Scala analysis: xen14-mclaren-nonoctave-phi-5
John McBryde's 5th root of phi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 166.618 cents 166.618059 2: 333.236 cents 333.236119 3: 499.854 cents 499.854178 4: 666.472 cents 666.472237 5: 833.090 cents 833.090296
SHOW/INTERVAL
0: 166.6181 cents 166.6181 1: 166.6181 cents 166.6181 2: 166.6181 cents 166.6181 3: 166.6181 cents 166.6181 4: 166.6181 cents 166.6181 5: 166.6181 cents 166.6181
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 166.61806 cents 2: 5 333.23612 cents 3: 5 499.85418 cents 4: 5 666.47224 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 166.6 333.2 499.9 666.5 833.1 166.6: 166.6 333.2 499.9 666.5 833.1 333.2: 166.6 333.2 499.9 666.5 833.1 499.9: 166.6 333.2 499.9 666.5 833.1 666.5: 166.6 333.2 499.9 666.5 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 166.6181 .. 166.6181 cents 1/1, 0.0000 cents 166.61806 cents 2: 333.2361 .. 333.2361 cents 1/1, 0.0000 cents 166.61806 cents 3: 499.8542 .. 499.8542 cents 1/1, 0.0000 cents 166.61806 cents 4: 666.4722 .. 666.4722 cents 1/1, 0.0000 cents 166.61806 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 166.61806 cents, class 1 Average step (divided formal octave): 166.6181 cents Largest one step interval : 166.61806 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 166.61806 cents, amount: 5 Most common interval of one step : 166.61806 cents, amount: 5 Least squares average step : 166.61806 cents, oct.: 833.09030 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 166.61806 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.200000 redundancy: 0.800000 Efficiency x scale size : 1.000000 Number of different interval sizes : 4 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 0 Number of recognisable fourths : 5, average 499.8542 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x 2 S SD: 366.9097 cents 2 x x x 3 x S SD: 35.4828 cents 3 x x 4 x 5 S SD: 25.6502 cents 4 x 5 x 6 x S SD: 31.9228 cents 5 x 6:7 x 8 S SD: 28.9030 cents 6 x 7:8:9:10 S SD: 22.7693 cents 7:8 x 9:10:11 S SD: 28.8556 cents 8:9:10:11:12:13 H SD: 18.0785 cents 9:10:11:12:13:15 SD: 12.6064 cents 13:14:16:17:19:21 SD: 11.8488 cents 15:17:18:20:22:24 SD: 11.3278 cents 18:20:22:24:26:29 SD: 7.4825 cents 19:21:23:25:28:31 SD: 5.9804 cents 27:30:33:36:40:44 S SD: 5.6621 cents 28:31:34:37:41:45 SD: 4.8021 cents 29:32:35:39:43:47 SD: 4.4318 cents 32:35:39:43:47:52 SD: 4.0474 cents 38:42:46:51:56:61 SD: 3.7579 cents 39:43:47:52:57:63 SD: 2.9083 cents 42:46:51:56:62:68 SD: 2.5032 cents 47:52:57:63:69:76 SD: 2.2783 cents 57:63:69:76:84:92 SD: 1.9535 cents 60:66:73:80:88:97 SD: 1.5393 cents 81:89:98:108:119:131 SD: 1.0663 cents 89:98:108:119:131:144 SD: 0.8936 cents 128:141:155:171:188:207 SD: 0.5826 cents 170:187:206:227:250:275 SD: 0.4583 cents 188:207:228:251:276:304 SD: 0.4475 cents 230:253:279:307:338:372 SD: 0.4167 cents 236:260:286:315:347:382 SD: 0.3268 cents 296:326:359:395:435:479 SD: 0.2116 cents 377:415:457:503:554:610 SD: 0.1527 cents 424:467:514:566:623:686 SD: 0.1435 cents 466:513:565:622:685:754 SD: 0.1188 cents 594:654:720:793:873:961 SD: 0.0986 cents