Scala analysis: 171_C7
Chromatic tetrachord 132/125 * 250/243 * 27/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 132/125 94.331802 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: 132/125 94.3318 2: 250/243 49.1661 maximal diesis, Porcupine comma 3: 27/22 354.5471 neutral third, Zalzal wosta of al-Farabi
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 250/243 49.166 cents maximal diesis, Porcupine comma 1: 1 132/125 94.332 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: 1 125/99 403.713 cents 2: 1 162/125 448.879 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 : 94.3 143.5 498.0 94.3 : 49.2 403.7 498.0 143.5: 354.5 448.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.1661 .. 354.5471 cents 6561/5500, 305.3809 cents 250/243, 49.1661 cents 2: 143.4979 .. 448.8789 cents 6561/5500, 305.3809 cents 1936/2187,-211.0491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 250/243, 49.1661 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 27/22, 354.5471 cents Average / Smallest step : 3.376613 Largest / Average step : 2.135633 Largest / Smallest step : 7.211204 Median interval of one step : 132/125, 94.3318 cents, amount: 1 Least squares average step : 133.96162 cents, oct.: 401.88486 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1246-tone equal temperament with octave 4/3 degrees: 236 359 1246 Least number of segments generator : 625 of 249.822 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1005 of 401.714 cents and inv. generated superset size: 33 = 30 more = 1100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 49.16614 cents Scale diversity : 0.703498 Lumma stability : 0.197437 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 : 16038/15625, 45.1657 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 11 Odd number limit : 243 (O: 125 U: 243) Highest odd numerator or denominator: 125 Scale harmonicity : 0.018617 Average absolute harmonicity : 0.089822 Specific harmonicity : 0.087915 Fundamental : 1/10125, -13.3056 octaves, 0.0258 Hz. Guide tone : 264, 8.0444 octaves, 69069.149 Hz. Exponens Consonantiae : 2.673000E+06, 21.35003 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 216.5, average 72.16667 Mersenne's string divisions : 304031 Sum of van Prooijen's expressibility: 4.48252, average 1.49417 Sum of Tenney's harmonic distance : 9.14963, average 3.04988 Vogel's harmonic complexity : 27.66667 Wille's k value : 1687 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 24.18243, average 4.03041 Lattice compactness (without 2's) : 21.17462, average 3.52910 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -4 .. 1 -1.33333 6 1 5: -3 .. 0 -1.00000 3 11: 0 .. 1 0.66667 2 2 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 11 / 3 = 3.66667 Scale is weakly epimorphic with val: <6 10 15 26| Scale is weakly epimorphic with val: <6 11 15 25| Scale is weakly epimorphic with val: <7 10 15 24| Scale is weakly epimorphic with val: <7 10 16 27| Scale is weakly epimorphic with val: <7 12 16 25| Scale is weakly epimorphic with val: <8 11 16 24| Scale is weakly epimorphic with val: <8 11 17 27| Scale is weakly epimorphic with val: <8 12 16 23| Scale is weakly epimorphic with val: <8 12 17 26|
FIT/MODE
3: 1 0 2 N G T3 SD: 43.3801 c. M:-71.6832 c. 4: 1 0 3 N G T3 SD: 20.5855 c. M:-30.1794 c. 6: 1 1 4 N M DE S SD: 14.5517 c. M:-22.5171 c. 7: 1 1 5 N M DE S SD: 13.4023 c. M: 23.1825 c. 9: 2 1 6 N T3 SD: 16.0642 c. M:-22.5171 c. 10: 2 1 7 N T3 SD: 4.5769 c. M:-5.9156 c. 17: 3 2 12 N T3 SD: 4.0991 c. M: 6.4415 c. 21: 4 2 15 N T3 SD: 0.7580 c. M: 1.1994 c. 52: 10 5 37 N T3 SD: 0.8406 c. M:-1.4461 c. 69: 13 7 49 N T3 SD: 0.5750 c. M:-0.8629 c. 80: 15 8 57 N T3 SD: 0.5760 c. M: 0.9484 c. 90: 17 9 64 N T3 SD: 0.2656 c. M:-0.3817 c. 111: 21 11 79 N T3 SD: 0.0781 c. M: 0.1071 c. 132: 25 13 94 N T3 SD: 0.0701 c. M: 0.1213 c. 243: 46 24 173 N T3 SD: 0.0340 c. M: 0.0517 c. 618: 117 61 440 N T3 SD: 0.0368 c. M: 0.0481 c. 628: 119 62 447 N T3 SD: 0.0367 c. M:-0.0469 c. 649: 123 64 462 N T3 SD: 0.0342 c. M:-0.0589 c. 739: 140 73 526 N T3 SD: 0.0324 c. M:-0.0522 c. 760: 144 75 541 N T3 SD: 0.0224 c. M:-0.0346 c. 871: 165 86 620 N T3 SD: 0.0178 c. M:-0.0259 c. 892: 169 88 635 N T3 SD: 0.0167 c. M:-0.0287 c. 1003: 190 99 714 N T3 SD: 0.0088 c. M:-0.0137 c. 1114: 211 110 793 N T3 SD: 0.0082 c. M:-0.0141 c. 1135: 215 112 808 N T3 SD: 0.0082 c. M:-0.0115 c. 1246: 236 123 887 N T3 SD: 0.0006 c. M:-0.0010 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 15:16 x 20 S SD: 8.6997 cents 16:17 x 21 SD: 14.6304 cents 17:18 x 23 SD: 12.8466 cents 19:20:21:25 SD: 12.6608 cents 20:21:22:27 SD: 10.6581 cents 21:22:23:28 SD: 6.5504 cents 27 x 29:36 SD: 9.8929 cents 28 x 30:37 SD: 14.3155 cents 29:31:32:39 SD: 12.4370 cents 30:32:33:40 SD: 9.2211 cents 31:33:34:41 SD: 8.5606 cents 32:34:35:43 SD: 6.9114 cents 33:35:36:44 SD: 3.4600 cents 36:38:39:48 SD: 1.6596 cents 69:73:75:92 SD: 1.1132 cents 105:111:114:140 SD: 0.7281 cents 126:133:137:168 SD: 0.5275 cents 162:171:176:216 SD: 0.2429 cents 231:244:251:308 SD: 0.1737 cents 393:415:427:524 SD: 0.0513 cents