Scala analysis: 389_D5
Diatonic tetrachord 40/39 * 39/34 * 17/15
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: 20/17 281.358304 septendecimal augmented second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/15 216.6867 septendecimal whole tone 1: 40/39 43.8311 tridecimal minor diesis 2: 39/34 237.5273 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 17/15 216.687 cents septendecimal whole tone 1: 1 39/34 237.527 cents 2: 1 136/117 260.518 cents 2: 1 20/17 281.358 cents septendecimal augmented second 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 : 43.8 281.4 498.0 43.8 : 237.5 454.2 498.0 281.4: 216.7 260.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 237.5273 cents 1521/1360, 193.6962 cents 40/39, 43.8311 cents 2: 260.5177 .. 454.2139 cents 1521/1360, 193.6962 cents 4624/4563, 22.9905 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 : 39/34, 237.5273 cents Average / Smallest step : 3.787612 Largest / Average step : 1.430758 Largest / Smallest step : 5.419155 Median interval of one step : 17/15, 216.6867 cents, amount: 1 Least squares average step : 150.04876 cents, oct.: 450.14628 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1602-tone equal temperament with octave 4/3 degrees: 141 905 1602 Least number of segments generator : 803 of 249.644 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1393 of 433.069 cents and inv. generated superset size: 51 = 48 more = 1700.000% 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 22.99049 cents Scale diversity : 0.628645 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.222174 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 : 585/578, 20.8406 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 193.6962 cents: 1 -- Rational properties -- Prime limit : 17 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.015543 Average absolute harmonicity : 0.089823 Specific harmonicity : 0.079176 Fundamental : 1/663, -9.3729 octaves, 0.3946 Hz. Guide tone : 40, 5.3219 octaves, 10465.023 Hz. Exponens Consonantiae : 2.652000E+04, 14.69479 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 61.5, average 20.50000 Mersenne's string divisions : 20461 Sum of van Prooijen's expressibility: 3.29863, average 1.09954 Sum of Tenney's harmonic distance : 6.80378, average 2.26793 Vogel's harmonic complexity : 26.66667 Wille's k value : 110 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.61376, average 2.26896 Lattice compactness (without 2's) : 9.02458, average 1.50410 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 0 -0.66667 2 1 5: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 18 25 27| Scale is weakly epimorphic with val: <6 10 19 26 28| Scale is weakly epimorphic with val: <6 11 18 26 27| Scale is weakly epimorphic with val: <6 11 19 27 28| Scale is weakly epimorphic with val: <7 10 16 25 27| Scale is weakly epimorphic with val: <7 10 17 25 29| Scale is weakly epimorphic with val: <7 10 17 25 32| Scale is weakly epimorphic with val: <7 10 17 26 28| Scale is weakly epimorphic with val: <7 10 18 26 27| Scale is weakly epimorphic with val: <7 10 18 26 30| Scale is weakly epimorphic with val: <7 10 18 26 33| Scale is weakly epimorphic with val: <7 10 18 27 29| Scale is weakly epimorphic with val: <7 10 19 25 30| Scale is weakly epimorphic with val: <7 10 19 27 28| Scale is weakly epimorphic with val: <7 10 19 27 31| Scale is weakly epimorphic with val: <7 10 19 28 30| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 27 27| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is weakly epimorphic with val: <7 11 15 29 31| Scale is weakly epimorphic with val: <7 11 15 30 30| Scale is weakly epimorphic with val: <7 11 15 30 33| Scale is JI-epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 27 29| Scale is weakly epimorphic with val: <7 11 16 27 32| Scale is weakly epimorphic with val: <7 11 16 28 28| Scale is weakly epimorphic with val: <7 11 16 28 31| Scale is weakly epimorphic with val: <7 11 16 30 32| Scale is weakly epimorphic with val: <7 11 17 25 27| Scale is weakly epimorphic with val: <7 11 17 25 30| Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is JI-epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 17 26 32| Scale is weakly epimorphic with val: <7 11 17 28 30| Scale is weakly epimorphic with val: <7 11 17 28 33| Scale is weakly epimorphic with val: <7 11 17 29 29| Scale is weakly epimorphic with val: <7 11 17 29 32| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 27| Scale is JI-epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 18 29 31| Scale is weakly epimorphic with val: <7 11 18 30 30| Scale is weakly epimorphic with val: <7 11 18 30 33| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 27 29| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 19 28 28| Scale is JI-epimorphic with val: <7 11 19 28 31| Scale is weakly epimorphic with val: <7 11 19 30 32| Scale is weakly epimorphic with val: <7 12 16 27 27| Scale is weakly epimorphic with val: <7 12 17 25 28| Scale is weakly epimorphic with val: <7 12 17 28 28| Scale is weakly epimorphic with val: <7 12 18 26 29| Scale is weakly epimorphic with val: <7 12 18 29 29| Scale is weakly epimorphic with val: <7 12 19 25 29| Scale is weakly epimorphic with val: <7 12 19 25 32| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 19 30 30| Scale is weakly epimorphic with val: <8 11 15 25 27| Scale is weakly epimorphic with val: <8 11 15 25 30| Scale is weakly epimorphic with val: <8 11 15 25 33| Scale is weakly epimorphic with val: <8 11 15 27 28| Scale is weakly epimorphic with val: <8 11 16 25 29| Scale is weakly epimorphic with val: <8 11 16 26 28| Scale is weakly epimorphic with val: <8 11 16 26 31| Scale is weakly epimorphic with val: <8 11 16 28 29| Scale is weakly epimorphic with val: <8 11 17 26 30| Scale is weakly epimorphic with val: <8 11 17 27 29| Scale is weakly epimorphic with val: <8 11 17 27 32| Scale is weakly epimorphic with val: <8 11 17 29 30| Scale is weakly epimorphic with val: <8 11 18 27 31| Scale is weakly epimorphic with val: <8 11 18 28 30| Scale is weakly epimorphic with val: <8 11 18 28 33| Scale is weakly epimorphic with val: <8 11 18 30 31| Scale is weakly epimorphic with val: <8 11 19 25 32| Scale is weakly epimorphic with val: <8 11 19 28 32| Scale is weakly epimorphic with val: <8 11 19 29 31| Scale is weakly epimorphic with val: <8 12 15 25 28| Scale is weakly epimorphic with val: <8 12 15 28 28| Scale is weakly epimorphic with val: <8 12 16 25 27| Scale is weakly epimorphic with val: <8 12 16 25 30| Scale is weakly epimorphic with val: <8 12 16 25 33| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 16 29 29| Scale is weakly epimorphic with val: <8 12 17 26 28| Scale is weakly epimorphic with val: <8 12 17 26 31| Scale is weakly epimorphic with val: <8 12 17 27 30| Scale is weakly epimorphic with val: <8 12 17 30 30| Scale is weakly epimorphic with val: <8 12 18 25 31| Scale is weakly epimorphic with val: <8 12 18 27 29| Scale is weakly epimorphic with val: <8 12 18 27 32| Scale is weakly epimorphic with val: <8 12 18 28 31| Scale is weakly epimorphic with val: <8 12 19 26 32| Scale is weakly epimorphic with val: <8 12 19 28 30| Scale is weakly epimorphic with val: <8 12 19 28 33| Scale is weakly epimorphic with val: <8 12 19 29 32|
FIT/MODE
3: 0 2 1 N G T3 SD: 38.6815 c. M:-50.6717 c. 4: 0 2 2 P M DE S SD: 31.4471 c. M: 43.8311 c. 5: 0 3 2 N G T3 SD: 27.2416 c. M: 43.8311 c. 6: 0 3 3 P M DE S SD: 31.4471 c. M: 43.8311 c. 7: 1 3 3 SP M DE S SD: 15.8827 c. M:-27.3182 c. 9: 1 4 4 SP M DE S SD: 7.1693 c. M:-11.5073 c. 11: 1 5 5 SP M DE S SD: 5.6607 c. M: 9.6974 c. 12: 1 6 5 P T3 SD: 5.4610 c. M:-9.1679 c. 14: 1 7 6 P T3 SD: 5.1205 c. M: 8.2564 c. 20: 2 9 9 SP M DE S SD: 5.5057 c. M: 7.4336 c. 21: 2 10 9 SP T3 SD: 2.7966 c. M:-3.6018 c. 23: 2 11 10 SP T3 SD: 0.3133 c. M: 0.5228 c. 124: 11 59 54 SP T3 SD: 0.2340 c. M:-0.3504 c. 147: 13 70 64 SP T3 SD: 0.1505 c. M:-0.2137 c. 170: 15 81 74 SP T3 SD: 0.0912 c. M:-0.1141 c. 193: 17 92 84 SP T3 SD: 0.0507 c. M: 0.0790 c. 216: 19 103 94 SP T3 SD: 0.0342 c. M: 0.0551 c. 455: 40 217 198 SP T3 SD: 0.0375 c. M: 0.0469 c. 625: 55 298 272 SP T3 SD: 0.0361 c. M: 0.0625 c. 671: 59 320 292 SP T3 SD: 0.0357 c. M: 0.0482 c. 841: 74 401 366 SP T3 SD: 0.0353 c. M: 0.0606 c. 887: 78 423 386 SP T3 SD: 0.0350 c. M: 0.0499 c. 908: 80 433 395 SP T3 SD: 0.0324 c. M:-0.0496 c. 931: 82 444 405 SP T3 SD: 0.0265 c. M:-0.0354 c. 954: 84 455 415 SP T3 SD: 0.0224 c. M:-0.0319 c. 977: 86 466 425 SP T3 SD: 0.0206 c. M:-0.0346 c. 1147: 101 547 499 SP T3 SD: 0.0162 c. M:-0.0247 c. 1170: 103 558 509 SP T3 SD: 0.0122 c. M:-0.0158 c. 1193: 105 569 519 SP T3 SD: 0.0108 c. M:-0.0183 c. 1363: 120 650 593 SP T3 SD: 0.0101 c. M:-0.0174 c. 1386: 122 661 603 SP T3 SD: 0.0056 c. M:-0.0084 c. 1409: 124 672 613 SP T3 SD: 0.0041 c. M:-0.0071 c. 1602: 141 764 697 SP T3 SD: 0.0032 c. M:-0.0044 c. 1625: 143 775 707 SP T3 SD: 0.0019 c. M: 0.0031 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: 104.9554 cents 5 x 6:7 S SD: 45.5797 cents 6 x 7:8 S SD: 7.2437 cents 7 x 8:9 S SD: 40.2571 cents 8 x 9:11 SD: 47.0007 cents 9 x 11:12 SD: 33.0248 cents 10 x 12:13 S SD: 27.8230 cents 15:16:18:20 S SD: 25.3547 cents 16:17:19:21 SD: 22.9504 cents 17:18:20:23 SD: 20.2138 cents 18:19:21:24 SD: 17.2792 cents 21:22:25:28 SD: 14.0123 cents 22:23:26:29 SD: 13.1251 cents 23:24:27:31 SD: 11.8110 cents 24:25:28:32 SD: 10.1672 cents 27:28:32:36 S SD: 7.6681 cents 29:30:34:39 SD: 7.2834 cents 30:31:35:40 SD: 6.4740 cents 33:34:39:44 SD: 3.7012 cents 39:40:46:52 SD: 1.4778 cents 84:86:99:112 SD: 1.4573 cents 108:111:127:144 SD: 1.2304 cents 114:117:134:152 SD: 0.6329 cents 153:157:180:204 SD: 0.2828 cents 198:203:233:264 SD: 0.2627 cents 312:320:367:416 SD: 0.0925 cents 351:360:413:468 SD: 0.0822 cents