Scala analysis: meanquar_16
1/4-comma mean-tone scale with split C#/Db, D#/Eb, G#/Ab and A#/Bb
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76.049 cents 76.049000 2: 117.109 cents 117.109000 3: 193.157 cents 193.157000 4: 269.206 cents 269.206000 5: 310.265 cents 310.265000 6: 5/4 386.313714 major third 7: 503.422 cents 503.422000 8: 579.471 cents 579.471000 9: 696.578 cents 696.578000 10: 25/16 772.627428 classic augmented fifth 11: 8/5 813.686286 minor sixth 12: 889.735 cents 889.735000 13: 965.784 cents 965.784000 14: 1006.843 cents 1006.843000 15: 1082.892 cents 1082.892000 16: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 117.1080 cents 117.1080 1: 76.0490 cents 76.0490 2: 41.0600 cents 41.0600 3: 76.0480 cents 76.0480 4: 76.0490 cents 76.0490 5: 41.0590 cents 41.0590 6: 76.0487 cents 76.0487 7: 117.1083 cents 117.1083 8: 76.0490 cents 76.0490 9: 117.1070 cents 117.1070 10: 76.0494 cents 76.0494 11: 128/125 41.0589 minor diesis, diesis 12: 76.0487 cents 76.0487 13: 76.0490 cents 76.0490 14: 41.0590 cents 41.0590 15: 76.0490 cents 76.0490 16: 117.1080 cents 117.1080
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 41.05900 cents 1: 1 41.06000 cents 1: 1 76.04800 cents 1: 2 76.04871 cents 1: 5 76.04900 cents 1: 1 76.04943 cents 1: 1 117.10700 cents 1: 1 117.10800 cents 1: 1 117.10829 cents 2: 2 117.10771 cents 2: 4 117.10800 cents 2: 1 117.10829 cents 2: 1 117.10900 cents 2: 1 152.09700 cents 2: 1 152.09771 cents 2: 1 193.15600 cents 2: 1 193.15643 cents 2: 3 193.15700 cents 2: 1 193.15729 cents 3: 1 193.15600 cents 3: 3 193.15671 cents 3: 4 193.15700 cents 3: 1 234.21529 cents 3: 2 234.21600 cents 3: 1 234.21700 cents 3: 1 269.20543 cents 3: 2 269.20600 cents 3: 1 310.26429 cents 4: 1 234.21557 cents 4: 1 234.21600 cents 4: 1 269.20471 cents 4: 1 269.20571 cents 4: 2 269.20600 cents 4: 1 310.26400 cents 4: 1 310.26429 cents 4: 5 310.26500 cents 4: 1 310.26600 cents 4: 1 386.31300 cents 4: 1 5/4 386.314 cents major third 5: 2 310.26471 cents 5: 2 310.26500 cents 5: 1 351.32500 cents 5: 3 386.31300 cents 5: 1 5/4 386.314 cents major third 5: 4 386.31400 cents 5: 1 427.37200 cents 5: 1 32/25 427.373 cents classic diminished fourth 5: 1 462.36243 cents 6: 1 5/4 386.314 cents major third 6: 1 386.31400 cents 6: 1 427.37200 cents 6: 1 32/25 427.373 cents classic diminished fourth 6: 3 427.37300 cents 6: 1 427.37400 cents 6: 2 462.36200 cents 6: 1 462.36271 cents 6: 1 462.36300 cents 6: 1 503.42100 cents 6: 3 503.42143 cents 7: 2 503.42100 cents 7: 2 503.42157 cents 7: 6 503.42200 cents 7: 1 503.42271 cents 7: 1 544.48029 cents 7: 1 579.46900 cents 7: 1 579.47000 cents 7: 2 579.47043 cents 8: 1 544.48100 cents 8: 1 544.48157 cents 8: 1 579.47000 cents 8: 2 579.47071 cents 8: 3 579.47100 cents 8: 3 620.52900 cents 8: 2 620.52929 cents 8: 1 620.53000 cents 8: 1 655.51843 cents 8: 1 655.51900 cents 9: 2 620.52957 cents 9: 1 620.53000 cents 9: 1 620.53100 cents 9: 1 655.51971 cents 9: 1 696.57729 cents 9: 6 696.57800 cents 9: 2 696.57843 cents 9: 2 696.57900 cents 10: 3 696.57857 cents 10: 1 696.57900 cents 10: 1 737.63700 cents 10: 1 737.63729 cents 10: 2 737.63800 cents 10: 1 772.62600 cents 10: 3 772.62700 cents 10: 1 25/16 772.627 cents classic augmented fifth 10: 1 772.62800 cents 10: 1 813.68600 cents 10: 1 8/5 813.686 cents minor sixth 11: 1 737.63757 cents 11: 1 25/16 772.627 cents classic augmented fifth 11: 1 772.62800 cents 11: 4 813.68600 cents 11: 1 8/5 813.686 cents minor sixth 11: 3 813.68700 cents 11: 1 848.67500 cents 11: 2 889.73500 cents 11: 2 889.73529 cents 12: 1 8/5 813.686 cents minor sixth 12: 1 813.68700 cents 12: 1 889.73400 cents 12: 5 889.73500 cents 12: 1 889.73571 cents 12: 1 889.73600 cents 12: 2 930.79400 cents 12: 1 930.79429 cents 12: 1 930.79529 cents 12: 1 965.78400 cents 12: 1 965.78443 cents 13: 1 889.73571 cents 13: 2 930.79400 cents 13: 1 930.79457 cents 13: 1 965.78300 cents 13: 2 965.78400 cents 13: 1 965.78471 cents 13: 4 1006.84300 cents 13: 3 1006.84329 cents 13: 1 1006.84400 cents 14: 1 1006.84271 cents 14: 3 1006.84300 cents 14: 1 1006.84357 cents 14: 1 1006.84400 cents 14: 1 1047.90229 cents 14: 1 1047.90300 cents 14: 1 1082.89100 cents 14: 1 1082.89171 cents 14: 4 1082.89200 cents 14: 2 1082.89229 cents 15: 1 1082.89171 cents 15: 1 1082.89200 cents 15: 1 1082.89300 cents 15: 1 1123.95057 cents 15: 5 1123.95100 cents 15: 2 1123.95129 cents 15: 1 1123.95200 cents 15: 1 1158.94000 cents 15: 3 1158.94100 cents Highest number of different intervals for one interval class: 11 Average number of different intervals per interval class: 9.60000 = 48/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.0 : 76.0 117.1 193.2 269.2 310.3 386.3 503.4 579.5 696.6 772.6 813.7 889.7 965.8 1006.8 1082.9 1200.0 76.0 : 41.1 117.1 193.2 234.2 310.3 427.4 503.4 620.5 696.6 737.6 813.7 889.7 930.8 1006.8 1124.0 1200.0 117.1 : 76.0 152.1 193.2 269.2 386.3 462.4 579.5 655.5 696.6 772.6 848.7 889.7 965.8 1082.9 1158.9 1200.0 193.2 : 76.0 117.1 193.2 310.3 386.3 503.4 579.5 620.5 696.6 772.6 813.7 889.7 1006.8 1082.9 1124.0 1200.0 269.2 : 41.1 117.1 234.2 310.3 427.4 503.4 544.5 620.5 696.6 737.6 813.7 930.8 1006.8 1047.9 1124.0 1200.0 310.3 : 76.0 193.2 269.2 386.3 462.4 503.4 579.5 655.5 696.6 772.6 889.7 965.8 1006.8 1082.9 1158.9 1200.0 386.3 : 117.1 193.2 310.3 386.3 427.4 503.4 579.5 620.5 696.6 813.7 889.7 930.8 1006.8 1082.9 1124.0 1200.0 503.4 : 76.0 193.2 269.2 310.3 386.3 462.4 503.4 579.5 696.6 772.6 813.7 889.7 965.8 1006.8 1082.9 1200.0 579.5 : 117.1 193.2 234.2 310.3 386.3 427.4 503.4 620.5 696.6 737.6 813.7 889.7 930.8 1006.8 1124.0 1200.0 696.6 : 76.0 117.1 193.2 269.2 310.3 386.3 503.4 579.5 620.5 696.6 772.6 813.7 889.7 1006.8 1082.9 1200.0 772.6 : 41.1 117.1 193.2 234.2 310.3 427.4 503.4 544.5 620.5 696.6 737.6 813.7 930.8 1006.8 1124.0 1200.0 813.7 : 76.0 152.1 193.2 269.2 386.3 462.4 503.4 579.5 655.5 696.6 772.6 889.7 965.8 1082.9 1158.9 1200.0 889.7 : 76.0 117.1 193.2 310.3 386.3 427.4 503.4 579.5 620.5 696.6 813.7 889.7 1006.8 1082.9 1124.0 1200.0 965.8 : 41.1 117.1 234.2 310.3 351.3 427.4 503.4 544.5 620.5 737.6 813.7 930.8 1006.8 1047.9 1124.0 1200.0 1006.8: 76.0 193.2 269.2 310.3 386.3 462.4 503.4 579.5 696.6 772.6 889.7 965.8 1006.8 1082.9 1158.9 1200.0 1082.9: 117.1 193.2 234.2 310.3 386.3 427.4 503.4 620.5 696.6 813.7 889.7 930.8 1006.8 1082.9 1124.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0590 .. 117.1083 cents 76.04929 cents 41.05900 cents 2: 117.1077 .. 193.1573 cents 76.04957 cents -0.00057 cents 3: 193.1560 .. 310.2643 cents 117.10829 cents -0.00129 cents 4: 234.2156 .. 386.3137 cents 152.09814 cents -76.04871 cents 5: 310.2647 .. 462.3624 cents 152.09771 cents -76.04900 cents 6: 386.3137 .. 503.4214 cents 117.10771 cents -76.04871 cents 7: 503.4210 .. 579.4704 cents 76.04943 cents -0.00043 cents 8: 544.4810 .. 655.5190 cents 111.03800 cents -34.98943 cents 9: 620.5296 .. 696.5790 cents 76.04943 cents -34.98943 cents 10: 696.5786 .. 813.6863 cents 117.10771 cents -0.00043 cents 11: 737.6376 .. 889.7353 cents 152.09771 cents -76.04871 cents 12: 813.6863 .. 965.7844 cents 152.09814 cents -76.04900 cents 13: 889.7357 .. 1006.8440 cents 117.10829 cents -76.04871 cents 14: 1006.8427 .. 1082.8923 cents 76.04957 cents -0.00129 cents 15: 1082.8917 .. 1158.9410 cents 76.04929 cents -0.00057 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 75.0000 cents Largest one step interval : 117.10829 cents Average / Smallest step : 1.826646 Largest / Average step : 1.561444 Largest / Smallest step : 2.852205 Median interval of one step : 76.04900 cents, amount: 5 Most common interval of one step : 76.04900 cents, amount: 5 Least squares average step : 73.33737 cents, oct.: 1173.39798 cents Scale is not proper Scale is a mode of a 789-tone equal temperament with octave 2/1 degrees: 50 77 127 177 204 254 331 381 458 508 535 585 635 662 712 789 Least number of segments generator : 395 of 600.760 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 458 of 696.578 cents and inv. generated superset size: 16 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCADEFAGHDEADAI Step pattern size order : DBCDADGDFEADDADG Scale is not a Constant Structure Scale diversity : 1.236475 Lumma stability : 0.068432 Lumma impropriety factor : 0.438564 Number of different interval sizes : 112 = 7.46667 / class Number of one step interval sizes : 9 Highest interval variety : 11 Mean interval variety : 9.60000 = 48/5 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 0.00029 cents Most common triad is 0.0 310.265 1006.843 cents, amount: 5 Number of recognisable fifths : 15, average 696.5783 cents Scale contains a complete diamond : 1 5 Formal octave complements present : 9 = 56.2500% Limited inverse transpositions : 15 Inversional symmetry on intervals : 7-8 15-16 -- Rational properties -- Prime limit : 5 (not all pitches rational)
FIT/MODE
16: 1 0 1 1 1 1 1 1 2 1 0 1 1 1 1 2 N T3 SD: 41.3014 c. M: 65.7840 c. 17: 1 0 1 1 1 1 2 1 1 1 1 1 1 1 1 2 N D3 SD: 39.5699 c. M: 66.7451 c. 18: 1 0 1 2 0 1 2 1 2 1 1 1 1 1 1 2 N SD: 34.3934 c. M: 59.8237 c. 19: 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 2 N D3 SD: 9.6573 c. M: 18.4156 c. 27: 2 1 1 2 1 2 2 2 3 1 1 2 2 1 1 3 N SD: 12.2666 c. M: 17.0719 c. 30: 2 1 2 2 1 2 3 1 3 2 1 2 2 1 2 3 N SD: 10.9783 c. M: 19.4710 c. 31: 2 1 2 2 1 2 3 2 3 2 1 2 2 1 2 3 N G SD: 1.0267 c. M:-1.9579 c. 112: 7 4 7 7 4 7 11 7 11 7 4 7 7 4 7 11 N G SD: 0.7858 c. M: 1.4983 c. 143: 9 5 9 9 5 9 14 9 14 9 5 9 9 5 9 14 N G SD: 0.3929 c. M: 0.7490 c. 174: 11 6 11 11 6 11 17 11 17 11 6 11 11 6 11 17 N G SD: 0.1400 c. M: 0.2668 c. 205: 13 7 13 13 7 13 20 13 20 13 7 13 13 7 13 20 N G SD: 0.0365 c. M:-0.0697 c. 584: 37 20 37 37 20 37 57 37 57 37 20 37 37 20 37 57 N G SD: 0.0161 c. M: 0.0306 c. 789: 50 27 50 50 27 50 77 50 77 50 27 50 50 27 50 77 N G SD: 0.0025 c. M: 0.0045 c. 1783: 113 61 113 113 61 113 174 113 174 113 61 113 113 61 113 174 N G SD: 0.0021 c. M:-0.0040 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.6885 cents 3 .. 6 match: 3 H SD: 2.5346 cents 4 .. 8 match: 4 H SD: 1.5445 cents 5 .. 10 match: 5 H SD: 2.4802 cents 6 .. 12 match: 6 H SD: 5.8128 cents 7 .. 14 match: 7 H SD: 11.5688 cents 8 .. 16 match: 8 H SD: 5.1474 cents 9 .. 18 match: 9 H SD: 8.1069 cents 10 .. 20 match: 10 H SD: 7.0948 cents 11 .. 22 match: 11 H SD: 9.1676 cents 12 .. 24 match: 11 S SD: 4.6074 cents 13 .. 26 match: 12 S SD: 6.9307 cents 14 .. 28 match: 13 S SD: 7.2268 cents 15 .. 30 match: 14 S SD: 4.3429 cents 16 .. 32 match: 14 S SD: 4.4312 cents 17 .. 34 match: 12 SD: 5.0849 cents 18 .. 36 match: 15 SD: 4.5779 cents 19 .. 38 match: 14 SD: 5.0318 cents 20 .. 40 match: 15 SD: 3.7053 cents 21 .. 42 match: 14 SD: 4.4477 cents 22 .. 44 match: 15 SD: 4.8879 cents 23 .. 46 match: 16 SD: 3.7357 cents 24 .. 48 match: 15 SD: 2.9261 cents 25 .. 50 match: 16 SD: 2.8061 cents 27 .. 54 match: 15 SD: 2.7950 cents 28 .. 56 match: 15 SD: 2.6728 cents 33 .. 66 match: 15 SD: 3.0072 cents 34 .. 68 match: 15 SD: 3.1658 cents 35 .. 70 match: 15 SD: 2.4314 cents 36 .. 72 match: 16 SD: 2.4072 cents 40 .. 80 match: 16 SD: 2.0094 cents 41 .. 82 match: 16 SD: 1.8082 cents 43 .. 86 match: 16 SD: 1.7510 cents 48 .. 96 match: 16 SD: 1.5529 cents 59 .. 118 match: 16 SD: 1.4678 cents 60 .. 120 match: 16 SD: 1.0811 cents 67 .. 134 match: 16 SD: 1.0808 cents 71 .. 142 match: 16 SD: 0.9071 cents 83 .. 166 match: 16 SD: 0.8150 cents 85 .. 170 match: 16 SD: 0.7991 cents 101 .. 202 match: 16 SD: 0.7401 cents 103 .. 206 match: 16 SD: 0.7346 cents 112 .. 224 match: 16 SD: 0.6633 cents 113 .. 226 match: 16 SD: 0.5661 cents 128 .. 256 match: 16 SD: 0.5509 cents 137 .. 274 match: 16 SD: 0.5293 cents 143 .. 286 match: 16 SD: 0.4943 cents 153 .. 306 match: 16 SD: 0.4360 cents 183 .. 366 match: 16 SD: 0.4148 cents 184 .. 368 match: 16 SD: 0.4001 cents 201 .. 402 match: 16 SD: 0.3930 cents 204 .. 408 match: 16 SD: 0.3169 cents 228 .. 456 match: 16 SD: 0.2867 cents 244 .. 488 match: 16 SD: 0.2461 cents 297 .. 594 match: 16 SD: 0.2366 cents 311 .. 622 match: 16 SD: 0.2365 cents 315 .. 630 match: 16 SD: 0.2070 cents 332 .. 664 match: 16 SD: 0.1817 cents 357 .. 714 match: 16 SD: 0.1805 cents 397 .. 794 match: 16 SD: 0.1713 cents 423 .. 846 match: 16 SD: 0.1698 cents 427 .. 854 match: 16 SD: 0.1692 cents 448 .. 896 match: 16 SD: 0.1575 cents 468 .. 936 match: 16 SD: 0.1416 cents 515 .. 1030 match: 16 SD: 0.1310 cents 560 .. 1120 match: 16 SD: 0.1099 cents