Scala analysis: 466_D15
Diatonic tetrachord 9/8 * 200/189 * 28/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 25/21 301.846520 BP second, quasi-equal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 28/25 196.1985 middle second 1: 9/8 203.9100 major whole tone 2: 200/189 97.9365 3: 28/25 196.1985 middle second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 200/189 97.937 cents 1: 1 28/25 196.198 cents middle second 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 63/50 400.108 cents quasi-equal 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 : 203.9 301.8 498.0 203.9: 97.9 294.1 498.0 301.8: 196.2 400.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.9365 .. 203.9100 cents 1701/1600, 105.9735 cents 200/189, 97.9365 cents 2: 294.1350 .. 400.1085 cents 1701/1600, 105.9735 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 200/189, 97.9365 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.695129 Largest / Average step : 1.228263 Largest / Smallest step : 2.082063 Median interval of one step : 28/25, 196.1985 cents, amount: 1 Least squares average step : 164.40986 cents, oct.: 493.22958 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1485-tone equal temperament with octave 4/3 degrees: 608 900 1485 Least number of segments generator : 743 of 249.190 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 779 of 261.264 cents and inv. generated superset size: 46 = 43 more = 1533.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.094055 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.574442 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 : 225/224, 7.7115 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Best minor thirds form a closed circle 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% -- Rational properties -- Prime limit : 7 Odd number limit : 189 (O: 63 U: 189) Highest odd numerator or denominator: 25 Scale harmonicity : 0.027712 Average absolute harmonicity : 0.124372 Specific harmonicity : 0.144243 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 900, 9.8138 octaves, 235463.009 Hz. Exponens Consonantiae : 1.512000E+05, 17.20610 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 35.0, average 11.66667 Mersenne's string divisions : 5474 Sum of van Prooijen's expressibility: 2.82930, average 0.94310 Sum of Tenney's harmonic distance : 5.65667, average 1.88556 Vogel's harmonic complexity : 13.66667 Wille's k value : 94 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 21.91789, average 3.65298 Lattice compactness (without 2's) : 14.42722, average 2.40454 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.33333 5 3: -1 .. 2 0.00000 4 2 5: 0 .. 2 0.66667 2 7: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 17 21| Scale is weakly epimorphic with val: <7 11 15 20| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 17 18| Scale is JI-epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <7 12 15 20| Scale is weakly epimorphic with val: <7 12 16 19| Scale is weakly epimorphic with val: <7 12 16 22| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 17 21| Scale is weakly epimorphic with val: <7 12 18 20| Scale is weakly epimorphic with val: <7 12 19 19| Scale is weakly epimorphic with val: <7 12 19 22| Scale is weakly epimorphic with val: <8 11 16 18| Scale is weakly epimorphic with val: <8 11 17 20| Scale is weakly epimorphic with val: <8 11 18 22|
FIT/MODE
3: 1 1 1 SP B ME I SD: 27.9707 c. M: 37.8950 c. 5: 2 1 2 SP M ME I SD: 3.2214 c. M: 4.6920 c. 36: 15 7 14 SP T3 SD: 2.5393 c. M:-3.6087 c. 41: 17 8 16 SP T3 SD: 1.8371 c. M:-2.5965 c. 46: 19 9 18 SP T3 SD: 1.2877 c. M:-1.8042 c. 51: 21 10 20 SP T3 SD: 0.8464 c. M:-1.1674 c. 56: 23 11 22 SP T3 SD: 0.4846 c. M:-0.6442 c. 61: 25 12 24 SP T3 SD: 0.1857 c. M:-0.2463 c. 66: 27 13 26 SP T3 SD: 0.0949 c. M: 0.1643 c. 127: 52 25 50 SP T3 SD: 0.0685 c. M:-0.1178 c. 193: 79 38 76 SP T3 SD: 0.0522 c. M:-0.0771 c. 259: 106 51 102 SP T3 SD: 0.0553 c. M: 0.0769 c. 320: 131 63 126 SP T3 SD: 0.0554 c. M:-0.0933 c. 452: 185 89 178 SP T3 SD: 0.0530 c. M:-0.0657 c. 645: 264 127 254 SP T3 SD: 0.0525 c. M:-0.0691 c. 779: 319 153 307 SP T3 SD: 0.0507 c. M: 0.0786 c. 784: 321 154 309 SP T3 SD: 0.0564 c. M: 0.0973 c. 833: 341 164 328 SP T3 SD: 0.0542 c. M:-0.0895 c. 835: 342 164 329 SP T3 SD: 0.0508 c. M:-0.0797 c. 840: 344 165 331 SP T3 SD: 0.0434 c. M: 0.0550 c. 845: 346 166 333 SP T3 SD: 0.0440 c. M: 0.0725 c. 901: 369 177 355 SP T3 SD: 0.0409 c. M:-0.0618 c. 906: 371 178 357 SP T3 SD: 0.0359 c. M: 0.0510 c. 911: 373 179 359 SP T3 SD: 0.0393 c. M: 0.0673 c. 967: 396 190 381 SP T3 SD: 0.0326 c. M:-0.0464 c. 972: 398 191 383 SP T3 SD: 0.0303 c. M: 0.0476 c. 1033: 423 203 407 SP T3 SD: 0.0258 c. M:-0.0329 c. 1038: 425 204 409 SP T3 SD: 0.0265 c. M: 0.0447 c. 1094: 448 215 431 SP T3 SD: 0.0261 c. M:-0.0426 c. 1099: 450 216 433 SP T3 SD: 0.0205 c. M: 0.0285 c. 1104: 452 217 435 SP T3 SD: 0.0243 c. M: 0.0421 c. 1160: 475 228 457 SP T3 SD: 0.0196 c. M:-0.0308 c. 1165: 477 229 459 SP T3 SD: 0.0167 c. M: 0.0270 c. 1226: 502 241 483 SP T3 SD: 0.0141 c. M:-0.0203 c. 1231: 504 242 485 SP T3 SD: 0.0148 c. M: 0.0256 c. 1292: 529 254 509 SP T3 SD: 0.0097 c. M: 0.0127 c. 1353: 554 266 533 SP T3 SD: 0.0114 c. M:-0.0197 c. 1358: 556 267 535 SP T3 SD: 0.0072 c. M: 0.0122 c. 1419: 581 279 559 SP T3 SD: 0.0065 c. M:-0.0112 c. 1424: 583 280 561 SP T3 SD: 0.0074 c. M: 0.0117 c. 1485: 608 292 585 SP T3 SD: 0.0020 c. M:-0.0034 c. 1551: 635 305 611 SP T3 SD: 0.0023 c. M: 0.0038 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: 84.4672 cents 5 x 6:7 S SD: 42.7931 cents 6 x 7:8 S SD: 17.4878 cents 7:8 x 9 S SD: 34.3053 cents 8:9:10:11 H SD: 33.2878 cents 9:10:11:12 H SD: 16.7941 cents 12 x 14:16 S SD: 17.4878 cents 13:15 x 17 SD: 27.6192 cents 14:16:17:19 SD: 17.8188 cents 15:17:18:20 SD: 6.2675 cents 31:35:37:41 SD: 5.3207 cents 32:36:38:43 SD: 4.7175 cents 33:37:39:44 SD: 4.6402 cents 41:46:49:55 SD: 4.4509 cents 42:47:50:56 SD: 3.0614 cents 48:54:57:64 SD: 1.4445 cents 63:71:75:84 SD: 1.0169 cents 105:118:125:140 SD: 0.6110 cents 120:135:143:160 SD: 0.5768 cents 168:189:200:224 SD: 0.0000 cents