Scala analysis: 674_T81
Tempered tetrachord in cents 233.3 + 16.7 + 250, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 233.300 cents 233.300000 2: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 233.3000 cents 233.3000 2: 16.7000 cents 16.7000 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16.70000 cents 1: 1 233.30000 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 266.70000 cents 2: 1 483.30000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 233.3 250.0 500.0 233.3: 16.7 266.7 500.0 250.0: 250.0 483.3 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 16.7000 .. 250.0000 cents 233.30000 cents 16.70000 cents 2: 250.0000 .. 483.3000 cents 233.30000 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 16.70000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 9.980040 Largest / Average step : 1.500000 Largest / Smallest step : 14.970060 Median interval of one step : 233.30000 cents, amount: 1 Least squares average step : 159.52143 cents, oct.: 478.56429 cents Scale is proper Scale has trivalence property Scale is a mode of a 868-tone equal temperament with octave 500.000 cents degrees: 405 434 868 Least number of segments generator : 435 of 250.576 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 435 of 250.576 cents and inv. generated superset size: 435 = 432 more = 14500.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 0.349577 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.066800 Rothenberg efficiency : 0.777778 redundancy: 0.222222 Efficiency x scale size : 2.333333 Number of different interval sizes : 5 = 2.50000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 16.70000 cents Most common intervals : 250.00000 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 483.3000 cents Number of appreciable fourths : 0 Formal octave complements present : 2 = 66.6667% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 1 0 2 N G T3 SD: 61.6021 c. M: 83.3333 c. 4: 2 0 2 P M DE I SD: 9.6417 c. M:-16.7000 c. 15: 7 0 8 N G T3 SD: 9.6225 c. M: 16.6667 c. 16: 7 1 8 P T3 SD: 8.4004 c. M: 14.5500 c. 18: 8 1 9 P T3 SD: 6.3958 c. M: 11.0778 c. 20: 9 1 10 P T3 SD: 4.7920 c. M: 8.3000 c. 22: 10 1 11 P T3 SD: 3.4798 c. M: 6.0273 c. 24: 11 1 12 P T3 SD: 2.3864 c. M: 4.1333 c. 26: 12 1 13 P T3 SD: 1.4611 c. M: 2.5308 c. 28: 13 1 14 P T3 SD: 0.6681 c. M: 1.1571 c. 30: 14 1 15 P T3 SD: 0.0192 c. M:-0.0333 c. 508: 237 17 254 P T3 SD: 0.0186 c. M: 0.0323 c. 538: 251 18 269 P T3 SD: 0.0165 c. M: 0.0286 c. 568: 265 19 284 P T3 SD: 0.0146 c. M: 0.0254 c. 598: 279 20 299 P T3 SD: 0.0129 c. M: 0.0224 c. 628: 293 21 314 P T3 SD: 0.0114 c. M: 0.0197 c. 658: 307 22 329 P T3 SD: 0.0100 c. M: 0.0173 c. 688: 321 23 344 P T3 SD: 0.0087 c. M: 0.0151 c. 718: 335 24 359 P T3 SD: 0.0076 c. M: 0.0131 c. 748: 349 25 374 P T3 SD: 0.0065 c. M: 0.0112 c. 778: 363 26 389 P T3 SD: 0.0055 c. M: 0.0095 c. 808: 377 27 404 P T3 SD: 0.0046 c. M: 0.0079 c. 838: 391 28 419 P T3 SD: 0.0037 c. M: 0.0064 c. 868: 405 29 434 P T3 SD: 0.0029 c. M: 0.0051 c. 898: 419 30 449 P T3 SD: 0.0022 c. M: 0.0038 c. 928: 433 31 464 P T3 SD: 0.0015 c. M: 0.0026 c. 958: 447 32 479 P T3 SD: 0.0008 c. M: 0.0015 c. 988: 461 33 494 P T3 SD: 0.0002 c. M: 0.0004 c. 2006: 936 67 1003 P T3 SD: 0.0001 c. M:-0.0001 c.
FIT/HARMONIC
1 x x 2 S SD: 700.0000 cents 2 x x 3 S SD: 201.9550 cents 3 x x 4 S SD: 1.9550 cents 4 x x 5 S SD: 113.6863 cents 5 x 6:7 S SD: 52.7187 cents 6 x 7:8 S SD: 8.4919 cents 7:8 x 9 S SD: 32.4754 cents 8:9 x 11 SD: 29.5690 cents 9:10 x 12 S SD: 25.4669 cents 11 x 13:15 SD: 26.9386 cents 12 x 14:16 S SD: 8.4919 cents 13 x 15:17 SD: 17.8220 cents 14:16 x 19 SD: 14.3829 cents 15:17 x 20 SD: 8.3640 cents 16:18 x 21 S SD: 20.7215 cents 17:19:20:23 SD: 18.8180 cents 18 x 21:24 S SD: 8.4919 cents 19 x 22:25 SD: 12.5874 cents 20 x 23:27 SD: 10.5698 cents 21:24 x 28 S SD: 1.4441 cents 22:25 x 29 SD: 12.4140 cents 24:27:28:32 S SD: 11.3148 cents 25 x 29:33 SD: 10.2822 cents 26 x 30:35 SD: 7.3928 cents 27:31 x 36 SD: 3.0938 cents 28:32 x 37 SD: 8.8053 cents 30:34:35:40 SD: 7.9194 cents 32 x 37:43 SD: 5.7979 cents 33 x 38:44 SD: 3.0413 cents 34:39 x 45 SD: 7.6631 cents 35:40 x 47 SD: 5.2914 cents 39 x 45:52 SD: 1.4937 cents 40 x 46:53 SD: 7.5615 cents 41:47 x 55 SD: 4.5639 cents 46 x 53:61 SD: 6.1740 cents 47:54 x 63 SD: 5.0518 cents 48:55 x 64 SD: 1.5387 cents 52 x 60:69 SD: 5.2716 cents 53 x 61:71 SD: 4.5322 cents 54:62 x 72 SD: 3.0938 cents 57:65:66:76 SD: 2.4364 cents 59 x 68:79 SD: 3.4118 cents 60 x 69:80 SD: 4.1368 cents 61:70 x 81 SD: 5.1653 cents 62:71:72:83 SD: 3.4274 cents 63:72:73:84 SD: 1.9402 cents 66 x 76:88 SD: 3.0413 cents 67:77 x 89 SD: 5.6528 cents 68:78:79:91 SD: 3.7862 cents 69:79:80:92 SD: 2.1566 cents 73 x 84:97 SD: 5.2782 cents 74:85 x 99 SD: 3.8398 cents 75:86:87:100 SD: 2.6944 cents 77:88:89:103 SD: 1.4311 cents 80 x 92:107 SD: 4.3735 cents 81:93:94:108 SD: 3.2892 cents 82:94:95:109 SD: 3.0735 cents 83:95:96:111 SD: 1.2668 cents 84:96:97:112 SD: 1.0070 cents 90:103:104:120 SD: 0.6659 cents 167:191:193:223 SD: 0.3867 cents 194:222:224:259 SD: 0.3697 cents 257:294:297:343 SD: 0.2255 cents 361:413:417:482 SD: 0.2158 cents 367:420:424:490 SD: 0.1558 cents 451:516:521:602 SD: 0.0999 cents 457:523:528:610 SD: 0.0828 cents