Scala analysis: 088_E10
Enharmonic tetrachord 36/35 * 35/34 * 34/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 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: 36/35 48.7704 septimal diesis, 1/4-tone 2: 35/34 50.1842 septendecimal 1/4-tone 3: 34/27 399.0904 septendecimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 35/34 50.184 cents septendecimal 1/4-tone 1: 1 34/27 399.090 cents septendecimal major third 2: 1 18/17 98.955 cents Arabic lute index finger 2: 1 136/105 447.861 cents 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 48.8 99.0 498.0 48.8 : 50.2 449.3 498.0 99.0 : 399.1 447.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 399.0904 cents 595/486, 350.3200 cents 36/35, 48.7704 cents 2: 98.9546 .. 449.2746 cents 595/486, 350.3200 cents 243/289,-300.1358 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 34/27, 399.0904 cents Average / Smallest step : 3.404013 Largest / Average step : 2.403942 Largest / Smallest step : 8.183049 Median interval of one step : 35/34, 50.1842 cents, amount: 1 Least squares average step : 124.34390 cents, oct.: 373.03169 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1062-tone equal temperament with octave 4/3 degrees: 104 211 1062 Least number of segments generator : 533 of 249.960 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 583 of 273.409 cents and inv. generated superset size: 50 = 47 more = 1666.667% 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 48.77038 cents Scale diversity : 0.421791 Lumma stability : 0.195847 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 : 1225/1224, 1.4138 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 : 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 with margin 348.9062 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 105 (O: 35 U: 105) Highest odd numerator or denominator: 35 Scale harmonicity : 0.017605 Average absolute harmonicity : 0.094451 Specific harmonicity : 0.090526 Fundamental : 1/1785, -10.8017 octaves, 0.1466 Hz. Guide tone : 36, 5.1699 octaves, 9418.520 Hz. Exponens Consonantiae : 6.426000E+04, 15.97163 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 56.5, average 18.83333 Mersenne's string divisions : 2485 Sum of van Prooijen's expressibility: 3.25164, average 1.08388 Sum of Tenney's harmonic distance : 6.66527, average 2.22176 Vogel's harmonic complexity : 27.00000 Wille's k value : 472 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.48108, average 2.74685 Lattice compactness (without 2's) : 13.89651, average 2.31609 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 2 1.00000 5 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 15 19 28| Scale is weakly epimorphic with val: <7 11 15 19 31| Scale is JI-epimorphic with val: <7 11 15 20 27| Scale is weakly epimorphic with val: <7 11 15 20 30| Scale is weakly epimorphic with val: <7 11 15 20 33| Scale is weakly epimorphic with val: <7 11 15 22 28| Scale is weakly epimorphic with val: <7 11 15 22 31| Scale is weakly epimorphic with val: <7 11 16 18 28| Scale is weakly epimorphic with val: <7 11 16 18 31| Scale is JI-epimorphic with val: <7 11 16 19 27| Scale is weakly epimorphic with val: <7 11 16 19 30| Scale is weakly epimorphic with val: <7 11 16 19 33| Scale is weakly epimorphic with val: <7 11 16 21 28| Scale is weakly epimorphic with val: <7 11 16 21 31| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 16 22 30| Scale is weakly epimorphic with val: <7 11 16 22 33| Scale is JI-epimorphic with val: <7 11 17 18 27| Scale is weakly epimorphic with val: <7 11 17 18 30| Scale is weakly epimorphic with val: <7 11 17 18 33| Scale is weakly epimorphic with val: <7 11 17 20 28| Scale is weakly epimorphic with val: <7 11 17 20 31| Scale is weakly epimorphic with val: <7 11 17 21 27| Scale is weakly epimorphic with val: <7 11 17 21 30| Scale is weakly epimorphic with val: <7 11 17 21 33| Scale is weakly epimorphic with val: <7 11 18 19 28| Scale is weakly epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 20 27| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 11 18 20 33| Scale is weakly epimorphic with val: <7 11 18 22 28| Scale is weakly epimorphic with val: <7 11 18 22 31| Scale is weakly epimorphic with val: <7 11 19 19 27| Scale is weakly epimorphic with val: <7 11 19 19 30| Scale is weakly epimorphic with val: <7 11 19 19 33| Scale is weakly epimorphic with val: <7 11 19 21 28| Scale is weakly epimorphic with val: <7 11 19 21 31| Scale is weakly epimorphic with val: <7 11 19 22 27| Scale is weakly epimorphic with val: <7 11 19 22 30| Scale is weakly epimorphic with val: <7 11 19 22 33| Scale is weakly epimorphic with val: <7 12 15 19 28| Scale is weakly epimorphic with val: <7 12 15 20 27| Scale is weakly epimorphic with val: <7 12 15 20 30| Scale is weakly epimorphic with val: <7 12 15 20 33| Scale is weakly epimorphic with val: <7 12 15 22 28| Scale is weakly epimorphic with val: <7 12 16 18 28| Scale is weakly epimorphic with val: <7 12 16 19 27| Scale is weakly epimorphic with val: <7 12 16 19 30| Scale is weakly epimorphic with val: <7 12 16 19 33| Scale is weakly epimorphic with val: <7 12 16 21 28| Scale is weakly epimorphic with val: <7 12 17 18 27| Scale is weakly epimorphic with val: <7 12 17 18 30| Scale is weakly epimorphic with val: <7 12 17 18 33| Scale is weakly epimorphic with val: <7 12 17 20 28| Scale is weakly epimorphic with val: <7 12 18 19 28| Scale is weakly epimorphic with val: <7 12 18 22 28| Scale is weakly epimorphic with val: <7 12 19 21 28| Scale is weakly epimorphic with val: <8 11 15 19 27| Scale is weakly epimorphic with val: <8 11 15 20 29| Scale is weakly epimorphic with val: <8 11 15 20 32| Scale is weakly epimorphic with val: <8 11 15 22 27| Scale is weakly epimorphic with val: <8 11 16 18 27| Scale is weakly epimorphic with val: <8 11 16 19 29| Scale is weakly epimorphic with val: <8 11 16 19 32| Scale is weakly epimorphic with val: <8 11 16 21 27| Scale is weakly epimorphic with val: <8 11 17 18 29| Scale is weakly epimorphic with val: <8 11 17 18 32| Scale is weakly epimorphic with val: <8 11 17 20 27| Scale is weakly epimorphic with val: <8 11 18 19 27| Scale is weakly epimorphic with val: <8 11 18 22 27| Scale is weakly epimorphic with val: <8 11 19 21 27| Scale is weakly epimorphic with val: <8 12 15 20 29| Scale is weakly epimorphic with val: <8 12 15 22 27| Scale is weakly epimorphic with val: <8 12 15 22 30| Scale is weakly epimorphic with val: <8 12 15 22 33| Scale is weakly epimorphic with val: <8 12 16 19 29| Scale is weakly epimorphic with val: <8 12 16 21 27| Scale is weakly epimorphic with val: <8 12 16 21 30| Scale is weakly epimorphic with val: <8 12 16 21 33| Scale is weakly epimorphic with val: <8 12 16 22 29| Scale is weakly epimorphic with val: <8 12 17 18 29| Scale is weakly epimorphic with val: <8 12 17 20 27| Scale is weakly epimorphic with val: <8 12 17 20 30| Scale is weakly epimorphic with val: <8 12 17 20 33| Scale is weakly epimorphic with val: <8 12 17 21 29| Scale is weakly epimorphic with val: <8 12 18 19 27| Scale is weakly epimorphic with val: <8 12 18 19 30| Scale is weakly epimorphic with val: <8 12 18 19 33| Scale is weakly epimorphic with val: <8 12 18 20 29| Scale is weakly epimorphic with val: <8 12 19 19 29| Scale is weakly epimorphic with val: <8 12 19 22 29|
FIT/MODE
3: 0 0 3 N M DE S SD: 63.6934 c. M: 98.9546 c. 4: 0 1 3 N G T3 SD: 31.7894 c. M: 48.7704 c. 5: 0 1 4 N G T3 SD: 28.1601 c. M: 48.7704 c. 6: 0 1 5 N G T3 SD: 29.6247 c. M: 48.7704 c. 7: 1 0 6 N G T3 SD: 20.6070 c. M: 27.8053 c. 8: 1 1 6 N M DE S SD: 16.6833 c. M:-25.5567 c. 9: 1 1 7 N M DE S SD: 7.7577 c. M:-11.7221 c. 10: 1 1 8 N M DE S SD: 0.7066 c. M:-1.0341 c. 61: 6 6 49 N M DE S SD: 0.5788 c. M: 0.9785 c. 71: 7 7 57 N M DE S SD: 0.4729 c. M: 0.7485 c. 81: 8 8 65 N M DE S SD: 0.4110 c. M: 0.5753 c. 91: 9 9 73 N M DE S SD: 0.3789 c. M:-0.4868 c. 101: 10 10 81 N M DE S SD: 0.3664 c. M:-0.5410 c. 111: 11 11 89 N M DE S SD: 0.3660 c. M:-0.5854 c. 121: 12 12 97 N M DE S SD: 0.3724 c. M:-0.6225 c. 131: 13 13 105 N M DE S SD: 0.3825 c. M:-0.6539 c. 141: 14 14 113 N M DE S SD: 0.3943 c. M:-0.6809 c. 151: 15 15 121 N M DE S SD: 0.4066 c. M:-0.7043 c. 172: 17 17 138 N M DE S SD: 0.3919 c. M: 0.5038 c. 176: 17 18 141 N T3 SD: 0.3866 c. M: 0.6638 c. 186: 18 19 149 N T3 SD: 0.3376 c. M: 0.5725 c. 196: 19 20 157 N T3 SD: 0.2955 c. M: 0.4905 c. 206: 20 21 165 N T3 SD: 0.2599 c. M: 0.4165 c. 216: 21 22 173 N T3 SD: 0.2305 c. M: 0.3493 c. 226: 22 23 181 N T3 SD: 0.2071 c. M: 0.2881 c. 236: 23 24 189 N T3 SD: 0.1896 c. M:-0.2323 c. 246: 24 25 197 N T3 SD: 0.1778 c. M:-0.2495 c. 256: 25 26 205 N T3 SD: 0.1714 c. M:-0.2653 c. 257: 25 26 206 N T3 SD: 0.1988 c. M: 0.3224 c. 266: 26 27 213 N T3 SD: 0.1696 c. M:-0.2799 c. 267: 26 27 214 N T3 SD: 0.1655 c. M: 0.2716 c. 277: 27 28 222 N T3 SD: 0.1349 c. M: 0.2245 c. 287: 28 29 230 N T3 SD: 0.1068 c. M: 0.1806 c. 297: 29 30 238 N T3 SD: 0.0812 c. M: 0.1397 c. 307: 30 31 246 N T3 SD: 0.0587 c. M: 0.1015 c. 317: 31 32 254 N T3 SD: 0.0408 c. M: 0.0657 c. 327: 32 33 262 N T3 SD: 0.0320 c. M:-0.0452 c. 337: 33 34 270 N T3 SD: 0.0365 c. M:-0.0633 c. 644: 63 65 516 N T3 SD: 0.0348 c. M: 0.0486 c. 664: 65 67 532 N T3 SD: 0.0327 c. M:-0.0544 c. 705: 69 71 565 N T3 SD: 0.0335 c. M: 0.0520 c. 715: 70 72 573 N T3 SD: 0.0251 c. M: 0.0422 c. 725: 71 73 581 N T3 SD: 0.0189 c. M: 0.0326 c. 735: 72 74 589 N T3 SD: 0.0168 c. M: 0.0232 c. 1032: 101 104 827 N T3 SD: 0.0201 c. M: 0.0276 c. 1042: 102 105 835 N T3 SD: 0.0132 c. M: 0.0174 c. 1052: 103 106 843 N T3 SD: 0.0065 c. M: 0.0084 c. 1062: 104 107 851 N T3 SD: 0.0019 c. M:-0.0024 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 x 21:27 SD: 12.9654 cents 21 x 22:28 SD: 9.2088 cents 22 x 23:29 SD: 14.7935 cents 23:24 x 31 SD: 15.5790 cents 24:25 x 32 SD: 10.9510 cents 25:26 x 33 SD: 12.9296 cents 26:27:28:35 S SD: 12.5166 cents 27:28:29:36 SD: 9.5120 cents 28:29:30:37 SD: 9.4539 cents 29:30:31:39 SD: 8.1079 cents 30:31:32:40 S SD: 5.0242 cents 33:34:35:44 SD: 1.3728 cents 69:71:73:92 SD: 0.5196 cents 102:105:108:136 SD: 0.4713 cents 171:176:181:228 SD: 0.4191 cents 321:330:340:428 SD: 0.3602 cents 354:364:375:472 SD: 0.3265 cents 357:367:378:476 SD: 0.3144 cents 390:401:413:520 SD: 0.2214 cents 423:435:448:564 SD: 0.1895 cents 459:472:486:612 SD: 0.1397 cents 492:506:521:656 SD: 0.0922 cents 561:577:594:748 SD: 0.0286 cents