Scala analysis: elevenlim
Eleven-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: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 7/4 968.825906 harmonic seventh 6: 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 7/6 266.8709 septimal minor third 6: 8/7 231.1741 septimal whole 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 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 2: 1 6/5 315.641 cents minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 5/4 386.314 cents major third 2: 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 4/3 498.045 cents perfect fourth 3: 1 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 1 10/7 617.488 cents Euler's tritone 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 3/2 701.955 cents perfect fifth 4: 1 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 4: 1 11/7 782.492 cents undecimal augmented fifth 4: 1 8/5 813.686 cents minor sixth 4: 1 18/11 852.592 cents undecimal neutral sixth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 1 7/4 968.826 cents harmonic seventh 5: 1 16/9 996.090 cents Pythagorean minor seventh 5: 1 9/5 1017.596 cents just minor seventh, BP seventh 5: 1 20/11 1034.996 cents large minor seventh 5: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 203.9 386.3 551.3 702.0 968.8 1200.0 203.9 : 182.4 347.4 498.0 764.9 996.1 1200.0 386.3 : 165.0 315.6 582.5 813.7 1017.6 1200.0 551.3 : 150.6 417.5 648.7 852.6 1035.0 1200.0 702.0 : 266.9 498.0 702.0 884.4 1049.4 1200.0 968.8 : 231.2 435.1 617.5 782.5 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 266.8709 cents 77/72, 116.2338 cents 12/11, 150.6371 cents 2: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 36/35, 48.7704 cents 3: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 1/1, 0.0000 cents 4: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 5: 933.1291 .. 1049.3629 cents 77/72, 116.2338 cents 36/35, 48.7704 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.327695 Largest / Average step : 1.334355 Largest / Smallest step : 1.771615 Median interval of one step : 193.15686 cents, amount: 0 Least squares average step : 192.11473 cents, oct.: 1152.68840 cents Scale is proper Step pattern alph. order: ABCDEF Step pattern size order : DCBAFE Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.609657 Rothenberg stability : 0.866667 = 13/15 Lumma stability : 0.332346 Rothenberg efficiency : 0.355556 redundancy: 0.644444 Efficiency x scale size : 2.133333 Number of different interval sizes : 28 = 5.60000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 6.00000 = 6 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 121/120, 14.3672 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 2 Most common triad is 0.0 498.045 1049.363 cents, amount: 1 Number of recognisable fifths : 2, average 701.9550 cents All steps are superparticular (epimoric) Scale is harmonic, base degree is : 4 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 16.6667% Scale is differentially coherent -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.022624 Average absolute harmonicity : 0.273396 Specific harmonicity : 0.169040 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 6930, 12.7586 octaves, 1813065.168 Hz. Exponens Consonantiae : 5.544000E+04, 15.75864 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 32.0, average 5.33333 Mersenne's string divisions : 159885 Sum of van Prooijen's expressibility: 4.01682, average 0.66947 Sum of Tenney's harmonic distance : 7.62918, average 1.27153 Vogel's harmonic complexity : 6.66667 Wille's k value : 5 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 50.97307, average 2.42729 Lattice compactness (without 2's) : 28.19349, average 1.34255 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.66667 12 1 3: 0 .. 2 0.50000 3 2 5: 0 .. 1 0.16667 1 1 7: 0 .. 1 0.16667 1 1 11: 0 .. 1 0.16667 1 1 Average exponent except 2's : 6 / 6 = 1.00000 Average absolute exponent except 2's: 6 / 6 = 1.00000 Scale is weakly epimorphic with val: <6 10 13 15 23| Scale is weakly epimorphic with val: <6 10 13 17 21| Scale is weakly epimorphic with val: <6 10 15 17 19| Scale is weakly epimorphic with val: <6 10 15 19 23| Scale is weakly epimorphic with val: <6 11 13 15 20| Scale is weakly epimorphic with val: <6 11 14 15 19| Scale is weakly epimorphic with val: <6 11 14 19 21| Scale is weakly epimorphic with val: <6 11 15 19 20|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 46.8280 c. M:-98.0450 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 9: 1 2 1 1 2 2 P D3 SD: 36.5076 c. M: 70.5767 c. 10: 2 1 2 1 2 2 P D3 SD: 28.1909 c. M:-48.6821 c. 12: 2 2 2 1 3 2 P T3 SD: 24.3180 c. M:-48.6821 c. 14: 2 2 2 2 3 3 P D3 S SD: 29.5890 c. M: 43.4566 c. 15: 3 2 2 2 3 3 P SD: 18.1140 c. M:-36.0900 c. 16: 3 2 2 2 4 3 N SD: 18.3944 c. M: 26.9550 c. 17: 3 2 3 2 4 3 P SD: 17.0627 c. M: 33.3725 c. 19: 3 3 3 2 4 4 P SD: 13.3399 c. M: 21.4575 c. 22: 4 3 3 3 5 4 P SD: 8.9256 c. M:-14.2718 c. 31: 5 5 4 4 7 6 P SD: 6.1104 c. M: 10.3616 c. 41: 7 6 6 5 9 8 P SD: 3.3365 c. M: 5.8259 c. 46: 8 7 6 6 10 9 P SD: 3.6228 c. M:-4.9906 c. 63: 11 9 9 8 14 12 P SD: 3.5600 c. M:-5.6138 c. 72: 12 11 10 9 16 14 P SD: 2.3942 c. M: 3.9100 c. 87: 15 13 12 11 19 17 P SD: 1.9267 c. M: 3.3087 c. 94: 16 14 13 12 21 18 P SD: 1.7733 c. M: 3.3350 c. 118: 20 18 16 15 26 23 P SD: 1.4413 c. M: 2.7242 c. 130: 22 20 18 16 29 25 P SD: 1.2466 c. M:-2.5282 c. 152: 26 23 21 19 34 29 P SD: 1.2418 c. M:-2.2267 c. 176: 30 27 24 22 39 34 P SD: 1.0974 c. M:-2.3226 c. 178: 30 27 25 22 40 34 P SD: 1.5112 c. M: 2.0441 c. 181: 31 27 25 23 40 35 P SD: 1.1749 c. M: 1.7833 c. 183: 31 28 25 23 41 35 P SD: 0.8009 c. M:-1.6659 c. 224: 38 34 31 28 50 43 P SD: 0.4811 c. M:-0.8170 c. 270: 46 41 37 34 60 52 P SD: 0.2967 c. M:-0.5344 c. 342: 58 52 47 43 76 66 P SD: 0.3369 c. M: 0.4407 c. 472: 80 72 65 59 105 91 P SD: 0.2971 c. M: 0.5202 c. 494: 84 75 68 62 110 95 P SD: 0.1844 c. M:-0.4049 c. 612: 104 93 84 77 136 118 P SD: 0.1607 c. M: 0.3376 c. 742: 126 113 102 93 165 143 P SD: 0.1308 c. M:-0.2092 c. 836: 142 127 115 105 186 161 P SD: 0.1037 c. M: 0.1893 c. 1106: 188 168 152 139 246 213 P SD: 0.0758 c. M: 0.1425 c. 1236: 210 188 170 155 275 238 P SD: 0.0818 c. M:-0.1384 c. 1354: 230 206 186 170 301 261 P SD: 0.0807 c. M: 0.1405 c. 1506: 256 229 207 189 335 290 P SD: 0.0838 c. M:-0.1405 c. 1578: 268 240 217 198 351 304 P SD: 0.0495 c. M: 0.1077 c. 1848: 314 281 254 232 411 356 P SD: 0.0228 c. M:-0.0499 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 0.0000 cents 3 x x 4 x 5:6 S SD: 33.2878 cents 4 x 5 x 6:7:8 S SD: 0.0000 cents 5 x 6:7:8:9:10 S SD: 28.8653 cents 6:7 x 8:9:11:12 SD: 23.0550 cents 7:8:9:10:11:12:14 S SD: 20.5891 cents 8:9:10:11:12:14:16 S SD: 0.0000 cents