Scala analysis: 506_M14
Miscellaneous tetrachord 13/10 * 250/247 * 76/75
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/10 454.213948 tridecimal semi-diminished fourth 2: 25/19 475.114412 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 76/75 22.9306 1: 13/10 454.2139 tridecimal semi-diminished fourth 2: 250/247 20.9005 3: 76/75 22.9306
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 250/247 20.900 cents 1: 1 76/75 22.931 cents 1: 1 13/10 454.214 cents tridecimal semi-diminished fourth 2: 1 40/39 43.831 cents tridecimal minor diesis 2: 1 25/19 475.114 cents 2: 1 494/375 477.145 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 : 454.2 475.1 498.0 454.2: 20.9 43.8 498.0 475.1: 22.9 477.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.9005 .. 454.2139 cents 3211/2500, 433.3135 cents 250/247, 20.9005 cents 2: 43.8311 .. 477.1445 cents 3211/2500, 433.3135 cents 400/507,-410.3829 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 250/247, 20.9005 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/10, 454.2139 cents Average / Smallest step : 7.943125 Largest / Average step : 2.735981 Largest / Smallest step : 21.732243 Median interval of one step : 76/75, 22.9306 cents, amount: 1 Least squares average step : 207.04127 cents, oct.: 621.12381 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1477-tone equal temperament with octave 4/3 degrees: 1347 1409 1477 Least number of segments generator : 739 of 249.191 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1220 of 411.384 cents and inv. generated superset size: 30 = 27 more = 1000.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 20.90046 cents Scale diversity : 0.019209 Lumma stability : 0.083930 Lumma impropriety factor : 0.823988 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 : 9386/9375, 2.0301 cents Number of recognisable fifths : 0 Number of recognisable fourths : 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 Limited inverse transpositions with margin 433.3135 cents: 1 -- Rational properties -- Prime limit : 19 Odd number limit : 375 (O: 247 U: 375) Highest odd numerator or denominator: 25 Scale harmonicity : 0.012327 Average absolute harmonicity : 0.089813 Specific harmonicity : 0.065741 Fundamental : 1/570, -9.1548 octaves, 0.4590 Hz. Guide tone : 1300, 10.3443 octaves, 340113.235 Hz. Exponens Consonantiae : 7.410000E+05, 19.49911 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 37.0, average 12.33333 Mersenne's string divisions : 7084 Sum of van Prooijen's expressibility: 2.98900, average 0.99633 Sum of Tenney's harmonic distance : 5.86982, average 1.95661 Vogel's harmonic complexity : 27.00000 Wille's k value : 370 Wilson's harmonic complexity : 50 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.29467, average 2.71578 Lattice compactness (without 2's) : 12.14845, average 2.02474 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 0 -0.33333 1 1 5: -1 .. 2 0.33333 3 13: 0 .. 1 0.33333 1 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 16 25 28| Scale is weakly epimorphic with val: <6 10 16 25 31| Scale is weakly epimorphic with val: <6 10 16 25 34| Scale is weakly epimorphic with val: <6 10 16 26 29| Scale is weakly epimorphic with val: <6 10 16 29 29| Scale is weakly epimorphic with val: <6 10 17 26 30| Scale is weakly epimorphic with val: <6 10 17 26 33| Scale is weakly epimorphic with val: <6 10 17 27 31| Scale is weakly epimorphic with val: <6 10 17 30 31| Scale is weakly epimorphic with val: <6 10 18 25 33| Scale is weakly epimorphic with val: <6 10 18 27 29| Scale is weakly epimorphic with val: <6 10 18 27 32| Scale is weakly epimorphic with val: <6 10 18 28 33| Scale is weakly epimorphic with val: <6 10 19 28 28| Scale is weakly epimorphic with val: <6 10 19 28 31| Scale is weakly epimorphic with val: <6 10 19 28 34| Scale is weakly epimorphic with val: <6 11 16 25 30| Scale is weakly epimorphic with val: <6 11 16 25 33| Scale is weakly epimorphic with val: <6 11 16 27 29| Scale is weakly epimorphic with val: <6 11 17 25 31| Scale is weakly epimorphic with val: <6 11 17 26 29| Scale is weakly epimorphic with val: <6 11 17 26 32| Scale is weakly epimorphic with val: <6 11 17 28 31| Scale is weakly epimorphic with val: <6 11 18 26 33| Scale is weakly epimorphic with val: <6 11 18 27 28| Scale is weakly epimorphic with val: <6 11 18 27 31| Scale is weakly epimorphic with val: <6 11 18 27 34| Scale is weakly epimorphic with val: <6 11 18 29 33| Scale is weakly epimorphic with val: <6 11 19 28 30| Scale is weakly epimorphic with val: <6 11 19 28 33| Scale is weakly epimorphic with val: <7 10 15 25 28| Scale is weakly epimorphic with val: <7 10 15 25 31| Scale is weakly epimorphic with val: <7 10 15 25 34| Scale is weakly epimorphic with val: <7 10 16 25 29| Scale is weakly epimorphic with val: <7 10 16 26 30| Scale is weakly epimorphic with val: <7 10 16 26 33| Scale is weakly epimorphic with val: <7 10 16 28 29| Scale is weakly epimorphic with val: <7 10 17 26 31| Scale is weakly epimorphic with val: <7 10 17 27 29| Scale is weakly epimorphic with val: <7 10 17 27 32| Scale is weakly epimorphic with val: <7 10 17 29 31| Scale is weakly epimorphic with val: <7 10 18 27 33| Scale is weakly epimorphic with val: <7 10 18 28 28| Scale is weakly epimorphic with val: <7 10 18 28 31| Scale is weakly epimorphic with val: <7 10 18 28 34| Scale is weakly epimorphic with val: <7 10 18 30 33| Scale is weakly epimorphic with val: <7 10 19 29 30| Scale is weakly epimorphic with val: <7 10 19 29 33| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 26 34| Scale is weakly epimorphic with val: <7 11 15 27 29| Scale is weakly epimorphic with val: <7 11 15 27 32| Scale is weakly epimorphic with val: <7 11 15 29 31| Scale is weakly epimorphic with val: <7 11 15 29 34| Scale is weakly epimorphic with val: <7 11 15 30 32| Scale is weakly epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 25 34| Scale is weakly epimorphic with val: <7 11 16 27 30| Scale is weakly epimorphic with val: <7 11 16 27 33| Scale is weakly epimorphic with val: <7 11 16 28 28| Scale is weakly epimorphic with val: <7 11 16 28 31| Scale is weakly epimorphic with val: <7 11 16 28 34| Scale is weakly epimorphic with val: <7 11 16 30 30| Scale is weakly epimorphic with val: <7 11 16 30 33| Scale is weakly epimorphic with val: <7 11 17 25 29| Scale is JI-epimorphic with val: <7 11 17 25 32| Scale is weakly epimorphic with val: <7 11 17 26 30| Scale is weakly epimorphic with val: <7 11 17 26 33| Scale is weakly epimorphic with val: <7 11 17 28 29| Scale is weakly epimorphic with val: <7 11 17 28 32| Scale is weakly epimorphic with val: <7 11 17 29 30| Scale is weakly epimorphic with val: <7 11 17 29 33| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is JI-epimorphic with val: <7 11 18 26 34| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 29 31| Scale is weakly epimorphic with val: <7 11 18 29 34| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 25 34| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 11 19 28 28| Scale is weakly epimorphic with val: <7 11 19 28 31| Scale is weakly epimorphic with val: <7 11 19 28 34| Scale is weakly epimorphic with val: <7 11 19 30 30| Scale is weakly epimorphic with val: <7 11 19 30 33| Scale is weakly epimorphic with val: <7 12 15 25 29| Scale is weakly epimorphic with val: <7 12 15 25 32| Scale is weakly epimorphic with val: <7 12 16 26 28| Scale is weakly epimorphic with val: <7 12 16 26 31| Scale is weakly epimorphic with val: <7 12 16 26 34| Scale is weakly epimorphic with val: <7 12 16 27 29| Scale is weakly epimorphic with val: <7 12 17 25 31| Scale is weakly epimorphic with val: <7 12 17 27 30| Scale is weakly epimorphic with val: <7 12 17 27 33| Scale is weakly epimorphic with val: <7 12 17 28 31| Scale is weakly epimorphic with val: <7 12 18 26 33| Scale is weakly epimorphic with val: <7 12 18 28 29| Scale is weakly epimorphic with val: <7 12 18 28 32| Scale is weakly epimorphic with val: <7 12 18 29 33| Scale is weakly epimorphic with val: <7 12 19 29 31| Scale is weakly epimorphic with val: <7 12 19 29 34| Scale is weakly epimorphic with val: <8 11 15 26 29| Scale is weakly epimorphic with val: <8 11 15 26 32| Scale is weakly epimorphic with val: <8 11 16 25 29| Scale is weakly epimorphic with val: <8 11 16 27 28| Scale is weakly epimorphic with val: <8 11 16 27 31| Scale is weakly epimorphic with val: <8 11 16 27 34| Scale is weakly epimorphic with val: <8 11 16 28 29| Scale is weakly epimorphic with val: <8 11 17 26 31| Scale is weakly epimorphic with val: <8 11 17 28 30| Scale is weakly epimorphic with val: <8 11 17 28 33| Scale is weakly epimorphic with val: <8 11 17 29 31| Scale is weakly epimorphic with val: <8 11 18 27 33| Scale is weakly epimorphic with val: <8 11 18 29 29| Scale is weakly epimorphic with val: <8 11 18 29 32| Scale is weakly epimorphic with val: <8 11 18 30 33| Scale is weakly epimorphic with val: <8 11 19 30 31| Scale is weakly epimorphic with val: <8 11 19 30 34| Scale is weakly epimorphic with val: <8 12 15 26 28| Scale is weakly epimorphic with val: <8 12 15 26 31| Scale is weakly epimorphic with val: <8 12 15 26 34| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 16 27 30| Scale is weakly epimorphic with val: <8 12 16 27 33| Scale is weakly epimorphic with val: <8 12 16 29 29| Scale is weakly epimorphic with val: <8 12 17 27 31| Scale is weakly epimorphic with val: <8 12 17 28 29| Scale is weakly epimorphic with val: <8 12 17 28 32| Scale is weakly epimorphic with val: <8 12 17 30 31| Scale is weakly epimorphic with val: <8 12 18 25 33| Scale is weakly epimorphic with val: <8 12 18 28 33| Scale is weakly epimorphic with val: <8 12 18 29 31| Scale is weakly epimorphic with val: <8 12 18 29 34| Scale is weakly epimorphic with val: <8 12 19 30 30| Scale is weakly epimorphic with val: <8 12 19 30 33|
FIT/MODE
3: 3 0 0 N M DE S SD: 28.5597 c. M:-43.8311 c. 4: 4 0 0 N M DE S SD: 28.5597 c. M:-43.8311 c. 5: 5 0 0 N M DE S SD: 28.5597 c. M:-43.8311 c. 7: 6 1 0 N G T3 SD: 20.5921 c. M: 27.3182 c. 9: 8 0 1 N G T3 SD: 19.8551 c. M: 32.4077 c. 10: 9 0 1 N G T3 SD: 15.8943 c. M: 26.8739 c. 11: 10 0 1 N G T3 SD: 12.9286 c. M: 22.3462 c. 12: 11 0 1 N G T3 SD: 10.8071 c. M: 18.5732 c. 13: 12 0 1 N G T3 SD: 9.4345 c. M: 15.3806 c. 14: 13 0 1 N G T3 SD: 8.7186 c. M: 12.6441 c. 15: 14 0 1 N G T3 SD: 8.5338 c. M:-10.6281 c. 17: 15 1 1 N M DE S SD: 9.2819 c. M: 14.7625 c. 18: 16 1 1 N M DE S SD: 7.1850 c. M: 11.5073 c. 19: 17 1 1 N M DE S SD: 5.3117 c. M: 8.5947 c. 20: 18 1 1 N M DE S SD: 3.6318 c. M: 5.9734 c. 21: 19 1 1 N M DE S SD: 2.1284 c. M: 3.6018 c. 22: 20 1 1 N M DE S SD: 0.8516 c. M: 1.4458 c. 23: 21 1 1 N M DE S SD: 0.7964 c. M:-1.2765 c. 45: 41 2 2 N M DE S SD: 0.5246 c. M:-0.7953 c. 67: 61 3 3 N M DE S SD: 0.5744 c. M: 0.7700 c. 68: 62 3 3 N M DE S SD: 0.5570 c. M:-0.9580 c. 91: 83 4 4 N M DE S SD: 0.6002 c. M:-1.0385 c. 112: 102 5 5 N M DE S SD: 0.5450 c. M:-0.6964 c. 113: 103 5 5 N M DE S SD: 0.5345 c. M:-0.8932 c. 125: 114 5 6 N T3 SD: 0.5632 c. M: 0.9756 c. 126: 115 5 6 N T3 SD: 0.4969 c. M: 0.7858 c. 127: 116 5 6 N T3 SD: 0.5290 c. M:-0.6933 c. 146: 133 6 7 N T3 SD: 0.6231 c. M: 0.9483 c. 147: 134 6 7 N T3 SD: 0.4702 c. M: 0.7858 c. 148: 135 6 7 N T3 SD: 0.3644 c. M: 0.6256 c. 149: 136 6 7 N T3 SD: 0.3469 c. M: 0.4675 c. 170: 155 7 8 N T3 SD: 0.2999 c. M: 0.5068 c. 171: 156 7 8 N T3 SD: 0.2289 c. M: 0.3698 c. 193: 176 8 9 N T3 SD: 0.1713 c. M: 0.2943 c. 194: 177 8 9 N T3 SD: 0.1481 c. M:-0.1879 c. 215: 196 9 10 N T3 SD: 0.1714 c. M: 0.2343 c. 216: 197 9 10 N T3 SD: 0.0744 c. M: 0.1271 c. 238: 217 10 11 N T3 SD: 0.0833 c. M: 0.1141 c. 239: 218 10 11 N T3 SD: 0.0405 c. M:-0.0698 c. 261: 238 11 12 N T3 SD: 0.0382 c. M: 0.0580 c. 455: 415 19 21 N T3 SD: 0.0422 c. M: 0.0561 c. 477: 435 20 22 N T3 SD: 0.0264 c. M: 0.0400 c. 500: 456 21 23 N T3 SD: 0.0120 c. M:-0.0205 c. 977: 891 41 45 N T3 SD: 0.0074 c. M: 0.0091 c. 1216: 1109 51 56 N T3 SD: 0.0049 c. M:-0.0064 c. 1477: 1347 62 68 N T3 SD: 0.0029 c. M: 0.0050 c. 1716: 1565 72 79 N T3 SD: 0.0033 c. M:-0.0054 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 4:5 x x S SD: 67.9002 cents 5 x x 7 SD: 84.4672 cents 6 x x 8 S SD: 0.0000 cents 7:9 x x SD: 19.1299 cents 8:10 x 11 S SD: 43.1522 cents 9 x x 12 S SD: 0.0000 cents 10:13 x x SD: 0.0000 cents 11:14 x 15 SD: 26.7441 cents 12 x x 16 S SD: 0.0000 cents 13:17 x x SD: 10.2138 cents 14:18 x 19 SD: 18.0616 cents 15 x x 20 S SD: 0.0000 cents 16 x 21 x SD: 4.3335 cents 17:22 x 23 SD: 13.2327 cents 18:23 x 24 SD: 14.9248 cents 19 x 25 x SD: 0.0000 cents 20:26 x 27 SD: 10.7531 cents 21:27 x 28 SD: 9.5649 cents 22 x 29 x SD: 3.1448 cents 23:30 x 31 SD: 9.7943 cents 24:31 x 32 SD: 5.5667 cents 25 x 33 x SD: 5.5311 cents 26:34 x 35 SD: 9.7312 cents 27:35 x 36 SD: 2.4697 cents 28:36:37 x SD: 10.2563 cents 29 x 38:39 SD: 8.2518 cents 30:39 x 40 SD: 0.0000 cents 31:40:41 x SD: 7.8544 cents 32 x 42:43 SD: 7.0762 cents 33:43 x 44 SD: 2.0154 cents 34:44:45 x SD: 6.4177 cents 35 x 46:47 SD: 6.2400 cents 36:47 x 48 SD: 3.6913 cents 37:48:49 x SD: 5.8795 cents 39:51 x 52 SD: 5.1069 cents 40:52 x 53 SD: 5.4271 cents 41:53:54:55 SD: 4.8201 cents 42 x 55:56 SD: 4.1318 cents 43:56 x 57 SD: 5.2791 cents 44:57:58:59 SD: 3.9843 cents 45 x 59:60 SD: 3.0832 cents 46:60 x 61 SD: 5.5323 cents 47:61:62:63 SD: 3.5258 cents 49:64 x 65 SD: 6.0122 cents 50:65:66:67 SD: 3.4181 cents 51:66:67:68 SD: 2.7695 cents 52:68 x 69 SD: 6.5942 cents 53:69:70:71 SD: 3.5777 cents 54:70:71:72 SD: 1.7011 cents 55 x 72:73 SD: 5.9221 cents 56:73:74:75 SD: 3.8993 cents 57:74:75:76 SD: 0.7793 cents 60:78:79:80 SD: 0.3846 cents 177:230:233:236 SD: 0.3618 cents 237:308:312:316 SD: 0.3470 cents 297:386:391:396 SD: 0.3449 cents 330:429:434:440 SD: 0.2799 cents 333:433:438:444 SD: 0.2470 cents 390:507:513:520 SD: 0.1776 cents 393:511:517:524 SD: 0.1630 cents 450:585:592:600 SD: 0.1026 cents 510:663:671:680 SD: 0.0453 cents 570:741:750:760 SD: 0.0000 cents