Scala analysis: 517_M25
Miscellaneous tetrachord 68/67 * 67/65 * 65/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/67 25.648381 2: 68/65 78.114034 Valentine semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 65/51 419.9310 1: 68/67 25.6484 2: 67/65 52.4657 3: 65/51 419.9310
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/67 25.648 cents 1: 1 67/65 52.466 cents 1: 1 65/51 419.931 cents 2: 1 68/65 78.114 cents Valentine semitone 2: 1 260/201 445.579 cents 2: 1 67/51 472.397 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 : 25.6 78.1 498.0 25.6 : 52.5 472.4 498.0 78.1 : 419.9 445.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.6484 .. 419.9310 cents 4355/3468, 394.2826 cents 68/67, 25.6484 cents 2: 78.1140 .. 472.3966 cents 4355/3468, 394.2826 cents 3468/4225,-341.8169 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 68/67, 25.6484 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 65/51, 419.9310 cents Average / Smallest step : 6.472728 Largest / Average step : 2.529476 Largest / Smallest step : 16.372611 Median interval of one step : 67/65, 52.4657 cents, amount: 1 Least squares average step : 119.71510 cents, oct.: 359.14531 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2136-tone equal temperament with octave 4/3 degrees: 110 335 2136 Least number of segments generator : 1069 of 249.256 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1349 of 314.542 cents and inv. generated superset size: 47 = 44 more = 1566.667% Number of contiguous 1-step segments: 0 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 25.64838 cents Scale diversity : 0.238649 Lumma stability : 0.102996 Lumma impropriety factor : 0.686317 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 : 68/67, 25.6484 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing 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% Limited inverse transpositions with margin 367.4653 cents: 2 -- Rational properties -- Prime limit : 67 Odd number limit : 201 (O: 67 U: 201) Highest odd numerator or denominator: 67 Scale harmonicity : 0.015788 Fundamental : 1/13065, -13.6734 octaves, 0.0200 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 8.884200E+05, 19.76088 octaves Euler's gradus suavitatis : 103 Sum of Mann's harmonic distance : 137.5, average 45.83333 Mersenne's string divisions : 17955 Sum of van Prooijen's expressibility: 4.11611, average 1.37204 Sum of Tenney's harmonic distance : 8.38319, average 2.79440 Vogel's harmonic complexity : 72.00000 Wille's k value : 2177 Wilson's harmonic complexity : 105 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 11.94631, average 1.99105 Lattice compactness (without 2's) : 8.56048, average 1.42675 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 67: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 16 26 29 44| Scale is JI-epimorphic with val: <7 11 16 26 30 43| Scale is weakly epimorphic with val: <7 11 16 27 30 45| Scale is JI-epimorphic with val: <7 11 16 27 31 44| Scale is weakly epimorphic with val: <7 11 16 28 29 45| Scale is weakly epimorphic with val: <7 11 16 28 31 43| Scale is weakly epimorphic with val: <7 11 17 26 30 45| Scale is JI-epimorphic with val: <7 11 17 26 31 44| Scale is weakly epimorphic with val: <7 11 17 27 29 45| Scale is weakly epimorphic with val: <7 11 17 27 31 43| Scale is weakly epimorphic with val: <7 11 17 28 29 44| Scale is weakly epimorphic with val: <7 11 17 28 30 43| Scale is weakly epimorphic with val: <7 11 18 26 29 45| Scale is weakly epimorphic with val: <7 11 18 26 31 43| Scale is weakly epimorphic with val: <7 11 18 27 29 44| Scale is weakly epimorphic with val: <7 11 18 27 30 43| Scale is weakly epimorphic with val: <7 11 18 28 30 45| Scale is weakly epimorphic with val: <7 11 18 28 31 44| Scale is weakly epimorphic with val: <7 12 16 26 31 44|
FIT/MODE
3: 0 0 3 N M DE S SD: 47.4680 c. M: 78.1140 c. 4: 0 1 3 N G T3 SD: 30.6080 c. M:-46.3972 c. 5: 0 1 4 N G T3 SD: 19.3207 c. M: 25.6484 c. 6: 0 1 5 N G T3 SD: 15.0752 c. M: 25.6484 c. 7: 0 1 6 N G T3 SD: 15.3443 c. M: 25.6484 c. 8: 0 1 7 N G T3 SD: 17.4100 c. M: 25.6484 c. 11: 1 1 9 N M DE S SD: 13.4166 c. M:-19.6284 c. 12: 1 1 10 N M DE S SD: 9.5802 c. M:-15.8554 c. 13: 1 1 11 N M DE S SD: 7.3614 c. M:-12.6628 c. 14: 1 1 12 N M DE S SD: 7.0009 c. M:-9.9263 c. 17: 1 2 14 N T3 SD: 6.0246 c. M:-9.7763 c. 18: 1 2 15 N T3 SD: 3.0567 c. M:-4.8935 c. 19: 1 2 16 N T3 SD: 0.4449 c. M:-0.5645 c. 77: 4 8 65 N T3 SD: 0.3146 c. M: 0.4966 c. 96: 5 10 81 N T3 SD: 0.2392 c. M: 0.2945 c. 115: 6 12 97 N T3 SD: 0.2150 c. M:-0.3366 c. 134: 7 14 113 N T3 SD: 0.2160 c. M:-0.3689 c. 153: 8 16 129 N T3 SD: 0.2271 c. M:-0.3932 c. 172: 9 18 145 N T3 SD: 0.2411 c. M:-0.4121 c. 211: 11 22 178 N T3 SD: 0.2226 c. M:-0.3161 c. 216: 11 23 182 N T3 SD: 0.2314 c. M: 0.2850 c. 217: 11 23 183 N T3 SD: 0.2365 c. M: 0.4019 c. 235: 12 25 198 N T3 SD: 0.2143 c. M:-0.3016 c. 236: 12 25 199 N T3 SD: 0.1879 c. M: 0.3241 c. 255: 13 27 215 N T3 SD: 0.1490 c. M: 0.2579 c. 274: 14 29 231 N T3 SD: 0.1190 c. M: 0.2008 c. 293: 15 31 247 N T3 SD: 0.0980 c. M: 0.1512 c. 312: 16 33 263 N T3 SD: 0.0866 c. M: 0.1076 c. 331: 17 35 279 N T3 SD: 0.0843 c. M:-0.1287 c. 351: 18 37 296 N T3 SD: 0.0750 c. M: 0.1076 c. 370: 19 39 312 N T3 SD: 0.0487 c. M: 0.0731 c. 389: 20 41 328 N T3 SD: 0.0256 c. M: 0.0420 c. 408: 21 43 344 N T3 SD: 0.0100 c. M: 0.0137 c. 1301: 67 137 1097 N T3 SD: 0.0112 c. M: 0.0194 c. 1320: 68 139 1113 N T3 SD: 0.0083 c. M: 0.0115 c. 1709: 88 180 1441 N T3 SD: 0.0072 c. M: 0.0122 c. 1728: 89 182 1457 N T3 SD: 0.0041 c. M: 0.0063 c. 2136: 110 225 1801 N T3 SD: 0.0018 c. M: 0.0030 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 7:8 S SD: 94.3784 cents 7 x 8:9 S SD: 82.7518 cents 8 x 9:11 SD: 68.3056 cents 9 x 10:12 S SD: 52.1448 cents 10 x 11:13 SD: 48.6597 cents 11 x 12:15 S SD: 41.1499 cents 12 x 13:16 SD: 30.2293 cents 13 x 14:17 SD: 30.2017 cents 14 x 15:19 SD: 25.7245 cents 15 x 16:20 S SD: 16.8086 cents 16 x 17:21 SD: 19.1298 cents 17 x 18:23 SD: 16.3791 cents 18 x 19:24 SD: 7.7445 cents 19 x 20:25 S SD: 12.6493 cents 20 x 21:27 SD: 11.2125 cents 21 x 22:28 SD: 1.2115 cents 22 x 23:29 SD: 9.9098 cents 23 x 24:31 SD: 9.6171 cents 24 x 25:32 SD: 3.7208 cents 25 x 26:33 SD: 10.0879 cents 26 x 27:35 SD: 10.4607 cents 27 x 28:36 SD: 7.5766 cents 28 x 29:37 SD: 11.6463 cents 29 x 30:39 SD: 12.2277 cents 30 x 31:40 SD: 10.6736 cents 31 x 32:41 SD: 13.5316 cents 32 x 33:43 SD: 14.1297 cents 33:34:35:44 SD: 11.7472 cents 34:35:36:45 S SD: 11.5450 cents 35:36:37:47 SD: 10.6130 cents 36:37:38:48 SD: 8.9102 cents 38:39:40:51 SD: 8.2758 cents 39:40:41:52 SD: 6.6856 cents 41:42:43:55 SD: 6.5647 cents 42:43:44:56 SD: 5.0939 cents 45:46:47:60 SD: 4.2404 cents 48:49:50:64 SD: 4.1680 cents 57:58:60:76 SD: 3.8601 cents 59:60:62:79 SD: 3.7348 cents 60:61:63:80 SD: 2.3374 cents 63:64:66:84 SD: 0.9708 cents 66:67:69:88 SD: 0.4067 cents 129:131:135:172 SD: 0.3835 cents 195:198:204:260 SD: 0.2611 cents 261:265:273:348 SD: 0.2476 cents 411:417:430:548 SD: 0.1904 cents 474:481:496:632 SD: 0.1689 cents 477:484:499:636 SD: 0.1435 cents 540:548:565:720 SD: 0.1006 cents