Scala analysis: 587_M95
Miscellaneous tetrachord 15/14 * 112/101 * 101/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 120/101 298.414935 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 101/90 199.6301 1: 15/14 119.4428 major diatonic semitone 2: 112/101 178.9721 3: 101/90 199.6301
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 112/101 178.972 cents 1: 1 101/90 199.630 cents 2: 1 120/101 298.415 cents 2: 1 101/84 319.073 cents 2: 1 56/45 378.602 cents septimal narrow 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 : 119.4 298.4 498.0 119.4: 179.0 378.6 498.0 298.4: 199.6 319.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 199.6301 cents 707/675, 80.1873 cents 15/14, 119.4428 cents 2: 298.4149 .. 378.6022 cents 707/675, 80.1873 cents 10800/10201, 98.7849 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 101/90, 199.6301 cents Average / Smallest step : 1.389912 Largest / Average step : 1.202482 Largest / Smallest step : 1.671344 Median interval of one step : 112/101, 178.9721 cents, amount: 1 Least squares average step : 157.88626 cents, oct.: 473.65879 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1205-tone equal temperament with octave 4/3 degrees: 289 722 1205 Least number of segments generator : 603 of 249.229 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 722 of 298.414 cents and inv. generated superset size: 50 = 47 more = 1666.667% 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 98.78487 cents Scale diversity : 1.269204 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.677992 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 : 10201/10080, 20.6579 cents 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 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 59.5293 cents: 1 -- Rational properties -- Prime limit : 101 Odd number limit : 101 (O: 101 U: 101) Highest odd numerator or denominator: 101 Scale harmonicity : 0.038433 Fundamental : 1/4242, -12.0505 octaves, 0.0617 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 5.090400E+05, 18.95742 octaves Euler's gradus suavitatis : 119 Sum of Mann's harmonic distance : 128.5, average 42.83333 Mersenne's string divisions : 44863 Sum of van Prooijen's expressibility: 3.65753, average 1.21918 Sum of Tenney's harmonic distance : 7.48490, average 2.49497 Vogel's harmonic complexity : 81.66667 Wille's k value : 2272 Wilson's harmonic complexity : 119 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 17.99827, average 2.99971 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 1 101: -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: <6 10 17 18 47| Scale is weakly epimorphic with val: <6 10 18 19 48| Scale is weakly epimorphic with val: <6 10 19 20 49| Scale is weakly epimorphic with val: <6 11 16 18 49| Scale is weakly epimorphic with val: <6 11 17 19 47| Scale is weakly epimorphic with val: <6 11 18 20 48| Scale is weakly epimorphic with val: <6 11 19 21 49| Scale is weakly epimorphic with val: <7 10 18 18 47| Scale is weakly epimorphic with val: <7 10 19 19 48| Scale is weakly epimorphic with val: <7 10 19 20 47| Scale is weakly epimorphic with val: <7 11 15 18 48| Scale is weakly epimorphic with val: <7 11 15 20 49| Scale is weakly epimorphic with val: <7 11 15 21 48| Scale is weakly epimorphic with val: <7 11 16 18 47| Scale is weakly epimorphic with val: <7 11 16 19 49| Scale is weakly epimorphic with val: <7 11 16 21 47| Scale is weakly epimorphic with val: <7 11 16 22 49| Scale is weakly epimorphic with val: <7 11 17 19 48| Scale is JI-epimorphic with val: <7 11 17 20 47| Scale is weakly epimorphic with val: <7 11 17 22 48| Scale is weakly epimorphic with val: <7 11 18 18 48| Scale is weakly epimorphic with val: <7 11 18 20 49| Scale is JI-epimorphic with val: <7 11 18 21 48| Scale is weakly epimorphic with val: <7 11 19 19 49| Scale is weakly epimorphic with val: <7 11 19 21 47| Scale is JI-epimorphic with val: <7 11 19 22 49| Scale is weakly epimorphic with val: <7 12 16 18 48| Scale is weakly epimorphic with val: <7 12 17 18 47| Scale is weakly epimorphic with val: <7 12 17 19 49| Scale is weakly epimorphic with val: <7 12 17 21 47| Scale is weakly epimorphic with val: <7 12 18 19 48| Scale is weakly epimorphic with val: <7 12 18 20 47| Scale is weakly epimorphic with val: <7 12 18 22 48| Scale is weakly epimorphic with val: <7 12 19 20 49| Scale is weakly epimorphic with val: <7 12 19 21 48| Scale is weakly epimorphic with val: <8 11 15 20 47| Scale is weakly epimorphic with val: <8 11 16 18 48| Scale is weakly epimorphic with val: <8 11 16 21 48| Scale is weakly epimorphic with val: <8 11 17 19 49| Scale is weakly epimorphic with val: <8 11 17 22 49| Scale is weakly epimorphic with val: <8 11 18 18 49| Scale is weakly epimorphic with val: <8 11 19 19 47| Scale is weakly epimorphic with val: <8 12 15 20 48| Scale is weakly epimorphic with val: <8 12 16 18 49| Scale is weakly epimorphic with val: <8 12 16 21 49| Scale is weakly epimorphic with val: <8 12 17 18 48| Scale is weakly epimorphic with val: <8 12 18 19 49| Scale is weakly epimorphic with val: <8 12 19 20 47|
FIT/MODE
3: 1 1 1 SP B ME I SD: 33.1609 c. M:-46.5722 c. 4: 1 1 2 P M ME S SD: 28.6665 c. M: 49.3924 c. 5: 1 2 2 SP M ME S SD: 11.4535 c. M: 19.8338 c. 8: 2 3 3 SP M ME S SD: 7.9823 c. M:-12.8632 c. 12: 3 4 5 SP T3 SD: 5.4136 c. M: 7.8887 c. Ute tritonic, Peruvian tritonic 2 13: 3 5 5 SP M DE S SD: 5.3394 c. M:-8.0743 c. 17: 4 6 7 SP T3 SD: 3.4040 c. M: 5.4473 c. 20: 5 7 8 SP T3 SD: 2.9359 c. M:-5.0684 c. 25: 6 9 10 SP T3 SD: 0.2433 c. M:-0.4121 c. 142: 34 51 57 SP T3 SD: 0.2007 c. M: 0.2894 c. 167: 40 60 67 SP T3 SD: 0.1375 c. M: 0.1844 c. 192: 46 69 77 SP T3 SD: 0.0925 c. M: 0.1195 c. 217: 52 78 87 SP T3 SD: 0.0615 c. M: 0.0956 c. 242: 58 87 97 SP T3 SD: 0.0443 c. M: 0.0767 c. 267: 64 96 107 SP T3 SD: 0.0419 c. M: 0.0612 c. 509: 122 183 204 SP T3 SD: 0.0413 c. M: 0.0686 c. 559: 134 201 224 SP T3 SD: 0.0450 c. M:-0.0557 c. 646: 155 232 259 SP T3 SD: 0.0440 c. M:-0.0572 c. 671: 161 241 269 SP T3 SD: 0.0388 c. M:-0.0583 c. 696: 167 250 279 SP T3 SD: 0.0357 c. M:-0.0594 c. 721: 173 259 289 SP T3 SD: 0.0349 c. M:-0.0604 c. 746: 179 268 299 SP T3 SD: 0.0360 c. M:-0.0613 c. 771: 185 277 309 SP T3 SD: 0.0386 c. M:-0.0622 c. 838: 201 301 336 SP T3 SD: 0.0378 c. M: 0.0634 c. 863: 207 310 346 SP T3 SD: 0.0306 c. M: 0.0496 c. 888: 213 319 356 SP T3 SD: 0.0243 c. M: 0.0366 c. 913: 219 328 366 SP T3 SD: 0.0191 c. M: 0.0243 c. 938: 225 337 376 SP T3 SD: 0.0158 c. M:-0.0243 c. 963: 231 346 386 SP T3 SD: 0.0150 c. M:-0.0259 c. 988: 237 355 396 SP T3 SD: 0.0167 c. M:-0.0275 c. 1130: 271 406 453 SP T3 SD: 0.0166 c. M: 0.0287 c. 1155: 277 415 463 SP T3 SD: 0.0111 c. M: 0.0191 c. 1180: 283 424 473 SP T3 SD: 0.0061 c. M: 0.0100 c. 1205: 289 433 483 SP T3 SD: 0.0032 c. M:-0.0053 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: 87.8988 cents 5 x 6:7 S SD: 43.1029 cents 6 x 7:8 S SD: 15.7720 cents 7 x 8:9 S SD: 46.0581 cents 8:9:10:11 H SD: 44.3457 cents 9:10:11:12 H SD: 26.5924 cents 10:11:12:13 H SD: 21.8422 cents 11:12:13:15 SD: 16.9032 cents 12:13:14:16 S SD: 12.2971 cents 15:16:18:20 S SD: 6.2912 cents 27:29:32:36 SD: 2.0151 cents 42:45:50:56 SD: 1.1439 cents 69:74:82:92 SD: 0.5745 cents 180:193:214:240 SD: 0.5678 cents 213:228:253:284 SD: 0.5647 cents 240:257:285:320 SD: 0.4396 cents 267:286:317:356 SD: 0.4387 cents 282:302:335:376 SD: 0.2859 cents 309:331:367:412 SD: 0.2376 cents 351:376:417:468 SD: 0.1171 cents 420:450:499:560 SD: 0.0115 cents