Scala analysis: 186_C9
Chromatic tetrachord 256/245 * 245/234 * 39/32
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/245 76.034473 septimal minor semitone 2: 128/117 155.562336 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina 1: 256/245 76.0345 septimal minor semitone 2: 245/234 79.5279 3: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/245 76.034 cents septimal minor semitone 1: 1 245/234 79.528 cents 1: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 1 128/117 155.562 cents 2: 1 312/245 418.517 cents 2: 1 245/192 422.011 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 : 76.0 155.6 498.0 76.0 : 79.5 422.0 498.0 155.6: 342.5 418.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.0345 .. 342.4827 cents 9555/8192, 266.4482 cents 256/245, 76.0345 cents 2: 155.5623 .. 422.0105 cents 9555/8192, 266.4482 cents 4096/4563,-186.9203 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/245, 76.0345 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 39/32, 342.4827 cents Average / Smallest step : 2.183418 Largest / Average step : 2.062962 Largest / Smallest step : 4.504308 Median interval of one step : 245/234, 79.5279 cents, amount: 1 Least squares average step : 134.37815 cents, oct.: 403.13446 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1572-tone equal temperament with octave 4/3 degrees: 240 491 1572 Least number of segments generator : 787 of 249.339 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 845 of 267.715 cents and inv. generated superset size: 90 = 87 more = 3000.000% 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 76.03447 cents Scale diversity : 0.839166 Lumma stability : 0.305332 Lumma impropriety factor : 0.375308 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 : 60025/59904, 3.4934 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 262.9548 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 245 (O: 245 U: 245) Highest odd numerator or denominator: 245 Scale harmonicity : 0.016011 Average absolute harmonicity : 0.090625 Specific harmonicity : 0.082033 Fundamental : 1/28665, -14.8070 octaves, 0.0091 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 7.338240E+06, 22.80700 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 376.5, average 125.50000 Mersenne's string divisions : 122745 Sum of van Prooijen's expressibility: 4.93447, average 1.64482 Sum of Tenney's harmonic distance : 10.05198, average 3.35066 Vogel's harmonic complexity : 30.00000 Wille's k value : 4777 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 32.88468, average 5.48078 Lattice compactness (without 2's) : 12.49812, average 2.08302 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 5.66667 17 3: -2 .. 0 -1.00000 3 1 5: -1 .. 0 -0.33333 1 7: -2 .. 0 -0.66667 2 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-7 / 3 =-2.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 10 15 18 26| Scale is weakly epimorphic with val: <7 10 15 19 27| Scale is weakly epimorphic with val: <7 10 15 19 30| Scale is weakly epimorphic with val: <7 10 15 21 26| Scale is weakly epimorphic with val: <7 10 16 19 26| Scale is weakly epimorphic with val: <7 10 16 22 26| Scale is weakly epimorphic with val: <7 10 17 18 27| Scale is weakly epimorphic with val: <7 10 17 18 30| Scale is weakly epimorphic with val: <7 10 17 20 26| Scale is weakly epimorphic with val: <7 10 18 18 26| Scale is weakly epimorphic with val: <7 10 18 21 26| Scale is weakly epimorphic with val: <7 10 19 19 26| Scale is weakly epimorphic with val: <7 10 19 22 26| Scale is weakly epimorphic with val: <7 11 15 18 26| Scale is weakly epimorphic with val: <7 11 15 18 29| Scale is JI-epimorphic with val: <7 11 15 20 25| Scale is weakly epimorphic with val: <7 11 15 20 28| Scale is weakly epimorphic with val: <7 11 15 21 26| Scale is weakly epimorphic with val: <7 11 15 21 29| Scale is weakly epimorphic with val: <7 11 16 18 25| Scale is weakly epimorphic with val: <7 11 16 18 28| Scale is weakly epimorphic with val: <7 11 16 19 26| Scale is weakly epimorphic with val: <7 11 16 19 29| Scale is weakly epimorphic with val: <7 11 16 21 25| Scale is weakly epimorphic with val: <7 11 16 21 28| Scale is weakly epimorphic with val: <7 11 16 22 26| Scale is weakly epimorphic with val: <7 11 16 22 29| Scale is JI-epimorphic with val: <7 11 17 19 25| Scale is weakly epimorphic with val: <7 11 17 19 28| Scale is weakly epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 22 25| Scale is weakly epimorphic with val: <7 11 17 22 28| Scale is weakly epimorphic with val: <7 11 18 18 26| Scale is weakly epimorphic with val: <7 11 18 18 29| Scale is weakly epimorphic with val: <7 11 18 20 25| Scale is weakly epimorphic with val: <7 11 18 20 28| Scale is weakly epimorphic with val: <7 11 18 21 26| Scale is weakly epimorphic with val: <7 11 18 21 29| Scale is weakly epimorphic with val: <7 11 19 19 26| Scale is weakly epimorphic with val: <7 11 19 19 29| Scale is weakly epimorphic with val: <7 11 19 21 25| Scale is weakly epimorphic with val: <7 11 19 21 28| Scale is weakly epimorphic with val: <7 11 19 22 26| Scale is weakly epimorphic with val: <7 11 19 22 29| Scale is weakly epimorphic with val: <7 12 15 19 27| Scale is weakly epimorphic with val: <7 12 15 19 30| Scale is weakly epimorphic with val: <7 12 17 18 27| Scale is weakly epimorphic with val: <7 12 17 18 30| Scale is weakly epimorphic with val: <8 11 17 22 27| Scale is weakly epimorphic with val: <8 11 17 22 30| Scale is weakly epimorphic with val: <8 11 19 21 27| Scale is weakly epimorphic with val: <8 11 19 21 30| Scale is weakly epimorphic with val: <8 12 15 19 29| Scale is weakly epimorphic with val: <8 12 15 22 29| Scale is weakly epimorphic with val: <8 12 16 20 29| Scale is weakly epimorphic with val: <8 12 17 18 29| Scale is weakly epimorphic with val: <8 12 17 21 29| Scale is weakly epimorphic with val: <8 12 17 22 27| Scale is weakly epimorphic with val: <8 12 17 22 30| Scale is weakly epimorphic with val: <8 12 18 19 29| Scale is weakly epimorphic with val: <8 12 18 22 29| Scale is weakly epimorphic with val: <8 12 19 20 29| Scale is weakly epimorphic with val: <8 12 19 21 27| Scale is weakly epimorphic with val: <8 12 19 21 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 44.3114 c. M: 76.0345 c. 4: 0 1 3 N G T3 SD: 47.4180 c. M: 76.0345 c. 5: 1 1 3 N M DE S SD: 28.6448 c. M:-43.6557 c. 6: 1 1 4 N M DE S SD: 7.2545 c. M:-10.4527 c. 13: 2 2 9 N M DE S SD: 1.3805 c. M: 2.3177 c. 32: 5 5 22 N M DE S SD: 1.0316 c. M:-1.7851 c. 45: 7 7 31 N M DE S SD: 0.9036 c. M:-1.4392 c. 58: 9 9 40 N M DE S SD: 0.9223 c. M:-1.2484 c. 71: 11 11 49 N M DE S SD: 0.9670 c. M: 1.2385 c. 77: 12 12 53 N M DE S SD: 0.9333 c. M:-1.5829 c. 80: 12 13 55 N T3 SD: 0.7678 c. M: 1.3277 c. 86: 13 14 59 N T3 SD: 0.6328 c. M:-0.8006 c. 93: 14 15 64 N T3 SD: 0.6298 c. M: 1.0600 c. 99: 15 16 68 N T3 SD: 0.4006 c. M: 0.5731 c. 112: 17 18 77 N T3 SD: 0.2569 c. M: 0.4384 c. 125: 19 20 86 N T3 SD: 0.2158 c. M: 0.3316 c. 131: 20 21 90 N T3 SD: 0.1815 c. M:-0.3143 c. 144: 22 23 99 N T3 SD: 0.0548 c. M:-0.0767 c. 301: 46 48 207 N T3 SD: 0.0480 c. M:-0.0787 c. 413: 63 66 284 N T3 SD: 0.0355 c. M: 0.0615 c. 557: 85 89 383 N T3 SD: 0.0217 c. M: 0.0312 c. 570: 87 91 392 N T3 SD: 0.0212 c. M: 0.0325 c. 701: 107 112 482 N T3 SD: 0.0202 c. M:-0.0323 c. 714: 109 114 491 N T3 SD: 0.0062 c. M: 0.0105 c. 858: 131 137 590 N T3 SD: 0.0049 c. M:-0.0074 c. 1572: 240 251 1081 N T3 SD: 0.0022 c. M:-0.0029 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: 90.4986 cents 6 x 7:8 S SD: 55.6543 cents 7 x 8:9 S SD: 49.1966 cents 8 x 9:11 SD: 35.9705 cents 9 x 10:12 S SD: 13.4207 cents 10 x 11:13 SD: 22.4182 cents 11 x 12:15 S SD: 19.6081 cents 12 x 13:16 SD: 8.4948 cents 13 x 14:17 SD: 21.6417 cents 14 x 15:19 SD: 23.6831 cents 15:16 x 20 S SD: 17.8484 cents 17:18:19:23 SD: 16.7755 cents 18:19:20:24 S SD: 10.6933 cents 19:20:21:25 SD: 10.5529 cents 20:21:22:27 SD: 8.3185 cents 21:22:23:28 SD: 1.6331 cents 87:91:95:116 SD: 1.2415 cents 108:113:118:144 SD: 1.0775 cents 129:135:141:172 SD: 1.0335 cents 138:144:151:184 SD: 0.7907 cents 159:166:174:212 SD: 0.5114 cents 180:188:197:240 SD: 0.3370 cents 201:210:220:268 SD: 0.2774 cents 267:279:292:356 SD: 0.2042 cents 288:301:315:384 SD: 0.1938 cents 426:445:466:568 SD: 0.1759 cents 447:467:489:596 SD: 0.0909 cents 468:489:512:624 SD: 0.0145 cents