Scala analysis: 069_E6
Enharmonic tetrachord 26/25 * 100/99 * 33/26
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 26/25 67.900234 tridecimal 1/3-tone 2: 104/99 85.299718 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/26 412.7453 tridecimal major third 1: 26/25 67.9002 tridecimal 1/3-tone 2: 100/99 17.3995 Ptolemy's comma 3: 33/26 412.7453 tridecimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 100/99 17.399 cents Ptolemy's comma 1: 1 26/25 67.900 cents tridecimal 1/3-tone 1: 1 33/26 412.745 cents tridecimal major third 2: 1 104/99 85.300 cents 2: 1 50/39 430.145 cents 2: 1 33/25 480.646 cents 2 pentatones 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 : 67.9 85.3 498.0 67.9 : 17.4 430.1 498.0 85.3 : 412.7 480.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 17.3995 .. 412.7453 cents 3267/2600, 395.3458 cents 100/99, 17.3995 cents 2: 85.2997 .. 480.6455 cents 3267/2600, 395.3458 cents 2704/3267,-327.4456 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 100/99, 17.3995 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/26, 412.7453 cents Average / Smallest step : 9.541375 Largest / Average step : 2.486193 Largest / Smallest step : 23.721697 Median interval of one step : 26/25, 67.9002 cents, amount: 1 Least squares average step : 123.75962 cents, oct.: 371.27886 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1775-tone equal temperament with octave 4/3 degrees: 242 304 1775 Least number of segments generator : 888 of 249.163 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1384 of 388.335 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 17.39948 cents Scale diversity : 0.250989 Lumma stability : 0.069871 Lumma impropriety factor : 0.657462 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 : 100/99, 17.3995 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 480.6455 cents Number of appreciable 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 : 13 Odd number limit : 99 (O: 33 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.016268 Average absolute harmonicity : 0.087548 Specific harmonicity : 0.076108 Fundamental : 1/2475, -11.2732 octaves, 0.1057 Hz. Guide tone : 104, 6.7004 octaves, 27209.059 Hz. Exponens Consonantiae : 2.574000E+05, 17.97365 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 130.5, average 43.50000 Mersenne's string divisions : 10353 Sum of van Prooijen's expressibility: 3.87070, average 1.29023 Sum of Tenney's harmonic distance : 7.90476, average 2.63492 Vogel's harmonic complexity : 27.66667 Wille's k value : 643 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.80984, average 2.80164 Lattice compactness (without 2's) : 12.86710, average 2.14452 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -2 .. 0 -1.00000 3 1 5: -2 .. 0 -0.66667 2 11: -1 .. 0 -0.33333 1 13: 0 .. 1 0.66667 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 23 28| Scale is weakly epimorphic with val: <6 10 15 24 27| Scale is weakly epimorphic with val: <6 10 15 27 27| Scale is weakly epimorphic with val: <6 10 16 23 29| Scale is weakly epimorphic with val: <6 10 16 25 30| Scale is weakly epimorphic with val: <6 10 16 26 29| Scale is weakly epimorphic with val: <6 10 17 24 29| Scale is weakly epimorphic with val: <6 10 18 23 28| Scale is weakly epimorphic with val: <6 10 19 25 30| Scale is weakly epimorphic with val: <6 11 15 24 27| Scale is weakly epimorphic with val: <6 11 15 27 27| Scale is weakly epimorphic with val: <6 11 16 23 29| Scale is weakly epimorphic with val: <6 11 16 26 29| Scale is weakly epimorphic with val: <6 11 17 23 30| Scale is weakly epimorphic with val: <7 10 15 23 25| Scale is weakly epimorphic with val: <7 10 15 25 26| Scale is weakly epimorphic with val: <7 10 15 26 28| Scale is weakly epimorphic with val: <7 10 16 24 28| Scale is weakly epimorphic with val: <7 10 16 25 27| Scale is weakly epimorphic with val: <7 10 16 27 28| Scale is weakly epimorphic with val: <7 10 17 23 30| Scale is weakly epimorphic with val: <7 10 17 24 26| Scale is weakly epimorphic with val: <7 10 17 26 30| Scale is weakly epimorphic with val: <7 10 17 27 29| Scale is weakly epimorphic with val: <7 10 18 23 25| Scale is weakly epimorphic with val: <7 10 18 26 28| Scale is weakly epimorphic with val: <7 10 19 25 27| Scale is weakly epimorphic with val: <7 11 15 23 25| Scale is weakly epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 24 27| Scale is weakly epimorphic with val: <7 11 15 24 30| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 27 27| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is JI-epimorphic with val: <7 11 16 23 26| Scale is weakly epimorphic with val: <7 11 16 23 29| Scale is weakly epimorphic with val: <7 11 16 25 27| Scale is weakly epimorphic with val: <7 11 16 25 30| Scale is weakly epimorphic with val: <7 11 16 26 26| Scale is weakly epimorphic with val: <7 11 16 26 29| Scale is weakly epimorphic with val: <7 11 17 24 26| Scale is weakly epimorphic with val: <7 11 17 24 29| Scale is weakly epimorphic with val: <7 11 17 25 25| Scale is JI-epimorphic with val: <7 11 17 25 28| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is weakly epimorphic with val: <7 11 18 23 25| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is weakly epimorphic with val: <7 11 18 24 27| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 27 27| Scale is JI-epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 19 23 26| Scale is weakly epimorphic with val: <7 11 19 23 29| Scale is weakly epimorphic with val: <7 11 19 25 27| Scale is weakly epimorphic with val: <7 11 19 25 30| Scale is weakly epimorphic with val: <7 11 19 26 26| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is weakly epimorphic with val: <7 12 15 24 30| Scale is weakly epimorphic with val: <7 12 15 25 26| Scale is weakly epimorphic with val: <7 12 16 23 29| Scale is weakly epimorphic with val: <7 12 16 24 28| Scale is weakly epimorphic with val: <7 12 16 27 28| Scale is weakly epimorphic with val: <7 12 17 23 30| Scale is weakly epimorphic with val: <7 12 17 26 30| Scale is weakly epimorphic with val: <7 12 18 24 30| Scale is weakly epimorphic with val: <7 12 19 23 29| Scale is weakly epimorphic with val: <8 11 15 23 25| Scale is weakly epimorphic with val: <8 11 15 25 26| Scale is weakly epimorphic with val: <8 11 16 24 25| Scale is weakly epimorphic with val: <8 11 16 25 27| Scale is weakly epimorphic with val: <8 11 16 27 28| Scale is weakly epimorphic with val: <8 11 17 24 29| Scale is weakly epimorphic with val: <8 11 17 26 27| Scale is weakly epimorphic with val: <8 11 17 27 29| Scale is weakly epimorphic with val: <8 11 18 25 26| Scale is weakly epimorphic with val: <8 11 19 24 25| Scale is weakly epimorphic with val: <8 11 19 27 28| Scale is weakly epimorphic with val: <8 12 15 23 25| Scale is weakly epimorphic with val: <8 12 15 24 27| Scale is weakly epimorphic with val: <8 12 15 27 30| Scale is weakly epimorphic with val: <8 12 16 23 26| Scale is weakly epimorphic with val: <8 12 16 25 27| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 17 24 29| Scale is weakly epimorphic with val: <8 12 17 25 28| Scale is weakly epimorphic with val: <8 12 17 27 29| Scale is weakly epimorphic with val: <8 12 18 24 27| Scale is weakly epimorphic with val: <8 12 18 27 30| Scale is weakly epimorphic with val: <8 12 19 23 26| Scale is weakly epimorphic with val: <8 12 19 26 29|
FIT/MODE
3: 0 0 3 N M DE S SD: 62.9457 c. M: 85.2997 c. 5: 1 0 4 N G T3 SD: 20.0848 c. M:-31.7088 c. 6: 1 0 5 N G T3 SD: 8.8220 c. M:-15.1073 c. 7: 1 0 6 N G T3 SD: 8.3823 c. M: 14.1504 c. 13: 2 0 11 N G T3 SD: 7.1033 c. M:-8.7221 c. 16: 2 1 13 N T3 SD: 5.6923 c. M:-8.0837 c. 17: 2 1 14 N T3 SD: 5.5775 c. M: 9.3067 c. 21: 3 1 17 N T3 SD: 5.8328 c. M:-9.5660 c. 22: 3 1 18 N T3 SD: 3.0334 c. M:-5.2539 c. 23: 3 1 19 N T3 SD: 1.8588 c. M: 2.9378 c. 29: 4 1 24 N T3 SD: 0.5651 c. M:-0.7956 c. 59: 8 2 49 N T3 SD: 0.5537 c. M: 0.8853 c. 81: 11 3 67 N T3 SD: 0.4767 c. M:-0.7821 c. 88: 12 3 73 N T3 SD: 0.2344 c. M: 0.4057 c. 117: 16 4 97 N T3 SD: 0.1531 c. M:-0.2085 c. 169: 23 6 140 N T3 SD: 0.1168 c. M:-0.1636 c. 198: 27 7 164 N T3 SD: 0.1291 c. M:-0.2232 c. 228: 31 8 189 N T3 SD: 0.1229 c. M: 0.1836 c. 257: 35 9 213 N T3 SD: 0.0459 c. M: 0.0731 c. 286: 39 10 237 N T3 SD: 0.0192 c. M:-0.0297 c. 543: 74 19 450 N T3 SD: 0.0154 c. M: 0.0267 c. 829: 113 29 687 N T3 SD: 0.0094 c. M: 0.0123 c. 1115: 152 39 924 N T3 SD: 0.0095 c. M:-0.0156 c. 1203: 164 42 997 N T3 SD: 0.0091 c. M: 0.0152 c. 1232: 168 43 1021 N T3 SD: 0.0087 c. M:-0.0150 c. 1489: 203 52 1234 N T3 SD: 0.0038 c. M: 0.0066 c. 1775: 242 62 1471 N T3 SD: 0.0014 c. M:-0.0022 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: 90.7856 cents 7 x 8:9 S SD: 79.4409 cents 8 x 9:11 SD: 65.0123 cents 9 x 10:12 S SD: 48.5520 cents 10 x 11:13 SD: 45.4807 cents 11 x 12:15 S SD: 38.0218 cents 12 x 13:16 SD: 26.6365 cents 13 x 14:17 SD: 27.2901 cents 14 x 15:19 SD: 22.9384 cents 15 x 16:20 S SD: 13.2158 cents 16 x 17:21 SD: 16.8053 cents 17 x 18:23 SD: 14.3634 cents 18 x 19:24 SD: 4.1516 cents 19 x 20:25 S SD: 11.5982 cents 20 x 21:27 SD: 10.7612 cents 21 x 22:28 SD: 2.3813 cents 22 x 23:29 SD: 10.7365 cents 23:24 x 31 SD: 9.7943 cents 24:25 x 32 SD: 1.3861 cents 25:26 x 33 SD: 8.6997 cents 26:27 x 35 SD: 8.3820 cents 27:28 x 36 SD: 2.4697 cents 28:29 x 37 SD: 8.5468 cents 29:30 x 39 SD: 8.7412 cents 33:34:35:44 SD: 7.7279 cents 36:37:38:48 SD: 7.3621 cents 38 x 40:51 SD: 5.9400 cents 39 x 41:52 SD: 0.6400 cents 40 x 42:53 SD: 5.4430 cents 41 x 43:55 SD: 5.4509 cents 42 x 44:56 SD: 2.3813 cents 43 x 45:57 SD: 6.0287 cents 44 x 46:59 SD: 6.4386 cents 45:47 x 60 SD: 3.6913 cents 46:48 x 61 SD: 5.5323 cents 47:49 x 63 SD: 5.0589 cents 48:50 x 64 SD: 1.3861 cents 49:51 x 65 SD: 4.4795 cents 54:56:57:72 SD: 3.2205 cents 57:59:60:76 SD: 2.9710 cents 63 x 66:84 SD: 2.3813 cents 64 x 67:85 SD: 4.5229 cents 65 x 68:87 SD: 4.8939 cents 66 x 69:88 SD: 4.1717 cents 67:70 x 89 SD: 5.1188 cents 68:71 x 91 SD: 4.6680 cents 69:72 x 92 SD: 2.8902 cents 74:77:78:99 SD: 2.7688 cents 75:78:79:100 SD: 1.5516 cents 78:81:82:104 SD: 0.9549 cents 88 x 92:117 SD: 4.8443 cents 89:93 x 119 SD: 4.7694 cents 90:94:95:120 SD: 3.7036 cents 91:95:96:121 SD: 3.6393 cents 92:96:97:123 SD: 3.2565 cents 93:97:98:124 SD: 2.4448 cents 95:99:100:127 SD: 2.2414 cents 96:100:101:128 SD: 1.2667 cents 99:103:104:132 SD: 0.2242 cents 276:287:290:368 SD: 0.1450 cents 375:390:394:500 SD: 0.0888 cents 474:493:498:632 SD: 0.0844 cents