Scala analysis: fib10
first thirteen fibonacci numbers reduced to the octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 9/8 203.910002 major whole tone 3: 5/4 386.313714 major third 4: 21/16 470.780907 narrow fourth 5: 89/64 570.880117 6: 3/2 701.955001 perfect fifth 7: 13/8 840.527662 tridecimal neutral sixth 8: 55/32 937.631656 9: 233/128 1037.023374 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/233 162.9766 1: 17/16 104.9554 17th harmonic 2: 18/17 98.9546 Arabic lute index finger 3: 10/9 182.4037 minor whole tone 4: 21/20 84.4672 minor semitone 5: 89/84 100.0992 quasi-equal semitone 6: 96/89 131.0749 7: 13/12 138.5727 tridecimal 2/3-tone 8: 55/52 97.1040 9: 233/220 99.3917 10: 256/233 162.9766
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21/20 84.467 cents minor semitone 1: 1 55/52 97.104 cents 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 233/220 99.392 cents 1: 1 89/84 100.099 cents quasi-equal semitone 1: 1 17/16 104.955 cents 17th harmonic 1: 1 96/89 131.075 cents 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 256/233 162.977 cents 1: 1 10/9 182.404 cents minor whole tone 2: 1 89/80 184.566 cents 2: 1 233/208 196.496 cents 2: 1 9/8 203.910 cents major whole tone 2: 1 8/7 231.174 cents septimal whole tone 2: 1 55/48 235.677 cents undecimal semi-augmented whole tone 2: 1 64/55 262.368 cents 2: 1 7/6 266.871 cents septimal minor third 2: 1 272/233 267.932 cents 2: 1 104/89 269.648 cents 2: 1 20/17 281.358 cents septendecimal augmented second 3: 1 6/5 315.641 cents minor third 3: 1 233/192 335.068 cents 3: 1 16/13 359.472 cents tridecimal neutral third 3: 1 21/17 365.825 cents submajor third 3: 1 110/89 366.752 cents 3: 1 288/233 366.887 cents 3: 1 89/72 366.970 cents 3: 1 68/55 367.324 cents 3: 1 26/21 369.747 cents 3: 1 5/4 386.314 cents major third 4: 1 13/10 454.214 cents tridecimal semi-diminished fourth 4: 1 17/13 464.428 cents 4: 1 89/68 465.925 cents 4: 1 233/178 466.143 cents 4: 1 72/55 466.278 cents undecimal semi-diminished fourth 4: 1 55/42 466.851 cents 4: 1 21/16 470.781 cents narrow fourth 4: 2 4/3 498.045 cents perfect fourth 4: 1 320/233 549.290 cents 5: 1 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 18/13 563.382 cents tridecimal augmented fourth 5: 1 233/168 566.242 cents 5: 1 89/64 570.880 cents 5: 1 24/17 597.000 cents 1st septendecimal tritone 5: 1 17/12 603.000 cents 2nd septendecimal tritone 5: 1 128/89 629.120 cents 5: 1 336/233 633.758 cents 5: 1 13/9 636.618 cents tridecimal diminished fifth 5: 1 16/11 648.682 cents undecimal semi-diminished fifth 6: 1 233/160 650.710 cents 6: 2 3/2 701.955 cents perfect fifth 6: 1 32/21 729.219 cents wide fifth 6: 1 84/55 733.149 cents 6: 1 55/36 733.722 cents undecimal semi-augmented fifth 6: 1 356/233 733.857 cents 6: 1 136/89 734.075 cents 6: 1 26/17 735.572 cents 6: 1 20/13 745.786 cents tridecimal semi-augmented fifth 7: 1 8/5 813.686 cents minor sixth 7: 1 21/13 830.253 cents 7: 1 55/34 832.676 cents 7: 1 144/89 833.030 cents 7: 1 233/144 833.113 cents 7: 1 89/55 833.248 cents 7: 1 34/21 834.175 cents supraminor sixth 7: 1 13/8 840.528 cents tridecimal neutral sixth 7: 1 384/233 864.932 cents 7: 1 5/3 884.359 cents major sixth, BP sixth 8: 1 17/10 918.642 cents septendecimal diminished seventh 8: 1 89/52 930.352 cents 8: 1 233/136 932.068 cents 8: 1 12/7 933.129 cents septimal major sixth 8: 1 55/32 937.632 cents 8: 1 96/55 964.323 cents 8: 1 7/4 968.826 cents harmonic seventh 8: 1 16/9 996.090 cents Pythagorean minor seventh 8: 1 416/233 1003.504 cents 8: 1 160/89 1015.434 cents 9: 1 9/5 1017.596 cents just minor seventh, BP seventh 9: 1 233/128 1037.023 cents 9: 1 24/13 1061.427 cents tridecimal neutral seventh 9: 1 89/48 1068.925 cents 9: 1 32/17 1095.045 cents 17th subharmonic 9: 1 168/89 1099.901 cents quasi-equal major seventh 9: 1 440/233 1100.608 cents 9: 1 17/9 1101.045 cents septendecimal major seventh 9: 1 104/55 1102.896 cents 9: 1 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 9.77778 = 88/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 105.0 203.9 386.3 470.8 570.9 702.0 840.5 937.6 1037.0 1200.0 105.0 : 99.0 281.4 365.8 465.9 597.0 735.6 832.7 932.1 1095.0 1200.0 203.9 : 182.4 266.9 367.0 498.0 636.6 733.7 833.1 996.1 1101.0 1200.0 386.3 : 84.5 184.6 315.6 454.2 551.3 650.7 813.7 918.6 1017.6 1200.0 470.8 : 100.1 231.2 369.7 466.9 566.2 729.2 834.2 933.1 1115.5 1200.0 570.9 : 131.1 269.6 366.8 466.1 629.1 734.1 833.0 1015.4 1099.9 1200.0 702.0 : 138.6 235.7 335.1 498.0 603.0 702.0 884.4 968.8 1068.9 1200.0 840.5 : 97.1 196.5 359.5 464.4 563.4 745.8 830.3 930.4 1061.4 1200.0 937.6 : 99.4 262.4 367.3 466.3 648.7 733.1 833.2 964.3 1102.9 1200.0 1037.0: 163.0 267.9 366.9 549.3 633.8 733.9 864.9 1003.5 1100.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 182.4037 cents 200/189, 97.9365 cents 21/20, 84.4672 cents 2: 184.5664 .. 281.3583 cents 1600/1513, 96.7919 cents 801/800, 2.1627 cents 3: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 51/50, 34.2830 cents 4: 454.2139 .. 549.2903 cents 3200/3029, 95.0764 cents 26/25, 67.9002 cents 5: 551.3179 .. 648.6821 cents 128/121, 97.3641 cents 2563/2560, 2.0276 cents 6: 650.7097 .. 745.7861 cents 3200/3029, 95.0764 cents 2563/2560, 2.0276 cents 7: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 26/25, 67.9002 cents 8: 918.6417 .. 1015.4336 cents 1600/1513, 96.7919 cents 51/50, 34.2830 cents 9: 1017.5963 .. 1115.5328 cents 200/189, 97.9365 cents 801/800, 2.1627 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.420670 Largest / Average step : 1.520031 Largest / Smallest step : 2.159462 Median interval of one step : 102.52731 cents, amount: 0 Least squares average step : 117.76345 cents, oct.: 1177.63449 cents Scale is strictly proper Step pattern alph. order: ABCDEFGHIJ Step pattern size order : FCJAEGHBDI Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.02760 cents Scale diversity : 1.508544 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.318068 Rothenberg efficiency : 0.204444 redundancy: 0.795556 Efficiency x scale size : 2.044444 Number of different interval sizes : 88 = 9.77778 / class Number of one step interval sizes : 10 Highest interval variety : 10 Mean interval variety : 9.77778 = 88/9 Median interval variety : 9 Lowest interval variety : 9 Smallest interval difference : 20737/20736, 0.0835 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 Length of longest harmonic part : 2 at degree 0 Formal octave complements present : 1 = 10.0000% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval class 4 Scale is n-1 differentially coherent in interval classes 6 and 7 combined Scale is n-1 differentially coherent in interval class 7 Limited inverse transpositions with margin 78.5094 cents: 2 -- Rational properties -- Prime limit : 233 Odd number limit : 233 (O: 233 U: 233) Highest odd numerator or denominator: 233 Scale harmonicity : 0.009953 Fundamental : 1/128, -7.0000 octaves, 2.0439 Hz. Guide tone : too high to compute Exponens Consonantiae : 4.065195E+12, 41.88646 octaves Euler's gradus suavitatis : 381 Sum of Mann's harmonic distance : 363.0, average 36.30000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.85405, average 1.18541 Sum of Tenney's harmonic distance : 22.69113, average 2.26911 Vogel's harmonic complexity : 42.80000 Wille's k value : 116 Wilson's harmonic complexity : 381 Rectangular lattice diameter : 9 Triangular lattice diameter : 2 Lattice compactness : 187.16644, average 3.40303 Lattice compactness (without 2's) : 69.76320, average 1.26842 Number of different primes : 9 Prime exponents' range, average, count, tones@limit: 2: -7 .. 1 -3.40000 36 1 3: 0 .. 2 0.40000 4 2 5: 0 .. 1 0.20000 2 1 7: 0 .. 1 0.10000 1 1 11: 0 .. 1 0.10000 1 1 13: 0 .. 1 0.10000 1 1 17: 0 .. 1 0.10000 1 1 89: 0 .. 1 0.10000 1 1 233: 0 .. 1 0.10000 1 1 Average exponent except 2's : 12 / 10 = 1.20000 Average absolute exponent except 2's: 12 / 10 = 1.20000 Scale is weakly epimorphic with val: <10 16 23 28 34 38 41 65 79| Scale is JI-epimorphic with val: <10 16 23 28 35 37 41 65 79| = patent Scale is weakly epimorphic with val: <10 16 23 28 36 37 41 65 78| Scale is weakly epimorphic with val: <10 16 23 29 34 38 41 64 79| Scale is weakly epimorphic with val: <10 16 23 29 35 37 41 64 79| Scale is weakly epimorphic with val: <10 16 23 29 36 37 41 64 78| Scale is weakly epimorphic with val: <10 16 24 27 34 37 41 65 79| Scale is weakly epimorphic with val: <10 16 24 27 35 37 41 65 78|
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 24.1401 c. M:-42.9766 c. 12: 1 1 2 1 1 1 1 1 1 2 N D3 S SD: 25.2231 c. M: 40.5277 c. 13: 1 1 2 1 1 1 2 1 1 2 P M ME SD: 22.5582 c. M: 55.8012 c. 15: 1 2 2 1 1 2 2 1 1 2 P D3 SD: 21.6998 c. M:-39.4723 c. 17: 1 2 2 2 1 2 2 1 2 2 P M ME SD: 19.6773 c. M: 34.3672 c. Beatles-10, Dichotic-10 21: 2 2 3 1 2 2 3 1 2 3 N SD: 14.9169 c. M:-24.6614 c. 22: 2 2 3 2 1 3 2 2 2 3 P D3 SD: 13.9664 c. M: 25.4256 c. 23: 2 2 3 2 2 2 3 2 2 3 SP M ME SD: 10.5704 c. M: 23.6941 c. 24: 2 2 4 1 2 3 3 2 2 3 N SD: 12.2878 c. M: 20.8801 c. 26: 2 2 4 2 2 3 3 2 2 4 P D3 S SD: 14.3806 c. M: 21.6388 c. 27: 2 3 4 2 2 3 3 2 2 4 N SD: 12.2188 c. M:-18.3122 c. 28: 2 3 4 2 2 3 4 2 2 4 P SD: 11.4277 c. M: 19.2411 c. 29: 3 2 4 2 3 3 3 3 2 4 SP D3 SD: 11.2230 c. M:-19.1825 c. 31: 3 2 5 2 3 3 4 2 3 4 P SD: 8.1076 c. M:-11.1736 c. 36: 3 3 5 3 3 4 4 3 3 5 SP D3 S SD: 7.4041 c. M: 19.6470 c. 43: 4 3 7 3 3 5 5 4 3 6 N SD: 6.9816 c. M: 12.7406 c. 44: 4 3 7 3 4 5 5 3 4 6 P SD: 6.6613 c. M: 13.0009 c. 46: 4 4 7 3 4 5 5 4 4 6 P SD: 3.7616 c. M:-6.4549 c. 59: 5 5 9 4 5 6 7 5 5 8 P SD: 4.2273 c. M: 10.4296 c. 69: 6 6 10 5 6 7 8 6 6 9 SP SD: 4.0536 c. M:-6.4549 c. 72: 6 6 11 5 6 8 8 6 6 10 P SD: 4.1362 c. M: 7.1943 c. 74: 6 7 11 5 6 8 9 6 6 10 P SD: 4.0492 c. M: 7.6581 c. 77: 7 6 12 5 7 8 9 6 7 10 P SD: 3.6357 c. M:-7.1325 c. 78: 7 6 12 6 6 9 9 6 6 11 P SD: 4.1290 c. M: 6.2541 c. 80: 7 7 12 5 7 9 9 7 6 11 P SD: 3.9091 c. M:-7.3683 c. 81: 7 7 12 6 7 8 10 6 7 11 P SD: 3.7327 c. M:-6.8977 c. 82: 7 7 12 6 7 9 9 7 7 11 SP SD: 3.0574 c. M: 6.3813 c. 84: 7 7 13 6 7 9 10 7 7 11 P SD: 3.3393 c. M:-5.8338 c. 87: 8 7 13 6 7 10 10 7 7 12 P SD: 2.8201 c. M:-5.3894 c. 90: 8 7 14 6 8 10 10 7 8 12 P SD: 3.0183 c. M:-4.7117 c. 94: 8 8 14 7 8 10 11 7 8 13 P SD: 2.8327 c. M: 5.7168 c. 105: 9 9 16 7 9 11 13 8 9 14 P SD: 2.7766 c. M:-5.1866 c. 111: 10 9 17 8 9 12 13 9 9 15 P SD: 2.5660 c. M:-4.8948 c. 113: 10 9 17 8 10 12 13 9 10 15 SP SD: 2.6119 c. M: 4.0128 c. 118: 10 10 18 8 10 13 14 9 10 16 P SD: 1.9641 c. M:-3.5401 c. 137: 12 11 21 10 11 15 16 11 11 19 P SD: 1.6667 c. M: 3.4467 c. 140: 12 12 21 10 12 15 16 11 12 19 P SD: 1.7982 c. M:-3.4056 c. 147: 13 12 22 11 12 16 17 12 12 20 SP SD: 1.3181 c. M:-2.6885 c. 164: 14 14 25 11 14 18 19 13 14 22 P SD: 1.4804 c. M: 2.5164 c. 170: 15 14 26 12 14 19 19 14 14 23 P SD: 1.6777 c. M:-3.9274 c. 171: 15 14 26 12 14 19 20 14 14 23 P SD: 1.3852 c. M:-2.7192 c. 183: 16 15 28 13 15 20 21 15 15 25 P SD: 0.7158 c. M:-1.3502 c. 296: 26 24 45 21 25 32 34 24 25 40 SP SD: 0.8939 c. M: 1.3385 c. 301: 26 25 46 21 25 33 35 24 25 41 P SD: 0.6525 c. M: 1.3009 c. 311: 27 26 47 22 26 34 36 25 26 42 SP SD: 0.5027 c. M:-0.9187 c. 441: 39 36 67 31 37 48 51 36 36 60 SP SD: 0.5641 c. M:-1.1670 c. 448: 39 37 68 32 37 49 52 36 37 61 SP SD: 0.4205 c. M:-0.6477 c. 494: 43 41 75 35 41 54 57 40 41 67 SP SD: 0.2367 c. M: 0.5020 c. 742: 65 61 113 52 62 81 86 60 61 101 SP SD: 0.2429 c. M:-0.4427 c. 788: 69 65 120 55 66 86 91 64 65 107 SP SD: 0.2380 c. M:-0.4883 c. 824: 72 68 125 58 69 90 95 67 68 112 SP SD: 0.2110 c. M: 0.3926 c. 935: 82 77 142 66 78 102 108 76 77 127 SP SD: 0.2327 c. M:-0.5502 c. 971: 85 80 148 68 81 106 112 79 80 132 SP SD: 0.2143 c. M:-0.5040 c. 1007: 88 83 153 71 84 110 116 82 83 137 SP SD: 0.1941 c. M: 0.4085 c. 1053: 92 87 160 74 88 115 122 85 87 143 SP SD: 0.1886 c. M:-0.4980 c. 1084: 95 89 165 76 91 118 125 88 90 147 SP SD: 0.2156 c. M:-0.3376 c. 1089: 95 90 166 76 91 119 126 88 90 148 SP SD: 0.2117 c. M:-0.4631 c. 1099: 96 91 167 77 92 120 127 89 91 149 SP SD: 0.2139 c. M:-0.3119 c. 1106: 97 91 168 78 92 121 128 89 92 150 SP SD: 0.1848 c. M:-0.3403 c. 1125: 98 93 171 79 94 123 130 91 93 153 SP SD: 0.2216 c. M: 0.4221 c. 1135: 99 94 172 80 95 124 131 92 94 154 SP SD: 0.2044 c. M: 0.4106 c. 1142: 100 94 174 80 95 125 132 92 95 155 SP SD: 0.1956 c. M:-0.3763 c. 1236: 108 102 188 87 103 135 143 100 102 168 SP SD: 0.1271 c. M:-0.2490 c. 1282: 112 106 195 90 107 140 148 104 106 174 SP SD: 0.1470 c. M:-0.2779 c. 1318: 115 109 200 93 110 144 152 107 109 179 SP SD: 0.1396 c. M: 0.2743 c. 1532: 134 126 233 108 128 167 177 124 127 208 SP SD: 0.1145 c. M: 0.2546 c. 1578: 138 130 240 111 132 172 182 128 131 214 SP SD: 0.1322 c. M:-0.2390 c. 1600: 140 132 243 113 133 175 185 129 133 217 SP SD: 0.1411 c. M:-0.2266 c. 1619: 142 133 246 114 135 177 187 131 134 220 SP SD: 0.1282 c. M:-0.2947 c. 1665: 146 137 253 117 139 182 192 135 138 226 SP SD: 0.1189 c. M:-0.2698 c. 1723: 151 142 262 121 144 188 199 139 143 234 SP SD: 0.1478 c. M:-0.2214 c. 1730: 151 143 263 122 144 189 200 140 143 235 SP SD: 0.1216 c. M: 0.2155 c. 1843: 161 152 280 130 154 201 213 149 153 250 SP SD: 0.1178 c. M: 0.2041 c. 1894: 166 156 288 133 158 207 219 153 157 257 SP SD: 0.1310 c. M:-0.2326 c. 1907: 167 157 290 134 159 209 220 154 158 259 SP SD: 0.1294 c. M:-0.2998 c. 1930: 169 159 293 136 161 211 223 156 160 262 SP SD: 0.0963 c. M: 0.1997 c. 1966: 172 162 299 138 164 215 227 159 163 267 SP SD: 0.0900 c. M: 0.1807 c. 2026: 177 167 308 143 169 221 234 164 168 275 SP SD: 0.0973 c. M: 0.1588 c. 2113: 185 174 321 149 176 231 244 171 175 287 SP SD: 0.0691 c. M: 0.1329 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x x 6 S SD: 17.2062 cents 4 x x 5 x x 6 x 7 x 8 S SD: 7.7986 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 15.7832 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 13.7243 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 13.3866 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 7.8877 cents 9 x 10:11:12 x 14:15 x 16:18 S SD: 14.4845 cents 10 x 11 x 13:14:15:16:17:18:20 SD: 7.2693 cents 11:12 x 14 x 15:17:18:19:20:22 SD: 10.5365 cents 12:13:14:15:16:17:18:20:21:22:24 S SD: 9.9578 cents 13:14:15:16:17:18:20:21:22:24:26 S SD: 8.1399 cents 14:15:16 x 18:19:21:23:24:25:28 SD: 8.2325 cents 15:16:17:19:20:21:23:24:26:27:30 SD: 6.6131 cents 16:17:18:20:21:22:24:26:28:29:32 SD: 3.7566 cents 29:31:33:36:38:40:44:47:50:53:58 SD: 3.6648 cents 31:33:35:39:41:43:47:50:53:56:62 SD: 3.3721 cents 32:34:36:40:42:45:48:52:55:58:64 SD: 2.0727 cents 48:51:54:60:63:67:72:78:83:87:96 SD: 1.4379 cents 64:68:72:80:84:89:96:104:110:117:128 SD: 0.7414 cents 96:102:108:120:126:134:144:156:165:175:192 SD: 0.6929 cents 112:119:126:140:147:156:168:182:193:204:224 SD: 0.5386 cents 128:136:144:160:168:178:192:208:220:233:256 SD: 0.0000 cents