Scala analysis: ninelim
Nine-limit otonal chord
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 3/2 701.955001 perfect fifth 4: 7/4 968.825906 harmonic seventh 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 6/5 315.6413 minor third 4: 7/6 266.8709 septimal minor third 5: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 2 4/3 498.045 cents perfect fourth 2: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 3: 2 3/2 701.955 cents perfect fifth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 8/5 813.686 cents minor sixth 4: 1 5/3 884.359 cents major sixth, BP sixth 4: 1 12/7 933.129 cents septimal major sixth 4: 1 7/4 968.826 cents harmonic seventh 4: 1 16/9 996.090 cents Pythagorean minor seventh 4: 1 9/5 1017.596 cents just minor seventh, BP seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.50000 = 9/2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 203.9 386.3 702.0 968.8 1200.0 203.9 : 182.4 498.0 764.9 996.1 1200.0 386.3 : 315.6 582.5 813.7 1017.6 1200.0 702.0 : 266.9 498.0 702.0 884.4 1200.0 968.8 : 231.2 435.1 617.5 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 182.4037 .. 315.6413 cents 27/25, 133.2376 cents 10/9, 182.4037 cents 2: 386.3137 .. 582.5122 cents 28/25, 196.1985 cents 25/24, 70.6724 cents 3: 617.4878 .. 813.6863 cents 28/25, 196.1985 cents 50/49, 34.9756 cents 4: 884.3587 .. 1017.5963 cents 27/25, 133.2376 cents 25/24, 70.6724 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 10/9, 182.4037 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 1.315763 Largest / Average step : 1.315172 Largest / Smallest step : 1.730454 Median interval of one step : 8/7, 231.1741 cents, amount: 1 Least squares average step : 235.59466 cents, oct.: 1177.97328 cents Scale is strictly proper Step pattern alph. order: ABCDE Step pattern size order : BAEDC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.573508 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.450940 Rothenberg efficiency : 0.440000 redundancy: 0.560000 Efficiency x scale size : 2.200000 Number of different interval sizes : 18 = 4.50000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.50000 = 9/2 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 81/80, 21.5063 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 2 Most common triad is 0.0 498.045 701.955 cents, amount: 1 Number of recognisable fifths : 2, average 701.9550 cents Best fifths form a closed circle All steps are superparticular (epimoric) Scale is harmonic, base degree is : 2 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 20.0000% Scale is differentially coherent -- Rational properties -- Prime limit : 7 Odd number limit : 9 (O: 9 U: 9) Highest odd numerator or denominator: 9 Scale harmonicity : 0.038433 Average absolute harmonicity : 0.318634 Specific harmonicity : 0.248112 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 630, 9.2992 octaves, 164824.106 Hz. Exponens Consonantiae : 5.040000E+03, 12.29921 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 22.5, average 4.50000 Mersenne's string divisions : 8415 Sum of van Prooijen's expressibility: 2.97543, average 0.59509 Sum of Tenney's harmonic distance : 5.68470, average 1.13694 Vogel's harmonic complexity : 5.80000 Wille's k value : 4 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 35.53802, average 2.36920 Lattice compactness (without 2's) : 19.71478, average 1.31432 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.40000 9 1 3: 0 .. 2 0.60000 3 2 5: 0 .. 1 0.20000 1 1 7: 0 .. 1 0.20000 1 1 Average exponent except 2's : 5 / 5 = 1.00000 Average absolute exponent except 2's: 5 / 5 = 1.00000 Scale is weakly epimorphic with val: <5 7 11 13| Scale is JI-epimorphic with val: <5 8 12 14| = patent
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 45.7889 c. M:-93.6863 c. 7: 1 1 2 2 1 N D3 S SD: 36.8152 c. M:-59.7455 c. 9: 1 2 2 2 2 SP M ME S SD: 39.1749 c. M: 70.5767 c. 10: 2 1 3 2 2 P T3 SD: 21.9017 c. M:-36.0900 c. 12: 2 2 3 3 2 P D3 S SD: 15.3509 c. M:-31.1741 c. Dominant Pentatonic 16: 3 2 4 4 3 P SD: 16.3553 c. M: 26.9550 c. 19: 3 3 5 4 4 SP SD: 12.4515 c. M: 21.4575 c. 22: 4 3 6 5 4 P SD: 9.4193 c. M:-14.2718 c. 31: 5 5 8 7 6 SP SD: 5.2152 c. M: 10.3616 c. 41: 7 6 11 9 8 SP SD: 2.9647 c. M: 5.8259 c. 46: 8 7 12 10 9 SP SD: 3.6484 c. M:-4.9906 c. 53: 9 8 14 12 10 SP SD: 2.2205 c. M:-4.7590 c. 72: 12 11 19 16 14 SP SD: 2.5556 c. M: 3.9100 c. 77: 13 12 20 17 15 SP SD: 1.9870 c. M:-3.2967 c. 94: 16 14 25 21 18 SP SD: 1.6245 c. M: 3.3350 c. 99: 17 15 26 22 19 SP SD: 1.3409 c. M:-2.1506 c. 118: 20 18 31 26 23 SP SD: 1.2471 c. M: 2.7242 c. 130: 22 20 34 29 25 SP SD: 0.7658 c. M:-1.3786 c. 171: 29 26 45 38 33 SP SD: 0.3120 c. M: 0.4049 c. 270: 46 41 71 60 52 SP SD: 0.3116 c. M:-0.5344 c. 441: 75 67 116 98 85 SP SD: 0.1071 c. M:-0.1716 c. 612: 104 93 161 136 118 SP SD: 0.0907 c. M: 0.1985 c. 935: 159 142 246 208 180 SP SD: 0.1046 c. M:-0.1581 c. 1053: 179 160 277 234 203 SP SD: 0.0837 c. M: 0.1649 c. 1106: 188 168 291 246 213 SP SD: 0.0531 c. M:-0.0710 c. 1277: 217 194 336 284 246 SP SD: 0.0431 c. M: 0.0960 c. 1677: 285 255 441 373 323 SP SD: 0.0474 c. M:-0.0906 c. 1718: 292 261 452 382 331 SP SD: 0.0349 c. M: 0.0506 c. 1848: 314 281 486 411 356 SP SD: 0.0235 c. M:-0.0499 c. 2019: 343 307 531 449 389 SP SD: 0.0278 c. M: 0.0467 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 0.0000 cents 3 x 4 x 5:6 S SD: 46.6888 cents 4 x 5:6:7:8 S SD: 0.0000 cents 5 x 6:8:9:10 S SD: 35.2287 cents 6:7:8:9:11:12 SD: 30.2881 cents 7:8:9:11:12:14 SD: 20.8637 cents 8:9:10:12:14:16 S SD: 0.0000 cents