Scala analysis: xen15-oconnell-golden-section-7
7-note scale in 25 parts of Golden Section
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 133.294 cents 133.294447 2: 233.265 cents 233.265283 3: 366.560 cents 366.559730 4: 466.531 cents 466.530566 5: 599.825 cents 599.825013 6: 699.796 cents 699.795849 7: 833.090 cents 833.090296
SHOW/INTERVAL
0: 133.2944 cents 133.2944 1: 133.2944 cents 133.2944 2: 99.9708 cents 99.9708 3: 133.2944 cents 133.2944 4: 99.9708 cents 99.9708 5: 133.2944 cents 133.2944 6: 99.9708 cents 99.9708 7: 133.2944 cents 133.2944
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 99.97084 cents 1: 4 133.29445 cents 2: 6 233.26528 cents 2: 1 266.58889 cents 3: 2 333.23612 cents 3: 5 366.55973 cents 4: 5 466.53057 cents 4: 2 499.85418 cents 5: 1 566.50140 cents 5: 6 599.82501 cents 6: 4 699.79585 cents 6: 3 733.11946 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 133.3 233.3 366.6 466.5 599.8 699.8 833.1 133.3: 100.0 233.3 333.2 466.5 566.5 699.8 833.1 233.3: 133.3 233.3 366.6 466.5 599.8 733.1 833.1 366.6: 100.0 233.3 333.2 466.5 599.8 699.8 833.1 466.5: 133.3 233.3 366.6 499.9 599.8 733.1 833.1 599.8: 100.0 233.3 366.6 466.5 599.8 699.8 833.1 699.8: 133.3 266.6 366.6 499.9 599.8 733.1 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.9708 .. 133.2944 cents 33.32361 cents 99.97084 cents 2: 233.2653 .. 266.5889 cents 33.32361 cents 99.97084 cents 3: 333.2361 .. 366.5597 cents 33.32361 cents 66.64723 cents 4: 466.5306 .. 499.8542 cents 33.32361 cents 99.97084 cents 5: 566.5014 .. 599.8250 cents 33.32361 cents 66.64723 cents 6: 699.7958 .. 733.1195 cents 33.32361 cents 99.97084 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 99.97084 cents, class 1 Average step (divided formal octave): 119.0129 cents Largest one step interval : 133.29445 cents Average / Smallest step : 1.190476 Largest / Average step : 1.120000 Largest / Smallest step : 1.333333 Median interval of one step : 133.29445 cents, amount: 4 Most common interval of one step : 133.29445 cents, amount: 4 Least squares average step : 118.53685 cents, oct.: 829.75793 cents Scale is strictly proper Scale has Myhill's property chromas: 33.32361 cents and 66.64723 cents, ratio: 2.000000 generators: 2 of 233.26528 cents and 5 of 599.82501 cents Scale is maximally even in 25-tone equal temperament ET pair of linear temperament : 25&277696607 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 25-tone equal temperament with octave 833.090 cents degrees: 4 7 11 14 18 21 25 generators: 7 and 18 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABA Step pattern size order : LSLSLSL Interval vector is [ 0 0 3 4 0 0 6 1 0 2 5 0 ] Scale is a Constant Structure, by a margin of 66.64723 cents Scale diversity : 1.113683 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.760000 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 33.32361 cents Most common intervals : 233.26528 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 233.265 466.531 cents Most common triad is 0.0 233.265 599.825 cents, amount: 5 Number of recognisable fifths : 4, average 699.7958 cents Number of recognisable fourths : 2, average 499.8542 cents Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 7 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 9.5210 c. M:-14.2815 c. Lebeng 18: 3 2 3 2 3 2 3 SP M ME I SD: 3.7026 c. M:-5.5539 c. 25: 4 3 4 3 4 3 4 SP M ME I SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 366.9097 cents 2 x x x x x 3 x S SD: 2.1592 cents 3 x x x 4 x x 5 S SD: 30.0899 cents 4 x x 5 x x 6 x S SD: 9.9358 cents 5 x x 6 x 7 x 8 S SD: 19.0582 cents 6 x 7 x 8 x 9:10 S SD: 17.2402 cents 7 x 8 x 9:10 x 11 S SD: 15.5431 cents 8 x 9:10 x 11:12:13 S SD: 12.1076 cents 9:10 x 11:12:13 x 15 SD: 17.6112 cents 10:11 x 12:13:14:15:16 S SD: 11.0941 cents 11:12:13 x 14:16 x 18 S SD: 18.5484 cents 12:13:14:15:16:17:18:19 H SD: 8.9943 cents 13:14:15:16:17:18:19:21 SD: 8.4007 cents 14:15:16:17:18:20:21:23 SD: 7.9828 cents 16:17:18:20:21:23:24:26 SD: 7.7492 cents 20:22:23:25:26:28:30:32 SD: 6.8571 cents 22:24:25:27:29:31:33:36 SD: 4.8400 cents 26:28:30:32:34:37:39:42 SD: 2.9370 cents 42:45:48:52:55:59:63:68 SD: 2.6461 cents 48:52:55:59:63:68:72:78 SD: 2.0657 cents 62:67:71:77:81:88:93:100 SD: 1.8439 cents 68:73:78:84:89:96:102:110 SD: 1.6982 cents 75:81:86:93:98:106:112:121 SD: 1.5431 cents 77:83:88:95:101:109:115:125 SD: 1.4207 cents 84:91:96:104:110:119:126:136 SD: 1.0918 cents 97:105:111:120:127:137:145:157 SD: 0.8765 cents 123:133:141:152:161:174:184:199 SD: 0.6603 cents 152:164:174:188:199:215:228:246 SD: 0.4685 cents 237:256:271:293:310:335:355:383 SD: 0.4475 cents 249:269:285:308:326:352:373:403 SD: 0.2667 cents 285:308:326:352:373:403:427:461 SD: 0.2581 cents 374:404:428:462:490:529:560:605 SD: 0.2578 cents 411:444:470:508:538:581:616:665 SD: 0.2177 cents 437:472:500:540:572:618:655:707 SD: 0.1453 cents 534:577:611:660:699:755:800:864 SD: 0.1338 cents