Scala analysis: magic16septimage
Magic[16] in regular Septimage tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57.719 cents 57.718713 2: 207.604 cents 207.604289 3: 265.323 cents 265.323002 4: 323.042 cents 323.041716 5: 380.760 cents 380.760429 6: 438.479 cents 438.479142 7: 496.198 cents 496.197856 8: 646.083 cents 646.083431 9: 703.802 cents 703.802144 10: 761.521 cents 761.520858 11: 819.240 cents 819.239571 12: 876.958 cents 876.958284 13: 1026.844 cents 1026.843860 14: 1084.563 cents 1084.562573 15: 1142.281 cents 1142.281287 16: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 57.7187 cents 57.7187 1: 57.7187 cents 57.7187 2: 149.8856 cents 149.8856 3: 57.7187 cents 57.7187 4: 57.7187 cents 57.7187 5: 57.7187 cents 57.7187 6: 57.7187 cents 57.7187 7: 57.7187 cents 57.7187 8: 149.8856 cents 149.8856 9: 57.7187 cents 57.7187 10: 57.7187 cents 57.7187 11: 57.7187 cents 57.7187 12: 57.7187 cents 57.7187 13: 149.8856 cents 149.8856 14: 57.7187 cents 57.7187 15: 57.7187 cents 57.7187 16: 57.7187 cents 57.7187
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 57.71871 cents 1: 3 149.88558 cents 2: 10 115.43743 cents 2: 6 207.60429 cents 3: 7 173.15614 cents 3: 9 265.32300 cents 4: 4 230.87485 cents 4: 12 323.04172 cents 5: 1 288.59357 cents 5: 15 380.76043 cents 6: 14 438.47914 cents 6: 2 530.64600 cents 7: 11 496.19786 cents 7: 5 588.36472 cents 8: 8 553.91657 cents 8: 8 646.08343 cents 9: 5 611.63528 cents 9: 11 703.80214 cents 10: 2 669.35400 cents 10: 14 761.52086 cents 11: 15 819.23957 cents 11: 1 911.40643 cents 12: 12 876.95828 cents 12: 4 969.12515 cents 13: 9 934.67700 cents 13: 7 1026.84386 cents 14: 6 992.39571 cents 14: 10 1084.56257 cents 15: 3 1050.11442 cents 15: 13 1142.28129 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 0.0 : 57.7 207.6 265.3 323.0 380.8 438.5 496.2 646.1 703.8 761.5 819.2 877.0 1026.8 1084.6 1142.3 1200.0 57.7 : 149.9 207.6 265.3 323.0 380.8 438.5 588.4 646.1 703.8 761.5 819.2 969.1 1026.8 1084.6 1142.3 1200.0 207.6 : 57.7 115.4 173.2 230.9 288.6 438.5 496.2 553.9 611.6 669.4 819.2 877.0 934.7 992.4 1050.1 1200.0 265.3 : 57.7 115.4 173.2 230.9 380.8 438.5 496.2 553.9 611.6 761.5 819.2 877.0 934.7 992.4 1142.3 1200.0 323.0 : 57.7 115.4 173.2 323.0 380.8 438.5 496.2 553.9 703.8 761.5 819.2 877.0 934.7 1084.6 1142.3 1200.0 380.8 : 57.7 115.4 265.3 323.0 380.8 438.5 496.2 646.1 703.8 761.5 819.2 877.0 1026.8 1084.6 1142.3 1200.0 438.5 : 57.7 207.6 265.3 323.0 380.8 438.5 588.4 646.1 703.8 761.5 819.2 969.1 1026.8 1084.6 1142.3 1200.0 496.2 : 149.9 207.6 265.3 323.0 380.8 530.6 588.4 646.1 703.8 761.5 911.4 969.1 1026.8 1084.6 1142.3 1200.0 646.1 : 57.7 115.4 173.2 230.9 380.8 438.5 496.2 553.9 611.6 761.5 819.2 877.0 934.7 992.4 1050.1 1200.0 703.8 : 57.7 115.4 173.2 323.0 380.8 438.5 496.2 553.9 703.8 761.5 819.2 877.0 934.7 992.4 1142.3 1200.0 761.5 : 57.7 115.4 265.3 323.0 380.8 438.5 496.2 646.1 703.8 761.5 819.2 877.0 934.7 1084.6 1142.3 1200.0 819.2 : 57.7 207.6 265.3 323.0 380.8 438.5 588.4 646.1 703.8 761.5 819.2 877.0 1026.8 1084.6 1142.3 1200.0 877.0 : 149.9 207.6 265.3 323.0 380.8 530.6 588.4 646.1 703.8 761.5 819.2 969.1 1026.8 1084.6 1142.3 1200.0 1026.8: 57.7 115.4 173.2 230.9 380.8 438.5 496.2 553.9 611.6 669.4 819.2 877.0 934.7 992.4 1050.1 1200.0 1084.6: 57.7 115.4 173.2 323.0 380.8 438.5 496.2 553.9 611.6 761.5 819.2 877.0 934.7 992.4 1142.3 1200.0 1142.3: 57.7 115.4 265.3 323.0 380.8 438.5 496.2 553.9 703.8 761.5 819.2 877.0 934.7 1084.6 1142.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.7187 .. 149.8856 cents 92.16686 cents 57.71871 cents 2: 115.4374 .. 207.6043 cents 92.16686 cents -34.44815 cents 3: 173.1561 .. 265.3230 cents 92.16686 cents -34.44815 cents 4: 230.8749 .. 323.0417 cents 92.16686 cents -34.44815 cents 5: 288.5936 .. 380.7604 cents 92.16686 cents -34.44815 cents 6: 438.4791 .. 530.6460 cents 92.16686 cents 57.71871 cents 7: 496.1979 .. 588.3647 cents 92.16686 cents -34.44815 cents 8: 553.9166 .. 646.0834 cents 92.16686 cents -34.44815 cents 9: 611.6353 .. 703.8021 cents 92.16686 cents -34.44815 cents 10: 669.3540 .. 761.5209 cents 92.16686 cents -34.44815 cents 11: 819.2396 .. 911.4064 cents 92.16686 cents 57.71871 cents 12: 876.9583 .. 969.1251 cents 92.16686 cents -34.44815 cents 13: 934.6770 .. 1026.8439 cents 92.16686 cents -34.44815 cents 14: 992.3957 .. 1084.5626 cents 92.16686 cents -34.44815 cents 15: 1050.1144 .. 1142.2813 cents 92.16686 cents -34.44815 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 57.71871 cents, class 1 Average step (divided formal octave): 75.0000 cents Largest one step interval : 149.88558 cents Average / Smallest step : 1.299405 Largest / Average step : 1.998474 Largest / Smallest step : 2.596828 Median interval of one step : 57.71871 cents, amount: 13 Most common interval of one step : 57.71871 cents, amount: 13 Least squares average step : 76.26298 cents, oct.: 1220.20771 cents Scale is not proper Scale has Myhill's property chromas: 92.16686 cents and 34.44815 cents, ratio: 2.675524 generators: 5 of 380.76043 cents and 11 of 819.23957 cents ET pair of linear temperament : 19&22 Scale is distributional even Scale is a mode of a 1289-tone equal temperament with octave 1200.000 cents degrees: 62 223 285 347 409 471 533 694 756 818 880 942 1103 1165 1227 1289 generators: 409 and 880 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAAAABAAAABAAA Step pattern size order : SLSSSSSLSSSSLSSS Scale is a Constant Structure, by a margin of 23.27056 cents Scale diversity : 1.194895 Lumma stability : 0.192396 Lumma impropriety factor : 0.344481 Rothenberg efficiency : 0.708333 redundancy: 0.291667 Efficiency x scale size : 11.333333 Number of different interval sizes : 30 = 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 : 23.27056 cents Most common intervals : 380.76043 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 553.917 819.240 cents Most common triad is 0.0 380.760 819.240 cents, amount: 14 Number of recognisable fifths : 11, average 703.8021 cents Formal octave complements present : 11 = 68.7500% Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 12-13 -- Rational properties --
FIT/MODE
16: 0 2 1 1 1 0 1 2 1 1 0 1 2 1 1 1 N T3 SD: 43.1309 c. M: 69.2396 c. 17: 1 2 1 1 0 1 1 2 1 1 1 0 3 0 1 1 N SD: 19.7351 c. M:-31.9797 c. 19: 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 P M ME SD: 9.5078 c. M: 18.1306 c. 22: 1 3 1 1 1 1 1 3 1 1 1 1 3 1 1 1 N M DE SD: 5.5469 c. M:-10.5775 c. 41: 2 5 2 2 2 2 2 5 2 2 2 2 5 2 2 2 N M DE SD: 1.4297 c. M: 2.7262 c. 63: 3 8 3 3 3 3 3 8 3 3 3 3 8 3 3 3 N M DE SD: 1.0066 c. M:-1.9195 c. 104: 5 13 5 5 5 5 5 13 5 5 5 5 13 5 5 5 N M DE SD: 0.0462 c. M:-0.0880 c. 665: 32 83 32 32 32 32 32 83 32 32 32 32 83 32 32 32 N M DE SD: 0.0448 c. M: 0.0855 c. 769: 37 96 37 37 37 37 37 96 37 37 37 37 96 37 37 37 N M DE SD: 0.0325 c. M: 0.0620 c. 873: 42 109 42 42 42 42 42 109 42 42 42 42 109 42 42 42 N M DE SD: 0.0232 c. M: 0.0442 c. 977: 47 122 47 47 47 47 47 122 47 47 47 47 122 47 47 47 N M DE SD: 0.0158 c. M: 0.0301 c. 1081: 52 135 52 52 52 52 52 135 52 52 52 52 135 52 52 52 N M DE SD: 0.0098 c. M: 0.0187 c. 1185: 57 148 57 57 57 57 57 148 57 57 57 57 148 57 57 57 N M DE SD: 0.0049 c. M: 0.0094 c. 1289: 62 161 62 62 62 62 62 161 62 62 62 62 161 62 62 62 N M DE SD: 0.0008 c. M: 0.0015 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.9236 cents 3 .. 6 match: 3 H SD: 2.5425 cents 4 .. 8 match: 4 H SD: 14.5781 cents 5 .. 10 match: 5 H SD: 12.9806 cents 6 .. 12 match: 6 H SD: 3.9829 cents 7 .. 14 match: 7 H SD: 10.2471 cents 8 .. 16 match: 8 H SD: 10.3977 cents 9 .. 18 match: 9 H SD: 5.6716 cents 10 .. 20 match: 9 SD: 7.6043 cents 11 .. 22 match: 10 S SD: 8.4653 cents 12 .. 24 match: 10 S SD: 5.7216 cents 13 .. 26 match: 11 SD: 8.4738 cents 14 .. 28 match: 13 SD: 6.8350 cents 15 .. 30 match: 13 SD: 5.3339 cents 16 .. 32 match: 14 SD: 5.2172 cents 17 .. 34 match: 14 SD: 5.1373 cents 18 .. 36 match: 15 S SD: 4.0993 cents 19 .. 38 match: 14 SD: 6.0677 cents 20 .. 40 match: 15 SD: 3.6208 cents 21 .. 42 match: 15 SD: 4.3412 cents 22 .. 44 match: 15 SD: 4.1384 cents 23 .. 46 match: 16 SD: 3.9073 cents 24 .. 48 match: 16 SD: 2.4498 cents 30 .. 60 match: 16 SD: 2.3640 cents 31 .. 62 match: 16 SD: 2.3194 cents 36 .. 72 match: 16 SD: 2.2254 cents 38 .. 76 match: 16 SD: 1.9277 cents 48 .. 96 match: 16 SD: 1.4281 cents 53 .. 106 match: 16 SD: 1.3804 cents 58 .. 116 match: 16 SD: 1.3286 cents 60 .. 120 match: 16 SD: 1.2267 cents 62 .. 124 match: 16 SD: 1.1247 cents 73 .. 146 match: 16 SD: 1.0670 cents 78 .. 156 match: 16 SD: 0.9257 cents 84 .. 168 match: 16 SD: 0.8760 cents 91 .. 182 match: 16 SD: 0.8584 cents 93 .. 186 match: 16 SD: 0.7589 cents 94 .. 188 match: 16 SD: 0.7306 cents 108 .. 216 match: 16 SD: 0.7232 cents 109 .. 218 match: 16 SD: 0.6862 cents 111 .. 222 match: 16 SD: 0.6772 cents 117 .. 234 match: 16 SD: 0.5726 cents 121 .. 242 match: 16 SD: 0.5580 cents 126 .. 252 match: 16 SD: 0.4882 cents 150 .. 300 match: 16 SD: 0.3972 cents 180 .. 360 match: 16 SD: 0.3907 cents 195 .. 390 match: 16 SD: 0.3671 cents 199 .. 398 match: 16 SD: 0.3464 cents 205 .. 410 match: 16 SD: 0.3095 cents 235 .. 470 match: 16 SD: 0.2426 cents 259 .. 518 match: 16 SD: 0.2387 cents 289 .. 578 match: 16 SD: 0.2242 cents 337 .. 674 match: 16 SD: 0.2161 cents 347 .. 694 match: 16 SD: 0.2087 cents 355 .. 710 match: 16 SD: 0.2022 cents 361 .. 722 match: 16 SD: 0.2019 cents 362 .. 724 match: 16 SD: 0.1865 cents 382 .. 764 match: 16 SD: 0.1816 cents 385 .. 770 match: 16 SD: 0.1414 cents 440 .. 880 match: 16 SD: 0.1228 cents 566 .. 1132 match: 16 SD: 0.1126 cents 590 .. 1180 match: 16 SD: 0.0790 cents