Scala analysis: xen18-erlich-garibaldi-17
12L 5s MOS for Garibaldi, L=89.08, s=26.36
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 89.080 cents 89.080000 2: 115.440 cents 115.440000 3: 204.520 cents 204.520000 4: 293.600 cents 293.600000 5: 382.680 cents 382.680000 6: 409.040 cents 409.040000 7: 498.120 cents 498.120000 8: 587.200 cents 587.200000 9: 613.560 cents 613.560000 10: 702.640 cents 702.640000 11: 791.720 cents 791.720000 12: 818.080 cents 818.080000 13: 907.160 cents 907.160000 14: 996.240 cents 996.240000 15: 1085.320 cents 1085.320000 16: 1111.680 cents 1111.680000 17: 1200.760 cents 1200.760000
SHOW/INTERVAL
0: 89.0800 cents 89.0800 1: 89.0800 cents 89.0800 2: 26.3600 cents 26.3600 3: 89.0800 cents 89.0800 4: 89.0800 cents 89.0800 5: 89.0800 cents 89.0800 6: 26.3600 cents 26.3600 7: 89.0800 cents 89.0800 8: 89.0800 cents 89.0800 9: 26.3600 cents 26.3600 10: 89.0800 cents 89.0800 11: 89.0800 cents 89.0800 12: 26.3600 cents 26.3600 13: 89.0800 cents 89.0800 14: 89.0800 cents 89.0800 15: 89.0800 cents 89.0800 16: 26.3600 cents 26.3600 17: 89.0800 cents 89.0800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 26.36000 cents 1: 12 89.08000 cents 2: 10 115.44000 cents 2: 7 178.16000 cents 3: 15 204.52000 cents 3: 2 267.24000 cents 4: 3 230.88000 cents 4: 14 293.60000 cents 5: 8 319.96000 cents 5: 9 382.68000 cents 6: 13 409.04000 cents 6: 4 471.76000 cents 7: 1 435.40000 cents 7: 16 498.12000 cents 8: 6 524.48000 cents 8: 11 587.20000 cents 9: 11 613.56000 cents 9: 6 676.28000 cents 10: 16 702.64000 cents 10: 1 765.36000 cents 11: 4 729.00000 cents 11: 13 791.72000 cents 12: 9 818.08000 cents 12: 8 880.80000 cents 13: 14 907.16000 cents 13: 3 969.88000 cents 14: 2 933.52000 cents 14: 15 996.24000 cents 15: 7 1022.60000 cents 15: 10 1085.32000 cents 16: 12 1111.68000 cents 16: 5 1174.40000 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 8 9 10 11 12 13 14 15 16 17 0.0 : 89.1 115.4 204.5 293.6 382.7 409.0 498.1 587.2 613.6 702.6 791.7 818.1 907.2 996.2 1085.3 1111.7 1200.8 89.1 : 26.4 115.4 204.5 293.6 320.0 409.0 498.1 524.5 613.6 702.6 729.0 818.1 907.2 996.2 1022.6 1111.7 1200.8 115.4 : 89.1 178.2 267.2 293.6 382.7 471.8 498.1 587.2 676.3 702.6 791.7 880.8 969.9 996.2 1085.3 1174.4 1200.8 204.5 : 89.1 178.2 204.5 293.6 382.7 409.0 498.1 587.2 613.6 702.6 791.7 880.8 907.2 996.2 1085.3 1111.7 1200.8 293.6 : 89.1 115.4 204.5 293.6 320.0 409.0 498.1 524.5 613.6 702.6 791.7 818.1 907.2 996.2 1022.6 1111.7 1200.8 382.7 : 26.4 115.4 204.5 230.9 320.0 409.0 435.4 524.5 613.6 702.6 729.0 818.1 907.2 933.5 1022.6 1111.7 1200.8 409.0 : 89.1 178.2 204.5 293.6 382.7 409.0 498.1 587.2 676.3 702.6 791.7 880.8 907.2 996.2 1085.3 1174.4 1200.8 498.1 : 89.1 115.4 204.5 293.6 320.0 409.0 498.1 587.2 613.6 702.6 791.7 818.1 907.2 996.2 1085.3 1111.7 1200.8 587.2 : 26.4 115.4 204.5 230.9 320.0 409.0 498.1 524.5 613.6 702.6 729.0 818.1 907.2 996.2 1022.6 1111.7 1200.8 613.6 : 89.1 178.2 204.5 293.6 382.7 471.8 498.1 587.2 676.3 702.6 791.7 880.8 969.9 996.2 1085.3 1174.4 1200.8 702.6 : 89.1 115.4 204.5 293.6 382.7 409.0 498.1 587.2 613.6 702.6 791.7 880.8 907.2 996.2 1085.3 1111.7 1200.8 791.7 : 26.4 115.4 204.5 293.6 320.0 409.0 498.1 524.5 613.6 702.6 791.7 818.1 907.2 996.2 1022.6 1111.7 1200.8 818.1 : 89.1 178.2 267.2 293.6 382.7 471.8 498.1 587.2 676.3 765.4 791.7 880.8 969.9 996.2 1085.3 1174.4 1200.8 907.2 : 89.1 178.2 204.5 293.6 382.7 409.0 498.1 587.2 676.3 702.6 791.7 880.8 907.2 996.2 1085.3 1111.7 1200.8 996.2 : 89.1 115.4 204.5 293.6 320.0 409.0 498.1 587.2 613.6 702.6 791.7 818.1 907.2 996.2 1022.6 1111.7 1200.8 1085.3: 26.4 115.4 204.5 230.9 320.0 409.0 498.1 524.5 613.6 702.6 729.0 818.1 907.2 933.5 1022.6 1111.7 1200.8 1111.7: 89.1 178.2 204.5 293.6 382.7 471.8 498.1 587.2 676.3 702.6 791.7 880.8 907.2 996.2 1085.3 1174.4 1200.8 1200.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.3600 .. 89.0800 cents 62.72000 cents 26.36000 cents 2: 115.4400 .. 178.1600 cents 62.72000 cents 26.36000 cents 3: 204.5200 .. 267.2400 cents 62.72000 cents 26.36000 cents 4: 230.8800 .. 293.6000 cents 62.72000 cents -36.36000 cents 5: 319.9600 .. 382.6800 cents 62.72000 cents 26.36000 cents 6: 409.0400 .. 471.7600 cents 62.72000 cents 26.36000 cents 7: 435.4000 .. 498.1200 cents 62.72000 cents -36.36000 cents 8: 524.4800 .. 587.2000 cents 62.72000 cents 26.36000 cents 9: 613.5600 .. 676.2800 cents 62.72000 cents 26.36000 cents 10: 702.6400 .. 765.3600 cents 62.72000 cents 26.36000 cents 11: 729.0000 .. 791.7200 cents 62.72000 cents -36.36000 cents 12: 818.0800 .. 880.8000 cents 62.72000 cents 26.36000 cents 13: 907.1600 .. 969.8800 cents 62.72000 cents 26.36000 cents 14: 933.5200 .. 996.2400 cents 62.72000 cents -36.36000 cents 15: 1022.6000 .. 1085.3200 cents 62.72000 cents 26.36000 cents 16: 1111.6800 .. 1174.4000 cents 62.72000 cents 26.36000 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 26.36000 cents, class 1 Average step (divided formal octave): 70.6329 cents Largest one step interval : 89.08000 cents Average / Smallest step : 2.679550 Largest / Average step : 1.261168 Largest / Smallest step : 3.379363 Median interval of one step : 89.08000 cents, amount: 12 Most common interval of one step : 89.08000 cents, amount: 12 Least squares average step : 70.56267 cents, oct.: 1199.56533 cents Scale is not proper Scale has Myhill's property chromas: 62.72000 cents and 36.36000 cents, ratio: 1.724972 generators: 7 of 498.12000 cents and 10 of 702.64000 cents ET pair of linear temperament : 12&41 Scale is distributional even Scale is a mode of a 1321-tone equal temperament with octave 1200.760 cents degrees: 98 127 225 323 421 450 548 646 675 773 871 900 998 1096 1194 1223 1321 generators: 548 and 773 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAABAABAAABA Step pattern size order : LSLLLSLLSLLSLLLSL Scale is a Constant Structure, by a margin of 26.36000 cents Scale diversity : 1.176826 Lumma stability : 0.285386 Lumma impropriety factor : 0.121123 Rothenberg efficiency : 0.705882 redundancy: 0.294118 Efficiency x scale size : 12.000000 Number of different interval sizes : 32 = 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 : 26.36000 cents Most common intervals : 498.12000 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 498.120 996.240 cents Most common triad is 0.0 498.120 702.640 cents, amount: 15 Number of recognisable fifths : 16, average 702.6400 cents Number of recognisable fourths : 16, average 498.1200 cents Scale contains two identical disjunct "tetrachords" of 8 notes Formal octave complements present : 17 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 8-9 -- Rational properties --
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.0744 c. M:-29.5153 c. 20: 1 1 1 2 1 1 1 2 0 2 1 1 1 2 1 1 1 N D3 I SD: 17.5742 c. M: 29.0420 c. 21: 2 0 2 1 2 0 2 1 1 1 2 0 2 1 2 0 2 N T3 I SD: 16.0162 c. M: 25.2781 c. 22: 2 0 2 1 2 0 2 2 0 2 1 1 2 1 2 0 2 N T3 SD: 15.4468 c. M: 27.6000 c. 23: 2 0 2 2 1 1 2 1 1 1 2 1 1 2 2 0 2 N D3 I SD: 14.8435 c. M: 23.9496 c. 24: 2 0 2 2 2 0 2 2 0 2 2 0 2 2 2 0 2 N M DE I SD: 10.7614 c. M:-17.5733 c. 29: 2 1 2 2 2 1 2 2 1 2 2 1 2 2 2 1 2 P M ME I SD: 6.1423 c. M: 10.0303 c. 41: 3 1 3 3 3 1 3 3 1 3 3 1 3 3 3 1 3 N M DE I SD: 1.1949 c. M:-1.9512 c. 94: 7 2 7 7 7 2 7 7 2 7 7 2 7 7 7 2 7 N M DE I SD: 0.3315 c. M:-0.5413 c. 135: 10 3 10 10 10 3 10 10 3 10 10 3 10 10 10 3 10 N M DE I SD: 0.1321 c. M:-0.2157 c. 229: 17 5 17 17 17 5 17 17 5 17 17 5 17 17 17 5 17 N M DE I SD: 0.0582 c. M:-0.0950 c. 364: 27 8 27 27 27 8 27 27 8 27 27 8 27 27 27 8 27 N M DE I SD: 0.0124 c. M:-0.0202 c. 957: 71 21 71 71 71 21 71 71 21 71 71 21 71 71 71 21 71 N M DE I SD: 0.0045 c. M:-0.0074 c. 1321: 98 29 98 98 98 29 98 98 29 98 98 29 98 98 98 29 98 N M DE I SD: 0.0001 c. M:-0.0002 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.7600 cents 2 .. 4 match: 2 H SD: 0.5116 cents 3 .. 6 match: 3 H SD: 7.6047 cents 4 .. 8 match: 4 H SD: 6.9182 cents 5 .. 10 match: 5 H SD: 6.2730 cents 6 .. 12 match: 6 H SD: 8.3804 cents 7 .. 14 match: 7 H SD: 6.9249 cents 8 .. 16 match: 8 H SD: 6.3323 cents 9 .. 18 match: 9 H SD: 6.6824 cents 10 .. 20 match: 10 H SD: 6.7864 cents 11 .. 22 match: 11 H SD: 8.9993 cents 12 .. 24 match: 12 H SD: 5.3805 cents 13 .. 26 match: 13 H SD: 7.3957 cents 14 .. 28 match: 13 S SD: 5.8631 cents 15 .. 30 match: 13 SD: 4.8420 cents 16 .. 32 match: 14 S SD: 4.5297 cents 17 .. 34 match: 13 SD: 5.1800 cents 18 .. 36 match: 15 S SD: 4.7076 cents 19 .. 38 match: 12 SD: 5.2558 cents 20 .. 40 match: 14 SD: 4.6871 cents 21 .. 42 match: 16 SD: 4.2095 cents 22 .. 44 match: 15 SD: 3.8466 cents 23 .. 46 match: 16 SD: 3.5585 cents 24 .. 48 match: 15 SD: 3.6706 cents 26 .. 52 match: 15 SD: 3.1995 cents 27 .. 54 match: 13 SD: 3.6747 cents 28 .. 56 match: 16 SD: 3.1665 cents 29 .. 58 match: 15 SD: 3.2288 cents 30 .. 60 match: 16 SD: 2.5417 cents 31 .. 62 match: 14 SD: 2.4706 cents 32 .. 64 match: 15 SD: 2.2297 cents 33 .. 66 match: 16 SD: 2.0391 cents 34 .. 68 match: 15 SD: 2.8018 cents 35 .. 70 match: 15 SD: 2.8349 cents 36 .. 72 match: 15 SD: 2.4227 cents 38 .. 76 match: 17 SD: 1.9114 cents 39 .. 78 match: 16 SD: 2.1565 cents 40 .. 80 match: 17 SD: 1.6744 cents 41 .. 82 match: 16 SD: 1.9593 cents 42 .. 84 match: 17 SD: 1.6645 cents 43 .. 86 match: 16 SD: 2.1872 cents 44 .. 88 match: 17 SD: 2.0222 cents 45 .. 90 match: 17 SD: 1.6616 cents 48 .. 96 match: 16 SD: 1.3614 cents 49 .. 98 match: 16 SD: 1.6202 cents 50 .. 100 match: 16 SD: 1.7045 cents 54 .. 108 match: 17 SD: 1.3007 cents 57 .. 114 match: 17 SD: 1.2908 cents 60 .. 120 match: 17 SD: 1.2248 cents 64 .. 128 match: 17 SD: 1.1687 cents 70 .. 140 match: 17 SD: 1.1248 cents 71 .. 142 match: 17 SD: 0.9931 cents 72 .. 144 match: 17 SD: 0.9217 cents 86 .. 172 match: 17 SD: 0.8896 cents 90 .. 180 match: 17 SD: 0.8208 cents 96 .. 192 match: 17 SD: 0.7772 cents 102 .. 204 match: 17 SD: 0.6851 cents 112 .. 224 match: 17 SD: 0.6234 cents 129 .. 258 match: 17 SD: 0.5056 cents 134 .. 268 match: 17 SD: 0.4736 cents 150 .. 300 match: 17 SD: 0.4617 cents 158 .. 316 match: 17 SD: 0.4480 cents 162 .. 324 match: 17 SD: 0.4446 cents 174 .. 348 match: 17 SD: 0.3316 cents 190 .. 380 match: 17 SD: 0.3168 cents 233 .. 466 match: 17 SD: 0.3078 cents 243 .. 486 match: 17 SD: 0.3035 cents 247 .. 494 match: 17 SD: 0.2666 cents 248 .. 496 match: 17 SD: 0.2660 cents 270 .. 540 match: 17 SD: 0.2417 cents 288 .. 576 match: 17 SD: 0.2389 cents 303 .. 606 match: 17 SD: 0.1818 cents 405 .. 810 match: 17 SD: 0.1789 cents 416 .. 832 match: 17 SD: 0.1725 cents 421 .. 842 match: 17 SD: 0.1544 cents 453 .. 906 match: 17 SD: 0.1516 cents 477 .. 954 match: 17 SD: 0.1452 cents 492 .. 984 match: 17 SD: 0.1303 cents 510 .. 1020 match: 17 SD: 0.1160 cents