Scala analysis: xen18-ayers-table-48
7 Iterated Reciprocals of Golden Means between 1/1 and 2/1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 283.282 cents 283.282000 2: 458.359 cents 458.359000 3: 633.437 cents 633.437000 4: 741.641 cents 741.641000 5: 916.719 cents 916.719000 6: 1024.920 cents 1024.920000 7: 1133.130 cents 1133.130000 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 66.8700 cents 66.8700 1: 283.2820 cents 283.2820 2: 175.0770 cents 175.0770 3: 175.0780 cents 175.0780 4: 108.2040 cents 108.2040 5: 175.0780 cents 175.0780 6: 108.2010 cents 108.2010 7: 108.2100 cents 108.2100 8: 66.8700 cents 66.8700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66.87000 cents 1: 1 108.20100 cents 1: 1 108.20400 cents 1: 1 108.21000 cents 1: 1 175.07700 cents 1: 2 175.07800 cents 1: 1 283.28200 cents 2: 1 175.08000 cents 2: 1 216.41100 cents 2: 1 283.27900 cents 2: 2 283.28200 cents 2: 1 350.15200 cents 2: 1 350.15500 cents 2: 1 458.35900 cents 3: 1 283.28100 cents 3: 1 391.48300 cents 3: 1 391.48900 cents 3: 1 458.35900 cents 3: 1 458.36000 cents 3: 1 458.36200 cents 3: 1 525.22900 cents 3: 1 633.43700 cents 4: 1 458.35900 cents 4: 1 499.69300 cents 4: 1 566.56100 cents 4: 1 566.56300 cents 4: 1 633.43700 cents 4: 1 633.43900 cents 4: 1 700.30700 cents 4: 1 741.64100 cents 5: 1 566.56300 cents 5: 1 674.77100 cents 5: 1 741.63800 cents 5: 1 741.64000 cents 5: 1 741.64100 cents 5: 1 808.51100 cents 5: 1 808.51700 cents 5: 1 916.71900 cents 6: 1 741.64100 cents 6: 1 849.84500 cents 6: 1 849.84800 cents 6: 2 916.71800 cents 6: 1 916.72100 cents 6: 1 983.58900 cents 6: 1 1024.92000 cents 7: 1 916.71800 cents 7: 2 1024.92200 cents 7: 1 1024.92300 cents 7: 1 1091.79000 cents 7: 1 1091.79600 cents 7: 1 1091.79900 cents 7: 1 1133.13000 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 7.42857 = 52/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 283.3 458.4 633.4 741.6 916.7 1024.9 1133.1 1200.0 283.3 : 175.1 350.2 458.4 633.4 741.6 849.8 916.7 1200.0 458.4 : 175.1 283.3 458.4 566.6 674.8 741.6 1024.9 1200.0 633.4 : 108.2 283.3 391.5 499.7 566.6 849.8 1024.9 1200.0 741.6 : 175.1 283.3 391.5 458.4 741.6 916.7 1091.8 1200.0 916.7 : 108.2 216.4 283.3 566.6 741.6 916.7 1024.9 1200.0 1024.9: 108.2 175.1 458.4 633.4 808.5 916.7 1091.8 1200.0 1133.1: 66.9 350.2 525.2 700.3 808.5 983.6 1091.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.8700 .. 283.2820 cents 216.41200 cents 66.87000 cents 2: 175.0800 .. 458.3590 cents 283.27900 cents -108.20200 cents 3: 283.2810 .. 633.4370 cents 350.15600 cents -175.07800 cents 4: 458.3590 .. 741.6410 cents 283.28200 cents -175.07800 cents 5: 566.5630 .. 916.7190 cents 350.15600 cents -175.07800 cents 6: 741.6410 .. 1024.9200 cents 283.27900 cents -175.07800 cents 7: 916.7180 .. 1133.1300 cents 216.41200 cents -108.20200 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 66.87000 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 283.28200 cents Average / Smallest step : 2.243158 Largest / Average step : 1.888547 Largest / Smallest step : 4.236309 Median interval of one step : 141.64350 cents, amount: 0 Most common interval of one step : 175.07800 cents, amount: 2 Least squares average step : 168.29363 cents, oct.: 1346.34902 cents Scale is not proper Scale is a mode of a 987-tone equal temperament with octave 1200.000 cents degrees: 233 377 521 610 754 843 932 987 Least number of segments generator : 494 of 600.608 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 610 of 741.641 cents and inv. generated superset size: 13 = 5 more = 162.500% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCEFG Step pattern size order : GEFCFBDA Scale is not a Constant Structure Scale diversity : 1.471158 Lumma stability : 0.111450 Lumma impropriety factor : 0.708200 Rothenberg efficiency : 0.303571 redundancy: 0.696429 Efficiency x scale size : 2.428571 Number of different interval sizes : 44 = 6.28571 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 7.42857 = 52/7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 0.00100 cents Number of recognisable fifths : 1, average 700.3070 cents Formal octave complements present : 3 = 37.5000% -- Rational properties --
FIT/MODE
8: 2 1 1 1 1 1 1 0 N T3 SD: 29.4054 c. M:-66.8700 c. 10: 2 2 1 1 2 1 0 1 N SD: 38.1737 c. M:-55.0800 c. 11: 3 1 2 1 1 1 1 1 N SD: 33.3991 c. M: 43.9917 c. 12: 3 1 2 1 2 1 1 1 N SD: 32.6638 c. M: 58.3590 c. 13: 3 2 2 1 2 1 1 1 N SD: 11.1848 c. M: 25.4377 c. 21: 5 3 3 2 3 2 2 1 N SD: 4.2781 c. M:-9.7271 c. 34: 8 5 5 3 5 3 3 2 N SD: 1.6342 c. M: 3.7182 c. 55: 13 8 8 5 8 5 5 3 N SD: 0.6233 c. M:-1.4155 c. 89: 21 13 13 8 13 8 8 5 N SD: 0.2391 c. M: 0.5457 c. 144: 34 21 21 13 21 13 13 8 N SD: 0.0903 c. M:-0.2033 c. 233: 55 34 34 21 34 21 21 13 N SD: 0.0356 c. M: 0.0828 c. 377: 89 55 55 34 55 34 34 21 N SD: 0.0126 c. M:-0.0265 c. 610: 144 89 89 55 89 55 55 34 N SD: 0.0060 c. M: 0.0152 c. 987: 233 144 144 89 144 89 89 55 N SD: 0.0018 c. M:-0.0040 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 19.8430 cents 3 x 4 x x 5 x x 6 S SD: 17.0690 cents 4 x 5 x 6:7 x x 8 S SD: 24.3421 cents 5:6 x 7:8 x 9 x 10 S SD: 18.8517 cents 6:7:8 x 9:10:11 x 12 S SD: 11.8602 cents 7:8:9:10:11:12:13 x 14 S SD: 12.4851 cents 8:9:10 x 12:14 x 15:16 S SD: 22.2318 cents 9:11:12:13:14:15:16:17:18 SD: 11.9548 cents 10:12:13:14:15:17:18:19:20 SD: 9.4958 cents 11:13:14:16:17:19:20:21:22 SD: 7.1123 cents 16:19:21:23:25:27:29:31:32 SD: 5.0387 cents 22:26:29:32:34:37:40:42:44 SD: 4.6342 cents 23:27:30:33:35:39:42:44:46 SD: 3.4048 cents 27:32:35:39:41:46:49:52:54 SD: 3.1436 cents 30:35:39:43:46:51:54:58:60 SD: 2.8427 cents 36:42:47:52:55:61:65:69:72 SD: 2.5526 cents 39:46:51:56:60:66:70:75:78 SD: 2.1550 cents 43:51:56:62:66:73:78:83:86 SD: 1.8273 cents 50:59:65:72:77:85:90:96:100 SD: 1.4725 cents 52:61:68:75:80:88:94:100:104 SD: 1.4714 cents 56:66:73:81:86:95:101:108:112 SD: 1.0239 cents 73:86:95:105:112:124:132:140:146 SD: 0.9440 cents 79:93:103:114:121:134:143:152:158 SD: 0.6351 cents 129:152:168:186:198:219:233:248:258 SD: 0.3120 cents 208:245:271:300:319:353:376:400:416 SD: 0.2569 cents 281:331:366:405:431:477:508:541:562 SD: 0.2382 cents 333:392:434:480:511:565:602:641:666 SD: 0.2377 cents 342:403:446:493:525:581:618:658:684 SD: 0.2363 cents 344:405:448:496:528:584:622:662:688 SD: 0.1784 cents 432:509:563:623:663:734:781:831:864 SD: 0.1755 cents 462:544:602:666:709:785:835:889:924 SD: 0.1507 cents 484:570:631:698:743:822:875:931:968 SD: 0.1507 cents 518:610:675:747:795:880:936:997:1036 SD: 0.1458 cents 541:637:705:780:830:919:978:1041:1082 SD: 0.1284 cents 557:656:726:803:855:946:1007:1072:1114 SD: 0.0890 cents