Scala analysis: xen12-wilson-08-4C3-tetrany-14
7-9-11-15 4C3 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 15/11 536.950772 undecimal augmented fourth 3: 5/3 884.358713 major sixth, BP sixth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 15/14 119.4428 major diatonic semitone 2: 14/11 417.5080 undecimal diminished fourth or major third 3: 11/9 347.4079 undecimal neutral third 4: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 6/5 315.641 cents minor third 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 15/11 536.951 cents undecimal augmented fourth 2: 1 22/15 663.049 cents undecimal 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 5/3 884.359 cents major sixth, BP sixth 3: 1 28/15 1080.557 cents grave major 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 : 119.4 537.0 884.4 1200.0 119.4 : 417.5 764.9 1080.6 1200.0 537.0 : 347.4 663.0 782.5 1200.0 884.4 : 315.6 435.1 852.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 417.5080 cents 196/165, 298.0652 cents 15/14, 119.4428 cents 2: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 99/98, 17.5761 cents 3: 782.4920 .. 1080.5572 cents 196/165, 298.0652 cents 99/98, 17.5761 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 14/11, 417.5080 cents Average / Smallest step : 2.511662 Largest / Average step : 1.391693 Largest / Smallest step : 3.495463 Median interval of one step : 331.52461 cents, amount: 0 Least squares average step : 288.21402 cents, oct.: 1152.85607 cents Scale is strictly proper Step pattern alph. order: ABCD Step pattern size order : ADCB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.609544 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.228365 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 harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 25.0000% -- Rational properties -- Prime limit : 11 Odd number limit : 15 (O: 15 U: 15) Highest odd numerator or denominator: 15 Scale harmonicity : 0.023696 Average absolute harmonicity : 0.299031 Specific harmonicity : 0.133735 Fundamental : 1/462, -8.8517 octaves, 0.5663 Hz. Guide tone : 30, 4.9069 octaves, 7848.767 Hz. Exponens Consonantiae : 1.386000E+04, 13.75864 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 33.0, average 8.25000 Mersenne's string divisions : 9048 Sum of van Prooijen's expressibility: 3.05115, average 0.76279 Sum of Tenney's harmonic distance : 6.01682, average 1.50421 Vogel's harmonic complexity : 22.00000 Wille's k value : 247 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 18.94168, average 1.89417 Lattice compactness (without 2's) : 15.64298, average 1.56430 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.00000 2 1 3: -1 .. 1 0.25000 3 5: 0 .. 1 0.75000 3 1 7: -1 .. 0 -0.25000 1 1 11: -1 .. 0 -0.25000 1 1 Average exponent except 2's : 2 / 4 = 0.50000 Average absolute exponent except 2's: 8 / 4 = 2.00000 Scale is weakly epimorphic with val: <4 5 8 12 15| Scale is weakly epimorphic with val: <4 5 10 12 13| Scale is weakly epimorphic with val: <4 6 8 11 13| Scale is JI-epimorphic with val: <4 6 9 10 13| Scale is weakly epimorphic with val: <4 7 8 12 13| Scale is weakly epimorphic with val: <4 7 9 11 13| Scale is JI-epimorphic with val: <4 7 10 12 15|
FIT/MODE
4: 0 2 1 1 N T3 SD: 67.9824 c. M: 119.4428 c. 7: 1 2 2 2 SP M ME SD: 31.4521 c. M:-51.9858 c. 8: 1 3 2 2 P T3 SD: 35.8943 c. M:-63.0492 c. 9: 1 3 3 2 P SD: 25.5174 c. M:-48.9746 c. 11: 1 4 3 3 P SD: 8.8708 c. M: 11.6314 c. 20: 2 7 6 5 P SD: 7.9727 c. M:-15.6413 c. 27: 3 9 8 7 SP SD: 7.5259 c. M:-13.8905 c. 31: 3 11 9 8 P SD: 4.2248 c. M:-5.9639 c. 38: 4 13 11 10 SP SD: 3.4377 c. M:-6.8730 c. 42: 4 15 12 11 P SD: 3.9786 c. M:-5.9064 c. 49: 5 17 14 13 SP SD: 2.2248 c. M:-3.0062 c. 69: 7 24 20 18 SP SD: 2.0477 c. M:-2.5978 c. 80: 8 28 23 21 SP SD: 1.5827 c. M:-3.0492 c. 92: 9 32 27 24 SP SD: 1.9785 c. M:-2.5978 c. 103: 10 36 30 27 SP SD: 1.6471 c. M: 2.9380 c. 110: 11 38 32 29 SP SD: 1.2863 c. M: 2.4053 c. 121: 12 42 35 32 SP SD: 1.1319 c. M: 1.7141 c. 141: 14 49 41 37 SP SD: 0.5601 c. M: 0.7806 c. 152: 15 53 44 40 SP SD: 0.5191 c. M: 1.0218 c. 190: 19 66 55 50 SP SD: 0.2934 c. M:-0.5572 c. 331: 33 115 96 87 SP SD: 0.2492 c. M: 0.3949 c. 342: 34 119 99 90 SP SD: 0.1169 c. M: 0.1482 c. 532: 53 185 154 140 SP SD: 0.1061 c. M: 0.1482 c. 753: 75 262 218 198 SP SD: 0.0824 c. M:-0.1034 c. 905: 90 315 262 238 SP SD: 0.0694 c. M: 0.1058 c. 1095: 109 381 317 288 SP SD: 0.0222 c. M:-0.0355 c. 1437: 143 500 416 378 SP SD: 0.0159 c. M: 0.0274 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 82.5021 cents 3 x 4:5:6 S SD: 12.9686 cents 4 x 5:7:8 SD: 57.5676 cents 5:6:7:8:10 S SD: 53.3645 cents 6:7:8:10:12 S SD: 38.1188 cents 7:8:10:12:14 S SD: 36.5279 cents 8:9:11:13:16 SD: 24.0602 cents 9:10:12:15:18 S SD: 18.5029 cents 10:11:14:17:20 SD: 18.2466 cents 11:12:15:18:22 SD: 11.1305 cents 12:13:16:20:24 SD: 10.8386 cents 13:14:18:22:26 SD: 9.6036 cents 14:15:19:23:28 SD: 6.5613 cents 24:26:33:40:48 SD: 5.9810 cents 25:27:34:42:50 SD: 5.0122 cents 27:29:37:45:54 SD: 2.3843 cents 30:32:41:50:60 SD: 2.1540 cents 42:45:57:70:84 SD: 2.0659 cents 55:59:75:92:110 SD: 1.6562 cents 57:61:78:95:114 SD: 1.5983 cents 69:74:94:115:138 SD: 0.5914 cents 99:106:135:165:198 SD: 0.2916 cents 168:180:229:280:336 SD: 0.1718 cents 267:286:364:445:534 SD: 0.1528 cents 294:315:401:490:588 SD: 0.0981 cents 363:389:495:605:726 SD: 0.0795 cents 462:495:630:770:924 SD: 0.0000 cents