Scala analysis: xen12-wilson-38-4C3-tetrany-14
5-7-9-11 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: 11/9 347.407941 undecimal neutral third 3: 11/7 782.492036 undecimal augmented fifth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 14/11 417.5080 undecimal diminished fourth or major third 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 10/9 182.4037 minor whole tone 3: 9/7 435.0841 septimal major third, BP third 4: 14/11 417.5080 undecimal diminished fourth or major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 14/11 417.508 cents undecimal diminished fourth or major third 1: 1 9/7 435.084 cents septimal major third, BP third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 2: 1 10/7 617.488 cents Euler's tritone 2: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 11/7 782.492 cents undecimal augmented fifth 3: 1 9/5 1017.596 cents just minor seventh, BP seventh 3: 1 20/11 1034.996 cents large minor seventh 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 : 165.0 347.4 782.5 1200.0 165.0 : 182.4 617.5 1035.0 1200.0 347.4 : 435.1 852.6 1017.6 1200.0 782.5 : 417.5 582.5 764.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 165.0042 .. 435.0841 cents 90/77, 270.0799 cents 11/10, 165.0042 cents 2: 347.4079 .. 852.5921 cents 162/121, 505.1841 cents 77/81,-87.6762 cents 3: 764.9159 .. 1034.9958 cents 90/77, 270.0799 cents 77/81,-87.6762 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 11/10, 165.0042 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 1.818135 Largest / Average step : 1.450280 Largest / Smallest step : 2.636806 Median interval of one step : 299.95584 cents, amount: 0 Least squares average step : 266.90987 cents, oct.: 1067.63950 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : ABDC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 70.10002 cents Scale diversity : 1.564296 Lumma stability : 0.275007 Lumma impropriety factor : 0.146127 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 : 100/99, 17.3995 cents Number of recognisable fifths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 25.0000% Limited inverse transpositions with margin 270.0799 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.023696 Average absolute harmonicity : 0.279185 Specific harmonicity : 0.121851 Fundamental : 1/630, -9.2992 octaves, 0.4153 Hz. Guide tone : 22, 4.4594 octaves, 5755.762 Hz. Exponens Consonantiae : 1.386000E+04, 13.75864 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 31.0, average 7.75000 Mersenne's string divisions : 1260 Sum of van Prooijen's expressibility: 3.12418, average 0.78104 Sum of Tenney's harmonic distance : 6.22455, average 1.55614 Vogel's harmonic complexity : 22.75000 Wille's k value : 346 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 19.43097, average 1.94310 Lattice compactness (without 2's) : 16.01534, average 1.60153 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.00000 2 1 3: -2 .. 0 -0.50000 2 5: -1 .. 0 -0.25000 1 7: -1 .. 0 -0.25000 1 11: 0 .. 1 0.75000 3 3 Average exponent except 2's :-1 / 4 =-0.25000 Average absolute exponent except 2's: 7 / 4 = 1.75000 Scale is weakly epimorphic with val: <4 5 8 11 13| Scale is weakly epimorphic with val: <4 5 9 12 15| Scale is weakly epimorphic with val: <4 6 9 10 15| Scale is JI-epimorphic with val: <4 6 9 11 14| = patent Scale is weakly epimorphic with val: <4 6 10 11 13| Scale is weakly epimorphic with val: <4 7 8 11 13| Scale is weakly epimorphic with val: <4 7 9 12 15|
FIT/MODE
4: 0 1 1 2 N T3 SD: 125.2769 c. M: 182.4920 c. 5: 0 1 2 2 N G SD: 103.2813 c. M: 165.0042 c. 6: 1 1 2 2 P D3 S SD: 32.7764 c. M:-52.5921 c. 8: 1 1 3 3 N D3 S SD: 29.7001 c. M: 47.4079 c. 13: 2 2 5 4 N SD: 28.2468 c. M:-48.2772 c. 14: 2 2 5 5 N D3 S SD: 6.7894 c. M: 11.0635 c. 31: 4 5 11 11 N SD: 6.5795 c. M: 10.1655 c. 35: 5 5 13 12 N SD: 4.9735 c. M:-6.4243 c. 45: 6 7 16 16 N SD: 5.2315 c. M: 9.1587 c. 49: 7 7 18 17 N SD: 3.9805 c. M:-6.4243 c. 51: 7 8 18 18 N SD: 4.0916 c. M: 6.0214 c. 52: 7 8 19 18 N SD: 2.1268 c. M: 3.4658 c. 66: 9 10 24 23 N SD: 1.2390 c. M: 1.9534 c. 124: 17 19 45 43 N SD: 0.8801 c. M:-1.3789 c. 138: 19 21 50 48 N SD: 0.2418 c. M:-0.4181 c. 204: 28 31 74 71 N SD: 0.2399 c. M: 0.3491 c. 342: 47 52 124 119 N SD: 0.0532 c. M: 0.0919 c. 480: 66 73 174 167 N SD: 0.0462 c. M:-0.0921 c. 822: 113 125 298 286 N SD: 0.0281 c. M: 0.0407 c. 1164: 160 177 422 405 N SD: 0.0302 c. M: 0.0558 c. 1986: 273 302 720 691 N SD: 0.0285 c. M: 0.0495 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x 3:4 S SD: 40.2685 cents 3 x 4:5:6 S SD: 60.6157 cents 4 x 5:6:8 S SD: 29.8140 cents 5 x 6:8:10 S SD: 14.8406 cents 6 x 7:9:12 SD: 37.9655 cents 7:8:9:11:14 SD: 27.4608 cents 8:9:10:13:16 SD: 19.9929 cents 9:10:11:14:18 SD: 6.1830 cents 19:21:23:30:38 SD: 5.0848 cents 28:31:34:44:56 SD: 3.9746 cents 31:34:38:49:62 SD: 3.1029 cents 40:44:49:63:80 SD: 1.3895 cents 49:54:60:77:98 SD: 1.1345 cents 81:89:99:127:162 SD: 1.0873 cents 89:98:109:140:178 SD: 1.0820 cents 91:100:111:143:182 SD: 0.9677 cents 100:110:122:157:200 SD: 0.8805 cents 112:123:137:176:224 SD: 0.7860 cents 121:133:148:190:242 SD: 0.5633 cents 131:144:160:206:262 SD: 0.5203 cents 140:154:171:220:280 SD: 0.2811 cents 180:198:220:283:360 SD: 0.2185 cents 189:208:231:297:378 SD: 0.2081 cents 301:331:368:473:602 SD: 0.1849 cents 310:341:379:487:620 SD: 0.1795 cents 320:352:391:503:640 SD: 0.1739 cents 329:362:402:517:658 SD: 0.1691 cents 369:406:451:580:738 SD: 0.1508 cents 441:485:539:693:882 SD: 0.0892 cents 450:495:550:707:900 SD: 0.0874 cents 490:539:599:770:980 SD: 0.0803 cents