Scala analysis: 549_M57
Miscellaneous tetrachord 16/15 * 1215/1024 * 256/243
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 81/64 407.820003 Pythagorean major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 16/15 111.7313 minor diatonic semitone 2: 1215/1024 296.0887 wide augmented second 3: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 1215/1024 296.089 cents wide augmented second 2: 1 4096/3645 201.956 cents narrow diminished third 2: 1 5/4 386.314 cents major third 2: 1 81/64 407.820 cents Pythagorean 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 : 111.7 407.8 498.0 111.7: 296.1 386.3 498.0 407.8: 90.2 202.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 296.0887 cents 295245/262144, 205.8637 cents 256/243, 90.2250 cents 2: 201.9563 .. 407.8200 cents 295245/262144, 205.8637 cents 4194304/4428675,-94.1324 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 1215/1024, 296.0887 cents Average / Smallest step : 1.840011 Largest / Average step : 1.783506 Largest / Smallest step : 3.281671 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 172.96473 cents, oct.: 518.89420 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1529-tone equal temperament with octave 4/3 degrees: 343 1252 1529 Least number of segments generator : 765 of 249.185 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1222 of 398.045 cents and inv. generated superset size: 32 = 29 more = 1066.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.092981 Lumma stability : 0.362317 Lumma impropriety factor : 0.189004 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 : 81/80, 21.5063 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 5 Odd number limit : 3645 (O: 1215 U: 3645) Highest odd numerator or denominator: 81 Scale harmonicity : 0.033632 Average absolute harmonicity : 0.116938 Specific harmonicity : 0.170454 Fundamental : 1/960, -9.9069 octaves, 0.2725 Hz. Guide tone : 1296, 10.3399 octaves, 339066.733 Hz. Exponens Consonantiae : 1.244160E+06, 20.24674 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 91.5, average 30.50000 Mersenne's string divisions : 31465 Sum of van Prooijen's expressibility: 3.56170, average 1.18723 Sum of Tenney's harmonic distance : 7.17406, average 2.39135 Vogel's harmonic complexity : 14.33333 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 36.58483, average 6.09747 Lattice compactness (without 2's) : 17.51323, average 2.91887 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 4 0.00000 12 3: -1 .. 4 0.66667 6 2 5: -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 JI-epimorphic with val: <7 11 16| Scale is weakly epimorphic with val: <7 11 19|
FIT/MODE
3: 0 2 1 N G T3 SD: 77.9487 c. M: 111.7313 c. 4: 1 2 1 P M ME I SD: 21.1256 c. M: 34.2863 c. 5: 1 3 1 N M DE I SD: 8.8508 c. M: 12.1223 c. 12: 3 7 2 N T3 SD: 8.4739 c. M:-12.7800 c. 13: 3 8 2 N T3 SD: 8.0682 c. M:-13.6027 c. 16: 4 9 3 N T3 SD: 7.6005 c. M:-12.7800 c. 17: 4 10 3 N T3 SD: 3.4262 c. M:-5.4558 c. 22: 5 13 4 N T3 SD: 0.8645 c. M:-1.4608 c. 49: 11 29 9 N T3 SD: 0.7245 c. M: 1.2527 c. 67: 15 40 12 N T3 SD: 0.6052 c. M:-1.0229 c. 71: 16 42 13 N T3 SD: 0.6293 c. M: 0.9663 c. 89: 20 53 16 N T3 SD: 0.4124 c. M:-0.6888 c. 94: 21 56 17 N T3 SD: 0.2831 c. M: 0.4659 c. 116: 26 69 21 N T3 SD: 0.0681 c. M: 0.1005 c. 254: 57 151 46 N T3 SD: 0.0257 c. M:-0.0347 c. 370: 83 220 67 N T3 SD: 0.0226 c. M:-0.0385 c. 624: 140 371 113 N T3 SD: 0.0205 c. M:-0.0342 c. 878: 197 522 159 N T3 SD: 0.0211 c. M:-0.0323 c. 905: 203 538 164 N T3 SD: 0.0186 c. M: 0.0285 c. 1021: 229 607 185 N T3 SD: 0.0178 c. M: 0.0248 c. 1043: 234 620 189 N T3 SD: 0.0148 c. M: 0.0248 c. 1159: 260 689 210 N T3 SD: 0.0096 c. M: 0.0161 c. 1275: 286 758 231 N T3 SD: 0.0091 c. M: 0.0130 c. 1413: 317 840 256 N T3 SD: 0.0050 c. M: 0.0082 c. 1529: 343 909 277 N T3 SD: 0.0034 c. M: 0.0050 c. 1783: 400 1060 323 N T3 SD: 0.0009 c. M:-0.0015 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: 21.5063 cents 5 x 6:7 S SD: 62.5132 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 61.2575 cents 8:9:10:11 H SD: 36.2053 cents 9:10:11:12 H SD: 30.9914 cents 10:11 x 13 SD: 34.4934 cents 11:12:14:15 S SD: 18.6225 cents 12:13:15:16 SD: 11.4648 cents 15:16:19:20 SD: 0.4748 cents 237:253:300:316 SD: 0.4652 cents 252:269:319:336 SD: 0.4439 cents 267:285:338:356 SD: 0.4265 cents 282:301:357:376 SD: 0.4124 cents 297:317:376:396 SD: 0.4010 cents 312:333:395:416 SD: 0.3919 cents 327:349:414:436 SD: 0.3845 cents 342:365:433:456 SD: 0.3787 cents 357:381:452:476 SD: 0.3741 cents 372:397:471:496 SD: 0.3706 cents 387:413:490:516 SD: 0.3679 cents 402:429:509:536 SD: 0.3660 cents 417:445:528:556 SD: 0.3646 cents 432:461:547:576 SD: 0.3637 cents 447:477:566:596 SD: 0.3632 cents 448:478:567:597 SD: 0.3601 cents 463:494:586:617 SD: 0.3488 cents 467:498:591:623 SD: 0.3483 cents 478:510:605:637 SD: 0.3388 cents 482:514:610:643 SD: 0.3359 cents 493:526:624:657 SD: 0.3301 cents 497:530:629:663 SD: 0.3248 cents 508:542:643:677 SD: 0.3225 cents 512:546:648:683 SD: 0.3150 cents 527:562:667:703 SD: 0.3063 cents 528:563:668:704 SD: 0.2977 cents 543:579:687:724 SD: 0.2801 cents 558:595:706:744 SD: 0.2638 cents 573:611:725:764 SD: 0.2486 cents 588:627:744:784 SD: 0.2346 cents