Scala analysis: 574_M82
Miscellaneous tetrachord 360/343 * 343/309 * 103/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 360/343 83.745996 2: 120/103 264.468082 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 103/90 233.5769 1: 360/343 83.7460 2: 343/309 180.7221 3: 103/90 233.5769
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 360/343 83.746 cents 1: 1 343/309 180.722 cents 1: 1 103/90 233.577 cents 2: 1 120/103 264.468 cents 2: 1 412/343 317.323 cents 2: 1 343/270 414.299 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 : 83.7 264.5 498.0 83.7 : 180.7 414.3 498.0 264.5: 233.6 317.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.7460 .. 233.5769 cents 35329/32400, 149.8309 cents 360/343, 83.7460 cents 2: 264.4681 .. 414.2990 cents 35329/32400, 149.8309 cents 10800/10609, 30.8912 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 360/343, 83.7460 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 103/90, 233.5769 cents Average / Smallest step : 1.982363 Largest / Average step : 1.406963 Largest / Smallest step : 2.789111 Median interval of one step : 343/309, 180.7221 cents, amount: 1 Least squares average step : 150.48694 cents, oct.: 451.46082 cents Scale is strictly proper Scale has trivalence property 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 30.89117 cents Scale diversity : 1.083230 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.398324 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 : 10800/10609, 30.8912 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 103 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 343 Scale harmonicity : 0.020722 Fundamental : 1/105987, -16.6935 octaves, 0.0025 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 3.815532E+07, 25.18538 octaves Euler's gradus suavitatis : 134 Sum of Mann's harmonic distance : 466.5, average 155.50000 Mersenne's string divisions : 1097383 Sum of van Prooijen's expressibility: 5.02525, average 1.67508 Sum of Tenney's harmonic distance : 10.26280, average 3.42093 Vogel's harmonic complexity : 93.66667 Wille's k value : 17664 Wilson's harmonic complexity : 138 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 20.43243, average 3.40540 Lattice compactness (without 2's) : 15.91312, average 2.65219 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 7: -3 .. 0 -1.00000 3 1 103: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 11 17 18 47| Scale is weakly epimorphic with val: <7 10 16 18 48| Scale is weakly epimorphic with val: <7 10 19 19 48| Scale is weakly epimorphic with val: <7 11 15 18 48| Scale is weakly epimorphic with val: <7 11 15 19 48| Scale is weakly epimorphic with val: <7 11 15 20 48| Scale is weakly epimorphic with val: <7 11 15 21 48| Scale is weakly epimorphic with val: <7 11 15 22 48| Scale is weakly epimorphic with val: <7 11 16 18 47| Scale is weakly epimorphic with val: <7 11 16 19 47| Scale is weakly epimorphic with val: <7 11 16 20 47| Scale is weakly epimorphic with val: <7 11 16 21 47| Scale is weakly epimorphic with val: <7 11 16 22 47| Scale is weakly epimorphic with val: <7 11 18 18 48| Scale is weakly epimorphic with val: <7 11 18 19 48| Scale is JI-epimorphic with val: <7 11 18 20 48| Scale is weakly epimorphic with val: <7 11 18 21 48| Scale is weakly epimorphic with val: <7 11 18 22 48| Scale is weakly epimorphic with val: <7 11 19 19 47| Scale is weakly epimorphic with val: <7 11 19 20 47| Scale is weakly epimorphic with val: <7 11 19 21 47| Scale is weakly epimorphic with val: <7 11 19 22 47| Scale is weakly epimorphic with val: <7 12 15 19 47| Scale is weakly epimorphic with val: <7 12 18 20 47| Scale is weakly epimorphic with val: <7 12 19 19 49| Scale is weakly epimorphic with val: <7 12 19 20 49| Scale is weakly epimorphic with val: <7 12 19 21 49| Scale is weakly epimorphic with val: <7 12 19 22 49| Scale is weakly epimorphic with val: <8 11 15 18 47| Scale is weakly epimorphic with val: <8 11 15 19 47| Scale is weakly epimorphic with val: <8 11 15 20 47| Scale is weakly epimorphic with val: <8 11 15 21 47| Scale is weakly epimorphic with val: <8 11 15 22 47| Scale is weakly epimorphic with val: <8 11 17 20 48| Scale is weakly epimorphic with val: <8 12 15 20 49| Scale is weakly epimorphic with val: <8 12 18 21 49|
FIT/MODE
3: 0 1 2 N G T3 SD: 74.6244 c. M: 98.4531 c. 4: 1 1 2 P M ME S SD: 25.1686 c. M:-40.7653 c. 5: 1 2 2 SP M ME S SD: 21.8493 c. M:-34.3589 c. 6: 1 2 3 P T3 SD: 8.9277 c. M: 15.4456 c. 11: 2 4 5 SP T3 SD: 5.7178 c. M:-7.1928 c. 13: 2 5 6 SP T3 SD: 4.6372 c. M: 7.1237 c. 17: 3 6 8 SP T3 SD: 2.4366 c. M:-4.1443 c. 30: 5 11 14 SP T3 SD: 0.7919 c. M:-1.1559 c. 47: 8 17 22 SP T3 SD: 0.6476 c. M:-1.0276 c. 66: 11 24 31 SP T3 SD: 0.4727 c. M: 0.7385 c. 77: 13 28 36 SP T3 SD: 0.4621 c. M:-0.7247 c. 83: 14 30 39 SP T3 SD: 0.2976 c. M: 0.4442 c. 113: 19 41 53 SP T3 SD: 0.0114 c. M: 0.0194 c. 1499: 252 544 703 SP T3 SD: 0.0110 c. M: 0.0186 c. 1546: 260 561 725 SP T3 SD: 0.0127 c. M:-0.0177 c. 1612: 271 585 756 SP T3 SD: 0.0103 c. M: 0.0176 c. 1659: 279 602 778 SP T3 SD: 0.0112 c. M:-0.0151 c. 1725: 290 626 809 SP T3 SD: 0.0097 c. M: 0.0167 c. 1772: 298 643 831 SP T3 SD: 0.0098 c. M:-0.0129 c. 1838: 309 667 862 SP T3 SD: 0.0092 c. M: 0.0159 c. 1885: 317 684 884 SP T3 SD: 0.0086 c. M:-0.0110 c. 1998: 336 725 937 SP T3 SD: 0.0076 c. M:-0.0093 c. 2111: 355 766 990 SP T3 SD: 0.0067 c. M:-0.0086 c. 2224: 374 807 1043 SP T3 SD: 0.0059 c. M:-0.0080 c. 2337: 393 848 1096 SP T3 SD: 0.0052 c. M:-0.0074 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: 49.3797 cents 6 x 7:8 S SD: 1.2014 cents 7 x 8:9 S SD: 35.6110 cents 8 x 9:11 SD: 40.3277 cents 9 x 10:12 S SD: 41.0322 cents 10:11:12:13 H SD: 35.1864 cents 11:12:13:15 SD: 27.0806 cents 12:13:14:16 S SD: 18.2931 cents 16:17:19:21 SD: 15.9344 cents 17:18:20:23 SD: 11.3302 cents 18:19:21:24 SD: 3.3819 cents 42:44:49:56 SD: 1.3363 cents 60:63:70:80 S SD: 0.8362 cents 162:170:189:216 SD: 0.8070 cents 182:191:212:243 SD: 0.8015 cents 183:192:213:244 SD: 0.5908 cents 201:211:234:268 SD: 0.4431 cents 243:255:283:324 SD: 0.2392 cents 261:274:304:348 SD: 0.2000 cents 303:318:353:404 SD: 0.0355 cents