Scala analysis: xen13-mclaren-finite-continued-fraction-1
Finite continued fraction scale #1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 48.765 cents 48.764600 2: 82.404 cents 82.403700 3: 231.172 cents 231.172400 4: 266.876 cents 266.875800 5: 315.641 cents 315.641200 6: 498.045 cents 498.044900 7: 884.359 cents 884.358600 8: 933.128 cents 933.128400 9: 1151.316 cents 1151.315600
SHOW/INTERVAL
0: 218.1872 cents 218.1872 1: 48.7646 cents 48.7646 2: 33.6391 cents 33.6391 3: 148.7687 cents 148.7687 4: 35.7034 cents 35.7034 5: 48.7654 cents 48.7654 6: 182.4037 cents 182.4037 7: 386.3137 cents 386.3137 8: 48.7698 cents 48.7698 9: 218.1872 cents 218.1872
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.63910 cents 1: 1 35.70340 cents 1: 1 48.76460 cents 1: 1 48.76540 cents 1: 1 48.76980 cents 1: 1 148.76870 cents 1: 1 182.40370 cents 1: 1 218.18720 cents 1: 1 386.31370 cents 2: 1 82.40370 cents 2: 1 84.46880 cents 2: 1 182.40780 cents 2: 1 184.47210 cents 2: 1 231.16910 cents 2: 1 266.95180 cents 2: 1 266.95700 cents 2: 1 435.08350 cents 2: 1 568.71740 cents 3: 1 218.11120 cents 3: 1 231.17240 cents 3: 1 233.23750 cents 3: 1 266.87250 cents 3: 1 300.59090 cents 3: 1 315.72160 cents 3: 1 617.48280 cents 3: 1 617.48720 cents 3: 1 653.27070 cents 4: 1 266.87580 cents 4: 1 266.87660 cents 4: 1 349.36070 cents 4: 1 415.64120 cents 4: 1 449.35960 cents 4: 1 653.18620 cents 4: 1 666.25260 cents 4: 1 702.03530 cents 4: 1 835.67440 cents 5: 1 315.64120 cents 5: 1 449.28030 cents 5: 1 485.06300 cents 5: 1 498.12940 cents 5: 1 701.95600 cents 5: 1 735.67440 cents 5: 1 801.95490 cents 5: 1 884.43900 cents 5: 1 884.43980 cents 6: 1 498.04490 cents 6: 1 533.82840 cents 6: 1 533.83280 cents 6: 1 835.59400 cents 6: 1 850.72470 cents 6: 1 884.44310 cents 6: 1 918.07810 cents 6: 1 920.14320 cents 6: 1 933.20440 cents 7: 1 582.59820 cents 7: 1 716.23210 cents 7: 1 884.35860 cents 7: 1 884.36380 cents 7: 1 920.14650 cents 7: 1 966.84350 cents 7: 1 968.90780 cents 7: 1 1066.84680 cents 7: 1 1068.91190 cents 8: 1 765.00190 cents 8: 1 933.12840 cents 8: 1 968.91190 cents 8: 1 1002.54690 cents 8: 1 1102.54580 cents 8: 1 1102.55020 cents 8: 1 1102.55100 cents 8: 1 1115.61220 cents 8: 1 1117.67650 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 9.00000 = 9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 48.8 82.4 231.2 266.9 315.6 498.0 884.4 933.1 1151.3 48.8 : 33.6 182.4 218.1 266.9 449.3 835.6 884.4 1102.6 1151.3 82.4 : 148.8 184.5 233.2 415.6 802.0 850.7 1068.9 1117.7 1151.3 231.2 : 35.7 84.5 266.9 653.2 702.0 920.1 968.9 1002.5 1151.3 266.9 : 48.8 231.2 617.5 666.3 884.4 933.2 966.8 1115.6 1151.3 315.6 : 182.4 568.7 617.5 835.7 884.4 918.1 1066.8 1102.6 1151.3 498.0 : 386.3 435.1 653.3 702.0 735.7 884.4 920.1 968.9 1151.3 884.4 : 48.8 267.0 315.7 349.4 498.1 533.8 582.6 765.0 1151.3 933.1 : 218.2 267.0 300.6 449.4 485.1 533.8 716.2 1102.5 1151.3 1151.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6391 .. 386.3137 cents 352.67460 cents 33.63910 cents 2: 82.4037 .. 568.7174 cents 486.31370 cents -303.91000 cents 3: 218.1112 .. 653.2707 cents 435.15950 cents -350.60620 cents 4: 266.8758 .. 835.6744 cents 568.79860 cents -386.39490 cents 5: 315.6412 .. 884.4398 cents 568.79860 cents -520.03320 cents 6: 498.0449 .. 933.2044 cents 435.15950 cents -386.39490 cents 7: 582.5982 .. 1068.9119 cents 486.31370 cents -350.60620 cents 8: 765.0019 .. 1117.6765 cents 352.67460 cents -303.91000 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 33.63910 cents, class 1 Average step (divided formal octave): 127.9240 cents Largest one step interval : 386.31370 cents Average / Smallest step : 3.802835 Largest / Average step : 3.019870 Largest / Smallest step : 11.484068 Median interval of one step : 48.76980 cents, amount: 1 Least squares average step : 107.22262 cents, oct.: 965.00355 cents Scale is not proper Step pattern alph. order: ABCDEFGHI Step pattern size order : CAFBDGIEH Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.00330 cents Scale diversity : 1.616748 Lumma stability : 0.058436 Lumma impropriety factor : 0.856853 Rothenberg efficiency : 0.222222 redundancy: 0.777778 Efficiency x scale size : 2.000000 Number of different interval sizes : 72 = 9.00000 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 9.00000 = 9 Median interval variety : 9 Lowest interval variety : 9 Smallest interval difference : 0.00080 cents Number of recognisable fifths : 3, average 706.7411 cents Number of appreciable fifths : 2, average 701.9956 cents Number of recognisable fourths : 3, average 493.7458 cents Number of appreciable fourths : 2, average 498.0871 cents Formal octave complements present : 1 = 11.1111% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
9: 0 1 1 0 0 2 3 0 2 N SD: 34.1303 c. M: 59.7933 c. 10: 0 1 1 0 1 1 4 0 2 N SD: 30.8682 c. M: 48.7646 c. 11: 0 1 1 1 0 2 3 1 2 N SD: 30.7385 c. M: 48.7646 c. 13: 1 0 2 0 1 2 4 1 2 N SD: 28.0950 c. M:-41.0617 c. 14: 1 0 2 0 1 2 5 0 3 N SD: 18.8279 c. M:-33.4722 c. 16: 1 0 2 1 0 3 5 1 3 N SD: 16.8875 c. M: 27.8123 c. 18: 1 0 3 0 1 3 6 1 3 N SD: 16.0570 c. M:-26.3013 c. 21: 1 1 2 1 1 3 7 1 4 N SD: 11.6598 c. M:-27.2454 c. 22: 1 1 2 1 1 4 7 1 4 N SD: 13.9875 c. M:-25.2804 c. 23: 1 1 3 0 1 4 8 1 4 N SD: 14.1293 c. M:-19.1136 c. 25: 1 1 3 1 1 4 8 1 5 N SD: 7.7668 c. M: 12.0759 c. 26: 1 1 3 1 1 4 9 1 5 N SD: 5.9521 c. M: 10.9498 c. 30: 1 1 4 1 1 5 10 1 6 N SD: 6.3903 c. M: 12.0759 c. 39: 2 1 5 1 2 6 13 2 7 N SD: 6.6820 c. M:-11.5408 c. 43: 2 1 6 1 2 7 14 2 8 N SD: 5.6425 c. M:-10.6759 c. 44: 2 1 6 1 2 7 15 2 8 N SD: 4.5194 c. M:-8.8571 c. 51: 2 2 6 2 2 8 17 2 10 N SD: 4.6646 c. M:-7.8956 c. 56: 2 2 7 2 2 9 19 2 11 N SD: 4.9595 c. M: 7.9641 c. 64: 3 2 8 2 3 10 21 3 12 N SD: 4.8572 c. M:-8.1663 c. 65: 3 2 8 2 3 10 22 3 12 N SD: 3.4513 c. M:-6.1590 c. 69: 3 2 9 2 3 11 23 3 13 N SD: 1.4359 c. M:-2.5271 c. 95: 4 3 12 3 4 15 32 4 18 N SD: 0.9798 c. M:-2.4301 c. 143: 6 4 19 4 6 23 48 6 27 N SD: 1.3655 c. M:-2.3112 c. 164: 7 5 21 5 7 26 55 7 31 N SD: 0.6956 c. M:-1.8389 c. 185: 8 5 24 6 8 29 62 8 35 N SD: 0.9601 c. M:-1.7485 c. 194: 8 6 25 6 8 31 65 8 37 N SD: 0.7904 c. M: 1.3936 c. 233: 10 7 30 7 10 37 78 10 44 N SD: 0.8255 c. M:-1.5979 c. 238: 10 7 31 7 10 38 80 10 45 N SD: 0.7034 c. M: 1.2063 c. 263: 11 8 34 8 11 42 88 11 50 N SD: 0.6149 c. M:-1.0044 c. 280: 12 8 36 9 12 44 94 12 53 N SD: 0.5490 c. M:-0.9706 c. 310: 13 9 40 10 13 49 104 13 59 N SD: 0.5813 c. M: 0.9342 c. 333: 14 10 43 10 14 53 112 14 63 N SD: 0.5639 c. M: 1.0174 c. 349: 15 10 45 11 15 55 117 15 66 N SD: 0.4817 c. M:-1.0531 c. 354: 15 10 46 11 15 56 119 15 67 N SD: 0.4320 c. M: 1.0961 c. 375: 16 11 48 12 16 59 126 16 71 N SD: 0.4847 c. M: 0.9093 c. 379: 16 11 49 12 16 60 127 16 72 N SD: 0.3313 c. M: 0.5324 c. 423: 18 12 55 13 18 67 142 18 80 N SD: 0.3201 c. M: 0.7501 c. 448: 19 13 58 14 19 71 150 19 85 N SD: 0.3052 c. M:-0.5159 c. 449: 19 13 58 14 19 71 151 19 85 N SD: 0.3110 c. M: 0.5945 c. 474: 20 14 61 15 20 75 159 20 90 N SD: 0.2567 c. M: 0.4235 c. 518: 22 15 67 16 22 82 174 22 98 N SD: 0.1830 c. M:-0.3707 c. 543: 23 16 70 17 23 86 182 23 103 N SD: 0.2039 c. M:-0.2875 c. 587: 25 17 76 18 25 93 197 25 111 N SD: 0.2292 c. M:-0.4768 c. 613: 26 18 79 19 26 97 206 26 116 N SD: 0.2125 c. M: 0.3310 c. 617: 26 18 80 19 26 98 207 26 117 N SD: 0.1955 c. M: 0.3002 c. 682: 29 20 88 21 29 108 229 29 129 N SD: 0.2105 c. M:-0.4164 c. 712: 30 21 92 22 30 113 239 30 135 N SD: 0.1548 c. M: 0.3230 c. 781: 33 23 101 24 33 124 262 33 148 N SD: 0.1520 c. M:-0.2700 c. 897: 38 26 116 28 38 142 301 38 170 N SD: 0.1097 c. M: 0.2586 c. 966: 41 28 125 30 41 153 324 41 183 N SD: 0.1130 c. M:-0.1959 c. 992: 42 29 128 31 42 157 333 42 188 N SD: 0.0903 c. M: 0.2129 c. 1061: 45 31 137 33 45 168 356 45 201 N SD: 0.0652 c. M:-0.1296 c. 1609: 68 47 208 50 68 255 540 68 305 N SD: 0.0684 c. M: 0.1158 c. 1678: 71 49 217 52 71 266 563 71 318 N SD: 0.0480 c. M:-0.0809 c. 1773: 75 52 229 55 75 281 595 75 336 N SD: 0.0423 c. M:-0.0700 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 48.6844 cents 2 x x x x x x 3 x 4 S SD: 94.3944 cents 3 x x x x x 4:5 x 6 S SD: 16.2281 cents 4 x x x x 5 x x 7:8 SD: 30.9822 cents 5 x x x x 6:7:8:9:10 S SD: 29.4172 cents 6 x x x 7 x 8:10 x 12 S SD: 12.1711 cents 7 x x 8 x x 9 x 12:14 S SD: 19.8970 cents 8 x x 9 x 10:11:13:14:16 SD: 19.8197 cents 9 x x 10 x 11:12:15 x 18 S SD: 15.1759 cents 10 x x 11 x 12:13 x 17:19 SD: 18.0206 cents 11 x 12 x 13 x 15:18:19:21 SD: 15.6903 cents 12 x 13 x 14 x 16:20:21:23 SD: 11.8487 cents 13 x 14:15 x 16:17 x 22:25 SD: 13.2291 cents 14 x 15:16 x 17:19:23:24:27 SD: 8.5176 cents 15 x 16:17 x 18:20:25:26:29 SD: 5.5989 cents 16 x 17:18 x 19:21:27 x 31 SD: 8.8596 cents 17 x 18:19:20 x 23:28:29:33 SD: 7.9727 cents 18 x 19 x 21:22:24:30:31:35 SD: 4.9456 cents 19 x 20 x 22:23:25:32:33:37 SD: 6.0833 cents 20 x 21:23 x 24:27:33:34:39 SD: 4.7795 cents 21 x 22:24 x 25:28:35:36:41 SD: 2.2237 cents 22 x 23:25:26 x 29:37:38:43 SD: 5.5556 cents 23 x 24:26:27:28:31:38:39:45 SD: 5.8887 cents 24 x 25:27:28:29:32:40:41:47 SD: 4.3488 cents 25 x 26 x 29:30:33:42:43:49 SD: 4.5693 cents 26:27 x 30 x 31:35:43:45:51 SD: 5.7637 cents 27:28 x 31 x 32:36:45:46:53 SD: 4.7582 cents 28:29 x 32:33:34:37:47:48:54 SD: 4.7908 cents 29:30 x 33:34:35:39:48:50:56 SD: 3.8193 cents 30:31 x 34:35:36:40:50:51:58 SD: 3.0204 cents 32:33:34 x 37:38:43:53:55:62 SD: 4.7727 cents 33:34:35:38:39:40:44:55:57:64 SD: 4.3765 cents 34:35:36:39:40:41:45:57:58:66 SD: 3.4164 cents 35:36:37:40:41:42:47:58:60:68 SD: 2.4661 cents 36:37:38:41:42:43:48:60:62:70 SD: 1.8985 cents 60:62:63:69:70:72:80:100:103:117 SD: 1.6255 cents 66:68:69:75:77:79:88:110:113:128 SD: 1.4926 cents 77:79:81:88:90:92:103:128:132:150 SD: 1.4703 cents 78:80:82:89:91:94:104:130:134:152 SD: 1.2739 cents 84:86:88:96:98:101:112:140:144:163 SD: 1.0705 cents 102:105:107:117:119:122:136:170:175:198 SD: 1.0286 cents 104:107:109:119:121:125:139:173:178:202 SD: 0.9702 cents 105:108:110:120:123:126:140:175:180:204 SD: 0.8270 cents 126:130:132:144:147:151:168:210:216:245 SD: 0.6783 cents 140:144:147:160:163:168:187:233:240:272 SD: 0.6547 cents 144:148:151:165:168:173:192:240:247:280 SD: 0.5788 cents 168:173:176:192:196:202:224:280:288:327 SD: 0.5225 cents 180:185:189:206:210:216:240:300:309:350 SD: 0.4661 cents 204:210:214:233:238:245:272:340:350:397 SD: 0.3372 cents 210:216:220:240:245:252:280:350:360:408 SD: 0.2661 cents 246:253:258:281:287:295:328:410:422:478 SD: 0.2542 cents 384:395:403:439:448:461:512:640:658:747 SD: 0.2045 cents 414:426:434:473:483:497:552:690:710:805 SD: 0.1675 cents 450:463:472:514:525:540:600:750:771:875 SD: 0.1648 cents 456:469:478:521:532:547:608:760:782:887 SD: 0.1589 cents 594:611:623:679:693:713:792:990:1018:1155 SD: 0.0885 cents