Scala analysis: xen12-wilson-38-4C3-tetrany-11
3-5-7-11 4C3 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 11/7 782.492036 undecimal augmented fifth 3: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 10/7 617.4878 Euler's tritone 3: 7/6 266.8709 septimal minor third 4: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 10/7 617.488 cents Euler's tritone 2: 1 6/5 315.641 cents minor third 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 11/7 782.492 cents undecimal augmented fifth 2: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 12/7 933.129 cents septimal major sixth 3: 1 20/11 1034.996 cents large minor seventh 3: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 0.0 : 165.0 782.5 1049.4 1200.0 165.0 : 617.5 884.4 1035.0 1200.0 782.5 : 266.9 417.5 582.5 1200.0 1049.4: 150.6 315.6 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 617.4878 cents 55/42, 466.8507 cents 12/11, 150.6371 cents 2: 315.6413 .. 884.3587 cents 25/18, 568.7174 cents 21/25,-301.8465 cents 3: 582.5122 .. 1049.3629 cents 55/42, 466.8507 cents 21/25,-301.8465 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 10/7, 617.4878 cents Average / Smallest step : 1.991542 Largest / Average step : 2.058293 Largest / Smallest step : 4.099176 Median interval of one step : 215.93757 cents, amount: 0 Least squares average step : 322.60257 cents, oct.: 1290.41028 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : BDCA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.642486 Lumma stability : 0.251062 Lumma impropriety factor : 0.473931 Rothenberg efficiency : 0.500000 redundancy: 0.500000 Efficiency x scale size : 2.000000 Number of different interval sizes : 12 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 121/120, 14.3672 cents Number of recognisable fifths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 25.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.025295 Average absolute harmonicity : 0.279996 Specific harmonicity : 0.127226 Fundamental : 1/210, -7.7142 octaves, 1.2458 Hz. Guide tone : 22, 4.4594 octaves, 5755.762 Hz. Exponens Consonantiae : 4.620000E+03, 12.17368 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 29.5, average 7.37500 Mersenne's string divisions : 2142 Sum of van Prooijen's expressibility: 3.12418, average 0.78104 Sum of Tenney's harmonic distance : 6.04846, average 1.51211 Vogel's harmonic complexity : 20.25000 Wille's k value : 192 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 17.38766, average 1.73877 Lattice compactness (without 2's) : 12.72792, average 1.27279 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 -0.25000 3 1 3: -1 .. 0 -0.25000 1 5: -1 .. 0 -0.25000 1 7: -1 .. 0 -0.25000 1 11: 0 .. 1 0.75000 3 3 Average exponent except 2's : 0 / 4 = 0.00000 Average absolute exponent except 2's: 6 / 4 = 1.50000 Scale is weakly epimorphic with val: <4 5 8 10 15| Scale is weakly epimorphic with val: <4 5 8 11 14| Scale is weakly epimorphic with val: <4 5 10 12 15| Scale is JI-epimorphic with val: <4 6 8 11 13| Scale is weakly epimorphic with val: <4 6 9 12 15| Scale is weakly epimorphic with val: <4 7 8 10 13| Scale is JI-epimorphic with val: <4 7 9 12 14| Scale is weakly epimorphic with val: <4 7 10 12 13|
FIT/MODE
4: 0 2 1 1 N T3 SD: 143.9088 c. M: 182.4920 c. 5: 0 3 1 1 N G SD: 98.8906 c. M: 165.0042 c. 6: 1 3 1 1 N M DE SD: 31.4958 c. M: 49.3629 c. 8: 1 4 2 1 N SD: 17.8974 c. M: 32.4920 c. 9: 1 5 2 1 N SD: 20.0561 c. M: 31.6709 c. 14: 2 7 3 2 N SD: 12.2061 c. M: 20.7915 c. 15: 2 8 3 2 N SD: 10.2376 c. M:-17.5080 c. 22: 3 11 5 3 N SD: 11.4716 c. M: 18.8557 c. 23: 3 12 5 3 N SD: 5.1623 c. M: 8.4825 c. 38: 5 20 8 5 N SD: 6.1636 c. M: 7.2577 c. 43: 6 22 10 5 N SD: 5.7097 c. M:-11.1022 c. 49: 7 25 11 6 N SD: 3.7532 c. M:-6.4243 c. 57: 8 29 13 7 N SD: 2.9548 c. M: 3.5447 c. 58: 8 30 13 7 N SD: 3.4574 c. M:-5.8095 c. 63: 9 32 14 8 N SD: 3.4163 c. M:-6.4243 c. 64: 9 33 14 8 N SD: 3.1431 c. M:-5.0080 c. 66: 9 34 15 8 N SD: 2.7011 c. M:-5.1825 c. 72: 10 37 16 9 N SD: 0.9845 c. M:-1.6624 c. 95: 13 49 21 12 N SD: 0.7001 c. M: 0.9419 c. 152: 21 78 34 19 N SD: 0.6812 c. M: 0.9131 c. 167: 23 86 37 21 N SD: 0.4148 c. M:-0.7415 c. 175: 24 90 39 22 N SD: 0.4584 c. M: 0.7778 c. 247: 34 127 55 31 N SD: 0.1775 c. M: 0.3058 c. 342: 47 176 76 43 N SD: 0.1298 c. M: 0.2401 c. 414: 57 213 92 52 N SD: 0.1291 c. M:-0.2132 c. 589: 81 303 131 74 N SD: 0.0985 c. M: 0.1491 c. 756: 104 389 168 95 N SD: 0.0901 c. M: 0.1566 c. 917: 126 472 204 115 N SD: 0.0988 c. M:-0.1463 c. 931: 128 479 207 117 N SD: 0.1005 c. M: 0.1685 c. 1003: 138 516 223 126 N SD: 0.0773 c. M: 0.1107 c. 1164: 160 599 259 146 N SD: 0.0675 c. M:-0.1216 c. 1236: 170 636 275 155 N SD: 0.0806 c. M:-0.1516 c. 1259: 173 648 280 158 N SD: 0.0618 c. M: 0.1115 c. 1331: 183 685 296 167 N SD: 0.0540 c. M:-0.0775 c. 1506: 207 775 335 189 N SD: 0.0392 c. M: 0.0640 c. 1578: 217 812 351 198 N SD: 0.0353 c. M:-0.0667 c. 1673: 230 861 372 210 N SD: 0.0316 c. M:-0.0543 c. 1920: 264 988 427 241 N SD: 0.0075 c. M:-0.0121 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 40.2685 cents 3 x 5 x 6 SD: 50.9333 cents 5:6:8:9:10 S SD: 39.2697 cents 6:7:9:11:12 SD: 32.4644 cents 7:8:11:13:14 SD: 17.4597 cents 9:10:14:17:18 SD: 14.3238 cents 10:11:16:18:20 SD: 11.1305 cents 11:12:17:20:22 SD: 8.8226 cents 12:13:19:22:24 SD: 7.3712 cents 18:20:28:33:36 SD: 6.1830 cents 19:21:30:35:38 SD: 3.5783 cents 30:33:47:55:60 SD: 1.3135 cents 49:54:77:90:98 SD: 1.1345 cents 61:67:96:112:122 SD: 1.1169 cents 79:87:124:145:158 SD: 0.8625 cents 89:98:140:163:178 SD: 0.7656 cents 91:100:143:167:182 SD: 0.6115 cents 119:131:187:218:238 SD: 0.4676 cents 149:164:234:273:298 SD: 0.4574 cents 161:177:253:295:322 SD: 0.3457 cents 180:198:283:330:360 SD: 0.2185 cents 210:231:330:385:420 SD: 0.0000 cents