Scala analysis: eikohole1
First eikohole ball <6 9 13 17 20|-epimorphic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 35/33 101.866677 2: 7/6 266.870906 septimal minor third 3: 14/11 417.507964 undecimal diminished fourth or major third 4: 5/3 884.358713 major sixth, BP sixth 5: 20/11 1034.995772 large minor seventh 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 11/10 165.0042 Ptolemy's second, 4/5-tone 1: 35/33 101.8667 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 55/42 466.8507 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 11/10 165.0042 Ptolemy's second, 4/5-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 35/33 101.867 cents 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 55/42 466.851 cents 2: 2 7/6 266.871 cents septimal minor third 2: 2 6/5 315.641 cents minor third 2: 2 10/7 617.488 cents Euler's tritone 3: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 77/60 431.875 cents 3: 1 120/77 768.125 cents 3: 2 11/7 782.492 cents undecimal augmented fifth 4: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 2 5/3 884.359 cents major sixth, BP sixth 4: 2 12/7 933.129 cents septimal major sixth 5: 1 84/55 733.149 cents 5: 2 20/11 1034.996 cents large minor seventh 5: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 5: 1 66/35 1098.133 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.60000 = 18/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 101.9 266.9 417.5 884.4 1035.0 1200.0 101.9 : 165.0 315.6 782.5 933.1 1098.1 1200.0 266.9 : 150.6 617.5 768.1 933.1 1035.0 1200.0 417.5 : 466.9 617.5 782.5 884.4 1049.4 1200.0 884.4 : 150.6 315.6 417.5 582.5 733.1 1200.0 1035.0: 165.0 266.9 431.9 582.5 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 101.8667 .. 466.8507 cents 121/98, 364.9841 cents 35/33, 101.8667 cents 2: 266.8709 .. 617.4878 cents 60/49, 350.6169 cents 49/55,-199.9798 cents 3: 417.5080 .. 782.4920 cents 121/98, 364.9841 cents 49/55,-199.9798 cents 4: 582.5122 .. 933.1291 cents 60/49, 350.6169 cents 49/55,-199.9798 cents 5: 733.1493 .. 1098.1333 cents 121/98, 364.9841 cents 49/55,-199.9798 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 35/33, 101.8667 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 55/42, 466.8507 cents Average / Smallest step : 1.963351 Largest / Average step : 2.334254 Largest / Smallest step : 4.582958 Median interval of one step : 157.82064 cents, amount: 0 Least squares average step : 195.61040 cents, oct.: 1173.66238 cents Scale is not proper Step pattern alph. order: ABCDCB Step pattern size order : ACBDBC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.471972 Lumma stability : 0.169778 Lumma impropriety factor : 0.555215 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 2.800000 Number of different interval sizes : 18 = 3.60000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.60000 = 18/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 121/120, 14.3672 cents Number of recognisable fifths : 0 Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 4 Formal octave complements present : 1 = 16.6667% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 3-4 -- Rational properties -- Prime limit : 11 Odd number limit : 77 (O: 77 U: 77) Highest odd numerator or denominator: 35 Scale harmonicity : 0.024671 Average absolute harmonicity : 0.213360 Specific harmonicity : 0.103286 Fundamental : 1/66, -6.0444 octaves, 3.9640 Hz. Guide tone : 140, 7.1293 octaves, 36627.579 Hz. Exponens Consonantiae : 9.240000E+03, 13.17368 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 74.0, average 12.33333 Mersenne's string divisions : 4110600 Sum of van Prooijen's expressibility: 5.17092, average 0.86182 Sum of Tenney's harmonic distance : 10.69290, average 1.78215 Vogel's harmonic complexity : 14.50000 Wille's k value : 38 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 41.42418, average 1.97258 Lattice compactness (without 2's) : 30.62742, average 1.45845 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.50000 5 1 3: -1 .. 0 -0.50000 3 5: 0 .. 1 0.50000 3 1 7: 0 .. 1 0.50000 3 1 11: -1 .. 0 -0.50000 3 3 Average exponent except 2's : 0 / 6 = 0.00000 Average absolute exponent except 2's: 12 / 6 = 2.00000 Scale is weakly epimorphic with val: <6 9 13 16 23| Scale is JI-epimorphic with val: <6 9 13 17 20| Scale is weakly epimorphic with val: <6 9 13 17 22| Scale is weakly epimorphic with val: <6 9 13 18 23| Scale is weakly epimorphic with val: <6 9 14 17 19| Scale is weakly epimorphic with val: <6 9 14 18 22| Scale is weakly epimorphic with val: <6 9 14 19 23| 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 13 18 20| Scale is weakly epimorphic with val: <6 10 14 18 19| Scale is JI-epimorphic with val: <6 10 14 18 21| Scale is weakly epimorphic with val: <6 10 14 18 23| Scale is weakly epimorphic with val: <6 10 15 17 19| Scale is weakly epimorphic with val: <6 10 15 18 20| 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 13 15 22| Scale is weakly epimorphic with val: <6 11 13 16 21| Scale is weakly epimorphic with val: <6 11 13 18 21| Scale is weakly epimorphic with val: <6 11 14 15 19| Scale is weakly epimorphic with val: <6 11 14 18 22| Scale is weakly epimorphic with val: <6 11 14 19 21| Scale is weakly epimorphic with val: <6 11 15 16 19| Scale is weakly epimorphic with val: <6 11 15 18 19| Scale is weakly epimorphic with val: <6 11 15 19 20| Scale is JI-epimorphic with val: <6 11 15 19 22|
FIT/MODE
6: 0 1 1 2 1 1 N D3 SD: 62.5782 c. M: 101.8667 c. 8: 1 1 1 3 1 1 N M DE SD: 28.6934 c. M:-48.1333 c. 9: 1 1 1 4 1 1 N M DE SD: 27.9830 c. M:-48.9746 c. 12: 1 2 1 5 1 2 N SD: 21.8971 c. M: 34.9958 c. 14: 1 2 2 5 2 2 N D3 SD: 14.4909 c. M: 27.2159 c. 15: 1 2 2 6 2 2 N D3 SD: 16.0767 c. M: 26.8709 c. 20: 2 2 3 8 2 3 N SD: 15.9509 c. M: 26.8709 c. 22: 2 3 3 8 3 3 N D3 SD: 9.8250 c. M:-18.8557 c. 23: 2 3 3 9 3 3 N D3 SD: 4.4886 c. M:-8.4825 c. 35: 3 5 4 14 4 5 N SD: 5.5404 c. M:-7.4148 c. 37: 3 5 5 14 5 5 N D3 SD: 5.4192 c. M: 8.6830 c. 45: 4 6 6 17 6 6 N D3 SD: 5.0167 c. M:-9.1587 c. 49: 4 7 6 19 6 7 N SD: 3.4569 c. M: 6.4243 c. 58: 5 8 7 23 7 8 N SD: 2.8579 c. M:-5.2965 c. 72: 6 10 9 28 9 10 N SD: 1.1582 c. M: 1.8667 c. 95: 8 13 12 37 12 13 N SD: 0.8508 c. M: 1.6077 c. 152: 13 21 19 59 19 21 N SD: 0.8622 c. M:-1.5501 c. 167: 14 23 21 65 21 23 N SD: 0.7649 c. M: 1.2679 c. 175: 15 24 22 68 22 24 N SD: 0.5957 c. M:-0.9905 c. 247: 21 34 31 96 31 34 N SD: 0.2178 c. M:-0.3356 c. 342: 29 47 43 133 43 47 N SD: 0.1197 c. M: 0.2042 c. 589: 50 81 74 229 74 81 N SD: 0.0867 c. M:-0.1491 c. 931: 79 128 117 362 117 128 N SD: 0.0809 c. M: 0.1482 c. 1201: 102 165 151 467 151 165 N SD: 0.1008 c. M:-0.1440 c. 1236: 105 170 155 481 155 170 N SD: 0.0757 c. M:-0.1194 c. 1331: 113 183 167 518 167 183 N SD: 0.0489 c. M:-0.0891 c. 1578: 134 217 198 614 198 217 N SD: 0.0337 c. M:-0.0519 c. 1920: 163 264 241 747 241 264 N SD: 0.0085 c. M:-0.0163 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 91.2019 cents 3 x x 4:5 x 6 S SD: 26.8457 cents 4 x x 5 x 7:8 SD: 24.3847 cents 5 x 6 x 8:9:10 S SD: 21.9030 cents 6 x 7:8:10:11:12 S SD: 16.3617 cents 7 x 8:9:12:13:14 S SD: 14.5727 cents 8 x 9:10:13:15:16 SD: 19.6940 cents 9:10 x 11:15:16:18 SD: 22.7279 cents 10:11:12:13:17:18:20 SD: 15.9777 cents 11:12:13:14:18:20:22 SD: 10.3906 cents 12:13:14:15:20:22:24 S SD: 8.3779 cents 16:17:19:20:27:29:32 SD: 8.1878 cents 17:18:20:22:28:31:34 SD: 6.4476 cents 18:19:21:23:30:33:36 SD: 2.9894 cents 36:38:42:46:60:65:72 SD: 2.6918 cents 47:50:55:60:78:85:94 SD: 2.4865 cents 48:51:56:61:80:87:96 SD: 1.1248 cents 66:70:77:84:110:120:132 SD: 0.0000 cents