Scala analysis: xen12-wilson-08-4C3-tetrany-06
1-7-9-11 4C3 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/9 347.407941 undecimal neutral third 2: 11/8 551.317942 undecimal semi-augmented fourth 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: 11/9 347.4079 undecimal neutral third 2: 9/8 203.9100 major whole tone 3: 8/7 231.1741 septimal whole tone 4: 14/11 417.5080 undecimal diminished fourth or major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 11/9 347.408 cents undecimal neutral third 1: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 16/11 648.682 cents undecimal semi-diminished fifth 2: 1 14/9 764.916 cents septimal minor sixth 3: 1 11/7 782.492 cents undecimal augmented fifth 3: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 7/4 968.826 cents harmonic seventh 3: 1 16/9 996.090 cents Pythagorean 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 : 347.4 551.3 782.5 1200.0 347.4 : 203.9 435.1 852.6 1200.0 551.3 : 231.2 648.7 996.1 1200.0 782.5 : 417.5 764.9 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 203.9100 .. 417.5080 cents 112/99, 213.5980 cents 9/8, 203.9100 cents 2: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 99/98, 17.5761 cents 3: 782.4920 .. 996.0900 cents 112/99, 213.5980 cents 99/98, 17.5761 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 9/8, 203.9100 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 14/11, 417.5080 cents Average / Smallest step : 1.471237 Largest / Average step : 1.391693 Largest / Smallest step : 2.047511 Median interval of one step : 289.29102 cents, amount: 0 Least squares average step : 286.58400 cents, oct.: 1146.33599 cents Scale is strictly proper Step pattern alph. order: ABCD Step pattern size order : CABD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.591247 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.369144 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 : 99/98, 17.5761 cents Number of recognisable fifths : 0 Best minor thirds form a closed circle Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 25.0000% -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.281216 Specific harmonicity : 0.133285 Fundamental : 1/504, -8.9773 octaves, 0.5191 Hz. Guide tone : 22, 4.4594 octaves, 5755.762 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 30.0, average 7.50000 Mersenne's string divisions : 3420 Sum of van Prooijen's expressibility: 3.12418, average 0.78104 Sum of Tenney's harmonic distance : 6.12764, average 1.53191 Vogel's harmonic complexity : 20.50000 Wille's k value : 346 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 25.12110, average 2.51211 Lattice compactness (without 2's) : 14.53663, average 1.45366 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.50000 4 1 3: -2 .. 0 -0.50000 2 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 11 13| Scale is weakly epimorphic with val: <4 7 11 13|
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 67.8704 c. M:-117.5080 c. 5: 1 1 1 2 P M ME SD: 71.6379 c. M: 107.4079 c. 6: 2 1 1 2 P D3 I SD: 36.8863 c. M:-52.5921 c. 9: 3 1 2 3 P SD: 29.1372 c. M:-52.5921 c. 11: 3 2 2 4 P SD: 14.1009 c. M: 20.1352 c. 17: 5 3 3 6 P SD: 7.8440 c. M:-13.3879 c. 20: 6 3 4 7 P SD: 8.5567 c. M:-12.5921 c. 28: 8 5 5 10 P SD: 6.6528 c. M: 11.0635 c. 31: 9 5 6 11 P SD: 6.2820 c. M: 9.3825 c. 35: 10 6 7 12 SP SD: 4.0377 c. M:-6.0794 c. 48: 14 8 9 17 P SD: 4.0183 c. M: 7.4920 c. 52: 15 9 10 18 SP SD: 1.7659 c. M:-2.5282 c. 72: 21 12 14 25 SP SD: 1.5136 c. M:-2.5921 c. 83: 24 14 16 29 SP SD: 1.3223 c. M: 1.9204 c. 124: 36 21 24 43 SP SD: 0.8584 c. M:-1.3789 c. 135: 39 23 26 47 SP SD: 0.4078 c. M: 0.7413 c. 207: 60 35 40 72 SP SD: 0.3676 c. M: 0.5933 c. 259: 75 44 50 90 SP SD: 0.2636 c. M:-0.5195 c. 342: 99 58 66 119 SP SD: 0.2220 c. M: 0.4407 c. 359: 104 61 69 125 SP SD: 0.2226 c. M: 0.3193 c. 394: 114 67 76 137 SP SD: 0.1615 c. M:-0.2491 c. 601: 174 102 116 209 SP SD: 0.1561 c. M: 0.2364 c. 618: 179 105 119 215 SP SD: 0.1088 c. M:-0.1649 c. 753: 218 128 145 262 SP SD: 0.0398 c. M:-0.0765 c. 1095: 317 186 211 381 SP SD: 0.0448 c. M: 0.0851 c. 1147: 332 195 221 399 SP SD: 0.0517 c. M:-0.0712 c. 1354: 392 230 261 471 SP SD: 0.0501 c. M:-0.0781 c. 1641: 475 279 316 571 SP SD: 0.0449 c. M: 0.0588 c. 1713: 496 291 330 596 SP SD: 0.0265 c. M:-0.0527 c. 1848: 535 314 356 643 SP SD: 0.0158 c. M: 0.0245 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: 38.3186 cents 4:5 x 6:8 S SD: 29.8140 cents 5:6:7:8:10 S SD: 13.5906 cents 13:16:18:20:26 SD: 10.1194 cents 14:17:19:22:28 SD: 6.3214 cents 18:22:25:28:36 SD: 6.1830 cents 19:23:26:30:38 SD: 5.0889 cents 26:32:36:41:52 SD: 4.5250 cents 32:39:44:50:64 SD: 2.7565 cents 35:43:48:55:70 SD: 2.5092 cents 40:49:55:63:80 SD: 1.3895 cents 72:88:99:113:144 SD: 0.5468 cents 112:137:154:176:224 SD: 0.3512 cents 184:225:253:289:368 SD: 0.3024 cents 189:231:260:297:378 SD: 0.2081 cents 301:368:414:473:602 SD: 0.1848 cents 315:385:433:495:630 SD: 0.1249 cents 392:479:539:616:784 SD: 0.1004 cents 432:528:594:679:864 SD: 0.0911 cents 504:616:693:792:1008 SD: 0.0000 cents