Scala analysis: 495_M3
Miscellaneous tetrachord 128/127 * 127/126 * 21/16
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 128/127 13.578376 2: 64/63 27.264092 septimal comma, Archytas' comma 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 21/16 470.7809 narrow fourth 1: 128/127 13.5784 2: 127/126 13.6857 3: 21/16 470.7809 narrow fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128/127 13.578 cents 1: 1 127/126 13.686 cents 1: 1 21/16 470.781 cents narrow fourth 2: 1 64/63 27.264 cents septimal comma, Archytas' comma 2: 1 168/127 484.359 cents 2: 1 127/96 484.467 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 : 13.6 27.3 498.0 13.6 : 13.7 484.5 498.0 27.3 : 470.8 484.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 13.5784 .. 470.7809 cents 2667/2048, 457.2025 cents 128/127, 13.5784 cents 2: 27.2641 .. 484.4666 cents 2667/2048, 457.2025 cents 1024/1323,-443.5168 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 128/127, 13.5784 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 21/16, 470.7809 cents Average / Smallest step : 12.226425 Largest / Average step : 2.835773 Largest / Smallest step : 34.671371 Median interval of one step : 127/126, 13.6857 cents, amount: 1 Least squares average step : 111.58868 cents, oct.: 334.76605 cents Scale is not proper Scale has trivalence property 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 13.57838 cents Scale diversity :-0.091934 Lumma stability : 0.054527 Lumma impropriety factor : 0.890516 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 : 16129/16128, 0.1073 cents Number of recognisable fifths : 0 Number of recognisable fourths : 2, average 484.4130 cents Number of appreciable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 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 class 1 Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 127 Odd number limit : 127 (O: 127 U: 127) Highest odd numerator or denominator: 127 Scale harmonicity : 0.044211 Fundamental : 1/8001, -12.9660 octaves, 0.0327 Hz. Guide tone : 128, 7.0000 octaves, 33488.072 Hz. Exponens Consonantiae : 1.024128E+06, 19.96596 octaves Euler's gradus suavitatis : 144 Sum of Mann's harmonic distance : 194.5, average 64.83333 Mersenne's string divisions : 226695 Sum of van Prooijen's expressibility: 4.38027, average 1.46009 Sum of Tenney's harmonic distance : 8.89572, average 2.96524 Vogel's harmonic complexity : 97.33333 Wille's k value : 1333 Wilson's harmonic complexity : 140 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 27.43034, average 4.57172 Lattice compactness (without 2's) : 7.88635, average 1.31439 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 7 5.00000 15 3: -2 .. 0 -1.00000 3 1 7: -1 .. 0 -0.33333 1 1 127: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 19 50| Scale is weakly epimorphic with val: <7 11 18 51| Scale is weakly epimorphic with val: <7 11 19 50| Scale is weakly epimorphic with val: <7 11 21 51| Scale is weakly epimorphic with val: <7 11 22 50| Scale is weakly epimorphic with val: <8 12 21 51|
FIT/MODE
3: 0 0 3 N M DE S SD: 17.5851 c. M: 27.2641 c. 13: 0 1 12 N G T3 SD: 10.1063 c. M: 13.5784 c. 14: 0 1 13 N G T3 SD: 9.1913 c. M: 13.5784 c. 15: 0 1 14 N G T3 SD: 8.5565 c. M: 13.5784 c. 16: 0 1 15 N G T3 SD: 8.1507 c. M: 13.5784 c. 17: 0 1 16 N G T3 SD: 7.9268 c. M: 13.5784 c. 18: 0 1 17 N G T3 SD: 7.8430 c. M: 13.5784 c. 19: 0 1 18 N G T3 SD: 7.8629 c. M: 13.5784 c. 20: 0 1 19 N G T3 SD: 7.9572 c. M: 13.5784 c. 21: 0 1 20 N G T3 SD: 8.1026 c. M: 13.5784 c. 22: 0 1 21 N G T3 SD: 8.2819 c. M: 13.5784 c. 23: 0 1 22 N G T3 SD: 8.4822 c. M: 13.5784 c. 24: 0 1 23 N G T3 SD: 8.6945 c. M: 13.5784 c. 26: 1 0 25 N G T3 SD: 5.6819 c. M: 8.1085 c. 27: 1 1 25 N M DE S SD: 6.2289 c. M:-9.6281 c. 28: 1 1 26 N M DE S SD: 5.3784 c. M:-8.3106 c. 29: 1 1 27 N M DE S SD: 4.5865 c. M:-7.0838 c. 30: 1 1 28 N M DE S SD: 3.8475 c. M:-5.9389 c. 31: 1 1 29 N M DE S SD: 3.1562 c. M:-4.8678 c. 32: 1 1 30 N M DE S SD: 2.5080 c. M:-3.8637 c. 33: 1 1 31 N M DE S SD: 1.8992 c. M:-2.9205 c. 34: 1 1 32 N M DE S SD: 1.3262 c. M:-2.0327 c. 35: 1 1 33 N M DE S SD: 0.7861 c. M:-1.1956 c. 36: 1 1 34 N M DE S SD: 0.2767 c. M:-0.4051 c. 37: 1 1 35 N M DE S SD: 0.2092 c. M: 0.3427 c. 73: 2 2 69 N M DE S SD: 0.0413 c. M:-0.0667 c. 183: 5 5 173 N M DE S SD: 0.0328 c. M: 0.0485 c. 256: 7 7 242 N M DE S SD: 0.0280 c. M:-0.0400 c. 329: 9 9 311 N M DE S SD: 0.0280 c. M:-0.0460 c. 402: 11 11 380 N M DE S SD: 0.0291 c. M:-0.0497 c. 439: 12 12 415 N M DE S SD: 0.0293 c. M: 0.0361 c. 475: 13 13 449 N M DE S SD: 0.0303 c. M:-0.0523 c. 548: 15 15 518 N M DE S SD: 0.0313 c. M:-0.0542 c. 585: 16 16 553 N M DE S SD: 0.0277 c. M:-0.0434 c. 1023: 28 28 967 N M DE S SD: 0.0308 c. M:-0.0534 c. 1060: 29 29 1002 N M DE S SD: 0.0283 c. M:-0.0474 c. 1097: 30 30 1037 N M DE S SD: 0.0278 c. M:-0.0418 c. 1426: 39 39 1348 N M DE S SD: 0.0277 c. M:-0.0428 c. 1571: 43 43 1485 N M DE S SD: 0.0310 c. M:-0.0537 c. 1572: 43 43 1486 N M DE S SD: 0.0278 c. M:-0.0450 c. 1609: 44 44 1521 N M DE S SD: 0.0278 c. M:-0.0413 c. 1938: 53 53 1832 N M DE S SD: 0.0277 c. M:-0.0420 c. 2011: 55 55 1901 N M DE S SD: 0.0277 c. M:-0.0429 c. 2320: 63 64 2193 N T3 SD: 0.0311 c. M: 0.0539 c. 2339: 64 64 2211 N M DE S SD: 0.0289 c. M:-0.0492 c. 2341: 64 64 2213 N M DE S SD: 0.0286 c. M:-0.0375 c. 2354: 64 65 2225 N T3 SD: 0.0274 c. M: 0.0376 c. 2355: 64 65 2226 N T3 SD: 0.0270 c. M: 0.0434 c. 2356: 64 65 2227 N T3 SD: 0.0286 c. M: 0.0491 c. 2357: 64 65 2228 N T3 SD: 0.0319 c. M: 0.0549 c. 2376: 65 65 2246 N M DE S SD: 0.0281 c. M:-0.0466 c. 2377: 65 65 2247 N M DE S SD: 0.0278 c. M:-0.0409 c. 2390: 65 66 2259 N T3 SD: 0.0277 c. M:-0.0346 c. 2391: 65 66 2260 N T3 SD: 0.0261 c. M: 0.0389 c. 2392: 65 66 2261 N T3 SD: 0.0266 c. M: 0.0445 c. 2393: 65 66 2262 N T3 SD: 0.0290 c. M: 0.0502 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 x 7 SD: 84.4672 cents 6 x x 8 S SD: 0.0000 cents 7 x 8:9 S SD: 106.7045 cents 8 x 9:11 SD: 92.2521 cents 9 x 10:12 S SD: 77.5698 cents 10 x 11:13 SD: 72.2729 cents 11 x 12:15 S SD: 64.6810 cents 12 x 13:16 SD: 55.6543 cents 13 x 14:17 SD: 53.2401 cents 14 x 15:19 SD: 48.5692 cents 15 x 16:20 S SD: 42.2336 cents 16 x 17:21 SD: 41.1682 cents 17 x 18:23 SD: 38.0076 cents 18 x 19:24 SD: 33.1695 cents 19 x 20:25 S SD: 32.8351 cents 20 x 21:27 SD: 30.5562 cents 21 x 22:28 SD: 26.6365 cents 22 x 23:29 SD: 26.7432 cents 23 x 24:31 SD: 25.0240 cents 24 x 25:32 SD: 21.7042 cents 25 x 26:33 SD: 22.1023 cents 26 x 27:35 SD: 20.7608 cents 27 x 28:36 SD: 17.8484 cents 28 x 29:37 SD: 18.4559 cents 29 x 30:39 SD: 17.3819 cents 30 x 31:40 SD: 14.7514 cents 31 x 32:41 SD: 15.5227 cents 32 x 33:43 SD: 14.6456 cents 33 x 34:44 SD: 12.2092 cents 34 x 35:45 SD: 13.1204 cents 35 x 36:47 SD: 12.3931 cents 36 x 37:48 SD: 10.0850 cents 37 x 38:49 SD: 11.1261 cents 38 x 39:51 SD: 10.5162 cents 39 x 40:52 SD: 8.2835 cents 40 x 41:53 SD: 9.4550 cents 41 x 42:55 SD: 8.9399 cents 42 x 43:56 SD: 6.7364 cents 43 x 44:57 SD: 8.0476 cents 44 x 45:59 SD: 7.6115 cents 45 x 46:60 SD: 5.3933 cents 46 x 47:61 SD: 6.8625 cents 47 x 48:63 SD: 6.4943 cents 48 x 49:64 SD: 4.2164 cents 49 x 50:65 SD: 5.8713 cents 50 x 51:67 SD: 5.5637 cents 51 x 52:68 SD: 3.1766 cents 52 x 53:69 SD: 5.0559 cents 53 x 54:71 SD: 4.8049 cents 54 x 55:72 SD: 2.2513 cents 55 x 56:73 SD: 4.4061 cents 56 x 57:75 SD: 4.2095 cents 57 x 58:76 SD: 1.4225 cents 58 x 59:77 SD: 3.9165 cents 59 x 60:79 SD: 3.7731 cents 60 x 61:80 SD: 0.6760 cents 61 x 62:81 SD: 3.5824 cents 62 x 63:83 SD: 3.4902 cents 63 x 64:84 SD: 0.0000 cents 64 x 65:85 SD: 3.3945 cents 65 x 66:87 SD: 3.3489 cents 66 x 67:88 SD: 0.6150 cents 67 x 68:89 SD: 3.3353 cents 68 x 69:91 SD: 3.3288 cents 69 x 70:92 SD: 1.1769 cents 70 x 71:93 SD: 3.3799 cents 71 x 72:95 SD: 3.4035 cents 72 x 73:96 SD: 1.6923 cents 73 x 74:97 SD: 3.5012 cents 74 x 75:99 SD: 3.5461 cents 75 x 76:100 SD: 2.1668 cents 76 x 77:101 SD: 3.6744 cents 77 x 78:103 SD: 3.7333 cents 78 x 79:104 SD: 2.6049 cents 79 x 80:105 SD: 3.8801 cents 80 x 81:107 SD: 3.9475 cents 81 x 82:108 SD: 3.0108 cents 82 x 83:109 SD: 4.1040 cents 83 x 84:111 SD: 4.1760 cents 84 x 85:112 SD: 3.3879 cents 85:86 x 113 SD: 4.1981 cents 86:87 x 115 SD: 4.0828 cents 87:88 x 116 SD: 3.1037 cents 88:89 x 117 SD: 3.8751 cents 89:90 x 119 SD: 3.7690 cents 90:91 x 120 SD: 2.7757 cents 91:92 x 121 SD: 3.5786 cents 92:93 x 123 SD: 3.4810 cents 93:94 x 124 SD: 2.4688 cents 94:95 x 125 SD: 3.3068 cents 96:97:98:128 SD: 3.1647 cents 99:100:101:132 SD: 2.7648 cents 102:103:104:136 SD: 2.3882 cents 105:106:107:140 SD: 2.0329 cents 108:109:110:144 SD: 1.6973 cents 111:112:113:148 SD: 1.3797 cents 114:115:116:152 SD: 1.0786 cents 117:118:119:156 SD: 0.7930 cents 120:121:122:160 SD: 0.5218 cents 123:124:125:164 SD: 0.2643 cents 126:127:128:168 SD: 0.0358 cents