Scala analysis: 575_M83
Miscellaneous tetrachord 40/39 * 143/125 * 25/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 88/75 276.735514 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/22 221.3095 undecimal acute whole tone 1: 40/39 43.8311 tridecimal minor diesis 2: 143/125 232.9045 3: 25/22 221.3095 undecimal acute whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 25/22 221.309 cents undecimal acute whole tone 1: 1 143/125 232.904 cents 2: 1 500/429 265.141 cents 2: 1 88/75 276.736 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 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 : 43.8 276.7 498.0 43.8 : 232.9 454.2 498.0 276.7: 221.3 265.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 232.9045 cents 5577/5000, 189.0734 cents 40/39, 43.8311 cents 2: 265.1405 .. 454.2139 cents 5577/5000, 189.0734 cents 62500/61347, 32.2361 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 143/125, 232.9045 cents Average / Smallest step : 3.787612 Largest / Average step : 1.402912 Largest / Smallest step : 5.313686 Median interval of one step : 25/22, 221.3095 cents, amount: 1 Least squares average step : 149.38836 cents, oct.: 448.16509 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1159-tone equal temperament with octave 4/3 degrees: 102 644 1159 Least number of segments generator : 580 of 249.237 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 939 of 403.507 cents and inv. generated superset size: 25 = 22 more = 833.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 32.23607 cents Scale diversity : 0.605873 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.240738 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 : 3146/3125, 11.5950 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 189.0734 cents: 1 -- Rational properties -- Prime limit : 13 Odd number limit : 429 (O: 143 U: 429) Highest odd numerator or denominator: 75 Scale harmonicity : 0.015337 Average absolute harmonicity : 0.090264 Specific harmonicity : 0.081380 Fundamental : 1/975, -9.9293 octaves, 0.2683 Hz. Guide tone : 440, 8.7814 octaves, 115115.249 Hz. Exponens Consonantiae : 4.290000E+05, 18.71062 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 124.5, average 41.50000 Mersenne's string divisions : 90139 Sum of van Prooijen's expressibility: 3.94325, average 1.31442 Sum of Tenney's harmonic distance : 8.09185, average 2.69728 Vogel's harmonic complexity : 23.33333 Wille's k value : 162 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.07132, average 2.84522 Lattice compactness (without 2's) : 12.14845, average 2.02474 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 ..-1 -1.00000 3 1 5: -2 .. 1 -0.33333 3 11: 0 .. 1 0.33333 1 1 13: -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 15 25 25| Scale is weakly epimorphic with val: <6 10 15 25 28| Scale is weakly epimorphic with val: <6 10 16 27 29| Scale is weakly epimorphic with val: <6 11 15 26 26| Scale is weakly epimorphic with val: <6 11 15 26 29| Scale is weakly epimorphic with val: <7 10 16 24 25| Scale is weakly epimorphic with val: <7 10 16 24 28| Scale is weakly epimorphic with val: <7 10 17 25 25| Scale is weakly epimorphic with val: <7 10 17 26 26| Scale is weakly epimorphic with val: <7 10 17 26 29| Scale is weakly epimorphic with val: <7 10 18 24 26| Scale is weakly epimorphic with val: <7 10 19 23 27| Scale is weakly epimorphic with val: <7 10 19 26 27| Scale is weakly epimorphic with val: <7 11 15 24 26| Scale is weakly epimorphic with val: <7 11 15 24 29| Scale is weakly epimorphic with val: <7 11 15 25 27| Scale is weakly epimorphic with val: <7 11 15 25 30| Scale is weakly epimorphic with val: <7 11 15 27 29| Scale is weakly epimorphic with val: <7 11 16 23 27| Scale is weakly epimorphic with val: <7 11 16 23 30| Scale is JI-epimorphic with val: <7 11 16 24 25| Scale is weakly epimorphic with val: <7 11 16 24 28| Scale is weakly epimorphic with val: <7 11 16 26 27| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is weakly epimorphic with val: <7 11 16 27 28| Scale is weakly epimorphic with val: <7 11 17 23 26| Scale is weakly epimorphic with val: <7 11 17 23 29| Scale is weakly epimorphic with val: <7 11 17 25 25| Scale is weakly epimorphic with val: <7 11 17 25 28| Scale is JI-epimorphic with val: <7 11 17 26 26| Scale is weakly epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 18 24 26| Scale is weakly epimorphic with val: <7 11 18 24 29| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 19 23 27| Scale is weakly epimorphic with val: <7 11 19 23 30| Scale is weakly epimorphic with val: <7 11 19 24 25| Scale is weakly epimorphic with val: <7 11 19 24 28| Scale is weakly epimorphic with val: <7 11 19 26 27| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 12 15 24 26| Scale is weakly epimorphic with val: <7 12 15 24 29| Scale is weakly epimorphic with val: <7 12 16 26 27| Scale is weakly epimorphic with val: <7 12 16 26 30| Scale is weakly epimorphic with val: <7 12 19 24 25| Scale is weakly epimorphic with val: <8 11 15 24 25| Scale is weakly epimorphic with val: <8 11 16 23 26| Scale is weakly epimorphic with val: <8 11 16 26 26| Scale is weakly epimorphic with val: <8 11 17 24 26| Scale is weakly epimorphic with val: <8 11 17 24 29| Scale is weakly epimorphic with val: <8 11 17 25 27| Scale is weakly epimorphic with val: <8 11 18 24 28| Scale is weakly epimorphic with val: <8 11 18 26 27| Scale is weakly epimorphic with val: <8 11 18 26 30| Scale is weakly epimorphic with val: <8 11 18 27 28| Scale is weakly epimorphic with val: <8 11 19 23 29| Scale is weakly epimorphic with val: <8 11 19 26 29| Scale is weakly epimorphic with val: <8 12 16 23 26| Scale is weakly epimorphic with val: <8 12 16 23 29| Scale is weakly epimorphic with val: <8 12 16 25 25| Scale is weakly epimorphic with val: <8 12 17 24 26| Scale is weakly epimorphic with val: <8 12 17 25 27| Scale is weakly epimorphic with val: <8 12 17 25 30| Scale is weakly epimorphic with val: <8 12 18 23 27| Scale is weakly epimorphic with val: <8 12 18 26 27| Scale is weakly epimorphic with val: <8 12 18 27 28| Scale is weakly epimorphic with val: <8 12 19 25 28|
FIT/MODE
3: 0 2 1 N G T3 SD: 40.7375 c. M:-55.2945 c. 4: 0 2 2 P M DE S SD: 29.9398 c. M: 43.8311 c. 5: 0 3 2 N G T3 SD: 28.3384 c. M: 43.8311 c. 6: 0 3 3 P M DE S SD: 29.9398 c. M: 43.8311 c. 7: 1 3 3 SP M DE S SD: 16.4123 c. M:-27.3182 c. 9: 1 4 4 SP M DE S SD: 6.6438 c. M:-11.5073 c. 11: 1 5 5 SP M DE S SD: 3.0464 c. M: 5.0746 c. 23: 2 11 10 SP T3 SD: 2.7694 c. M:-4.7682 c. 25: 2 12 11 SP T3 SD: 2.6209 c. M: 3.9875 c. 32: 3 15 14 SP T3 SD: 2.5719 c. M:-3.4148 c. 34: 3 16 15 SP T3 SD: 0.9167 c. M:-1.5838 c. 45: 4 21 20 SP T3 SD: 0.2551 c. M:-0.4396 c. 124: 11 58 55 SP T3 SD: 0.3081 c. M:-0.4024 c. 126: 11 59 56 SP T3 SD: 0.2042 c. M: 0.3509 c. 160: 14 75 71 SP T3 SD: 0.2271 c. M:-0.3020 c. 171: 15 80 76 SP T3 SD: 0.0863 c. M: 0.1429 c. 216: 19 101 96 SP T3 SD: 0.0282 c. M: 0.0438 c. 477: 42 223 212 SP T3 SD: 0.0283 c. M: 0.0438 c. 682: 60 319 303 SP T3 SD: 0.0232 c. M:-0.0373 c. 727: 64 340 323 SP T3 SD: 0.0202 c. M:-0.0323 c. 898: 79 420 399 SP T3 SD: 0.0140 c. M:-0.0178 c. 943: 83 441 419 SP T3 SD: 0.0091 c. M:-0.0148 c. 1159: 102 542 515 SP T3 SD: 0.0023 c. M:-0.0039 c. 1375: 121 643 611 SP T3 SD: 0.0027 c. M: 0.0036 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: 109.5782 cents 5 x 6:7 S SD: 46.4983 cents 6 x 7:8 S SD: 4.9323 cents 7 x 8:9 S SD: 38.8585 cents 8 x 9:11 SD: 45.1153 cents 9 x 11:12 SD: 35.3362 cents 10 x 12:13 S SD: 29.3037 cents 15:16:18:20 S SD: 26.0855 cents 16:17:19:21 SD: 23.3600 cents 17:18:20:23 SD: 20.2724 cents 18:19:21:24 SD: 16.9134 cents 21:22:25:28 SD: 14.8245 cents 22:23:26:29 SD: 13.5169 cents 23:24:27:31 SD: 11.7475 cents 24:25:28:32 SD: 9.5322 cents 27:28:32:36 S SD: 8.6197 cents 28:29:33:37 SD: 8.0750 cents 29:30:34:39 SD: 7.0199 cents 30:31:35:40 SD: 5.4226 cents 33:34:39:44 SD: 4.9131 cents 35:36:41:47 SD: 4.5233 cents 36:37:42:48 SD: 3.5007 cents 39:40:46:52 SD: 3.0187 cents 45:46:53:60 SD: 2.9108 cents 69:71:81:92 SD: 1.9002 cents 75:77:88:100 SD: 0.5768 cents 156:160:183:208 SD: 0.1261 cents 507:520:595:676 SD: 0.1164 cents 588:603:690:784 SD: 0.0995 cents