Scala analysis: 297_C22
Chromatic tetrachord 184/173 * 173/162 * 27/23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 184/173 106.720474 2: 92/81 220.454344 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/23 277.5907 vicesimotertial minor third 1: 184/173 106.7205 2: 173/162 113.7339 3: 27/23 277.5907 vicesimotertial minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 184/173 106.720 cents 1: 1 173/162 113.734 cents 1: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 92/81 220.454 cents 2: 1 216/173 384.311 cents 2: 1 173/138 391.325 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 : 106.7 220.5 498.0 106.7: 113.7 391.3 498.0 220.5: 277.6 384.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 106.7205 .. 277.5907 cents 4671/4232, 170.8702 cents 184/173, 106.7205 cents 2: 220.4543 .. 391.3245 cents 4671/4232, 170.8702 cents 2116/2187,-57.1363 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 184/173, 106.7205 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 27/23, 277.5907 cents Average / Smallest step : 1.555606 Largest / Average step : 1.672082 Largest / Smallest step : 2.601100 Median interval of one step : 173/162, 113.7339 cents, amount: 1 Least squares average step : 145.84030 cents, oct.: 437.52089 cents Scale is not proper Scale has trivalence property Scale is a mode of a 924-tone equal temperament with octave 4/3 degrees: 198 409 924 Least number of segments generator : 463 of 249.562 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 515 of 277.590 cents and inv. generated superset size: 67 = 64 more = 2233.333% 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 57.13631 cents Scale diversity : 1.130819 Lumma stability : 0.428558 Lumma impropriety factor : 0.114721 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 : 29929/29808, 7.0134 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 163.8568 cents: 2 -- Rational properties -- Prime limit : 173 Odd number limit : 173 (O: 173 U: 173) Highest odd numerator or denominator: 173 Scale harmonicity : 0.017936 Fundamental : 1/14013, -13.7745 octaves, 0.0187 Hz. Guide tone : 184, 7.5236 octaves, 48139.104 Hz. Exponens Consonantiae : 2.578392E+06, 21.29804 octaves Euler's gradus suavitatis : 206 Sum of Mann's harmonic distance : 268.5, average 89.50000 Mersenne's string divisions : 61761 Sum of van Prooijen's expressibility: 4.62365, average 1.54122 Sum of Tenney's harmonic distance : 9.45432, average 3.15144 Vogel's harmonic complexity : 140.00000 Wille's k value : 2335 Wilson's harmonic complexity : 208 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 18.99836, average 3.16639 Lattice compactness (without 2's) : 14.69960, average 2.44993 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -4 .. 0 -1.66667 5 1 23: 0 .. 1 0.66667 2 1 173: -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: <6 10 31 54| Scale is weakly epimorphic with val: <6 11 35 54| Scale is weakly epimorphic with val: <7 11 31 53| Scale is weakly epimorphic with val: <7 11 32 55| Scale is weakly epimorphic with val: <7 11 34 53| Scale is weakly epimorphic with val: <7 11 35 55| Scale is weakly epimorphic with val: <7 12 35 53| Scale is weakly epimorphic with val: <8 11 31 54| Scale is weakly epimorphic with val: <8 11 32 53| Scale is weakly epimorphic with val: <8 12 34 55| Scale is weakly epimorphic with val: <8 12 35 54|
FIT/MODE
3: 0 1 2 N G T3 SD: 69.1686 c. M: 106.7205 c. 4: 1 1 2 P M ME S SD: 19.4307 c. M:-28.5682 c. 5: 1 1 3 N M DE S SD: 12.9300 c. M: 21.2363 c. 9: 2 2 5 N M DE S SD: 2.3423 c. M:-3.9562 c. 23: 5 5 13 N M DE S SD: 2.4300 c. M: 3.9130 c. 29: 6 7 16 N T3 SD: 2.6707 c. M: 3.6767 c. 32: 7 7 18 N M DE S SD: 1.9588 c. M: 2.5597 c. 38: 8 9 21 N T3 SD: 1.7359 c. M:-2.3553 c. 43: 9 10 24 N T3 SD: 1.4484 c. M: 2.4785 c. 47: 10 11 26 N T3 SD: 1.2753 c. M:-2.0764 c. 52: 11 12 29 N T3 SD: 0.7937 c. M: 1.3648 c. 61: 13 14 34 N T3 SD: 0.3347 c. M: 0.5797 c. 70: 15 16 39 N T3 SD: 0.0626 c. M:-0.1084 c. 341: 73 78 190 N T3 SD: 0.0771 c. M: 0.1009 c. 411: 88 94 229 N T3 SD: 0.0712 c. M:-0.0911 c. 434: 93 99 242 N T3 SD: 0.0699 c. M: 0.1211 c. 481: 103 110 268 N T3 SD: 0.0677 c. M:-0.0936 c. 495: 106 113 276 N T3 SD: 0.0734 c. M: 0.1072 c. 504: 108 115 281 N T3 SD: 0.0515 c. M: 0.0892 c. 513: 110 117 286 N T3 SD: 0.0591 c. M:-0.0728 c. 565: 121 129 315 N T3 SD: 0.0578 c. M: 0.0805 c. 574: 123 131 320 N T3 SD: 0.0376 c. M: 0.0651 c. 583: 125 133 325 N T3 SD: 0.0472 c. M:-0.0645 c. 635: 136 145 354 N T3 SD: 0.0459 c. M: 0.0596 c. 644: 138 147 359 N T3 SD: 0.0268 c. M: 0.0462 c. 714: 153 163 398 N T3 SD: 0.0180 c. M: 0.0311 c. 784: 168 179 437 N T3 SD: 0.0109 c. M: 0.0186 c. 854: 183 195 476 N T3 SD: 0.0051 c. M: 0.0082 c. 924: 198 211 515 N T3 SD: 0.0020 c. M:-0.0035 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: 63.6303 cents 6 x 7:8 S SD: 23.2083 cents 7 x 8:9 S SD: 31.9335 cents 8 x 9:11 SD: 27.8914 cents 9 x 10:12 S SD: 19.0253 cents 10 x 11:13 SD: 35.3408 cents 11:12:13:15 SD: 30.1287 cents 12:13:14:16 S SD: 18.7648 cents 13:14:15:17 SD: 16.1255 cents 14:15:16:19 SD: 11.6223 cents 15:16:17:20 SD: 2.0897 cents 66:70:75:88 SD: 1.6429 cents 81:86:92:108 SD: 1.0076 cents 96:102:109:128 SD: 0.6202 cents 111:118:126:148 SD: 0.4415 cents 237:252:269:316 SD: 0.4277 cents 315:335:358:420 SD: 0.3618 cents 330:351:375:440 SD: 0.2865 cents 345:367:392:460 SD: 0.2400 cents 360:383:409:480 SD: 0.2280 cents 426:453:484:568 SD: 0.2083 cents 441:469:501:588 SD: 0.1373 cents 456:485:518:608 SD: 0.0828 cents 471:501:535:628 SD: 0.0720 cents 567:603:644:756 SD: 0.0498 cents 582:619:661:776 SD: 0.0328 cents