Scala analysis: 407_D7
Diatonic tetrachord 150/139 * 139/128 * 256/225
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 150/139 131.853141 2: 75/64 274.582429 classic augmented second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 256/225 223.4626 Neapolitan diminished third 1: 150/139 131.8531 2: 139/128 142.7293 3: 256/225 223.4626 Neapolitan diminished third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 150/139 131.853 cents 1: 1 139/128 142.729 cents 1: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 75/64 274.582 cents classic augmented second 2: 1 512/417 355.316 cents 2: 1 278/225 366.192 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 : 131.9 274.6 498.0 131.9: 142.7 366.2 498.0 274.6: 223.5 355.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 131.8531 .. 223.4626 cents 17792/16875, 91.6094 cents 150/139, 131.8531 cents 2: 274.5824 .. 366.1919 cents 17792/16875, 91.6094 cents 16875/16384, 51.1199 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 150/139, 131.8531 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 256/225, 223.4626 cents Average / Smallest step : 1.259090 Largest / Average step : 1.346038 Largest / Smallest step : 1.694784 Median interval of one step : 139/128, 142.7293 cents, amount: 1 Least squares average step : 155.36807 cents, oct.: 466.10421 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1832-tone equal temperament with octave 4/3 degrees: 485 1010 1832 Least number of segments generator : 917 of 249.294 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1119 of 304.210 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 51.11986 cents Scale diversity : 1.311729 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.632124 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 : 19321/19200, 10.8761 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 80.7333 cents: 2 -- Rational properties -- Prime limit : 139 Odd number limit : 417 (O: 139 U: 417) Highest odd numerator or denominator: 139 Scale harmonicity : 0.038265 Fundamental : 1/26688, -14.7039 octaves, 0.0098 Hz. Guide tone : 300, 8.2288 octaves, 78487.670 Hz. Exponens Consonantiae : 8.006400E+06, 22.93272 octaves Euler's gradus suavitatis : 159 Sum of Mann's harmonic distance : 217.5, average 72.50000 Mersenne's string divisions : 281197 Sum of van Prooijen's expressibility: 4.49520, average 1.49840 Sum of Tenney's harmonic distance : 9.07953, average 3.02651 Vogel's harmonic complexity : 108.33333 Wille's k value : 15637 Wilson's harmonic complexity : 155 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 29.57396, average 4.92899 Lattice compactness (without 2's) : 11.12899, average 1.85483 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 2 -1.00000 9 3: -1 .. 1 0.33333 3 1 5: 0 .. 2 1.33333 4 1 139: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 4 / 3 = 1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 11 18 50| Scale is weakly epimorphic with val: <7 11 15 50| Scale is weakly epimorphic with val: <7 11 16 51| Scale is weakly epimorphic with val: <7 11 18 50| Scale is weakly epimorphic with val: <7 11 19 51| Scale is weakly epimorphic with val: <7 12 17 50|
FIT/MODE
3: 1 1 1 SP B ME I SD: 38.5887 c. M:-57.4476 c. 4: 1 1 2 P M ME S SD: 15.3538 c. M: 25.5599 c. 7: 2 2 3 SP M ME S SD: 8.3547 c. M:-10.4454 c. 11: 3 3 5 SP M DE S SD: 2.8492 c. M:-3.9773 c. 27: 7 8 12 SP T3 SD: 1.9920 c. M: 2.7304 c. 31: 8 9 14 SP T3 SD: 2.0970 c. M: 3.3254 c. 38: 10 11 17 SP T3 SD: 0.5911 c. M: 0.7887 c. 49: 13 14 22 SP T3 SD: 0.1839 c. M:-0.2812 c. 87: 23 25 39 SP T3 SD: 0.1581 c. M:-0.2010 c. 136: 36 39 61 SP T3 SD: 0.0443 c. M:-0.0747 c. 185: 49 53 83 SP T3 SD: 0.0366 c. M:-0.0615 c. 321: 85 92 144 SP T3 SD: 0.0284 c. M:-0.0405 c. 506: 134 145 227 SP T3 SD: 0.0294 c. M:-0.0402 c. 778: 206 223 349 SP T3 SD: 0.0292 c. M:-0.0465 c. 827: 219 237 371 SP T3 SD: 0.0287 c. M:-0.0354 c. 1054: 279 302 473 SP T3 SD: 0.0271 c. M: 0.0434 c. 1141: 302 327 512 SP T3 SD: 0.0227 c. M: 0.0305 c. 1190: 315 341 534 SP T3 SD: 0.0201 c. M: 0.0299 c. 1277: 338 366 573 SP T3 SD: 0.0187 c. M: 0.0292 c. 1326: 351 380 595 SP T3 SD: 0.0151 c. M: 0.0192 c. 1375: 364 394 617 SP T3 SD: 0.0143 c. M: 0.0238 c. 1462: 387 419 656 SP T3 SD: 0.0119 c. M: 0.0177 c. 1511: 400 433 678 SP T3 SD: 0.0098 c. M: 0.0149 c. 1647: 436 472 739 SP T3 SD: 0.0067 c. M: 0.0088 c. 1783: 472 511 800 SP T3 SD: 0.0055 c. M: 0.0095 c. 1832: 485 525 822 SP T3 SD: 0.0032 c. M: 0.0052 c. 1968: 521 564 883 SP T3 SD: 0.0016 c. M: 0.0028 c. 2153: 570 617 966 SP T3 SD: 0.0018 c. M:-0.0027 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 46.9589 cents 6 x 7:8 S SD: 3.8558 cents 7 x 8:9 S SD: 38.2373 cents 8 x 9:11 SD: 44.2510 cents 9:10:11:12 H SD: 29.5502 cents 10:11:12:13 H SD: 22.8667 cents 11:12:13:15 SD: 15.2040 cents 12:13:14:16 S SD: 3.4095 cents 51:55:60:68 SD: 2.2899 cents 63:68:74:84 SD: 1.3474 cents 75:81:88:100 SD: 0.8533 cents 87:94:102:116 SD: 0.7552 cents 180:194:211:240 SD: 0.7470 cents 192:207:225:256 SD: 0.5413 cents 204:220:239:272 SD: 0.4064 cents 216:233:253:288 SD: 0.3673 cents 267:288:313:356 SD: 0.3286 cents 279:301:327:372 SD: 0.1728 cents 291:314:341:388 SD: 0.0591 cents