Scala analysis: 711_S20
Semi-tempered tetrachord 1.13847 * 1.125 * 1.041
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 224.516 cents 224.515530 2: 428.426 cents 428.425530 3: 497.990 cents 497.989610
SHOW/INTERVAL
0: 69.5641 cents 69.5641 1: 224.5155 cents 224.5155 2: 203.9100 cents 203.9100 3: 69.5641 cents 69.5641
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 69.56408 cents 1: 1 203.91000 cents 1: 1 224.51553 cents 2: 1 273.47408 cents 2: 1 294.07961 cents 2: 1 428.42553 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 : 224.5 428.4 498.0 224.5: 203.9 273.5 498.0 428.4: 69.6 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 69.5641 .. 224.5155 cents 154.95145 cents 69.56408 cents 2: 273.4741 .. 428.4255 cents 154.95145 cents 48.95855 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 69.56408 cents, class 1 Average step (divided formal octave): 165.9965 cents Largest one step interval : 224.51553 cents Average / Smallest step : 2.386239 Largest / Average step : 1.352531 Largest / Smallest step : 3.227464 Median interval of one step : 203.91000 cents, amount: 1 Least squares average step : 183.95253 cents, oct.: 551.85759 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1353-tone equal temperament with octave 497.990 cents degrees: 610 1164 1353 Least number of segments generator : 677 of 249.179 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1084 of 398.981 cents and inv. generated superset size: 52 = 49 more = 1733.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LMS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 48.95855 cents Scale diversity : 0.889227 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.377692 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / 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 : 20.60553 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly decreasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 134.3459 cents: 2 -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 65.1247 c. M: 96.4325 c. 4: 2 1 1 P M ME S SD: 34.7223 c. M: 54.9333 c. 5: 2 2 1 SP M ME S SD: 22.6798 c. M: 30.0338 c. 6: 3 2 1 P T3 SD: 16.1215 c. M:-24.4793 c. 7: 3 3 1 SP M DE S SD: 6.4681 c. M: 11.0914 c. 13: 6 5 2 SP T3 SD: 5.1011 c. M: 7.0497 c. 15: 7 6 2 SP T3 SD: 4.9027 c. M:-7.8796 c. 20: 9 8 3 SP T3 SD: 2.9742 c. M: 5.1344 c. 22: 10 9 3 SP T3 SD: 1.4308 c. M:-1.8434 c. 29: 13 12 4 SP T3 SD: 0.8949 c. M: 1.2788 c. 49: 22 20 7 SP T3 SD: 1.0567 c. M: 1.5773 c. 51: 23 21 7 SP T3 SD: 0.7012 c. M:-1.2126 c. 64: 29 26 9 SP T3 SD: 0.7089 c. M:-1.1360 c. 71: 32 29 10 SP T3 SD: 0.3346 c. M: 0.5753 c. 93: 42 38 13 SP T3 SD: 0.2228 c. M:-0.3830 c. 100: 45 41 14 SP T3 SD: 0.2585 c. M: 0.4202 c. 122: 55 50 17 SP T3 SD: 0.0996 c. M:-0.1721 c. 193: 87 79 27 SP T3 SD: 0.0624 c. M: 0.1029 c. 286: 129 117 40 SP T3 SD: 0.0767 c. M:-0.1022 c. 315: 142 129 44 SP T3 SD: 0.0146 c. M: 0.0250 c. 845: 381 346 118 SP T3 SD: 0.0180 c. M:-0.0223 c. 916: 413 375 128 SP T3 SD: 0.0162 c. M: 0.0240 c. 1038: 468 425 145 SP T3 SD: 0.0067 c. M:-0.0116 c. 1353: 610 554 189 SP T3 SD: 0.0018 c. M:-0.0031 c. 1668: 752 683 233 SP T3 SD: 0.0014 c. M: 0.0022 c.
FIT/HARMONIC
1 x x 2 S SD: 702.0104 cents 2 x x 3 S SD: 203.9654 cents 3 x x 4 S SD: 0.0554 cents 4 x 5 x S SD: 42.1118 cents 5:6 x 7 S SD: 62.1449 cents 6:7 x 8 S SD: 21.1777 cents 7:8:9 x S SD: 4.7083 cents 9:10 x 12 S SD: 21.0559 cents 10:11:13 x SD: 32.4293 cents 11:13:14:15 SD: 25.4351 cents 12:14:15:16 S SD: 19.9092 cents 13:15 x 17 SD: 20.4073 cents 14:16:18:19 S SD: 10.7031 cents 15:17:19:20 SD: 6.9058 cents 21:24:27:28 S SD: 3.1389 cents 36:41:46:48 SD: 1.3704 cents 57:65:73:76 SD: 0.9534 cents 93:106:119:124 SD: 0.8608 cents 150:171:192:200 SD: 0.8510 cents 153:174:196:204 SD: 0.6282 cents 174:198:223:232 SD: 0.4636 cents 210:239:269:280 SD: 0.2063 cents 246:280:315:328 SD: 0.1863 cents 267:304:342:356 SD: 0.0787 cents 513:584:657:684 SD: 0.0524 cents