Scala analysis: 091_E10
Enharmonic tetrachord 24/23 * 69/68 * 34/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 2: 18/17 98.954592 Arabic lute index finger 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 34/27 399.0904 septendecimal major third 1: 24/23 73.6807 vicesimotertial minor semitone 2: 69/68 25.2739 3: 34/27 399.0904 septendecimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 69/68 25.274 cents 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 34/27 399.090 cents septendecimal major third 2: 1 18/17 98.955 cents Arabic lute index finger 2: 1 23/18 424.364 cents vicesimotertial major third 2: 1 272/207 472.771 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 : 73.7 99.0 498.0 73.7 : 25.3 424.4 498.0 99.0 : 399.1 472.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.2739 .. 399.0904 cents 2312/1863, 373.8165 cents 69/68, 25.2739 cents 2: 98.9546 .. 472.7711 cents 2312/1863, 373.8165 cents 243/289,-300.1358 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 69/68, 25.2739 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 34/27, 399.0904 cents Average / Smallest step : 6.568624 Largest / Average step : 2.403942 Largest / Smallest step : 15.790590 Median interval of one step : 24/23, 73.6807 cents, amount: 1 Least squares average step : 126.12320 cents, oct.: 378.36961 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1379-tone equal temperament with octave 4/3 degrees: 204 274 1379 Least number of segments generator : 690 of 249.203 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1172 of 423.284 cents and inv. generated superset size: 20 = 17 more = 666.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 25.27394 cents Scale diversity : 0.357539 Lumma stability : 0.101493 Lumma impropriety factor : 0.602628 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 : 69/68, 25.2739 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 : 23 Odd number limit : 207 (O: 69 U: 207) Highest odd numerator or denominator: 23 Scale harmonicity : 0.012019 Average absolute harmonicity : 0.087553 Specific harmonicity : 0.063171 Fundamental : 1/1173, -10.1960 octaves, 0.2230 Hz. Guide tone : 72, 6.1699 octaves, 18837.041 Hz. Exponens Consonantiae : 8.445600E+04, 16.36591 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 44.5, average 14.83333 Mersenne's string divisions : 1645 Sum of van Prooijen's expressibility: 3.06930, average 1.02310 Sum of Tenney's harmonic distance : 6.30684, average 2.10228 Vogel's harmonic complexity : 33.66667 Wille's k value : 310 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.41405, average 2.73567 Lattice compactness (without 2's) : 11.78068, average 1.96345 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 .. 2 0.66667 4 1 17: -1 .. 0 -0.33333 1 1 23: -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 JI-epimorphic with val: <7 11 27 31| Scale is weakly epimorphic with val: <7 11 27 34| Scale is weakly epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 28 33| Scale is weakly epimorphic with val: <7 11 28 36| Scale is weakly epimorphic with val: <7 11 30 31| Scale is weakly epimorphic with val: <7 11 30 34| Scale is weakly epimorphic with val: <7 11 31 33| Scale is weakly epimorphic with val: <7 11 31 36| Scale is weakly epimorphic with val: <7 11 33 34| Scale is weakly epimorphic with val: <7 12 27 30| Scale is weakly epimorphic with val: <7 12 28 32| Scale is weakly epimorphic with val: <7 12 28 35| Scale is weakly epimorphic with val: <7 12 30 30| Scale is weakly epimorphic with val: <8 11 27 31| Scale is weakly epimorphic with val: <8 11 27 34| Scale is weakly epimorphic with val: <8 11 29 32| Scale is weakly epimorphic with val: <8 11 32 32| Scale is weakly epimorphic with val: <8 12 27 33| Scale is weakly epimorphic with val: <8 12 29 31| Scale is weakly epimorphic with val: <8 12 29 34| Scale is weakly epimorphic with val: <8 12 30 33| Scale is weakly epimorphic with val: <8 12 33 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 57.5208 c. M: 73.6807 c. 4: 1 0 3 N G T3 SD: 32.8476 c. M:-50.8306 c. 5: 1 0 4 N G T3 SD: 14.9745 c. M:-25.9283 c. 6: 1 0 5 N G T3 SD: 10.6661 c. M: 15.9471 c. 13: 2 1 10 N T3 SD: 9.3804 c. M:-15.9789 c. 14: 2 1 11 N T3 SD: 4.7177 c. M:-7.7693 c. 15: 2 1 12 N T3 SD: 4.2170 c. M: 7.2747 c. 19: 3 1 15 N T3 SD: 4.4481 c. M:-5.8970 c. 20: 3 1 16 N T3 SD: 0.7026 c. M:-1.0261 c. 61: 9 3 49 N T3 SD: 0.5765 c. M: 0.9785 c. 75: 11 4 60 N T3 SD: 0.5261 c. M:-0.6544 c. 81: 12 4 65 N T3 SD: 0.3375 c. M: 0.5753 c. 101: 15 5 81 N T3 SD: 0.2531 c. M: 0.3318 c. 121: 18 6 97 N T3 SD: 0.2553 c. M:-0.4087 c. 136: 20 7 109 N T3 SD: 0.2573 c. M: 0.4387 c. 156: 23 8 125 N T3 SD: 0.1452 c. M: 0.2509 c. 176: 26 9 141 N T3 SD: 0.0796 c. M: 0.1058 c. 196: 29 10 157 N T3 SD: 0.0846 c. M:-0.1462 c. 257: 38 13 206 N T3 SD: 0.0734 c. M: 0.1208 c. 277: 41 14 222 N T3 SD: 0.0431 c. M: 0.0648 c. 433: 64 22 347 N T3 SD: 0.0436 c. M: 0.0666 c. 453: 67 23 363 N T3 SD: 0.0110 c. M: 0.0184 c. 926: 137 47 742 N T3 SD: 0.0057 c. M:-0.0090 c. 1379: 204 70 1105 N T3 SD: 0.0031 c. M:-0.0043 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: 83.9582 cents 7 x 8:9 S SD: 73.2224 cents 8 x 9:11 SD: 58.8508 cents 9 x 10:12 S SD: 41.7246 cents 10 x 11:13 SD: 39.6349 cents 11 x 12:15 S SD: 32.3448 cents 12 x 13:16 SD: 19.8090 cents 13 x 14:17 SD: 22.3113 cents 14 x 15:19 SD: 18.4303 cents 15 x 16:20 S SD: 6.3883 cents 16 x 17:21 SD: 13.9583 cents 17 x 18:23 SD: 12.6370 cents 18 x 19:24 SD: 2.6758 cents 19 x 20:25 S SD: 12.5391 cents 20:21 x 27 SD: 12.0299 cents 21:22 x 28 SD: 3.4282 cents 22:23 x 29 SD: 10.0275 cents 23:24 x 31 SD: 9.3581 cents 24:25 x 32 SD: 1.5041 cents 25:26 x 33 SD: 9.1673 cents 27:28:29:36 SD: 8.9929 cents 29:30:31:39 SD: 8.9311 cents 30:31:32:40 S SD: 7.0657 cents 35 x 37:47 SD: 6.3126 cents 36 x 38:48 SD: 2.6758 cents 37 x 39:49 SD: 7.0507 cents 38 x 40:51 SD: 7.6154 cents 39 x 41:52 SD: 6.1874 cents 40:42 x 53 SD: 7.6512 cents 41:43 x 55 SD: 6.8512 cents 42:44 x 56 SD: 3.4282 cents 48:50:51:64 SD: 2.2375 cents 58 x 61:77 SD: 6.9206 cents 59:62 x 79 SD: 7.1066 cents 60:63:64:80 S SD: 5.5737 cents 61:64:65:81 SD: 5.3811 cents 62:65:66:83 SD: 4.7226 cents 63:66:67:84 SD: 3.4160 cents 65:68:69:87 SD: 3.0455 cents 66:69:70:88 SD: 1.4610 cents 69:72:73:92 SD: 0.4648 cents 186:194:197:248 SD: 0.3108 cents 255:266:270:340 SD: 0.1886 cents 324:338:343:432 SD: 0.1784 cents 390:407:413:520 SD: 0.1027 cents 459:479:486:612 SD: 0.0524 cents