Scala analysis: 583_M91
Miscellaneous tetrachord 38/35 * 35/32 * 64/57
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 38/35 142.373396 2: 19/16 297.513016 19th harmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/57 200.5320 1: 38/35 142.3734 2: 35/32 155.1396 septimal neutral second 3: 64/57 200.5320
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 38/35 142.373 cents 1: 1 35/32 155.140 cents septimal neutral second 1: 1 64/57 200.532 cents 2: 1 19/16 297.513 cents 19th harmonic 2: 1 128/105 342.905 cents septimal neutral third 2: 1 70/57 355.672 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 : 142.4 297.5 498.0 142.4: 155.1 355.7 498.0 297.5: 200.5 342.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 142.3734 .. 200.5320 cents 1120/1083, 58.1586 cents 38/35, 142.3734 cents 2: 297.5130 .. 355.6716 cents 1120/1083, 58.1586 cents 1083/1024, 96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 38/35, 142.3734 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 64/57, 200.5320 cents Average / Smallest step : 1.166054 Largest / Average step : 1.207915 Largest / Smallest step : 1.408493 Median interval of one step : 35/32, 155.1396 cents, amount: 1 Least squares average step : 159.39532 cents, oct.: 478.18595 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 96.98103 cents Scale diversity : 1.349616 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.766452 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 : 1225/1216, 12.7662 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle 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% Limited inverse transpositions with margin 45.3924 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 105 (O: 35 U: 105) Highest odd numerator or denominator: 35 Scale harmonicity : 0.016819 Average absolute harmonicity : 0.086612 Specific harmonicity : 0.074949 Fundamental : 1/1680, -10.7142 octaves, 0.1557 Hz. Guide tone : 76, 6.2479 octaves, 19883.543 Hz. Exponens Consonantiae : 1.276800E+05, 16.96217 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 57.5, average 19.16667 Mersenne's string divisions : 2555 Sum of van Prooijen's expressibility: 3.29994, average 1.09998 Sum of Tenney's harmonic distance : 6.68591, average 2.22864 Vogel's harmonic complexity : 26.33333 Wille's k value : 997 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 21.95581, average 3.65930 Lattice compactness (without 2's) : 8.56048, average 1.42675 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.33333 7 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 15 19 31| Scale is weakly epimorphic with val: <6 10 15 22 34| Scale is weakly epimorphic with val: <6 10 16 18 31| Scale is weakly epimorphic with val: <6 10 16 21 34| Scale is weakly epimorphic with val: <6 10 17 20 34| Scale is weakly epimorphic with val: <6 10 18 19 34| Scale is weakly epimorphic with val: <6 11 15 20 32| Scale is weakly epimorphic with val: <6 11 16 19 32| Scale is weakly epimorphic with val: <6 11 17 18 32| Scale is weakly epimorphic with val: <7 10 15 18 31| Scale is weakly epimorphic with val: <7 10 15 19 30| Scale is weakly epimorphic with val: <7 10 15 21 31| Scale is weakly epimorphic with val: <7 10 15 22 33| Scale is weakly epimorphic with val: <7 10 16 18 30| Scale is weakly epimorphic with val: <7 10 16 20 31| Scale is weakly epimorphic with val: <7 10 16 21 33| Scale is weakly epimorphic with val: <7 10 17 19 31| Scale is weakly epimorphic with val: <7 10 17 20 33| Scale is weakly epimorphic with val: <7 10 17 22 31| Scale is weakly epimorphic with val: <7 10 18 18 31| Scale is weakly epimorphic with val: <7 10 18 19 33| Scale is weakly epimorphic with val: <7 10 18 21 31| Scale is weakly epimorphic with val: <7 10 19 20 31| Scale is weakly epimorphic with val: <7 11 15 18 30| Scale is weakly epimorphic with val: <7 11 15 18 33| Scale is weakly epimorphic with val: <7 11 15 19 29| Scale is weakly epimorphic with val: <7 11 15 19 32| Scale is JI-epimorphic with val: <7 11 15 21 30| Scale is weakly epimorphic with val: <7 11 15 21 33| Scale is weakly epimorphic with val: <7 11 15 22 29| Scale is weakly epimorphic with val: <7 11 15 22 32| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is weakly epimorphic with val: <7 11 16 18 32| Scale is JI-epimorphic with val: <7 11 16 20 30| Scale is weakly epimorphic with val: <7 11 16 20 33| Scale is weakly epimorphic with val: <7 11 16 21 29| Scale is weakly epimorphic with val: <7 11 16 21 32| Scale is JI-epimorphic with val: <7 11 17 19 30| Scale is weakly epimorphic with val: <7 11 17 19 33| Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is weakly epimorphic with val: <7 11 17 20 32| Scale is weakly epimorphic with val: <7 11 17 22 30| Scale is weakly epimorphic with val: <7 11 17 22 33| Scale is JI-epimorphic with val: <7 11 18 18 30| Scale is weakly epimorphic with val: <7 11 18 18 33| Scale is weakly epimorphic with val: <7 11 18 19 29| Scale is weakly epimorphic with val: <7 11 18 19 32| Scale is weakly epimorphic with val: <7 11 18 21 30| Scale is weakly epimorphic with val: <7 11 18 21 33| Scale is weakly epimorphic with val: <7 11 18 22 29| Scale is weakly epimorphic with val: <7 11 18 22 32| Scale is weakly epimorphic with val: <7 11 19 20 30| Scale is weakly epimorphic with val: <7 11 19 20 33| Scale is weakly epimorphic with val: <7 11 19 21 29| Scale is weakly epimorphic with val: <7 11 19 21 32| Scale is weakly epimorphic with val: <7 12 15 18 29| Scale is weakly epimorphic with val: <7 12 15 19 31| Scale is weakly epimorphic with val: <7 12 15 21 32| Scale is weakly epimorphic with val: <7 12 15 22 31| Scale is weakly epimorphic with val: <7 12 16 18 31| Scale is weakly epimorphic with val: <7 12 16 20 32| Scale is weakly epimorphic with val: <7 12 16 21 31| Scale is weakly epimorphic with val: <7 12 17 19 32| Scale is weakly epimorphic with val: <7 12 17 20 31| Scale is weakly epimorphic with val: <7 12 18 18 32| Scale is weakly epimorphic with val: <7 12 18 19 31| Scale is weakly epimorphic with val: <7 12 18 22 31| Scale is weakly epimorphic with val: <7 12 19 21 31| Scale is weakly epimorphic with val: <8 11 15 20 30| Scale is weakly epimorphic with val: <8 11 16 19 30| Scale is weakly epimorphic with val: <8 11 16 22 33| Scale is weakly epimorphic with val: <8 11 17 18 30| Scale is weakly epimorphic with val: <8 11 17 21 33| Scale is weakly epimorphic with val: <8 11 18 20 33| Scale is weakly epimorphic with val: <8 11 19 19 33| Scale is weakly epimorphic with val: <8 12 15 18 28| Scale is weakly epimorphic with val: <8 12 15 21 31| Scale is weakly epimorphic with val: <8 12 16 20 31| Scale is weakly epimorphic with val: <8 12 17 19 31| Scale is weakly epimorphic with val: <8 12 17 22 34| Scale is weakly epimorphic with val: <8 12 18 18 31| Scale is weakly epimorphic with val: <8 12 18 21 34| Scale is weakly epimorphic with val: <8 12 19 20 34|
FIT/MODE
3: 1 1 1 SP B ME I SD: 24.1547 c. M:-34.5170 c. 7: 2 2 3 SP M ME S SD: 7.4571 c. M: 12.9159 c. 10: 3 3 4 SP M ME S SD: 4.1348 c. M:-7.0401 c. 17: 5 5 7 SP M DE S SD: 3.5382 c. M: 4.5454 c. 22: 6 7 9 SP T3 SD: 4.2086 c. M: 6.5429 c. 25: 7 8 10 SP T3 SD: 1.8491 c. M: 2.9208 c. 32: 9 10 13 SP T3 SD: 1.6850 c. M: 2.2982 c. 35: 10 11 14 SP T3 SD: 0.7599 c. M:-1.3140 c. 42: 12 13 17 SP T3 SD: 0.6122 c. M: 1.0577 c. 77: 22 24 31 SP T3 SD: 0.0448 c. M: 0.0748 c. 472: 135 147 190 SP T3 SD: 0.0518 c. M:-0.0759 c. 514: 147 160 207 SP T3 SD: 0.0442 c. M:-0.0636 c. 549: 157 171 221 SP T3 SD: 0.0405 c. M:-0.0548 c. 591: 169 184 238 SP T3 SD: 0.0329 c. M:-0.0456 c. 626: 179 195 252 SP T3 SD: 0.0326 c. M:-0.0410 c. 668: 191 208 269 SP T3 SD: 0.0244 c. M:-0.0317 c. 703: 201 219 283 SP T3 SD: 0.0271 c. M:-0.0388 c. 745: 213 232 300 SP T3 SD: 0.0179 c. M: 0.0231 c. 822: 235 256 331 SP T3 SD: 0.0129 c. M: 0.0190 c. 899: 257 280 362 SP T3 SD: 0.0094 c. M: 0.0156 c. 976: 279 304 393 SP T3 SD: 0.0075 c. M: 0.0128 c. 1053: 301 328 424 SP T3 SD: 0.0073 c. M: 0.0104 c. 1679: 480 523 676 SP T3 SD: 0.0077 c. M:-0.0099 c. 1756: 502 547 707 SP T3 SD: 0.0065 c. M:-0.0093 c. 1833: 524 571 738 SP T3 SD: 0.0059 c. M:-0.0098 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 5 x S SD: 88.8007 cents 5 x 6:7 S SD: 43.1953 cents 6 x 7:8 S SD: 15.3211 cents 7 x 8:9 S SD: 45.7300 cents 8:9:10:11 H SD: 40.1529 cents 9:10:11:12 H SD: 21.3227 cents 10:11:12:13 H SD: 17.5181 cents 11:12:13:15 SD: 13.5437 cents 12:13:14:16 S SD: 10.2923 cents 21:23:25:28 SD: 5.2429 cents 33:36:39:44 SD: 3.9049 cents 36:39:43:48 SD: 3.5955 cents 48:52:57:64 SD: 1.2669 cents 69:75:82:92 SD: 0.7931 cents 117:127:139:156 SD: 0.2902 cents 267:290:317:356 SD: 0.2543 cents 315:342:374:420 SD: 0.0964 cents 432:469:513:576 SD: 0.0352 cents