Scala analysis: 102_E12
Enharmonic tetrachord 68/67 * 67/64 * 64/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/67 25.648381 2: 17/16 104.955410 17th harmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/51 393.0896 1: 68/67 25.6484 2: 67/64 79.3070 3: 64/51 393.0896
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/67 25.648 cents 1: 1 67/64 79.307 cents 1: 1 64/51 393.090 cents 2: 1 17/16 104.955 cents 17th harmonic 2: 1 256/201 418.738 cents 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 : 25.6 105.0 498.0 25.6 : 79.3 472.4 498.0 105.0: 393.1 418.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.6484 .. 393.0896 cents 1072/867, 367.4412 cents 68/67, 25.6484 cents 2: 104.9554 .. 472.3966 cents 1072/867, 367.4412 cents 867/1024,-288.1342 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 : 64/51, 393.0896 cents Average / Smallest step : 6.472728 Largest / Average step : 2.367796 Largest / Smallest step : 15.326098 Median interval of one step : 67/64, 79.3070 cents, amount: 1 Least squares average step : 123.54959 cents, oct.: 370.64876 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2311-tone equal temperament with octave 4/3 degrees: 119 487 2311 Least number of segments generator : 1156 of 249.130 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1510 of 325.421 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 25.64838 cents Scale diversity : 0.391481 Lumma stability : 0.102996 Lumma impropriety factor : 0.578530 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 Steps are strictly increasing 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% -- Rational properties -- Prime limit : 67 Odd number limit : 201 (O: 67 U: 201) Highest odd numerator or denominator: 67 Scale harmonicity : 0.025784 Fundamental : 1/3216, -11.6511 octaves, 0.0814 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 2.186880E+05, 17.73851 octaves Euler's gradus suavitatis : 91 Sum of Mann's harmonic distance : 87.5, average 29.16667 Mersenne's string divisions : 10395 Sum of van Prooijen's expressibility: 3.53364, average 1.17788 Sum of Tenney's harmonic distance : 7.17233, average 2.39078 Vogel's harmonic complexity : 62.00000 Wille's k value : 1708 Wilson's harmonic complexity : 87 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 22.17387, average 3.69564 Lattice compactness (without 2's) : 5.82843, average 0.97140 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 0.00000 8 3: -1 .. 0 -0.33333 1 1 17: 0 .. 1 0.66667 2 1 67: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <6 10 27 44| Scale is weakly epimorphic with val: <6 11 27 43| Scale is weakly epimorphic with val: <7 10 31 43| Scale is weakly epimorphic with val: <7 10 33 44| Scale is weakly epimorphic with val: <7 11 27 43| Scale is weakly epimorphic with val: <7 11 29 44| Scale is JI-epimorphic with val: <7 11 30 43| Scale is weakly epimorphic with val: <7 11 32 44| Scale is weakly epimorphic with val: <7 11 33 43| Scale is weakly epimorphic with val: <7 12 31 44| Scale is weakly epimorphic with val: <7 12 32 43| Scale is weakly epimorphic with val: <8 11 30 43| Scale is weakly epimorphic with val: <8 12 31 44|
FIT/MODE
3: 0 1 2 N G T3 SD: 38.2366 c. M:-61.0596 c. 4: 0 1 3 N G T3 SD: 18.6214 c. M: 25.6484 c. 5: 0 1 4 N G T3 SD: 15.1264 c. M: 25.6484 c. 11: 0 2 9 N G T3 SD: 16.9828 c. M: 25.6484 c. 13: 1 2 10 N T3 SD: 9.3078 c. M:-12.6628 c. 14: 1 2 11 N T3 SD: 5.8212 c. M:-9.9263 c. 15: 1 2 12 N T3 SD: 5.3434 c. M:-7.5546 c. 18: 1 3 14 N T3 SD: 3.5032 c. M:-5.7213 c. 19: 1 3 15 N T3 SD: 0.3314 c. M:-0.5645 c. 118: 6 19 93 N T3 SD: 0.3748 c. M:-0.5626 c. 119: 6 19 94 N T3 SD: 0.3621 c. M: 0.5369 c. 137: 7 22 108 N T3 SD: 0.2952 c. M:-0.4702 c. 138: 7 22 109 N T3 SD: 0.2797 c. M: 0.3852 c. 156: 8 25 123 N T3 SD: 0.2393 c. M:-0.4003 c. 157: 8 25 124 N T3 SD: 0.2209 c. M: 0.2708 c. 175: 9 28 138 N T3 SD: 0.2005 c. M:-0.3455 c. 176: 9 28 139 N T3 SD: 0.1792 c. M: 0.2528 c. 194: 10 31 153 N T3 SD: 0.1746 c. M:-0.3015 c. 195: 10 31 154 N T3 SD: 0.1509 c. M: 0.2383 c. 214: 11 34 169 N T3 SD: 0.1336 c. M: 0.2263 c. 232: 12 37 183 N T3 SD: 0.1505 c. M:-0.2351 c. 233: 12 37 184 N T3 SD: 0.1249 c. M: 0.2163 c. 251: 13 40 198 N T3 SD: 0.1477 c. M:-0.2095 c. 252: 13 40 199 N T3 SD: 0.1227 c. M: 0.2079 c. 270: 14 43 213 N T3 SD: 0.1485 c. M:-0.1874 c. 271: 14 43 214 N T3 SD: 0.1249 c. M: 0.2006 c. 313: 16 50 247 N T3 SD: 0.1153 c. M: 0.1892 c. 328: 17 52 259 N T3 SD: 0.1426 c. M: 0.1837 c. 332: 17 53 262 N T3 SD: 0.0899 c. M: 0.1461 c. 351: 18 56 277 N T3 SD: 0.0675 c. M: 0.1076 c. 370: 19 59 292 N T3 SD: 0.0475 c. M: 0.0731 c. 389: 20 62 307 N T3 SD: 0.0301 c. M: 0.0420 c. 408: 21 65 322 N T3 SD: 0.0163 c. M:-0.0247 c. 427: 22 68 337 N T3 SD: 0.0130 c. M:-0.0189 c. 835: 43 133 659 N T3 SD: 0.0126 c. M:-0.0217 c. 1262: 65 201 996 N T3 SD: 0.0122 c. M:-0.0208 c. 1438: 74 229 1135 N T3 SD: 0.0131 c. M: 0.0188 c. 1457: 75 232 1150 N T3 SD: 0.0103 c. M: 0.0139 c. 1476: 76 235 1165 N T3 SD: 0.0090 c. M: 0.0150 c. 1865: 96 297 1472 N T3 SD: 0.0075 c. M: 0.0117 c. 1884: 97 300 1487 N T3 SD: 0.0051 c. M: 0.0064 c. 1903: 98 303 1502 N T3 SD: 0.0043 c. M: 0.0074 c. 2292: 118 365 1809 N T3 SD: 0.0043 c. M: 0.0073 c. 2311: 119 368 1824 N T3 SD: 0.0018 c. M: 0.0026 c. 2330: 120 371 1839 N T3 SD: 0.0019 c. M: 0.0026 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: 80.9577 cents 7 x 8:9 S SD: 70.5252 cents 8 x 9:11 SD: 56.1917 cents 9 x 10:12 S SD: 38.7242 cents 10 x 11:13 SD: 37.1720 cents 11 x 12:15 S SD: 30.0020 cents 12 x 13:16 SD: 16.8086 cents 13 x 14:17 SD: 20.4634 cents 14 x 15:19 SD: 16.9472 cents 15 x 16:20 S SD: 3.3879 cents 16 x 17:21 SD: 13.6320 cents 17 x 18:23 SD: 12.9883 cents 18 x 19:24 SD: 5.6762 cents 19 x 20:25 S SD: 14.0249 cents 20 x 21:27 SD: 14.8517 cents 21 x 22:28 SD: 12.2092 cents 22 x 23:29 SD: 17.1422 cents 23 x 24:31 SD: 18.2237 cents 24 x 26:32 SD: 16.8086 cents 25 x 27:33 SD: 16.6029 cents 26 x 28:35 S SD: 14.3122 cents 27:28:29:36 SD: 13.9206 cents 28:29:30:37 SD: 13.6755 cents 29:30:31:39 SD: 12.5742 cents 30:31:32:40 S SD: 10.6159 cents 32:33:34:43 SD: 10.2449 cents 33:34:35:44 SD: 8.7389 cents 36:37:38:48 SD: 8.1887 cents 42:43:45:56 SD: 6.9725 cents 44:45:47:59 SD: 6.3001 cents 45:46:48:60 S SD: 4.7108 cents 48:49:51:64 SD: 3.3495 cents 51:52:54:68 SD: 3.3252 cents 60:61:64:80 SD: 2.4658 cents 63:64:67:84 SD: 0.7617 cents 129:131:137:172 SD: 0.4212 cents 192:195:204:256 SD: 0.3977 cents 207:210:220:276 SD: 0.2957 cents 270:274:287:360 SD: 0.2591 cents 273:277:290:364 SD: 0.1991 cents 336:341:357:448 SD: 0.0253 cents