scale is weakly epimorphic with val: <8 11 19 23 28| Scale is weakly epimorphic with val: <8 11 19 24 29| Scale is weakly epimorphic with val: <8 11 19 27 29| Scale is weakly epimorphic with val: <8 12 15 27 28| Scale is weakly epimorphic with val: <8 12 16 23 25| Scale is weakly epimorphic with val: <8 12 16 27 29| Scale is weakly epimorphic with val: <8 12 17 23 26| Scale is weakly epimorphic with val: <8 12 17 26 26| Scale is weakly epimorphic with val: <8 12 17 27 27| Scale is weakly epimorphic with val: <8 12 17 27 30| Scale is weakly epimorphic with val: <8 12 18 23 27| Scale is weakly epimorphic with val: <8 12 18 26 27| Scale is weakly epimorphic with val: <8 12 18 27 28| Scale is weakly epimorphic with val: <8 12 19 23 28| Scale is weakly epimorphic with val: <8 12 19 26 28| Scale is weakly epimorphic with val: <8 12 19 27 29|
FIT/MODE
3: 0 1 2 N G T3 SD: 28.4498 c. M: 43.8311 c. 4: 0 1 3 N G T3 SD: 27.5781 c. M: 43.8311 c. 7: 1 1 5 N M DE S SD: 15.7874 c. M:-27.3182 c. 8: 1 1 6 N M DE S SD: 15.2748 c. M: 18.9867 c. 9: 1 2 6 N T3 SD: 14.5995 c. M:-22.5171 c. 10: 1 2 7 N T3 SD: 4.8537 c. M:-5.9734 c. 11: 1 2 8 N T3 SD: 4.5048 c. M: 7.6675 c. 21: 2 4 15 N T3 SD: 2.1918 c. M:-3.6018 c. 24: 2 5 17 N T3 SD: 1.6864 c. M: 2.3273 c. 34: 3 7 24 N T3 SD: 1.7252 c. M:-2.9859 c. 35: 3 7 25 N T3 SD: 0.9559 c. M: 1.1994 c. 45: 4 9 32 N T3 SD: 0.3361 c. M:-0.4396 c. 80: 7 16 57 N T3 SD: 0.2307 c. M: 0.3100 c. 125: 11 25 89 N T3 SD: 0.0353 c. M: 0.0610 c. 420: 37 84 299 N T3 SD: 0.0268 c. M:-0.0443 c. 545: 48 109 388 N T3 SD: 0.0239 c. M:-0.0335 c. 670: 59 134 477 N T3 SD: 0.0237 c. M: 0.0312 c. 944: 83 189 672 N T3 SD: 0.0240 c. M: 0.0411 c. 989: 87 198 704 N T3 SD: 0.0176 c. M:-0.0236 c. 1114: 98 223 793 N T3 SD: 0.0129 c. M: 0.0174 c. 1239: 109 248 882 N T3 SD: 0.0100 c. M: 0.0160 c. 1284: 113 257 914 N T3 SD: 0.0114 c. M:-0.0197 c. 1364: 120 273 971 N T3 SD: 0.0085 c. M: 0.0148 c. 1409: 124 282 1003 N T3 SD: 0.0072 c. M:-0.0125 c. 1489: 131 298 1060 N T3 SD: 0.0084 c. M: 0.0138 c. 1534: 135 307 1092 N T3 SD: 0.0038 c. M:-0.0066 c. 1659: 146 332 1181 N T3 SD: 0.0009 c. M:-0.0015 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: 95.8750 cents 6 x 7:8 S SD: 61.6865 cents 7 x 8:9 S SD: 53.9703 cents 8 x 9:11 SD: 40.2729 cents 9 x 10:12 S SD: 19.4529 cents 10 x 11:13 SD: 24.4115 cents 11 x 12:15 S SD: 19.7777 cents 12 x 13:16 SD: 2.4626 cents 13 x 14:17 SD: 18.4469 cents 14 x 15:19 SD: 19.4781 cents 15 x 16:20 S SD: 15.8833 cents 16 x 17:21 SD: 23.6054 cents 17 x 18:23 SD: 25.6070 cents 18:19:20:24 S SD: 21.0579 cents 19:20:21:25 SD: 19.5344 cents 20:21:22:27 SD: 16.9192 cents 21:22:23:28 SD: 13.0945 cents 22:23:24:29 SD: 13.0798 cents 23:24:25:31 SD: 11.7475 cents 24:25:26:32 SD: 9.0965 cents 30:31:33:40 SD: 8.3656 cents 31:32:34:41 SD: 8.0976 cents 32:33:35:43 SD: 6.7181 cents 33:34:36:44 SD: 3.5373 cents 36:37:39:48 SD: 2.0341 cents 69:71:75:92 SD: 1.9002 cents 78:80:85:104 SD: 1.7628 cents 81:83:88:108 SD: 0.5346 cents 117:120:127:156 SD: 0.5047 cents 195:200:212:260 SD: 0.4034 cents 198:203:215:264 SD: 0.3697 cents 231:237:251:308 SD: 0.2058 cents 312:320:339:416 SD: 0.0631 cents