Scala analysis: xen13-mclaren-recurrence-2
Recurrence scale #2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 65/64 26.841376 13th-partial chroma 2: 2273/2048 180.458363 3: 321/256 391.715385 4: 3/2 701.955001 perfect fifth 5: 107587/65536 858.173086 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 65/64 26.8414 13th-partial chroma 2: 2273/2080 153.6170 3: 2568/2273 211.2570 4: 128/107 310.2396 5: 107587/98304 156.2181 6: 114688/107587 110.6528 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 65/64 26.841 cents 13th-partial chroma 1: 1 114688/107587 110.653 cents 1: 1 2273/2080 153.617 cents 1: 1 107587/98304 156.218 cents 1: 1 2568/2273 211.257 cents 1: 1 8/7 231.174 cents septimal whole tone 1: 1 128/107 310.240 cents 2: 1 2273/2048 180.458 cents 2: 1 65/56 258.015 cents 2: 1 7/6 266.871 cents septimal minor third 2: 1 131072/107587 341.827 cents 2: 1 321/260 364.874 cents 2: 1 107587/82176 466.458 cents 2: 1 3072/2273 521.497 cents 3: 1 133120/107587 368.668 cents 3: 1 321/256 391.715 cents 3: 1 2273/1792 411.632 cents 3: 1 4/3 498.045 cents perfect fourth 3: 1 448/321 577.111 cents 3: 1 96/65 675.114 cents 3: 1 107587/72736 677.715 cents 4: 1 145472/107587 522.285 cents 4: 1 65/48 524.886 cents 4: 1 321/224 622.889 cents 4: 1 3/2 701.955 cents perfect fifth 4: 1 3584/2273 788.368 cents 4: 1 512/321 808.285 cents 4: 1 107587/66560 831.332 cents 5: 1 2273/1536 678.503 cents 5: 1 164352/107587 733.542 cents 5: 1 520/321 835.126 cents 5: 1 107587/65536 858.173 cents 5: 1 12/7 933.129 cents septimal major sixth 5: 1 112/65 941.985 cents 5: 1 4096/2273 1019.542 cents 6: 1 107/64 889.760 cents 6: 1 7/4 968.826 cents harmonic seventh 6: 1 2273/1284 988.743 cents 6: 1 196608/107587 1043.782 cents 6: 1 4160/2273 1046.383 cents 6: 1 107587/57344 1089.347 cents 6: 1 128/65 1173.159 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 26.8 180.5 391.7 702.0 858.2 968.8 1200.0 26.8 : 153.6 364.9 675.1 831.3 942.0 1173.2 1200.0 180.5 : 211.3 521.5 677.7 788.4 1019.5 1046.4 1200.0 391.7 : 310.2 466.5 577.1 808.3 835.1 988.7 1200.0 702.0 : 156.2 266.9 498.0 524.9 678.5 889.8 1200.0 858.2 : 110.7 341.8 368.7 522.3 733.5 1043.8 1200.0 968.8 : 231.2 258.0 411.6 622.9 933.1 1089.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.8414 .. 310.2396 cents 8192/6955, 283.3982 cents 65/64, 26.8414 cents 2: 180.4584 .. 521.4966 cents 6291456/5166529, 341.0383 cents 243211/262144,-129.7813 cents 3: 368.6683 .. 677.7147 cents 309.04643 cents 295490/322761,-152.8283 cents 4: 522.2853 .. 831.3317 cents 309.04643 cents -155.42945 cents 5: 678.5034 .. 1019.5416 cents 6291456/5166529, 341.0383 cents 295490/322761,-152.8283 cents 6: 889.7604 .. 1173.1586 cents 8192/6955, 283.3982 cents 243211/262144,-129.7813 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 65/64, 26.8414 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 128/107, 310.2396 cents Average / Smallest step : 6.386728 Largest / Average step : 1.809731 Largest / Smallest step : 11.558261 Median interval of one step : 107587/98304, 156.2181 cents, amount: 1 Least squares average step : 163.38961 cents, oct.: 1143.72726 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : ACEGDBF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.78864 cents Scale diversity : 1.726534 Lumma stability : 0.044736 Lumma impropriety factor : 0.600541 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 5166529/5164176, 0.7886 cents Number of recognisable fifths : 1, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% -- Rational properties -- Prime limit : 2273 Odd number limit : 107587 (O: 107587 U: 107587) Highest odd numerator or denominator: 107587 Harmonicity values : limit above prime count Fundamental : 1/65536, -16.0000 octaves, 0.0040 Hz. Guide tone : too high to compute Sum of Mann's harmonic distance : 89084.5, average 12726.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.03000, average 2.00429 Sum of Tenney's harmonic distance : 27.57635, average 3.93948 Vogel's harmonic complexity : 449.71429 Wille's k value : 53793 Lattice compactness : 203.35915, average 7.26283 Lattice compactness (without 2's) : 25.68143, average 0.91719 Number of different primes : 9 Prime exponents' range, average, count, tones@limit: 2: -16 .. 1 -6.14286 45 1 3: 0 .. 1 0.28571 2 1 5: 0 .. 1 0.14286 1 7: 0 .. 1 0.14286 1 1 13: 0 .. 1 0.14286 1 1 107: 0 .. 1 0.14286 1 1 271: 0 .. 1 0.14286 1 397: 0 .. 1 0.14286 1 1 2273: 0 .. 1 0.14286 1 1 Average exponent except 2's : 9 / 7 = 1.28571 Average absolute exponent except 2's: 9 / 7 = 1.28571
FIT/MODE
7: 0 1 1 2 1 1 1 N T3 SD: 31.6758 c. M:-59.7455 c. 9: 0 1 2 2 1 1 2 N SD: 35.6550 c. M: 58.1731 c. 10: 0 1 2 3 1 1 2 N SD: 29.5570 c. M: 60.4584 c. 11: 0 2 2 2 2 1 2 N SD: 31.0881 c. M: 47.4095 c. 12: 0 2 2 3 2 1 2 N SD: 23.5921 c. M:-41.8269 c. 14: 0 2 2 4 2 1 3 N SD: 24.2850 c. M: 48.8582 c. 15: 0 2 3 4 2 1 3 N SD: 17.2692 c. M: 26.8414 c. 21: 0 3 4 5 3 2 4 N SD: 12.7740 c. M: 26.8414 c. 24: 1 3 4 6 3 2 5 N SD: 14.2020 c. M:-23.1586 c. 25: 1 3 4 7 3 2 5 N SD: 12.4091 c. M:-21.1586 c. 27: 1 3 5 7 3 3 5 N SD: 10.2688 c. M:-17.6031 c. 31: 1 4 5 8 4 3 6 N SD: 7.6025 c. M:-13.0900 c. 36: 1 4 7 9 5 3 7 N SD: 7.3835 c. M: 13.7917 c. 38: 1 5 6 10 5 4 7 N SD: 8.0356 c. M: 12.7680 c. 39: 1 5 7 10 5 4 7 N SD: 7.5109 c. M:-15.7895 c. 40: 1 5 7 10 6 3 8 N SD: 7.3078 c. M: 11.9550 c. 41: 1 5 7 11 5 4 8 N SD: 6.0089 c. M: 11.2276 c. 45: 1 6 8 11 6 4 9 N SD: 6.3568 c. M: 8.8259 c. 46: 1 6 8 12 6 4 9 N SD: 2.1173 c. M: 3.6085 c. 94: 2 12 17 24 12 9 18 N SD: 2.1064 c. M:-4.0293 c. 120: 3 15 21 31 16 11 23 N SD: 1.7594 c. M:-3.1586 c. 126: 3 16 22 33 16 12 24 N SD: 1.7108 c. M:-2.8069 c. 140: 3 18 25 36 18 13 27 N SD: 1.1968 c. M:-2.5703 c. 166: 4 21 29 43 22 15 32 N SD: 1.2574 c. M:-2.0743 c. 171: 4 22 30 44 22 16 33 N SD: 1.2785 c. M: 2.0327 c. 172: 4 22 30 45 22 16 33 N SD: 1.2653 c. M:-2.6962 c. 178: 4 23 31 46 23 17 34 N SD: 1.2799 c. M: 1.9933 c. 186: 4 24 33 48 24 17 36 N SD: 1.0189 c. M:-1.8330 c. 193: 4 25 34 50 25 18 37 N SD: 0.8936 c. M: 1.9709 c. 214: 5 27 38 55 28 20 41 N SD: 0.9120 c. M:-1.2676 c. 224: 5 29 39 58 29 21 43 N SD: 0.8462 c. M:-1.6845 c. 239: 5 31 42 62 31 22 46 N SD: 0.7808 c. M: 1.7368 c. 260: 6 33 46 67 34 24 50 N SD: 0.4936 c. M:-0.8509 c. 306: 7 39 54 79 40 28 59 N SD: 0.3842 c. M:-0.6504 c. 453: 10 58 80 117 59 42 87 N SD: 0.3506 c. M:-0.7105 c. 484: 11 62 85 125 63 45 93 N SD: 0.3818 c. M:-0.5956 c. 499: 11 64 88 129 65 46 96 N SD: 0.2701 c. M: 0.3885 c. 674: 15 86 119 174 88 62 130 N SD: 0.3217 c. M: 0.6364 c. 711: 16 91 125 184 92 66 137 N SD: 0.3200 c. M: 0.7891 c. 716: 16 92 126 185 93 66 138 N SD: 0.2953 c. M:-0.5472 c. 720: 16 92 127 186 94 66 139 N SD: 0.2914 c. M: 0.4926 c. 723: 16 93 127 187 94 67 139 N SD: 0.2749 c. M:-0.4687 c. 759: 17 97 134 196 99 70 146 N SD: 0.2446 c. M:-0.3795 c. 800: 18 102 141 207 104 74 154 N SD: 0.2217 c. M: 0.4584 c. 805: 18 103 142 208 105 74 155 N SD: 0.2298 c. M:-0.4605 c. 836: 19 107 147 216 109 77 161 N SD: 0.2444 c. M:-0.4314 c. 846: 19 108 149 219 110 78 163 N SD: 0.1666 c. M: 0.3165 c. 892: 20 114 157 231 116 82 172 N SD: 0.1851 c. M:-0.2872 c. 898: 20 115 158 232 117 83 173 N SD: 0.1987 c. M: 0.3960 c. 944: 21 121 166 244 123 87 182 N SD: 0.1584 c. M: 0.2601 c. 1063: 24 136 187 275 138 98 205 N SD: 0.1868 c. M:-0.2518 c. 1070: 24 137 188 277 139 99 206 N SD: 0.1683 c. M: 0.3135 c. 1116: 25 143 196 289 145 103 215 N SD: 0.1636 c. M: 0.3175 c. 1152: 26 147 203 298 150 106 222 N SD: 0.1565 c. M: 0.2500 c. 1204: 27 154 212 311 157 111 232 N SD: 0.1191 c. M: 0.2939 c. 1250: 28 160 220 323 163 115 241 N SD: 0.1071 c. M: 0.1950 c. 1376: 31 176 242 356 179 127 265 N SD: 0.1036 c. M:-0.1935 c. 1422: 32 182 250 368 185 131 274 N SD: 0.1178 c. M:-0.1628 c. 1443: 32 185 254 373 188 133 278 N SD: 0.0946 c. M: 0.2301 c. 1516: 34 194 267 392 197 140 292 N SD: 0.0911 c. M:-0.1558 c. 1703: 38 218 300 440 222 157 328 N SD: 0.0757 c. M: 0.1347 c. 1749: 39 224 308 452 228 161 337 N SD: 0.0733 c. M:-0.1460 c. 1875: 42 240 330 485 244 173 361 N SD: 0.0768 c. M:-0.1341 c. 2096: 47 268 369 542 273 193 404 N SD: 0.0835 c. M: 0.1236 c. 2181: 49 279 384 564 284 201 420 N SD: 0.0900 c. M:-0.1488 c. 2190: 49 280 386 566 285 202 422 N SD: 0.0857 c. M: 0.1844 c. 2233: 50 286 393 577 291 206 430 N SD: 0.0748 c. M: 0.1189 c. 2279: 51 292 401 589 297 210 439 N SD: 0.0734 c. M:-0.1472 c. 2289: 51 293 403 592 298 211 441 N SD: 0.0720 c. M: 0.1176 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 36.5022 cents 4 x x 5:6 x 7:8 S SD: 1.3504 cents 5 x x 6 x 8:9:10 S SD: 25.1805 cents 6 x 7:8:9:10:11:12 S SD: 26.8458 cents 7 x 8:9 x x 12:14 S SD: 18.9196 cents 8 x 9:10:12:13:14:16 S SD: 4.9736 cents 9 x 10:11:14:15:16:18 SD: 14.2984 cents 10 x 11:13:15:16:18:20 SD: 15.3682 cents 11 x 12:14:17:18:19:22 SD: 11.5096 cents 12 x 13:15:18:20:21:24 SD: 8.2820 cents 13 x 14:16:20:21:23:26 SD: 13.7628 cents 14 x 16:18:21:23:25:28 SD: 12.5586 cents 15 x 17:19:23:25:26:30 SD: 10.5774 cents 16 x 18:20:24:26:28:32 S SD: 4.9736 cents 28:29:31:35:42:46:49:56 SD: 4.9461 cents 34:35:38:43:51:56:60:68 SD: 4.8531 cents 35:36:39:44:53:57:61:70 SD: 4.6495 cents 36:37:40:45:54:59:63:72 SD: 3.0822 cents 44:45:49:55:66:72:77:88 SD: 2.2150 cents 48:49:53:60:72:79:84:96 SD: 2.0524 cents 52:53:58:65:78:85:91:104 SD: 1.9993 cents 55:56:61:69:83:90:96:110 SD: 1.9274 cents 56:57:62:70:84:92:98:112 SD: 1.1366 cents 64:65:71:80:96:105:112:128 SD: 0.7944 cents 118:120:131:148:177:194:207:236 SD: 0.7767 cents 126:128:140:158:189:207:221:252 SD: 0.6542 cents 176:179:195:221:264:289:308:352 SD: 0.6533 cents 180:183:200:226:270:295:315:360 SD: 0.6482 cents 181:184:201:227:272:297:317:362 SD: 0.5779 cents 182:185:202:228:273:299:319:364 SD: 0.5289 cents 184:187:204:231:276:302:322:368 SD: 0.4343 cents 192:195:213:241:288:315:336:384 SD: 0.3185 cents 248:252:275:311:372:407:434:496 SD: 0.2659 cents 256:260:284:321:384:420:448:512 SD: 0.1886 cents 444:451:493:557:666:729:777:888 SD: 0.1694 cents 500:508:555:627:750:821:875:1000 SD: 0.1115 cents 508:516:564:637:762:834:889:1016 SD: 0.0895 cents