Scala analysis: 472_D15
Diatonic tetrachord 35/32 * 1024/945 * 9/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35/32 155.139620 septimal neutral second 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 35/32 155.1396 septimal neutral second 2: 1024/945 138.9954 3: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1024/945 138.995 cents 1: 1 35/32 155.140 cents septimal neutral second 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 128/105 342.905 cents septimal neutral third 2: 1 315/256 359.050 cents 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 : 155.1 294.1 498.0 155.1: 139.0 342.9 498.0 294.1: 203.9 359.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.9954 .. 203.9100 cents 8505/8192, 64.9146 cents 1024/945, 138.9954 cents 2: 294.1350 .. 359.0496 cents 8505/8192, 64.9146 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 1024/945, 138.9954 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.194392 Largest / Average step : 1.228263 Largest / Smallest step : 1.467027 Median interval of one step : 35/32, 155.1396 cents, amount: 1 Least squares average step : 159.82462 cents, oct.: 479.47385 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1358-tone equal temperament with octave 4/3 degrees: 423 802 1358 Least number of segments generator : 681 of 249.756 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 935 of 342.910 cents and inv. generated superset size: 35 = 32 more = 1166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.355550 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.739322 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 : 33075/32768, 16.1442 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 64.9146 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 945 (O: 315 U: 945) Highest odd numerator or denominator: 35 Scale harmonicity : 0.028830 Average absolute harmonicity : 0.112440 Specific harmonicity : 0.147161 Fundamental : 1/864, -9.7549 octaves, 0.3028 Hz. Guide tone : 1120, 10.1293 octaves, 293020.633 Hz. Exponens Consonantiae : 9.676800E+05, 19.88417 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 66.5, average 22.16667 Mersenne's string divisions : 27671 Sum of van Prooijen's expressibility: 3.45255, average 1.15085 Sum of Tenney's harmonic distance : 7.06491, average 2.35497 Vogel's harmonic complexity : 14.66667 Wille's k value : 472 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 34.61548, average 5.76925 Lattice compactness (without 2's) : 12.46289, average 2.07715 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 5 0.66667 12 3: -3 .. 0 -1.33333 4 2 5: 0 .. 1 0.33333 1 7: 0 .. 1 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: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 17 21| Scale is weakly epimorphic with val: <7 10 18 20| Scale is weakly epimorphic with val: <7 10 19 19| Scale is weakly epimorphic with val: <7 11 15 18| Scale is JI-epimorphic with val: <7 11 15 21| Scale is JI-epimorphic with val: <7 11 16 20| Scale is JI-epimorphic with val: <7 11 17 19| Scale is weakly epimorphic with val: <7 11 17 22| Scale is JI-epimorphic with val: <7 11 18 18| Scale is weakly epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 11 19 20|
FIT/MODE
3: 1 1 1 SP B ME I SD: 22.7618 c. M:-37.8950 c. 7: 2 2 3 SP M ME S SD: 9.2351 c. M: 12.8410 c. 10: 3 3 4 SP M ME S SD: 4.2741 c. M: 5.7261 c. 17: 5 5 7 SP M DE S SD: 5.0427 c. M: 8.6558 c. 19: 6 5 8 SP T3 SD: 3.5651 c. M: 5.7932 c. 22: 7 6 9 SP T3 SD: 1.9245 c. M:-3.3292 c. 29: 9 8 12 SP T3 SD: 1.3002 c. M: 2.1776 c. 32: 10 9 13 SP T3 SD: 0.9563 c. M:-1.5792 c. 51: 16 14 21 SP T3 SD: 0.9299 c. M: 1.1674 c. 61: 19 17 25 SP T3 SD: 0.1196 c. M: 0.2068 c. 154: 48 43 63 SP T3 SD: 0.1096 c. M:-0.1643 c. 215: 67 60 88 SP T3 SD: 0.0507 c. M:-0.0651 c. 276: 86 77 113 SP T3 SD: 0.0279 c. M:-0.0483 c. 337: 105 94 138 SP T3 SD: 0.0305 c. M:-0.0376 c. 613: 191 171 251 SP T3 SD: 0.0272 c. M:-0.0424 c. 745: 232 208 305 SP T3 SD: 0.0262 c. M: 0.0437 c. 806: 251 225 330 SP T3 SD: 0.0239 c. M: 0.0412 c. 867: 270 242 355 SP T3 SD: 0.0250 c. M: 0.0391 c. 928: 289 259 380 SP T3 SD: 0.0279 c. M: 0.0372 c. 960: 299 268 393 SP T3 SD: 0.0173 c. M:-0.0228 c. 1021: 318 285 418 SP T3 SD: 0.0121 c. M: 0.0188 c. 1082: 337 302 443 SP T3 SD: 0.0108 c. M: 0.0184 c. 1143: 356 319 468 SP T3 SD: 0.0131 c. M: 0.0180 c. 1236: 385 345 506 SP T3 SD: 0.0106 c. M:-0.0178 c. 1297: 404 362 531 SP T3 SD: 0.0049 c. M:-0.0072 c. 1358: 423 379 556 SP T3 SD: 0.0031 c. M: 0.0048 c. 1634: 509 456 669 SP T3 SD: 0.0026 c. M:-0.0041 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: 92.1787 cents 5 x 6:7 S SD: 43.5810 cents 6 x 7:8 S SD: 13.6320 cents 7 x 8:9 S SD: 44.5201 cents 8:9 x 11 SD: 36.1129 cents 9:10:11:12 H SD: 19.9481 cents 10:11:12:13 H SD: 16.6032 cents 11:12:13:15 SD: 13.1580 cents 12:13:14:16 S SD: 10.6343 cents 21:23:25:28 SD: 2.6876 cents 33:36:39:44 SD: 2.2244 cents 54:59:64:72 SD: 0.6110 cents 129:141:153:172 SD: 0.5682 cents 183:200:217:244 SD: 0.5389 cents 222:243:263:296 SD: 0.5078 cents 243:266:288:324 SD: 0.4748 cents 255:279:302:340 SD: 0.4667 cents 276:302:327:368 SD: 0.3091 cents 297:325:352:396 SD: 0.2775 cents 330:361:391:440 SD: 0.1920 cents 351:384:416:468 SD: 0.1409 cents 384:420:455:512 SD: 0.1409 cents 405:443:480:540 SD: 0.0407 cents 459:502:544:612 SD: 0.0359 cents