Scala analysis: 436_D11
Diatonic tetrachord 24/23 * 115/102 * 17/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 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: 24/23 73.6807 vicesimotertial minor semitone 2: 115/102 207.6777 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 115/102 207.678 cents 1: 1 17/15 216.687 cents septendecimal whole tone 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 136/115 290.367 cents 2: 1 23/18 424.364 cents vicesimotertial major third 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 : 73.7 281.4 498.0 73.7 : 207.7 424.4 498.0 281.4: 216.7 290.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 216.6867 cents 391/360, 143.0060 cents 24/23, 73.6807 cents 2: 281.3583 .. 424.3643 cents 391/360, 143.0060 cents 300/289, 64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/15, 216.6867 cents Average / Smallest step : 2.253169 Largest / Average step : 1.305224 Largest / Smallest step : 2.940890 Median interval of one step : 115/102, 207.6777 cents, amount: 1 Least squares average step : 152.18088 cents, oct.: 456.54263 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1602-tone equal temperament with octave 4/3 degrees: 237 905 1602 Least number of segments generator : 803 of 249.644 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 977 of 303.739 cents and inv. generated superset size: 38 = 35 more = 1266.667% Number of contiguous 1-step segments: 0 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 64.67161 cents Scale diversity : 0.892396 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.425730 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 : 578/575, 9.0090 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Steps are strictly increasing 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 133.9970 cents: 1 -- Rational properties -- Prime limit : 23 Odd number limit : 115 (O: 115 U: 115) Highest odd numerator or denominator: 23 Scale harmonicity : 0.011502 Average absolute harmonicity : 0.087062 Specific harmonicity : 0.061346 Fundamental : 1/1173, -10.1960 octaves, 0.2230 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 1.407600E+05, 17.10288 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 45.5, average 15.16667 Mersenne's string divisions : 12173 Sum of van Prooijen's expressibility: 3.06930, average 1.02310 Sum of Tenney's harmonic distance : 6.35260, average 2.11753 Vogel's harmonic complexity : 33.66667 Wille's k value : 195 Wilson's harmonic complexity : 51 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.41979, average 2.40330 Lattice compactness (without 2's) : 9.79655, average 1.63276 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.33333 1 17: -1 .. 0 -0.33333 1 1 23: -1 .. 0 -0.33333 1 1 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 18 27 30| Scale is weakly epimorphic with val: <6 10 18 27 33| Scale is weakly epimorphic with val: <6 10 18 27 36| Scale is weakly epimorphic with val: <6 10 19 28 30| Scale is weakly epimorphic with val: <6 10 19 28 33| Scale is weakly epimorphic with val: <6 10 19 28 36| Scale is weakly epimorphic with val: <6 11 18 27 30| Scale is weakly epimorphic with val: <6 11 18 27 33| Scale is weakly epimorphic with val: <6 11 18 27 36| Scale is weakly epimorphic with val: <6 11 19 28 30| Scale is weakly epimorphic with val: <6 11 19 28 33| Scale is weakly epimorphic with val: <6 11 19 28 36| Scale is weakly epimorphic with val: <7 10 16 27 32| Scale is weakly epimorphic with val: <7 10 16 27 35| Scale is weakly epimorphic with val: <7 10 17 28 32| Scale is weakly epimorphic with val: <7 10 17 28 35| Scale is weakly epimorphic with val: <7 10 18 29 32| Scale is weakly epimorphic with val: <7 10 18 29 35| Scale is weakly epimorphic with val: <7 10 19 30 32| Scale is weakly epimorphic with val: <7 10 19 30 35| Scale is JI-epimorphic with val: <7 11 15 27 31| Scale is weakly epimorphic with val: <7 11 15 27 34| Scale is weakly epimorphic with val: <7 11 15 28 30| Scale is weakly epimorphic with val: <7 11 15 28 33| Scale is weakly epimorphic with val: <7 11 15 28 36| Scale is weakly epimorphic with val: <7 11 15 30 31| Scale is weakly epimorphic with val: <7 11 15 30 34| Scale is weakly epimorphic with val: <7 11 15 31 33| Scale is weakly epimorphic with val: <7 11 15 31 36| Scale is weakly epimorphic with val: <7 11 15 33 34| Scale is JI-epimorphic with val: <7 11 16 28 31| Scale is weakly epimorphic with val: <7 11 16 28 34| Scale is weakly epimorphic with val: <7 11 16 29 30| Scale is weakly epimorphic with val: <7 11 16 29 33| Scale is weakly epimorphic with val: <7 11 16 29 36| Scale is weakly epimorphic with val: <7 11 16 31 31| Scale is weakly epimorphic with val: <7 11 16 31 34| Scale is weakly epimorphic with val: <7 11 16 32 33| Scale is weakly epimorphic with val: <7 11 16 32 36| Scale is weakly epimorphic with val: <7 11 17 27 30| Scale is weakly epimorphic with val: <7 11 17 27 33| Scale is weakly epimorphic with val: <7 11 17 27 36| Scale is JI-epimorphic with val: <7 11 17 29 31| Scale is weakly epimorphic with val: <7 11 17 29 34| Scale is weakly epimorphic with val: <7 11 17 30 30| Scale is weakly epimorphic with val: <7 11 17 30 33| = patent Scale is weakly epimorphic with val: <7 11 17 30 36| Scale is weakly epimorphic with val: <7 11 17 32 34| Scale is weakly epimorphic with val: <7 11 17 33 33| Scale is weakly epimorphic with val: <7 11 17 33 36| Scale is weakly epimorphic with val: <7 11 18 27 31| Scale is weakly epimorphic with val: <7 11 18 27 34| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is weakly epimorphic with val: <7 11 18 28 36| Scale is JI-epimorphic with val: <7 11 18 30 31| Scale is weakly epimorphic with val: <7 11 18 30 34| Scale is weakly epimorphic with val: <7 11 18 31 33| Scale is weakly epimorphic with val: <7 11 18 31 36| Scale is weakly epimorphic with val: <7 11 18 33 34| Scale is weakly epimorphic with val: <7 11 19 28 31| Scale is weakly epimorphic with val: <7 11 19 28 34| Scale is weakly epimorphic with val: <7 11 19 29 30| Scale is weakly epimorphic with val: <7 11 19 29 33| Scale is weakly epimorphic with val: <7 11 19 29 36| Scale is JI-epimorphic with val: <7 11 19 31 31| Scale is weakly epimorphic with val: <7 11 19 31 34| Scale is weakly epimorphic with val: <7 11 19 32 33| Scale is weakly epimorphic with val: <7 11 19 32 36| Scale is weakly epimorphic with val: <7 12 15 28 30| Scale is weakly epimorphic with val: <7 12 16 27 32| Scale is weakly epimorphic with val: <7 12 16 27 35| Scale is weakly epimorphic with val: <7 12 16 29 30| Scale is weakly epimorphic with val: <7 12 17 27 30| Scale is weakly epimorphic with val: <7 12 17 28 32| Scale is weakly epimorphic with val: <7 12 17 28 35| Scale is weakly epimorphic with val: <7 12 17 30 30| Scale is weakly epimorphic with val: <7 12 18 28 30| Scale is weakly epimorphic with val: <7 12 18 29 32| Scale is weakly epimorphic with val: <7 12 18 29 35| Scale is weakly epimorphic with val: <7 12 19 29 30| Scale is weakly epimorphic with val: <7 12 19 30 32| Scale is weakly epimorphic with val: <7 12 19 30 35| Scale is weakly epimorphic with val: <8 11 15 27 32| Scale is weakly epimorphic with val: <8 11 15 28 31| Scale is weakly epimorphic with val: <8 11 15 28 34| Scale is weakly epimorphic with val: <8 11 15 30 32| Scale is weakly epimorphic with val: <8 11 16 28 32| Scale is weakly epimorphic with val: <8 11 16 29 31| Scale is weakly epimorphic with val: <8 11 16 29 34| Scale is weakly epimorphic with val: <8 11 16 31 32| Scale is weakly epimorphic with val: <8 11 17 29 32| Scale is weakly epimorphic with val: <8 11 17 30 31| Scale is weakly epimorphic with val: <8 11 17 30 34| Scale is weakly epimorphic with val: <8 11 17 32 32| Scale is weakly epimorphic with val: <8 11 18 27 32| Scale is weakly epimorphic with val: <8 11 18 30 32| Scale is weakly epimorphic with val: <8 11 18 31 31| Scale is weakly epimorphic with val: <8 11 18 31 34| Scale is weakly epimorphic with val: <8 11 19 28 32| Scale is weakly epimorphic with val: <8 11 19 31 32| Scale is weakly epimorphic with val: <8 11 19 32 34| Scale is weakly epimorphic with val: <8 12 15 28 31| Scale is weakly epimorphic with val: <8 12 15 28 34| Scale is weakly epimorphic with val: <8 12 15 29 33| Scale is weakly epimorphic with val: <8 12 15 32 33| Scale is weakly epimorphic with val: <8 12 16 27 33| Scale is weakly epimorphic with val: <8 12 16 29 31| Scale is weakly epimorphic with val: <8 12 16 29 34| Scale is weakly epimorphic with val: <8 12 16 30 33| Scale is weakly epimorphic with val: <8 12 16 33 33| Scale is weakly epimorphic with val: <8 12 17 28 33| Scale is weakly epimorphic with val: <8 12 17 30 31| Scale is weakly epimorphic with val: <8 12 17 30 34| Scale is weakly epimorphic with val: <8 12 17 31 33| Scale is weakly epimorphic with val: <8 12 18 29 33| Scale is weakly epimorphic with val: <8 12 18 31 31| Scale is weakly epimorphic with val: <8 12 18 31 34| Scale is weakly epimorphic with val: <8 12 18 32 33| Scale is weakly epimorphic with val: <8 12 19 27 33| Scale is weakly epimorphic with val: <8 12 19 30 33| Scale is weakly epimorphic with val: <8 12 19 32 34| Scale is weakly epimorphic with val: <8 12 19 33 33|
FIT/MODE
3: 0 2 1 N G T3 SD: 51.6283 c. M: 73.6807 c. 4: 0 2 2 P M DE S SD: 46.4559 c. M: 73.6807 c. 5: 1 2 2 SP M ME S SD: 18.0502 c. M:-25.9283 c. 7: 1 3 3 SP M DE S SD: 2.3733 c. M:-3.2388 c. 27: 4 11 12 SP T3 SD: 2.6950 c. M: 4.6666 c. 32: 5 13 14 SP T3 SD: 2.4893 c. M:-4.1389 c. 34: 5 14 15 SP T3 SD: 1.7728 c. M: 3.0390 c. 39: 6 16 17 SP T3 SD: 1.7148 c. M:-2.9417 c. 41: 6 17 18 SP T3 SD: 1.2252 c. M: 1.9672 c. 46: 7 19 20 SP T3 SD: 1.2204 c. M:-2.1088 c. 48: 7 20 21 SP T3 SD: 0.9237 c. M: 1.2080 c. 53: 8 22 23 SP T3 SD: 0.9210 c. M:-1.4960 c. 55: 8 23 24 SP T3 SD: 0.8050 c. M: 1.2377 c. 60: 9 25 26 SP T3 SD: 0.7757 c. M:-1.0261 c. 67: 10 28 29 SP T3 SD: 0.7464 c. M:-1.1150 c. 87: 13 36 38 SP T3 SD: 0.6507 c. M: 0.8502 c. 94: 14 39 41 SP T3 SD: 0.4259 c. M: 0.5457 c. 101: 15 42 44 SP T3 SD: 0.2326 c. M:-0.2864 c. 108: 16 45 47 SP T3 SD: 0.0678 c. M:-0.1038 c. 223: 33 93 97 SP T3 SD: 0.0304 c. M:-0.0483 c. 331: 49 138 144 SP T3 SD: 0.0290 c. M:-0.0481 c. 554: 82 231 241 SP T3 SD: 0.0269 c. M:-0.0372 c. 777: 115 324 338 SP T3 SD: 0.0271 c. M:-0.0339 c. 933: 138 389 406 SP T3 SD: 0.0248 c. M: 0.0403 c. 940: 139 392 409 SP T3 SD: 0.0214 c. M: 0.0336 c. 1048: 155 437 456 SP T3 SD: 0.0161 c. M: 0.0199 c. 1156: 171 482 503 SP T3 SD: 0.0141 c. M: 0.0232 c. 1163: 172 485 506 SP T3 SD: 0.0135 c. M: 0.0231 c. 1271: 188 530 553 SP T3 SD: 0.0085 c. M: 0.0123 c. 1379: 204 575 600 SP T3 SD: 0.0070 c. M: 0.0116 c. 1494: 221 623 650 SP T3 SD: 0.0042 c. M: 0.0073 c. 1602: 237 668 697 SP T3 SD: 0.0019 c. M: 0.0033 c. 1825: 270 761 794 SP T3 SD: 0.0023 c. M:-0.0030 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 11:12:13:15 SD: 28.8629 cents 12:13:14:16 S SD: 22.1632 cents 15:16:18:20 S SD: 17.0723 cents 16:17:19:21 SD: 14.8414 cents 17:18:20:23 SD: 11.9142 cents 18:19:21:24 SD: 8.2110 cents 21:22:25:28 SD: 7.2017 cents 22:23:26:29 SD: 7.1791 cents 23:24:27:31 SD: 6.3639 cents 24:25:28:32 SD: 4.9321 cents 39:41:46:52 SD: 4.5466 cents 44:46:52:59 SD: 4.3280 cents 45:47:53:60 SD: 0.8342 cents 114:119:134:152 SD: 0.5486 cents 159:166:187:212 SD: 0.3527 cents 255:266:300:340 SD: 0.1886 cents 300:313:353:400 SD: 0.1252 cents 414:432:487:552 SD: 0.0697 cents 459:479:540:612 SD: 0.0524 cents