Scala analysis: xen18-ayers-table-33
Logarithmic Means scale from Table 33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 176.997 cents 176.997000 2: 400.000 cents 400.000000 3: 490.809 cents 490.809000 4: 709.191 cents 709.191000 5: 800.000 cents 800.000000 6: 1023.000 cents 1023.000000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 177.0000 cents 177.0000 1: 176.9970 cents 176.9970 2: 223.0030 cents 223.0030 3: 90.8090 cents 90.8090 4: 218.3820 cents 218.3820 5: 90.8090 cents 90.8090 6: 223.0000 cents 223.0000 7: 177.0000 cents 177.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 90.80900 cents 1: 1 176.99700 cents 1: 1 177.00000 cents 1: 1 218.38200 cents 1: 1 223.00000 cents 1: 1 223.00300 cents 2: 2 309.19100 cents 2: 1 313.80900 cents 2: 1 313.81200 cents 2: 1 353.99700 cents 2: 2 400.00000 cents 3: 1 400.00000 cents 3: 2 490.80900 cents 3: 1 532.19100 cents 3: 1 532.19400 cents 3: 1 576.99700 cents 3: 1 577.00000 cents 4: 1 623.00000 cents 4: 1 623.00300 cents 4: 1 667.80600 cents 4: 1 667.80900 cents 4: 2 709.19100 cents 4: 1 800.00000 cents 5: 2 800.00000 cents 5: 1 846.00300 cents 5: 1 886.18800 cents 5: 1 886.19100 cents 5: 2 890.80900 cents 6: 1 976.99700 cents 6: 1 977.00000 cents 6: 1 981.61800 cents 6: 1 1023.00000 cents 6: 1 1023.00300 cents 6: 2 1109.19100 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.66667 = 17/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 177.0 400.0 490.8 709.2 800.0 1023.0 1200.0 177.0 : 223.0 313.8 532.2 623.0 846.0 1023.0 1200.0 400.0 : 90.8 309.2 400.0 623.0 800.0 977.0 1200.0 490.8 : 218.4 309.2 532.2 709.2 886.2 1109.2 1200.0 709.2 : 90.8 313.8 490.8 667.8 890.8 981.6 1200.0 800.0 : 223.0 400.0 577.0 800.0 890.8 1109.2 1200.0 1023.0: 177.0 354.0 577.0 667.8 886.2 977.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.8090 .. 223.0030 cents 132.19400 cents 90.80900 cents 2: 309.1910 .. 400.0000 cents 90.80900 cents 86.18800 cents 3: 400.0000 .. 577.0000 cents 177.00000 cents 1/1, 0.0000 cents 4: 623.0000 .. 800.0000 cents 177.00000 cents 46.00000 cents 5: 800.0000 .. 890.8090 cents 90.80900 cents 1/1, 0.0000 cents 6: 976.9970 .. 1109.1910 cents 132.19400 cents 86.18800 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 90.80900 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 223.00300 cents Average / Smallest step : 1.887793 Largest / Average step : 1.300851 Largest / Smallest step : 2.455737 Median interval of one step : 177.00000 cents, amount: 1 Most common interval of one step : 90.80900 cents, amount: 2 Least squares average step : 170.17277 cents, oct.: 1191.20940 cents Scale is proper Step pattern alph. order: ABCDCEF Step pattern size order : BFADAEC Scale is not a Constant Structure Scale diversity : 1.465037 Rothenberg stability : 0.857143 = 6/7 Lumma stability : 0.333328 Rothenberg efficiency : 0.351020 redundancy: 0.648980 Efficiency x scale size : 2.457143 Number of different interval sizes : 32 = 5.33333 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.66667 = 17/3 Median interval variety : 5.5 Lowest interval variety : 5 Smallest interval difference : 0.00300 cents Most common intervals : 400.00000 cents & inv., amount: 3 Most common triad is 0.0 400.000 800.000 cents, amount: 3 Number of recognisable fifths : 2, average 709.1910 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 5 = 71.4286% 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: 33.1554 c. M: 57.1429 c. Lebeng 8: 1 2 0 2 0 2 1 N D3 I SD: 37.3948 c. M:-50.0000 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 32.5794 c. M:-43.6667 c. 12: 2 2 1 2 1 2 2 P D3 I SD: 13.2400 c. M:-23.0030 c. Major-Minor, Melodic Major, Mischung 6, Mixolydian flat 6, Mela Carukesi, Raga Charukeshi, Tarangini, Heptatonia secunda 15: 2 3 1 3 1 3 2 P D3 I SD: 10.7675 c. M:-17.0000 c. 27: 4 5 2 5 2 5 4 P I SD: 1.1076 c. M:-1.9201 c. 156: 23 29 12 28 12 29 23 P I SD: 0.8021 c. M:-1.4987 c. 183: 27 34 14 33 14 34 27 P I SD: 0.5322 c. M:-0.9943 c. 210: 31 39 16 38 16 39 31 P I SD: 0.3400 c. M:-0.6196 c. 237: 35 44 18 43 18 44 35 P I SD: 0.2111 c. M:-0.3302 c. 264: 39 49 20 48 20 49 39 P I SD: 0.1560 c. M:-0.2757 c. 501: 74 93 38 91 38 93 74 P I SD: 0.1729 c. M:-0.2485 c. 516: 76 96 39 94 39 96 76 P I SD: 0.1484 c. M:-0.2558 c. 543: 80 101 41 99 41 101 80 P I SD: 0.1528 c. M:-0.2044 c. 699: 103 130 53 127 53 130 103 P I SD: 0.1333 c. M:-0.1781 c. 726: 107 135 55 132 55 135 107 P I SD: 0.0916 c. M:-0.1405 c. 753: 111 140 57 137 57 140 111 P I SD: 0.0586 c. M:-0.1076 c. 780: 115 145 59 142 59 145 115 P I SD: 0.0456 c. M:-0.0769 c. 1017: 150 189 77 185 77 189 150 P I SD: 0.0252 c. M:-0.0465 c. 1044: 154 194 79 190 79 194 154 P I SD: 0.0074 c. M:-0.0145 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: 3.6180 cents 3 x x 4 x 5 x 6 S SD: 28.2228 cents 4 x 5 x 6 x 7:8 S SD: 14.0857 cents 5 x 6:7 x 8:9:10 S SD: 25.0937 cents 6:7 x 8:9:10:11:12 S SD: 21.0775 cents 7:8:9 x x 11:13:14 SD: 16.5462 cents 8:9:10:11:12:13:14:16 S SD: 13.7043 cents 9:10:11:12 x 14:16:18 S SD: 11.5501 cents 10:11 x 13:15:16:18:20 SD: 6.9759 cents 11:12:14:15:17 x 20:22 SD: 12.0759 cents 12:13:15:16:18:19:22:24 SD: 7.1188 cents 16:18:20:21:24:25:29:32 SD: 6.6357 cents 18:20:23:24:27:29:33:36 SD: 6.5175 cents 19:21:24:25:29:30:34:38 SD: 4.8036 cents 26:29:33:35:39:41:47:52 SD: 4.6555 cents 27:30:34:36:41:43:49:54 SD: 2.8131 cents 36:40:45:48:54:57:65:72 SD: 2.6380 cents 39:43:49:52:59:62:70:78 SD: 2.5104 cents 46:51:58:61:69:73:83:92 SD: 1.1368 cents 73:81:92:97:110:116:132:146 SD: 0.6532 cents 119:132:150:158:179:189:215:238 SD: 0.5445 cents 138:153:174:183:208:219:249:276 SD: 0.4987 cents 150:166:189:199:226:238:271:300 SD: 0.3576 cents 196:217:247:260:295:311:354:392 SD: 0.3496 cents 223:247:281:296:336:354:403:446 SD: 0.2397 cents 269:298:339:357:405:427:486:538 SD: 0.2313 cents 308:341:388:409:464:489:556:616 SD: 0.1451 cents 381:422:480:506:574:605:688:762 SD: 0.1135 cents 427:473:538:567:643:678:771:854 SD: 0.0997 cents 577:639:727:766:869:916:1042:1154 SD: 0.0807 cents