Scala analysis: 103_E13
Enharmonic tetrachord 32/31 * 31/30 * 5/4, Didymos
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/31 54.964428 Greek enharmonic 1/4-tone 2: 16/15 111.731285 minor diatonic semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 32/31 54.9644 Greek enharmonic 1/4-tone 2: 31/30 56.7669 31st-partial chroma 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 32/31 54.964 cents Greek enharmonic 1/4-tone 1: 1 31/30 56.767 cents 31st-partial chroma 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 40/31 441.278 cents 2: 1 31/24 443.081 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 : 55.0 111.7 498.0 55.0 : 56.8 443.1 498.0 111.7: 386.3 441.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.9644 .. 386.3137 cents 155/128, 331.3493 cents 32/31, 54.9644 cents 2: 111.7313 .. 443.0806 cents 155/128, 331.3493 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 32/31, 54.9644 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.020408 Largest / Average step : 2.326981 Largest / Smallest step : 7.028431 Median interval of one step : 31/30, 56.7669 cents, amount: 1 Least squares average step : 126.61157 cents, oct.: 379.83471 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1939-tone equal temperament with octave 4/3 degrees: 214 435 1939 Least number of segments generator : 970 of 249.151 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1219 of 313.108 cents and inv. generated superset size: 42 = 39 more = 1400.000% 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 54.96443 cents Scale diversity : 0.518449 Lumma stability : 0.220721 Lumma impropriety factor : 0.551321 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 : 961/960, 1.8024 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 Limited inverse transpositions with margin 329.5469 cents: 2 -- Rational properties -- Prime limit : 31 Odd number limit : 31 (O: 31 U: 31) Highest odd numerator or denominator: 31 Scale harmonicity : 0.071090 Fundamental : 1/465, -8.8611 octaves, 0.5626 Hz. Guide tone : 32, 5.0000 octaves, 8372.018 Hz. Exponens Consonantiae : 1.488000E+04, 13.86109 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 50.5, average 16.83333 Mersenne's string divisions : 1953 Sum of van Prooijen's expressibility: 3.14457, average 1.04819 Sum of Tenney's harmonic distance : 6.45590, average 2.15197 Vogel's harmonic complexity : 28.66667 Wille's k value : 77 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 18.60911, average 3.10152 Lattice compactness (without 2's) : 5.82843, average 0.97140 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.66667 11 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 1 31: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <7 10 15 33| Scale is weakly epimorphic with val: <7 10 15 36| Scale is weakly epimorphic with val: <7 10 15 39| Scale is JI-epimorphic with val: <7 11 15 34| Scale is weakly epimorphic with val: <7 11 15 37| Scale is weakly epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 16 36| Scale is weakly epimorphic with val: <7 11 16 39| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 18 37| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 11 19 36| Scale is weakly epimorphic with val: <7 11 19 39| Scale is weakly epimorphic with val: <8 11 17 37| Scale is weakly epimorphic with val: <8 11 18 33| Scale is weakly epimorphic with val: <8 11 18 36| Scale is weakly epimorphic with val: <8 11 18 39| Scale is weakly epimorphic with val: <8 12 15 37| Scale is weakly epimorphic with val: <8 12 17 35| Scale is weakly epimorphic with val: <8 12 17 38| Scale is weakly epimorphic with val: <8 12 18 37|
FIT/MODE
3: 0 1 2 N G T3 SD: 44.6012 c. M: 54.9644 c. 4: 0 1 3 N G T3 SD: 32.5802 c. M: 54.9644 c. 5: 0 1 4 N G T3 SD: 32.4963 c. M: 54.9644 c. 6: 1 0 5 N G T3 SD: 23.1766 c. M: 28.7238 c. 7: 1 1 5 N M DE S SD: 19.9692 c. M:-30.5673 c. 8: 1 1 6 N M DE S SD: 8.4949 c. M:-12.7800 c. 9: 1 1 7 N M DE S SD: 0.6460 c. M: 1.0546 c. 71: 8 8 55 N M DE S SD: 0.7267 c. M:-1.1533 c. 80: 9 9 62 N M DE S SD: 0.6439 c. M:-1.0656 c. 89: 10 10 69 N M DE S SD: 0.5851 c. M:-0.9957 c. 98: 11 11 76 N M DE S SD: 0.5436 c. M:-0.9386 c. 107: 12 12 83 N M DE S SD: 0.5146 c. M:-0.8911 c. 116: 13 13 90 N M DE S SD: 0.4947 c. M:-0.8510 c. 125: 14 14 97 N M DE S SD: 0.4815 c. M:-0.8166 c. 134: 15 15 104 N M DE S SD: 0.4731 c. M:-0.7869 c. 143: 16 16 111 N M DE S SD: 0.4682 c. M:-0.7609 c. 147: 16 17 114 N T3 SD: 0.4383 c. M: 0.7554 c. 152: 17 17 118 N M DE S SD: 0.4659 c. M:-0.7380 c. 155: 17 18 120 N T3 SD: 0.4652 c. M:-0.7305 c. 156: 17 18 121 N T3 SD: 0.3986 c. M: 0.6903 c. 164: 18 19 127 N T3 SD: 0.4044 c. M:-0.6325 c. 165: 18 19 128 N T3 SD: 0.3661 c. M: 0.6322 c. 173: 19 20 134 N T3 SD: 0.3500 c. M:-0.5448 c. 174: 19 20 135 N T3 SD: 0.3400 c. M: 0.5802 c. 182: 20 21 141 N T3 SD: 0.3009 c. M:-0.4657 c. 183: 20 21 142 N T3 SD: 0.3194 c. M: 0.5333 c. 191: 21 22 148 N T3 SD: 0.2566 c. M:-0.3940 c. 192: 21 22 149 N T3 SD: 0.3038 c. M: 0.4908 c. 200: 22 23 155 N T3 SD: 0.2163 c. M:-0.3288 c. 209: 23 24 162 N T3 SD: 0.1796 c. M:-0.2693 c. 218: 24 25 169 N T3 SD: 0.1460 c. M:-0.2146 c. 227: 25 26 176 N T3 SD: 0.1153 c. M:-0.1643 c. 236: 26 27 183 N T3 SD: 0.0874 c. M:-0.1178 c. 245: 27 28 190 N T3 SD: 0.0623 c. M: 0.0778 c. 254: 28 29 197 N T3 SD: 0.0409 c. M: 0.0618 c. 263: 29 30 204 N T3 SD: 0.0271 c. M: 0.0469 c. 272: 30 31 211 N T3 SD: 0.0288 c. M: 0.0374 c. 535: 59 61 415 N T3 SD: 0.0258 c. M: 0.0398 c. 798: 88 91 619 N T3 SD: 0.0257 c. M: 0.0422 c. 807: 89 92 626 N T3 SD: 0.0264 c. M: 0.0375 c. 1061: 117 121 823 N T3 SD: 0.0259 c. M: 0.0433 c. 1079: 119 123 837 N T3 SD: 0.0268 c. M: 0.0364 c. 1114: 123 127 864 N T3 SD: 0.0268 c. M:-0.0382 c. 1123: 124 128 871 N T3 SD: 0.0239 c. M:-0.0295 c. 1132: 125 129 878 N T3 SD: 0.0219 c. M:-0.0317 c. 1141: 126 130 885 N T3 SD: 0.0211 c. M:-0.0344 c. 1377: 152 157 1068 N T3 SD: 0.0189 c. M:-0.0304 c. 1386: 153 158 1075 N T3 SD: 0.0159 c. M:-0.0234 c. 1395: 154 159 1082 N T3 SD: 0.0136 c. M:-0.0169 c. 1404: 155 160 1089 N T3 SD: 0.0124 c. M:-0.0192 c. 1649: 182 188 1279 N T3 SD: 0.0115 c. M:-0.0193 c. 1658: 183 189 1286 N T3 SD: 0.0087 c. M:-0.0134 c. 1667: 184 190 1293 N T3 SD: 0.0067 c. M:-0.0087 c. 1676: 185 191 1300 N T3 SD: 0.0063 c. M:-0.0107 c. 1930: 213 220 1497 N T3 SD: 0.0037 c. M:-0.0063 c. 1939: 214 221 1504 N T3 SD: 0.0018 c. M:-0.0029 c. 2202: 243 251 1708 N T3 SD: 0.0018 c. M: 0.0031 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: 77.5698 cents 7 x 8:9 S SD: 67.5105 cents 8 x 9:11 SD: 53.2328 cents 9 x 10:12 S SD: 35.3362 cents 10 x 11:13 SD: 34.4934 cents 11 x 12:15 S SD: 27.5105 cents 12 x 13:16 SD: 13.4207 cents 13 x 14:17 SD: 18.7389 cents 14 x 15:19 SD: 15.7988 cents 15 x 16:20 S SD: 0.0000 cents 16 x 17:21 SD: 14.0467 cents 17 x 18:23 SD: 14.1599 cents 18 x 19:24 SD: 9.0641 cents 19 x 20:25 S SD: 16.2144 cents 20 x 21:27 SD: 17.3627 cents 21:22 x 28 SD: 12.7863 cents 22:23 x 29 SD: 14.7912 cents 23:24:25:31 SD: 14.0031 cents 24:25:26:32 SD: 10.3666 cents 25:26:27:33 SD: 10.1795 cents 26:27:28:35 S SD: 8.5409 cents 27:28:29:36 SD: 4.8015 cents 30:31:32:40 S SD: 0.6008 cents 243:251:259:324 SD: 0.5797 cents 252:260:269:336 SD: 0.5159 cents 255:263:272:340 SD: 0.4953 cents 282:291:301:376 SD: 0.4289 cents 285:294:304:380 SD: 0.3798 cents 312:322:333:416 SD: 0.3655 cents 315:325:336:420 SD: 0.2863 cents 345:356:368:460 SD: 0.2091 cents 375:387:400:500 SD: 0.1443 cents 405:418:432:540 SD: 0.0891 cents 435:449:464:580 SD: 0.0415 cents 465:480:496:620 S SD: 0.0000 cents