Scala analysis: 591_M99
Miscellaneous tetrachord 19/17 * 1156/1083 * 19/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/17 192.557607 quasi-meantone 2: 68/57 305.487393 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/17 192.5576 quasi-meantone 1: 19/17 192.5576 quasi-meantone 2: 1156/1083 112.9298 3: 19/17 192.5576 quasi-meantone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1156/1083 112.930 cents 1: 2 19/17 192.558 cents quasi-meantone 2: 2 68/57 305.487 cents 2: 1 361/289 385.115 cents two (quasi-meantone) Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 192.6 305.5 498.0 192.6: 112.9 305.5 498.0 305.5: 192.6 385.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 112.9298 .. 192.5576 cents 20577/19652, 79.6278 cents 1156/1083, 112.9298 cents 2: 305.4874 .. 385.1152 cents 20577/19652, 79.6278 cents 1156/1083, 112.9298 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 1156/1083, 112.9298 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/17, 192.5576 cents Average / Smallest step : 1.470073 Largest / Average step : 1.159881 Largest / Smallest step : 1.705109 Median interval of one step : 19/17, 192.5576 cents, amount: 2 Most common interval of one step : 19/17, 192.5576 cents, amount: 2 Least squares average step : 164.11910 cents, oct.: 492.35730 cents Scale is strictly proper Scale has Myhill's property chromas: 20577/19652, 79.6278 cents and 22717712/22284891, 33.3020 cents, ratio: 2.391085 generators: 1 of 192.55761 cents and 2 of 305.48739 cents ET pair of linear temperament : 26&62 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 269-tone equal temperament with octave 4/3 degrees: 104 165 269 generators: 104 and 165 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : LSL Scale is a Constant Structure, by a margin of 112.92979 cents Scale diversity : 1.151353 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.680238 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 20577/19652, 79.6278 cents Most common intervals : 19/17, 192.5576 cents & inv., amount: 2 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 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 19 Odd number limit : 1083 (O: 361 U: 1083) Highest odd numerator or denominator: 57 Scale harmonicity : 0.007512 Average absolute harmonicity : 0.081457 Specific harmonicity : 0.039603 Fundamental : 1/969, -9.9204 octaves, 0.2700 Hz. Guide tone : 1292, 10.3354 octaves, 338020.230 Hz. Exponens Consonantiae : 1.251948E+06, 20.25574 octaves Euler's gradus suavitatis : 73 Sum of Mann's harmonic distance : 84.0, average 28.00000 Mersenne's string divisions : 31500 Sum of van Prooijen's expressibility: 3.51175, average 1.17058 Sum of Tenney's harmonic distance : 7.17677, average 2.39226 Vogel's harmonic complexity : 38.33333 Wille's k value : 541 Wilson's harmonic complexity : 75 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.96155, average 2.32692 Lattice compactness (without 2's) : 10.29253, average 1.71542 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -1 .. 0 -0.66667 2 1 17: -1 .. 1 0.00000 2 19: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is JI-epimorphic with val: <7 11 27 28| Scale is weakly epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 27 31| Scale is weakly epimorphic with val: <7 11 27 32| Scale is weakly epimorphic with val: <7 11 27 34| Scale is JI-epimorphic with val: <7 11 28 29| Scale is weakly epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 28 32| Scale is weakly epimorphic with val: <7 11 28 33| Scale is JI-epimorphic with val: <7 11 29 30| Scale is weakly epimorphic with val: <7 11 29 31| Scale is weakly epimorphic with val: <7 11 29 33| Scale is weakly epimorphic with val: <7 11 29 34| Scale is JI-epimorphic with val: <7 11 30 31| = patent Scale is weakly epimorphic with val: <7 11 30 32| Scale is weakly epimorphic with val: <7 11 30 34| Scale is JI-epimorphic with val: <7 11 31 32| Scale is weakly epimorphic with val: <7 11 31 33| Scale is JI-epimorphic with val: <7 11 32 33| Scale is weakly epimorphic with val: <7 11 32 34| Scale is JI-epimorphic with val: <7 11 33 34|
FIT/MODE
3: 1 1 1 SP B ME I SD: 21.6719 c. M:-26.5426 c. 5: 2 1 2 SP M ME I SD: 5.4382 c. M: 6.6604 c. 8: 3 2 3 SP M ME I SD: 4.7281 c. M: 5.7907 c. 13: 5 3 5 SP M DE I SD: 0.8180 c. M: 1.0018 c. 31: 12 7 12 SP M DE I SD: 0.1911 c. M:-0.2340 c. 44: 17 10 17 SP M DE I SD: 0.1071 c. M: 0.1311 c. 75: 29 17 29 SP M DE I SD: 0.0162 c. M: 0.0198 c. 194: 75 44 75 SP M DE I SD: 0.0118 c. M: 0.0144 c. 269: 104 61 104 SP M DE I SD: 0.0040 c. M: 0.0049 c. 344: 133 78 133 SP M DE I SD: 0.0004 c. M: 0.0005 c. 1645: 636 373 636 SP M DE I SD: 0.0003 c. M:-0.0004 c. 1989: 769 451 769 SP M DE I SD: 0.0002 c. M:-0.0002 c. 2333: 902 529 902 SP M DE I SD: 0.0001 c. M: 0.0001 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: 80.8263 cents 5 x 6:7 S SD: 42.5377 cents 6 x 7:8 S SD: 19.3082 cents 7:8 x 9 S SD: 36.9300 cents 8:9:10:11 H SD: 32.4889 cents 9:10:11:12 H SD: 14.3776 cents 15:17:18:20 SD: 8.7262 cents 24:27:29:32 SD: 8.2921 cents 25:28:30:33 SD: 6.8240 cents 26:29:31:35 SD: 5.6542 cents 27:30:32:36 S SD: 5.0769 cents 36:40:43:48 SD: 3.4576 cents 42:47:50:56 SD: 1.4125 cents 78:87:93:104 SD: 1.2141 cents 93:104:111:124 SD: 0.4260 cents 171:191:204:228 SD: 0.3553 cents 213:238:254:284 SD: 0.2784 cents 264:295:315:352 SD: 0.1501 cents 306:342:365:408 SD: 0.0832 cents 399:446:476:532 SD: 0.0761 cents 570:637:680:760 SD: 0.0533 cents