Scala analysis: xen13-mclaren-recurrence-1
Fibonacci scale (recurrence scale #1)
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: 5/4 386.313714 major third 3: 21/16 470.780907 narrow fourth 4: 89/64 570.880117 5: 3/2 701.955001 perfect fifth 6: 13/8 840.527662 tridecimal neutral sixth 7: 55/32 937.631656 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 64/55 262.3683 1: 17/16 104.9554 17th harmonic 2: 20/17 281.3583 septendecimal augmented second 3: 21/20 84.4672 minor semitone 4: 89/84 100.0992 quasi-equal semitone 5: 96/89 131.0749 6: 13/12 138.5727 tridecimal 2/3-tone 7: 55/52 97.1040 8: 64/55 262.3683
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 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 64/55 262.368 cents 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 89/80 184.566 cents 2: 1 8/7 231.174 cents septimal whole tone 2: 1 55/48 235.677 cents undecimal semi-augmented whole tone 2: 1 104/89 269.648 cents 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 21/17 365.825 cents submajor third 2: 1 68/55 367.324 cents 2: 1 5/4 386.314 cents major third 3: 1 6/5 315.641 cents minor third 3: 1 110/89 366.752 cents 3: 1 26/21 369.747 cents 3: 1 17/13 464.428 cents 3: 1 89/68 465.925 cents 3: 1 21/16 470.781 cents narrow fourth 3: 1 4/3 498.045 cents perfect fourth 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 13/10 454.214 cents tridecimal semi-diminished fourth 4: 1 55/42 466.851 cents 4: 1 89/64 570.880 cents 4: 1 24/17 597.000 cents 1st septendecimal tritone 4: 1 17/12 603.000 cents 2nd septendecimal tritone 4: 1 128/89 629.120 cents 4: 1 84/55 733.149 cents 4: 1 20/13 745.786 cents tridecimal semi-augmented fifth 5: 1 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 3/2 701.955 cents perfect fifth 5: 1 32/21 729.219 cents wide fifth 5: 1 136/89 734.075 cents 5: 1 26/17 735.572 cents 5: 1 21/13 830.253 cents 5: 1 89/55 833.248 cents 5: 1 5/3 884.359 cents major sixth, BP sixth 6: 1 8/5 813.686 cents minor sixth 6: 1 55/34 832.676 cents 6: 1 34/21 834.175 cents supraminor sixth 6: 1 13/8 840.528 cents tridecimal neutral sixth 6: 1 89/52 930.352 cents 6: 1 96/55 964.323 cents 6: 1 7/4 968.826 cents harmonic seventh 6: 1 160/89 1015.434 cents 7: 1 17/10 918.642 cents septendecimal diminished seventh 7: 1 55/32 937.632 cents 7: 1 24/13 1061.427 cents tridecimal neutral seventh 7: 1 89/48 1068.925 cents 7: 1 32/17 1095.045 cents 17th subharmonic 7: 1 168/89 1099.901 cents quasi-equal major seventh 7: 1 104/55 1102.896 cents 7: 1 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 105.0 386.3 470.8 570.9 702.0 840.5 937.6 1200.0 105.0 : 281.4 365.8 465.9 597.0 735.6 832.7 1095.0 1200.0 386.3 : 84.5 184.6 315.6 454.2 551.3 813.7 918.6 1200.0 470.8 : 100.1 231.2 369.7 466.9 729.2 834.2 1115.5 1200.0 570.9 : 131.1 269.6 366.8 629.1 734.1 1015.4 1099.9 1200.0 702.0 : 138.6 235.7 498.0 603.0 884.4 968.8 1068.9 1200.0 840.5 : 97.1 359.5 464.4 745.8 830.3 930.4 1061.4 1200.0 937.6 : 262.4 367.3 648.7 733.1 833.2 964.3 1102.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 281.3583 cents 400/357, 196.8911 cents 21/20, 84.4672 cents 2: 184.5664 .. 386.3137 cents 100/89, 201.7473 cents 1513/1600,-96.7919 cents 3: 315.6413 .. 648.6821 cents 40/33, 333.0408 cents 24/25,-70.6724 cents 4: 454.2139 .. 745.7861 cents 200/169, 291.5721 cents 143/160,-194.4681 cents 5: 551.3179 .. 884.3587 cents 40/33, 333.0408 cents 143/160,-194.4681 cents 6: 813.6863 .. 1015.4336 cents 100/89, 201.7473 cents 24/25,-70.6724 cents 7: 918.6417 .. 1115.5328 cents 400/357, 196.8911 cents 1513/1600,-96.7919 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 1.775837 Largest / Average step : 1.875722 Largest / Smallest step : 3.330977 Median interval of one step : 118.01515 cents, amount: 0 Least squares average step : 143.57749 cents, oct.: 1148.61994 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : DHACEFBG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.57221 cents Scale diversity : 1.595442 Lumma stability : 0.140779 Lumma impropriety factor : 0.522084 Rothenberg efficiency : 0.250000 redundancy: 0.750000 Efficiency x scale size : 2.000000 Number of different interval sizes : 56 = 8.00000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 8.00000 = 8 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 3026/3025, 0.5722 cents Number of recognisable fifths : 1, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 12.5000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is 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 classes 5 and 6 combined -- Rational properties -- Prime limit : 89 Odd number limit : 89 (O: 89 U: 89) Highest odd numerator or denominator: 89 Scale harmonicity : 0.010330 Fundamental : 1/64, -6.0000 octaves, 4.0879 Hz. Guide tone : 45435390, 25.4373 octaves, 11887059593.421 Hz. Exponens Consonantiae : 2.907865E+09, 31.43731 octaves Euler's gradus suavitatis : 146 Sum of Mann's harmonic distance : 174.0, average 21.75000 Mersenne's string divisions : 63205065 Sum of van Prooijen's expressibility: 8.53246, average 1.06656 Sum of Tenney's harmonic distance : 16.35924, average 2.04490 Vogel's harmonic complexity : 22.12500 Wille's k value : 44 Wilson's harmonic complexity : 145 Rectangular lattice diameter : 7 Triangular lattice diameter : 2 Lattice compactness : 116.51234, average 3.23645 Lattice compactness (without 2's) : 43.36287, average 1.20452 Number of different primes : 8 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -3.00000 26 1 3: 0 .. 1 0.25000 2 1 5: 0 .. 1 0.25000 2 1 7: 0 .. 1 0.12500 1 1 11: 0 .. 1 0.12500 1 1 13: 0 .. 1 0.12500 1 1 17: 0 .. 1 0.12500 1 1 89: 0 .. 1 0.12500 1 1 Average exponent except 2's : 9 / 8 = 1.12500 Average absolute exponent except 2's: 9 / 8 = 1.12500 Scale is weakly epimorphic with val: <8 12 18 21 28 31 35 53| Scale is weakly epimorphic with val: <8 12 18 21 29 30 35 53| Scale is weakly epimorphic with val: <8 12 18 23 28 31 33 53| Scale is weakly epimorphic with val: <8 12 18 23 29 30 33 53| Scale is weakly epimorphic with val: <8 12 19 21 27 31 34 53| Scale is weakly epimorphic with val: <8 12 19 21 28 30 34 53| Scale is weakly epimorphic with val: <8 12 19 22 27 31 33 53| Scale is weakly epimorphic with val: <8 12 19 22 28 30 33 53| Scale is weakly epimorphic with val: <8 13 18 22 28 31 33 52| Scale is JI-epimorphic with val: <8 13 18 22 29 30 33 52| Scale is weakly epimorphic with val: <8 13 18 23 28 31 33 51| Scale is weakly epimorphic with val: <8 13 18 23 29 30 33 51| Scale is weakly epimorphic with val: <8 13 19 21 27 31 33 52| Scale is weakly epimorphic with val: <8 13 19 21 28 30 33 52| Scale is weakly epimorphic with val: <8 13 20 21 27 30 33 51| Scale is weakly epimorphic with val: <8 14 18 21 27 31 33 52| Scale is weakly epimorphic with val: <8 14 18 21 29 29 33 52| Scale is weakly epimorphic with val: <8 14 18 22 27 31 33 51| Scale is weakly epimorphic with val: <8 14 18 22 29 29 33 51| Scale is weakly epimorphic with val: <8 14 20 21 29 31 34 53| Scale is weakly epimorphic with val: <8 14 20 23 29 31 34 51|
FIT/MODE
8: 0 2 1 0 1 1 1 2 N T3 SD: 81.7892 c. M: 120.8801 c. 9: 1 2 0 1 1 1 1 2 N SD: 35.9141 c. M: 70.7809 c. 10: 1 2 1 1 1 1 1 2 N D3 SD: 18.2960 c. M:-29.1199 c. 19: 2 4 1 2 2 2 2 4 N SD: 15.2686 c. M: 28.6756 c. 21: 2 5 1 2 2 3 1 5 N SD: 13.8993 c. M: 23.3459 c. 23: 2 5 2 2 2 3 2 5 N SD: 11.4715 c. M: 23.6941 c. 24: 2 6 1 2 3 3 2 5 N SD: 12.8755 c. M: 20.8801 c. 26: 2 6 2 2 3 3 2 6 N SD: 12.3870 c. M: 17.0829 c. 27: 2 7 2 2 3 3 2 6 N SD: 10.8315 c. M:-18.1080 c. 31: 3 7 2 3 3 4 2 7 N SD: 7.7761 c. M:-11.1736 c. 34: 3 8 2 3 4 4 3 7 N SD: 7.7307 c. M:-15.3095 c. 38: 3 9 3 3 4 5 3 8 N SD: 7.6368 c. M:-12.1039 c. 41: 4 9 3 4 4 5 3 9 N SD: 7.6342 c. M:-14.4857 c. 43: 4 10 3 3 5 5 4 9 N SD: 7.0196 c. M: 12.7406 c. 44: 4 10 3 4 5 5 3 10 N SD: 5.8552 c. M: 10.3589 c. 46: 4 11 3 4 5 5 4 10 N SD: 3.1010 c. M: 5.7451 c. 77: 7 18 5 7 8 9 6 17 N SD: 3.1541 c. M:-5.7433 c. 84: 7 20 6 7 9 10 7 18 N SD: 2.7881 c. M:-5.2255 c. 90: 8 21 6 8 10 10 7 20 N SD: 2.8929 c. M:-4.7117 c. 91: 8 21 7 7 10 11 7 20 N SD: 2.9322 c. M:-3.9444 c. 97: 8 23 7 8 11 11 8 21 N SD: 2.8465 c. M: 5.9863 c. 99: 9 23 7 8 11 11 8 22 N SD: 2.7774 c. M: 4.2983 c. 111: 10 26 8 9 12 13 9 24 N SD: 2.8049 c. M:-4.8948 c. 113: 10 26 8 10 12 13 9 25 N SD: 2.5017 c. M: 4.0128 c. 114: 10 27 8 9 13 13 9 25 N SD: 2.1969 c. M:-3.3082 c. 118: 10 28 8 10 13 14 9 26 N SD: 2.1862 c. M:-3.5401 c. 124: 11 29 9 10 14 14 10 27 N SD: 2.1757 c. M:-4.4966 c. 127: 11 30 9 10 14 15 10 28 N SD: 2.0346 c. M: 3.9510 c. 128: 11 30 9 11 14 15 10 28 N SD: 1.7318 c. M:-3.2223 c. 137: 12 32 10 11 15 16 11 30 N SD: 1.1123 c. M:-2.2118 c. 173: 15 41 12 14 19 20 14 38 N SD: 1.3873 c. M:-2.1256 c. 174: 15 41 12 15 19 20 14 38 N SD: 1.1713 c. M: 1.8154 c. 183: 16 43 13 15 20 21 15 40 N SD: 0.6899 c. M:-1.3502 c. 296: 26 69 21 25 32 34 24 65 N SD: 0.8566 c. M: 1.3385 c. 298: 26 70 21 25 32 35 24 65 N SD: 0.7369 c. M: 1.2839 c. 301: 26 71 21 25 33 35 24 66 N SD: 0.6786 c. M: 1.3009 c. 311: 27 73 22 26 34 36 25 68 N SD: 0.4082 c. M: 0.7753 c. 357: 31 84 25 30 39 41 29 78 N SD: 0.4115 c. M: 0.7537 c. 444: 39 104 31 37 49 51 36 97 N SD: 0.4282 c. M:-0.7477 c. 448: 39 105 32 37 49 52 36 98 N SD: 0.4302 c. M:-0.6477 c. 494: 43 116 35 41 54 57 40 108 N SD: 0.2477 c. M: 0.5020 c. 708: 62 166 50 59 77 82 57 155 N SD: 0.2498 c. M:-0.4055 c. 742: 65 174 52 62 81 86 60 162 N SD: 0.2339 c. M:-0.4427 c. 814: 71 191 57 68 89 94 66 178 N SD: 0.2721 c. M: 0.5106 c. 824: 72 193 58 69 90 95 67 180 N SD: 0.2312 c. M: 0.3926 c. 925: 81 217 65 77 101 107 75 202 N SD: 0.1752 c. M:-0.3143 c. 1015: 89 238 71 85 111 117 82 222 N SD: 0.2074 c. M:-0.3110 c. 1019: 89 239 72 85 111 118 82 223 N SD: 0.2011 c. M:-0.2967 c. 1038: 91 243 73 87 113 120 84 227 N SD: 0.1830 c. M: 0.2607 c. 1152: 101 270 81 96 126 133 93 252 N SD: 0.1290 c. M:-0.2529 c. 1221: 107 286 86 102 133 141 99 267 N SD: 0.1478 c. M: 0.2351 c. 1236: 108 290 87 103 135 143 100 270 N SD: 0.1341 c. M:-0.2490 c. 1335: 117 313 94 111 146 154 108 292 N SD: 0.1457 c. M:-0.2303 c. 1395: 122 327 98 117 152 161 113 305 N SD: 0.1444 c. M:-0.3027 c. 1419: 124 333 100 118 155 164 115 310 N SD: 0.1382 c. M:-0.2550 c. 1463: 128 343 103 122 160 169 118 320 N SD: 0.1030 c. M:-0.2105 c. 1509: 132 354 106 126 165 174 122 330 N SD: 0.1090 c. M:-0.2319 c. 1522: 133 357 107 127 166 176 123 333 N SD: 0.1202 c. M: 0.2467 c. 1532: 134 359 108 128 167 177 124 335 N SD: 0.0890 c. M: 0.1518 c. 1646: 144 386 116 137 180 190 133 360 N SD: 0.0889 c. M:-0.1790 c. 1957: 171 459 138 163 214 226 158 428 N SD: 0.0986 c. M:-0.1468 c. 1976: 173 463 139 165 216 228 160 432 N SD: 0.0732 c. M: 0.1331 c. 2113: 185 495 149 176 231 244 171 462 N SD: 0.0763 c. M: 0.1329 c. 2159: 189 506 152 180 236 249 175 472 N SD: 0.0653 c. M: 0.1386 c. 2274: 199 533 160 190 248 263 184 497 N SD: 0.0799 c. M: 0.1080 c. 2287: 200 536 161 191 250 264 185 500 N SD: 0.0747 c. M: 0.1309 c. 2388: 209 560 168 199 261 276 193 522 N SD: 0.0881 c. M:-0.1759 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x x 5 x 6 S SD: 17.2062 cents 4 x 5 x x 6 x 7:8 S SD: 7.7986 cents 5 x 6 x 7 x 8:9:10 S SD: 22.1312 cents 6 x x 8 x 9:10 x 12 S SD: 12.9047 cents 7:8 x 9:10 x 11:12:14 S SD: 25.1474 cents 8:9:10 x 11:12:13:14:16 S SD: 15.0833 cents 9:10:11:12 x 14:15 x 18 S SD: 19.8189 cents 10:11 x 13:14:15:16:17:20 SD: 10.1987 cents 11:12:14 x 15:17:18:19:22 SD: 12.0383 cents 12:13:15:16:17:18:20:21:24 SD: 9.5192 cents 13:14:16:17:18:20:21:22:26 SD: 8.0128 cents 14:15 x 18:19:21:23:24:28 SD: 8.6221 cents 15:16:19:20:21:23:24:26:30 SD: 7.7385 cents 16:17:20:21:22:24:26:28:32 SD: 4.6026 cents 28:30:35:37:39:42:46:48:56 SD: 3.3857 cents 32:34:40:42:45:48:52:55:64 SD: 2.4179 cents 48:51:60:63:67:72:78:83:96 SD: 1.5376 cents 64:68:80:84:89:96:104:110:128 SD: 0.0000 cents