Scala analysis: 498_M6
Miscellaneous tetrachord 17/13 * 429/425 * 100/99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/13 464.427748 2: 33/25 480.645516 2 pentatones 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 100/99 17.3995 Ptolemy's comma 1: 17/13 464.4277 2: 429/425 16.2178 3: 100/99 17.3995 Ptolemy's comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 429/425 16.218 cents 1: 1 100/99 17.399 cents Ptolemy's comma 1: 1 17/13 464.428 cents 2: 1 52/51 33.617 cents 2: 1 33/25 480.646 cents 2 pentatones 2: 1 1700/1287 481.827 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 : 464.4 480.6 498.0 464.4: 16.2 33.6 498.0 480.6: 17.4 481.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 16.2178 .. 464.4277 cents 7225/5577, 448.2100 cents 429/425, 16.2178 cents 2: 33.6173 .. 481.8272 cents 7225/5577, 448.2100 cents 676/867,-430.8105 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 429/425, 16.2178 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/13, 464.4277 cents Average / Smallest step : 10.236612 Largest / Average step : 2.797505 Largest / Smallest step : 28.636971 Median interval of one step : 100/99, 17.3995 cents, amount: 1 Least squares average step : 208.56098 cents, oct.: 625.68295 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1689-tone equal temperament with octave 4/3 degrees: 1575 1630 1689 Least number of segments generator : 845 of 249.170 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1253 of 369.479 cents and inv. generated superset size: 40 = 37 more = 1333.333% 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 16.21777 cents Scale diversity :-0.050087 Lumma stability : 0.065126 Lumma impropriety factor : 0.865003 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 : 42500/42471, 1.1817 cents Number of recognisable fifths : 0 Number of recognisable fourths : 2, average 481.2364 cents Number of appreciable 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 448.2100 cents: 1 -- Rational properties -- Prime limit : 17 Odd number limit : 1287 (O: 429 U: 1287) Highest odd numerator or denominator: 33 Scale harmonicity : 0.011039 Average absolute harmonicity : 0.087711 Specific harmonicity : 0.058875 Fundamental : 1/975, -9.9293 octaves, 0.2683 Hz. Guide tone : 2244, 11.1319 octaves, 587087.769 Hz. Exponens Consonantiae : 2.187900E+06, 21.06112 octaves Euler's gradus suavitatis : 53 Sum of Mann's harmonic distance : 47.5, average 15.83333 Mersenne's string divisions : 6090 Sum of van Prooijen's expressibility: 3.22608, average 1.07536 Sum of Tenney's harmonic distance : 6.34003, average 2.11334 Vogel's harmonic complexity : 28.33333 Wille's k value : 643 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 15.17950, average 2.52992 Lattice compactness (without 2's) : 12.42418, average 2.07070 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 1 0.00000 2 1 5: -2 .. 0 -0.66667 2 11: 0 .. 1 0.33333 1 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 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 weakly epimorphic with val: <7 11 16 25 26 31| Scale is weakly epimorphic with val: <7 11 16 25 27 29| Scale is weakly epimorphic with val: <7 11 16 25 28 30| Scale is weakly epimorphic with val: <7 11 16 26 26 30| Scale is weakly epimorphic with val: <7 11 16 26 27 31| Scale is weakly epimorphic with val: <7 11 16 26 28 29| Scale is weakly epimorphic with val: <7 11 17 24 26 31| Scale is weakly epimorphic with val: <7 11 17 24 27 29| Scale is weakly epimorphic with val: <7 11 17 24 28 30| Scale is weakly epimorphic with val: <7 11 17 25 26 30| Scale is weakly epimorphic with val: <7 11 17 25 27 31| Scale is JI-epimorphic with val: <7 11 17 25 28 29| Scale is weakly epimorphic with val: <7 11 18 24 26 30| Scale is weakly epimorphic with val: <7 11 18 24 27 31| Scale is weakly epimorphic with val: <7 11 18 24 28 29| Scale is weakly epimorphic with val: <7 11 18 26 26 31| Scale is weakly epimorphic with val: <7 11 18 26 27 29| Scale is weakly epimorphic with val: <7 11 18 26 28 30| Scale is weakly epimorphic with val: <7 12 16 24 26 29| Scale is weakly epimorphic with val: <7 12 16 24 27 30| Scale is weakly epimorphic with val: <7 12 16 24 28 31| Scale is weakly epimorphic with val: <7 12 17 25 26 30| Scale is weakly epimorphic with val: <7 12 17 25 27 31| Scale is weakly epimorphic with val: <7 12 17 25 28 29| Scale is weakly epimorphic with val: <7 12 17 26 26 29| Scale is weakly epimorphic with val: <7 12 17 26 27 30| Scale is weakly epimorphic with val: <7 12 17 26 28 31| Scale is weakly epimorphic with val: <7 12 18 25 26 29| Scale is weakly epimorphic with val: <7 12 18 25 27 30| Scale is weakly epimorphic with val: <7 12 18 25 28 31|
FIT/MODE
3: 3 0 0 N M DE S SD: 21.8545 c. M:-33.6173 c. 4: 4 0 0 N M DE S SD: 21.8545 c. M:-33.6173 c. 5: 5 0 0 N M DE S SD: 21.8545 c. M:-33.6173 c. 8: 7 1 0 N G T3 SD: 19.3468 c. M: 28.6384 c. 9: 8 1 0 N G T3 SD: 16.0681 c. M: 21.7211 c. 11: 10 0 1 N G T3 SD: 17.4460 c. M: 27.8773 c. 12: 11 0 1 N G T3 SD: 14.6425 c. M: 24.1043 c. 13: 12 0 1 N G T3 SD: 12.3738 c. M: 20.9117 c. 14: 13 0 1 N G T3 SD: 10.5541 c. M: 18.1752 c. 15: 14 0 1 N G T3 SD: 9.1273 c. M: 15.8035 c. 16: 15 0 1 N G T3 SD: 8.0553 c. M: 13.7283 c. 17: 16 0 1 N G T3 SD: 7.3078 c. M: 11.8973 c. 18: 17 0 1 N G T3 SD: 6.8519 c. M: 10.2697 c. 19: 18 0 1 N G T3 SD: 6.6458 c. M: 8.8134 c. 22: 20 1 1 N M DE S SD: 7.3800 c. M: 11.6596 c. 23: 21 1 1 N M DE S SD: 6.1106 c. M: 9.6910 c. 24: 22 1 1 N M DE S SD: 4.9476 c. M: 7.8865 c. 25: 23 1 1 N M DE S SD: 3.8786 c. M: 6.2263 c. 26: 24 1 1 N M DE S SD: 2.8935 c. M: 4.6939 c. 27: 25 1 1 N M DE S SD: 1.9850 c. M: 3.2750 c. 28: 26 1 1 N M DE S SD: 1.1521 c. M: 1.9574 c. 29: 27 1 1 N M DE S SD: 0.4415 c. M: 0.7307 c. 30: 28 1 1 N M DE S SD: 0.5191 c. M:-0.7980 c. 59: 55 2 2 N M DE S SD: 0.3103 c. M:-0.5166 c. 88: 82 3 3 N M DE S SD: 0.3124 c. M:-0.4207 c. 89: 83 3 3 N M DE S SD: 0.3538 c. M:-0.6114 c. 117: 109 4 4 N M DE S SD: 0.3315 c. M: 0.4371 c. 147: 137 5 5 N M DE S SD: 0.3056 c. M:-0.4592 c. 148: 138 5 5 N M DE S SD: 0.3318 c. M:-0.5736 c. 205: 191 7 7 N M DE S SD: 0.3220 c. M: 0.3956 c. 206: 192 7 7 N M DE S SD: 0.3051 c. M:-0.4756 c. 222: 207 7 8 N T3 SD: 0.3171 c. M: 0.5481 c. 223: 208 7 8 N T3 SD: 0.2782 c. M: 0.4676 c. 224: 209 7 8 N T3 SD: 0.2715 c. M: 0.3878 c. 251: 234 8 9 N T3 SD: 0.2730 c. M: 0.4587 c. 252: 235 8 9 N T3 SD: 0.2242 c. M: 0.3878 c. 253: 236 8 9 N T3 SD: 0.2032 c. M: 0.3175 c. 254: 237 8 9 N T3 SD: 0.2174 c. M:-0.2835 c. 280: 261 9 10 N T3 SD: 0.2465 c. M: 0.3878 c. 281: 262 9 10 N T3 SD: 0.1904 c. M: 0.3245 c. 282: 263 9 10 N T3 SD: 0.1551 c. M: 0.2617 c. 283: 264 9 10 N T3 SD: 0.1549 c. M: 0.1993 c. 310: 289 10 11 N T3 SD: 0.1725 c. M: 0.2731 c. 311: 290 10 11 N T3 SD: 0.1251 c. M: 0.2163 c. 312: 291 10 11 N T3 SD: 0.1073 c. M: 0.1598 c. 340: 317 11 12 N T3 SD: 0.1116 c. M: 0.1786 c. 341: 318 11 12 N T3 SD: 0.0747 c. M: 0.1270 c. 342: 319 11 12 N T3 SD: 0.0834 c. M:-0.1230 c. 370: 345 12 13 N T3 SD: 0.0607 c. M: 0.0994 c. 371: 346 12 13 N T3 SD: 0.0443 c. M:-0.0563 c. 400: 373 13 14 N T3 SD: 0.0185 c. M: 0.0321 c. 430: 401 14 15 N T3 SD: 0.0221 c. M:-0.0282 c. 829: 773 27 29 N T3 SD: 0.0202 c. M: 0.0263 c. 830: 774 27 29 N T3 SD: 0.0083 c. M:-0.0142 c. 859: 801 28 30 N T3 SD: 0.0071 c. M: 0.0109 c. 1259: 1174 41 44 N T3 SD: 0.0058 c. M: 0.0077 c. 1689: 1575 55 59 N T3 SD: 0.0013 c. M:-0.0018 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: 78.1140 cents 5 x x 7 SD: 84.4672 cents 6 x x 8 S SD: 0.0000 cents 7:9 x x SD: 29.3437 cents 8:10 x 11 S SD: 47.2753 cents 9 x x 12 S SD: 0.0000 cents 10:13 x x SD: 10.2138 cents 11:14 x 15 SD: 30.4759 cents 12 x x 16 S SD: 0.0000 cents 13:17 x x SD: 0.0000 cents 14:18 x 19 SD: 21.2131 cents 15 x x 20 S SD: 0.0000 cents 16:21 x x SD: 6.3532 cents 17:22 x 23 SD: 15.5332 cents 18 x x 24 S SD: 0.0000 cents 19 x 25 x SD: 5.5311 cents 20:26 x 27 SD: 11.9042 cents 21:27 x 28 SD: 14.6718 cents 22 x 29 x SD: 2.3863 cents 23:30 x 31 SD: 9.6171 cents 24:31 x 32 SD: 10.6736 cents 25 x 33 x SD: 0.0000 cents 26:34 x 35 SD: 8.2835 cents 27:35 x 36 SD: 7.5766 cents 28 x 37 x SD: 1.8726 cents 29:38 x 39 SD: 7.6345 cents 30:39 x 40 SD: 5.1069 cents 31 x 41 x SD: 3.3813 cents 32:42 x 43 SD: 7.4478 cents 33:43 x 44 SD: 3.0915 cents 34:44:45 x SD: 9.3237 cents 35 x 46:47 SD: 7.2153 cents 36:47 x 48 SD: 1.4156 cents 37:48:49 x SD: 7.4660 cents 38 x 50:51 SD: 6.3141 cents 39:51 x 52 SD: 0.0000 cents 40:52:53 x SD: 6.0655 cents 41 x 54:55 SD: 5.6020 cents 42:55 x 56 SD: 1.2115 cents 43:56:57 x SD: 5.1002 cents 44 x 58:59 SD: 5.0474 cents 45:59 x 60 SD: 2.2601 cents 46:60:61 x SD: 4.5578 cents 48:63 x 64 SD: 3.1766 cents 49:64:65 x SD: 4.3967 cents 51:67 x 68 SD: 3.9844 cents 52:68 x 69 SD: 4.1717 cents 53:69:70:71 SD: 3.7519 cents 54 x 71:72 SD: 3.4070 cents 55:72 x 73 SD: 4.0507 cents 56:73:74:75 SD: 3.2116 cents 57 x 75:76 SD: 2.7656 cents 58:76 x 77 SD: 4.1301 cents 59:77:78:79 SD: 2.8408 cents 61:80 x 81 SD: 4.3463 cents 62:81:82:83 SD: 2.6388 cents 64:84 x 85 SD: 4.6442 cents 65:85:86:87 SD: 2.5909 cents 66:86:87:88 SD: 2.2092 cents 67:88 x 89 SD: 4.9847 cents 68:89:90:91 SD: 2.6661 cents 69:90:91:92 SD: 1.5624 cents 70 x 92:93 SD: 4.8677 cents 71:93:94:95 SD: 2.8268 cents 72:94:95:96 SD: 0.9745 cents 75:98:99:100 SD: 0.4528 cents 78:102:103:104 SD: 0.2242 cents 231:302:305:308 SD: 0.2110 cents 309:404:408:412 SD: 0.2022 cents 387:506:511:516 SD: 0.2009 cents 510:667:673:680 SD: 0.1839 cents 585:765:772:780 SD: 0.1495 cents 588:769:776:784 SD: 0.1322 cents