Scala analysis: 547_M55
Miscellaneous tetrachord 360/347 * 347/321 * 107/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 360/347 63.673493 2: 120/107 198.508331 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 107/90 299.5367 1: 360/347 63.6735 2: 347/321 134.8348 3: 107/90 299.5367
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 360/347 63.673 cents 1: 1 347/321 134.835 cents 1: 1 107/90 299.537 cents 2: 1 120/107 198.508 cents 2: 1 428/347 363.210 cents 2: 1 347/270 434.372 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 : 63.7 198.5 498.0 63.7 : 134.8 434.4 498.0 198.5: 299.5 363.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.6735 .. 299.5367 cents 37129/32400, 235.8632 cents 360/347, 63.6735 cents 2: 198.5083 .. 434.3715 cents 37129/32400, 235.8632 cents 10800/11449,-101.0283 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 360/347, 63.6735 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 107/90, 299.5367 cents Average / Smallest step : 2.607286 Largest / Average step : 1.804275 Largest / Smallest step : 4.704260 Median interval of one step : 347/321, 134.8348 cents, amount: 1 Least squares average step : 139.63037 cents, oct.: 418.89110 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1400-tone equal temperament with octave 4/3 degrees: 179 558 1400 Least number of segments generator : 701 of 249.378 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1121 of 398.792 cents and inv. generated superset size: 102 = 99 more = 3400.000% 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 63.67349 cents Scale diversity : 0.982062 Lumma stability : 0.255694 Lumma impropriety factor : 0.202850 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 : 360/347, 63.6735 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% -- Rational properties -- Prime limit : 347 Odd number limit : 347 (O: 347 U: 347) Highest odd numerator or denominator: 347 Scale harmonicity : 0.057471 Fundamental : 1/111387, -16.7652 octaves, 0.0023 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 4.009932E+07, 25.25707 octaves Euler's gradus suavitatis : 466 Sum of Mann's harmonic distance : 470.5, average 156.83333 Mersenne's string divisions : 160489 Sum of van Prooijen's expressibility: 5.04683, average 1.68228 Sum of Tenney's harmonic distance : 10.28438, average 3.42813 Vogel's harmonic complexity : 313.66667 Wille's k value : 18564 Wilson's harmonic complexity : 468 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 16.06046, average 2.67674 Lattice compactness (without 2's) : 11.04863, average 1.84144 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.66667 2 107: -1 .. 0 -0.33333 1 1 347: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 15 48 60| Scale is weakly epimorphic with val: <7 11 15 49 62| Scale is weakly epimorphic with val: <7 11 16 49 61| Scale is weakly epimorphic with val: <7 11 16 50 60| Scale is weakly epimorphic with val: <7 11 17 48 61| Scale is weakly epimorphic with val: <7 11 17 50 62| Scale is JI-epimorphic with val: <7 11 18 48 60| Scale is weakly epimorphic with val: <7 11 18 49 62| Scale is JI-epimorphic with val: <7 11 19 49 61| Scale is weakly epimorphic with val: <7 11 19 50 60| Scale is weakly epimorphic with val: <7 12 18 48 62| Scale is weakly epimorphic with val: <7 12 18 50 60| Scale is weakly epimorphic with val: <7 12 19 48 61| Scale is weakly epimorphic with val: <7 12 19 49 60| Scale is weakly epimorphic with val: <8 11 16 48 61| Scale is weakly epimorphic with val: <8 11 17 48 60| Scale is weakly epimorphic with val: <8 11 17 49 62| Scale is weakly epimorphic with val: <8 11 18 49 61| Scale is weakly epimorphic with val: <8 11 18 50 60| Scale is weakly epimorphic with val: <8 11 19 50 62| Scale is weakly epimorphic with val: <8 12 15 48 61| Scale is weakly epimorphic with val: <8 12 15 49 60| Scale is weakly epimorphic with val: <8 12 16 49 62| Scale is weakly epimorphic with val: <8 12 16 50 61| Scale is weakly epimorphic with val: <8 12 17 48 62| Scale is weakly epimorphic with val: <8 12 17 50 60|
FIT/MODE
3: 0 1 2 N G T3 SD: 41.2720 c. M: 63.6735 c. 5: 1 1 3 N M DE S SD: 20.7514 c. M:-35.9355 c. 6: 1 1 4 N M DE S SD: 21.8298 c. M: 32.4933 c. 7: 1 2 4 N T3 SD: 9.6450 c. M:-14.9395 c. 8: 1 2 5 N T3 SD: 6.8282 c. M: 11.7415 c. 15: 2 4 9 N T3 SD: 1.6300 c. M:-2.7325 c. 38: 5 10 23 N T3 SD: 1.5394 c. M: 1.9116 c. 40: 5 11 24 N T3 SD: 0.9154 c. M: 1.4179 c. 48: 6 13 29 N T3 SD: 1.1365 c. M: 1.4179 c. 55: 7 15 33 N T3 SD: 0.4417 c. M:-0.7097 c. 70: 9 19 42 N T3 SD: 0.4597 c. M:-0.7097 c. 78: 10 21 47 N T3 SD: 0.3434 c. M: 0.5674 c. 118: 15 32 71 N T3 SD: 0.2233 c. M: 0.3627 c. 133: 17 36 80 N T3 SD: 0.0240 c. M: 0.0393 c. 587: 75 159 353 N T3 SD: 0.0288 c. M: 0.0391 c. 720: 92 195 433 N T3 SD: 0.0224 c. M: 0.0344 c. 735: 94 199 442 N T3 SD: 0.0225 c. M:-0.0321 c. 853: 109 231 513 N T3 SD: 0.0187 c. M: 0.0312 c. 868: 111 235 522 N T3 SD: 0.0155 c. M:-0.0211 c. 1001: 128 271 602 N T3 SD: 0.0105 c. M:-0.0131 c. 1134: 145 307 682 N T3 SD: 0.0068 c. M:-0.0095 c. 1267: 162 343 762 N T3 SD: 0.0043 c. M:-0.0071 c. 1400: 179 379 842 N T3 SD: 0.0031 c. M:-0.0051 c. 1533: 196 415 922 N T3 SD: 0.0036 c. M: 0.0051 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: 72.2060 cents 6 x 7:8 S SD: 34.1813 cents 7 x 8:9 S SD: 35.4652 cents 8 x 9:11 SD: 26.7730 cents 9 x 10:12 S SD: 8.0523 cents 10 x 11:13 SD: 27.5848 cents 11 x 12:15 S SD: 30.8436 cents 12 x 13:16 SD: 29.9678 cents 13:14:15:17 SD: 29.3074 cents 14:15:16:19 SD: 23.8426 cents 15:16:17:20 SD: 17.1270 cents 16:17:18:21 S SD: 16.5888 cents 17:18:19:23 SD: 14.6019 cents 18:19:20:24 S SD: 11.3291 cents 22:23:25:29 SD: 10.9940 cents 23:24:26:31 SD: 8.4286 cents 24:25:27:32 SD: 2.9470 cents 51:53:57:68 SD: 2.2096 cents 57:59:64:76 SD: 1.4853 cents 81:84:91:108 SD: 1.0360 cents 108:112:121:144 SD: 0.6260 cents 132:137:148:176 SD: 0.2729 cents 189:196:212:252 SD: 0.2584 cents 321:333:360:428 SD: 0.0449 cents