Scala analysis: 519_M27
Miscellaneous tetrachord 68/67 * 67/54 * 18/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/67 25.648381 2: 34/27 399.090407 septendecimal major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 18/17 98.9546 Arabic lute index finger 1: 68/67 25.6484 2: 67/54 373.4420 3: 18/17 98.9546 Arabic lute index finger
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/67 25.648 cents 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 67/54 373.442 cents 2: 1 72/67 124.603 cents 2: 1 34/27 399.090 cents septendecimal major third 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 : 25.6 399.1 498.0 25.6 : 373.4 472.4 498.0 399.1: 99.0 124.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.6484 .. 373.4420 cents 4489/3672, 347.7936 cents 68/67, 25.6484 cents 2: 124.6030 .. 472.3966 cents 4489/3672, 347.7936 cents 3888/4489,-248.8391 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 : 67/54, 373.4420 cents Average / Smallest step : 6.472728 Largest / Average step : 2.249447 Largest / Smallest step : 14.560062 Median interval of one step : 18/17, 98.9546 cents, amount: 1 Least squares average step : 165.56887 cents, oct.: 496.70661 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1359-tone equal temperament with octave 4/3 degrees: 70 1089 1359 Least number of segments generator : 680 of 249.206 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1349 of 494.380 cents and inv. generated superset size: 35 = 32 more = 1166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 25.64838 cents Scale diversity : 0.487240 Lumma stability : 0.102996 Lumma impropriety factor : 0.499632 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 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 67 Odd number limit : 67 (O: 67 U: 67) Highest odd numerator or denominator: 67 Scale harmonicity : 0.024927 Fundamental : 1/1809, -10.8210 octaves, 0.1446 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.230120E+05, 16.90844 octaves Euler's gradus suavitatis : 91 Sum of Mann's harmonic distance : 101.5, average 33.83333 Mersenne's string divisions : 57645 Sum of van Prooijen's expressibility: 3.73456, average 1.24485 Sum of Tenney's harmonic distance : 7.70061, average 2.56687 Vogel's harmonic complexity : 62.66667 Wille's k value : 569 Wilson's harmonic complexity : 93 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.81474, average 2.46912 Lattice compactness (without 2's) : 11.81256, average 1.96876 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -3 .. 0 -1.33333 4 1 17: 0 .. 1 0.66667 2 1 67: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 27 44| Scale is weakly epimorphic with val: <6 11 30 43| Scale is weakly epimorphic with val: <7 11 27 45| Scale is weakly epimorphic with val: <7 11 28 44| Scale is weakly epimorphic with val: <7 11 30 45| Scale is weakly epimorphic with val: <7 11 31 44| Scale is weakly epimorphic with val: <7 11 33 45| Scale is weakly epimorphic with val: <7 12 32 45| Scale is weakly epimorphic with val: <7 12 33 44| Scale is weakly epimorphic with val: <8 11 28 43| Scale is weakly epimorphic with val: <8 11 32 45| Scale is weakly epimorphic with val: <8 12 30 43| Scale is weakly epimorphic with val: <8 12 31 45|
FIT/MODE
3: 0 2 1 N G T3 SD: 41.4525 c. M: 67.0604 c. 4: 0 3 1 N G T3 SD: 20.9044 c. M: 25.6484 c. 5: 0 4 1 N G T3 SD: 14.8129 c. M: 25.6484 c. 9: 0 7 2 N G T3 SD: 16.2813 c. M: 25.6484 c. 10: 0 8 2 N G T3 SD: 14.8129 c. M: 25.6484 c. 11: 1 8 2 N T3 SD: 12.3268 c. M:-19.6284 c. 13: 1 9 3 N T3 SD: 11.7710 c. M: 15.9789 c. 14: 1 10 3 N T3 SD: 7.2777 c. M:-9.9263 c. 15: 1 11 3 N T3 SD: 4.3780 c. M:-7.5546 c. 16: 1 12 3 N T3 SD: 4.5115 c. M:-5.5712 c. 19: 1 14 4 N T3 SD: 3.4202 c. M: 5.8970 c. 20: 1 15 4 N T3 SD: 0.5730 c. M: 0.7461 c. 76: 4 57 15 N T3 SD: 0.4998 c. M:-0.6562 c. 95: 5 71 19 N T3 SD: 0.4990 c. M: 0.6544 c. 96: 5 72 19 N T3 SD: 0.2780 c. M:-0.3832 c. 116: 6 87 23 N T3 SD: 0.1347 c. M:-0.2043 c. 136: 7 102 27 N T3 SD: 0.0457 c. M:-0.0780 c. 292: 15 219 58 N T3 SD: 0.0402 c. M: 0.0639 c. 428: 22 321 85 N T3 SD: 0.0375 c. M: 0.0479 c. 775: 40 581 154 N T3 SD: 0.0337 c. M:-0.0572 c. 795: 41 596 158 N T3 SD: 0.0267 c. M:-0.0370 c. 815: 42 611 162 N T3 SD: 0.0270 c. M: 0.0433 c. 911: 47 683 181 N T3 SD: 0.0269 c. M:-0.0466 c. 931: 48 698 185 N T3 SD: 0.0185 c. M:-0.0296 c. 951: 49 713 189 N T3 SD: 0.0168 c. M: 0.0260 c. 1067: 55 800 212 N T3 SD: 0.0139 c. M:-0.0240 c. 1087: 56 815 216 N T3 SD: 0.0094 c. M: 0.0130 c. 1223: 63 917 243 N T3 SD: 0.0045 c. M:-0.0072 c. 1359: 70 1019 270 N T3 SD: 0.0042 c. M:-0.0053 c. 1379: 71 1034 274 N T3 SD: 0.0041 c. M: 0.0057 c. 1515: 78 1136 301 N T3 SD: 0.0041 c. M: 0.0065 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: 12.7767 cents 5 x 6:7 S SD: 59.3685 cents 6 x x 8 S SD: 0.0000 cents 7 x 9 x SD: 35.9937 cents 10:11 x 13 SD: 73.0432 cents 11:12:14:15 S SD: 44.0644 cents 12:13:15:16 SD: 37.8816 cents 14:15:18:19 S SD: 35.0109 cents 15:16:19:20 SD: 28.8932 cents 16:17:20:21 SD: 28.2768 cents 17:18:21:23 SD: 28.1250 cents 18:19:23:24 SD: 24.1675 cents 19:20:24:25 S SD: 22.4664 cents 20:21:25:27 SD: 21.3058 cents 21:22:26:28 SD: 20.7467 cents 22:23:28:29 SD: 19.3310 cents 23:24:29:31 SD: 17.1991 cents 24:25:30:32 S SD: 15.6006 cents 26:27:33:35 SD: 15.0412 cents 27:28:34:36 SD: 12.4375 cents 30:31:38:40 SD: 10.9111 cents 31:32:39:41 SD: 10.8456 cents 33:34:42:44 SD: 10.6300 cents 34:35:43:45 SD: 9.5515 cents 35:36:44:47 SD: 8.7872 cents 36:37:45:48 SD: 8.4186 cents 38:39:48:51 SD: 7.6799 cents 39:40:49:52 SD: 6.2002 cents 42:43:53:56 SD: 5.1732 cents 46:47:58:61 SD: 5.0342 cents 50:51:63:67 SD: 4.0845 cents 51:52:64:68 SD: 3.3252 cents 54:55:68:72 SD: 2.0394 cents 66:67:83:88 SD: 0.7826 cents 69:70:87:92 SD: 0.7774 cents 135:137:170:180 SD: 0.0629 cents