Scala analysis: 566_M74
Miscellaneous tetrachord 40/37 * 37/32 * 16/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/37 134.969675 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 40/37 134.9697 2: 37/32 251.3440 37th harmonic 3: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 40/37 134.970 cents 1: 1 37/32 251.344 cents 37th harmonic 2: 1 128/111 246.701 cents 2: 1 37/30 363.075 cents 2: 1 5/4 386.314 cents 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 : 135.0 386.3 498.0 135.0: 251.3 363.1 498.0 386.3: 111.7 246.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 251.3440 cents 555/512, 139.6128 cents 16/15, 111.7313 cents 2: 246.7010 .. 386.3137 cents 555/512, 139.6128 cents 4096/4107,-4.6431 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 37/32, 251.3440 cents Average / Smallest step : 1.485842 Largest / Average step : 1.513984 Largest / Smallest step : 2.249540 Median interval of one step : 40/37, 134.9697 cents, amount: 1 Least squares average step : 171.55229 cents, oct.: 514.65688 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2144-tone equal temperament with octave 4/3 degrees: 581 1663 2144 Least number of segments generator : 1073 of 249.255 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1603 of 372.372 cents and inv. generated superset size: 12 = 9 more = 400.000% 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 4.64308 cents Scale diversity : 1.141077 Lumma stability : 0.448679 Lumma impropriety factor : 0.009323 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 : 4107/4096, 4.6431 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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 : 37 Odd number limit : 111 (O: 37 U: 111) Highest odd numerator or denominator: 37 Scale harmonicity : 0.071090 Fundamental : 1/444, -8.7944 octaves, 0.5892 Hz. Guide tone : 40, 5.3219 octaves, 10465.023 Hz. Exponens Consonantiae : 1.776000E+04, 14.11634 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 46.5, average 15.50000 Mersenne's string divisions : 693 Sum of van Prooijen's expressibility: 2.74429, average 0.91476 Sum of Tenney's harmonic distance : 5.55047, average 1.85016 Vogel's harmonic complexity : 33.00000 Wille's k value : 277 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 18.60911, average 3.10152 Lattice compactness (without 2's) : 5.82843, average 0.97140 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 1.00000 7 3: -1 .. 0 -0.33333 1 1 5: 0 .. 1 0.66667 2 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <6 10 15 35| Scale is weakly epimorphic with val: <6 10 15 38| Scale is weakly epimorphic with val: <6 10 15 41| Scale is weakly epimorphic with val: <6 11 15 37| Scale is weakly epimorphic with val: <6 11 15 40| Scale is weakly epimorphic with val: <7 10 17 36| Scale is weakly epimorphic with val: <7 10 17 39| Scale is weakly epimorphic with val: <7 10 19 37| Scale is weakly epimorphic with val: <7 11 15 37| Scale is weakly epimorphic with val: <7 11 15 40| Scale is JI-epimorphic with val: <7 11 16 36| Scale is weakly epimorphic with val: <7 11 16 39| Scale is weakly epimorphic with val: <7 11 18 37| Scale is weakly epimorphic with val: <7 11 18 40| Scale is weakly epimorphic with val: <7 11 19 36| Scale is weakly epimorphic with val: <7 11 19 39| Scale is weakly epimorphic with val: <7 12 17 37| Scale is weakly epimorphic with val: <7 12 17 40| Scale is weakly epimorphic with val: <7 12 18 36| Scale is weakly epimorphic with val: <8 11 17 38| Scale is weakly epimorphic with val: <8 11 19 36| Scale is weakly epimorphic with val: <8 11 19 39| Scale is weakly epimorphic with val: <8 12 15 36| Scale is weakly epimorphic with val: <8 12 18 39| Scale is weakly epimorphic with val: <8 12 19 35| Scale is weakly epimorphic with val: <8 12 19 38| Scale is weakly epimorphic with val: <8 12 19 41|
FIT/MODE
3: 1 1 1 SP B ME I SD: 36.1042 c. M: 54.2837 c. 4: 1 2 1 P M ME I SD: 9.5343 c. M: 12.7800 c. 14: 4 7 3 P T3 SD: 5.1247 c. M:-7.3289 c. 18: 5 9 4 P T3 SD: 2.0421 c. M:-3.3762 c. 22: 6 11 5 P T3 SD: 0.9789 c. M: 1.4608 c. 59: 16 30 13 N T3 SD: 1.1517 c. M:-1.9926 c. 62: 17 31 14 P T3 SD: 1.0108 c. M:-1.5911 c. 63: 17 32 14 N T3 SD: 0.6939 c. M:-1.0546 c. 67: 18 34 15 N T3 SD: 0.6863 c. M: 1.1665 c. 81: 22 41 18 N T3 SD: 0.6333 c. M:-1.0546 c. 85: 23 43 19 N T3 SD: 0.2612 c. M:-0.4036 c. 107: 29 54 24 N T3 SD: 0.0144 c. M:-0.0203 c. 1288: 349 650 289 N T3 SD: 0.0153 c. M: 0.0195 c. 1395: 378 704 313 N T3 SD: 0.0131 c. M: 0.0164 c. 1502: 407 758 337 N T3 SD: 0.0111 c. M: 0.0138 c. 1609: 436 812 361 N T3 SD: 0.0094 c. M: 0.0116 c. 1716: 465 866 385 N T3 SD: 0.0080 c. M: 0.0099 c. 1823: 494 920 409 N T3 SD: 0.0067 c. M: 0.0085 c. 1930: 523 974 433 N T3 SD: 0.0055 c. M: 0.0072 c. 2037: 552 1028 457 N T3 SD: 0.0045 c. M: 0.0061 c. 2144: 581 1082 481 N T3 SD: 0.0036 c. M: 0.0051 c. 2251: 610 1136 505 N T3 SD: 0.0028 c. M: 0.0041 c. 2358: 639 1190 529 N T3 SD: 0.0021 c. M: 0.0033 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: 0.0000 cents 5 x 6:7 S SD: 55.0665 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 53.9301 cents 8:9:10:11 H SD: 29.0417 cents 9:10:11:12 H SD: 20.4495 cents 10:11 x 13 SD: 26.5671 cents 11:12:14:15 S SD: 17.4235 cents 12:13:15:16 SD: 1.2010 cents 99:107:124:132 SD: 1.1737 cents 111:120:139:148 SD: 1.0388 cents 123:133:154:164 SD: 0.9449 cents 135:146:169:180 SD: 0.8806 cents 147:159:184:196 SD: 0.8380 cents 159:172:199:212 SD: 0.8111 cents 171:185:214:228 SD: 0.7955 cents 183:198:229:244 SD: 0.7880 cents 195:211:244:260 SD: 0.7861 cents 208:225:260:277 SD: 0.7758 cents 220:238:275:293 SD: 0.7650 cents 224:242:280:299 SD: 0.7509 cents 236:255:295:315 SD: 0.6832 cents 248:268:310:331 SD: 0.6263 cents 249:269:311:332 SD: 0.6161 cents 260:281:325:347 SD: 0.5791 cents 261:282:326:348 SD: 0.5529 cents 272:294:340:363 SD: 0.5407 cents 273:295:341:364 SD: 0.4987 cents 285:308:356:380 SD: 0.4529 cents 297:321:371:396 SD: 0.4152 cents 309:334:386:412 SD: 0.3851 cents 321:347:401:428 SD: 0.3625 cents 333:360:416:444 SD: 0.3467 cents 345:373:431:460 SD: 0.3372 cents 348:376:435:464 SD: 0.3317 cents 360:389:450:480 SD: 0.2806 cents 372:402:465:496 SD: 0.2327 cents 384:415:480:512 SD: 0.1879 cents 396:428:495:528 SD: 0.1457 cents 408:441:510:544 SD: 0.1061 cents 420:454:525:560 SD: 0.0687 cents 432:467:540:576 SD: 0.0334 cents 444:480:555:592 SD: 0.0000 cents