Scala analysis: vines_ovovo22eb9w14w15_00_D
8:9:14:15 equal beating in 3 of 22 keysigs, a Mark L. Vines ovovo temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 67.112 cents 67.111770 2: 127.500 cents 127.500200 3: 171.672 cents 171.672420 4: 215.845 cents 215.844630 5: 276.233 cents 276.233060 6: 343.345 cents 343.344830 7: 387.517 cents 387.517040 8: 431.689 cents 431.689260 9: 492.078 cents 492.077690 10: 559.189 cents 559.189460 11: 619.578 cents 619.577890 12: 663.750 cents 663.750100 13: 707.922 cents 707.922320 14: 768.311 cents 768.310740 15: 835.423 cents 835.422520 16: 879.595 cents 879.594730 17: 923.767 cents 923.766940 18: 984.155 cents 984.155370 19: 1051.267 cents 1051.267150 20: 1095.439 cents 1095.439360 21: 1155.828 cents 1155.827790 22: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 44.1722 cents 44.1722 1: 67.1118 cents 67.1118 2: 60.3884 cents 60.3884 3: 44.1722 cents 44.1722 4: 44.1722 cents 44.1722 5: 60.3884 cents 60.3884 6: 67.1118 cents 67.1118 7: 44.1722 cents 44.1722 8: 44.1722 cents 44.1722 9: 60.3884 cents 60.3884 10: 67.1118 cents 67.1118 11: 60.3884 cents 60.3884 12: 44.1722 cents 44.1722 13: 44.1722 cents 44.1722 14: 60.3884 cents 60.3884 15: 67.1118 cents 67.1118 16: 44.1722 cents 44.1722 17: 44.1722 cents 44.1722 18: 60.3884 cents 60.3884 19: 67.1118 cents 67.1118 20: 44.1722 cents 44.1722 21: 60.3884 cents 60.3884 22: 44.1722 cents 44.1722
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 44.17222 cents 1: 7 60.38843 cents 1: 5 67.11177 cents 2: 4 88.34443 cents 2: 8 104.56065 cents 2: 4 111.28398 cents 2: 6 127.50020 cents 3: 7 148.73286 cents 3: 2 155.45620 cents 3: 12 171.67242 cents 3: 1 187.88863 cents 4: 2 209.12129 cents 4: 16 215.84463 cents 4: 4 232.06085 cents 5: 6 260.01684 cents 5: 13 276.23306 cents 5: 3 282.95640 cents 6: 2 304.18906 cents 6: 11 320.40527 cents 6: 1 327.12862 cents 6: 1 336.62148 cents 6: 7 343.34483 cents 7: 7 364.57749 cents 7: 2 380.79370 cents 7: 10 387.51704 cents 7: 3 403.73326 cents 8: 4 424.96592 cents 8: 10 431.68926 cents 8: 8 447.90547 cents 9: 2 475.86147 cents 9: 19 492.07769 cents 9: 1 498.80103 cents 10: 12 536.24990 cents 10: 4 552.46612 cents 10: 6 559.18946 cents 11: 5 580.42212 cents 11: 6 596.63833 cents 11: 6 603.36167 cents 11: 5 619.57789 cents 12: 6 640.81055 cents 12: 4 647.53388 cents 12: 12 663.75010 cents 13: 1 701.19897 cents 13: 19 707.92232 cents 13: 2 724.13853 cents 14: 8 752.09453 cents 14: 10 768.31074 cents 14: 4 775.03409 cents 15: 3 796.26674 cents 15: 10 812.48296 cents 15: 2 819.20630 cents 15: 7 835.42252 cents 16: 7 856.65517 cents 16: 1 863.37852 cents 16: 1 872.87138 cents 16: 11 879.59473 cents 16: 2 895.81094 cents 17: 3 917.04360 cents 17: 13 923.76694 cents 17: 6 939.98316 cents 18: 4 967.93916 cents 18: 16 984.15537 cents 18: 2 990.87871 cents 19: 1 1012.11137 cents 19: 12 1028.32759 cents 19: 2 1044.54380 cents 19: 7 1051.26715 cents 20: 6 1072.49980 cents 20: 4 1088.71602 cents 20: 8 1095.43936 cents 20: 4 1111.65557 cents 21: 5 1132.88823 cents 21: 7 1139.61157 cents 21: 10 1155.82779 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.52381 = 74/21
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0.0 : 67.1 127.5 171.7 215.8 276.2 343.3 387.5 431.7 492.1 559.2 619.6 663.8 707.9 768.3 835.4 879.6 923.8 984.2 1051.3 1095.4 1155.8 1200.0 67.1 : 60.4 104.6 148.7 209.1 276.2 320.4 364.6 425.0 492.1 552.5 596.6 640.8 701.2 768.3 812.5 856.7 917.0 984.2 1028.3 1088.7 1132.9 1200.0 127.5 : 44.2 88.3 148.7 215.8 260.0 304.2 364.6 431.7 492.1 536.2 580.4 640.8 707.9 752.1 796.3 856.7 923.8 967.9 1028.3 1072.5 1139.6 1200.0 171.7 : 44.2 104.6 171.7 215.8 260.0 320.4 387.5 447.9 492.1 536.2 596.6 663.8 707.9 752.1 812.5 879.6 923.8 984.2 1028.3 1095.4 1155.8 1200.0 215.8 : 60.4 127.5 171.7 215.8 276.2 343.3 403.7 447.9 492.1 552.5 619.6 663.8 707.9 768.3 835.4 879.6 940.0 984.2 1051.3 1111.7 1155.8 1200.0 276.2 : 67.1 111.3 155.5 215.8 283.0 343.3 387.5 431.7 492.1 559.2 603.4 647.5 707.9 775.0 819.2 879.6 923.8 990.9 1051.3 1095.4 1139.6 1200.0 343.3 : 44.2 88.3 148.7 215.8 276.2 320.4 364.6 425.0 492.1 536.2 580.4 640.8 707.9 752.1 812.5 856.7 923.8 984.2 1028.3 1072.5 1132.9 1200.0 387.5 : 44.2 104.6 171.7 232.1 276.2 320.4 380.8 447.9 492.1 536.2 596.6 663.8 707.9 768.3 812.5 879.6 940.0 984.2 1028.3 1088.7 1155.8 1200.0 431.7 : 60.4 127.5 187.9 232.1 276.2 336.6 403.7 447.9 492.1 552.5 619.6 663.8 724.1 768.3 835.4 895.8 940.0 984.2 1044.5 1111.7 1155.8 1200.0 492.1 : 67.1 127.5 171.7 215.8 276.2 343.3 387.5 431.7 492.1 559.2 603.4 663.8 707.9 775.0 835.4 879.6 923.8 984.2 1051.3 1095.4 1139.6 1200.0 559.2 : 60.4 104.6 148.7 209.1 276.2 320.4 364.6 425.0 492.1 536.2 596.6 640.8 707.9 768.3 812.5 856.7 917.0 984.2 1028.3 1072.5 1132.9 1200.0 619.6 : 44.2 88.3 148.7 215.8 260.0 304.2 364.6 431.7 475.9 536.2 580.4 647.5 707.9 752.1 796.3 856.7 923.8 967.9 1012.1 1072.5 1139.6 1200.0 663.8 : 44.2 104.6 171.7 215.8 260.0 320.4 387.5 431.7 492.1 536.2 603.4 663.8 707.9 752.1 812.5 879.6 923.8 967.9 1028.3 1095.4 1155.8 1200.0 707.9 : 60.4 127.5 171.7 215.8 276.2 343.3 387.5 447.9 492.1 559.2 619.6 663.8 707.9 768.3 835.4 879.6 923.8 984.2 1051.3 1111.7 1155.8 1200.0 768.3 : 67.1 111.3 155.5 215.8 283.0 327.1 387.5 431.7 498.8 559.2 603.4 647.5 707.9 775.0 819.2 863.4 923.8 990.9 1051.3 1095.4 1139.6 1200.0 835.4 : 44.2 88.3 148.7 215.8 260.0 320.4 364.6 431.7 492.1 536.2 580.4 640.8 707.9 752.1 796.3 856.7 923.8 984.2 1028.3 1072.5 1132.9 1200.0 879.6 : 44.2 104.6 171.7 215.8 276.2 320.4 387.5 447.9 492.1 536.2 596.6 663.8 707.9 752.1 812.5 879.6 940.0 984.2 1028.3 1088.7 1155.8 1200.0 923.8 : 60.4 127.5 171.7 232.1 276.2 343.3 403.7 447.9 492.1 552.5 619.6 663.8 707.9 768.3 835.4 895.8 940.0 984.2 1044.5 1111.7 1155.8 1200.0 984.2 : 67.1 111.3 171.7 215.8 283.0 343.3 387.5 431.7 492.1 559.2 603.4 647.5 707.9 775.0 835.4 879.6 923.8 984.2 1051.3 1095.4 1139.6 1200.0 1051.3: 44.2 104.6 148.7 215.8 276.2 320.4 364.6 425.0 492.1 536.2 580.4 640.8 707.9 768.3 812.5 856.7 917.0 984.2 1028.3 1072.5 1132.9 1200.0 1095.4: 60.4 104.6 171.7 232.1 276.2 320.4 380.8 447.9 492.1 536.2 596.6 663.8 724.1 768.3 812.5 872.9 940.0 984.2 1028.3 1088.7 1155.8 1200.0 1155.8: 44.2 111.3 171.7 215.8 260.0 320.4 387.5 431.7 475.9 536.2 603.4 663.8 707.9 752.1 812.5 879.6 923.8 967.9 1028.3 1095.4 1139.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.1722 .. 67.1118 cents 22.93955 cents 44.17222 cents 2: 88.3444 .. 127.5002 cents 39.15577 cents 21.23266 cents 3: 148.7329 .. 187.8886 cents 39.15577 cents 21.23266 cents 4: 209.1213 .. 232.0609 cents 22.93956 cents 21.23266 cents 5: 260.0168 .. 282.9564 cents 22.93956 cents 27.95599 cents 6: 304.1891 .. 343.3448 cents 39.15577 cents 21.23266 cents 7: 364.5775 .. 403.7333 cents 39.15577 cents 21.23266 cents 8: 424.9659 .. 447.9055 cents 22.93955 cents 21.23266 cents 9: 475.8615 .. 498.8010 cents 22.93956 cents 27.95600 cents 10: 536.2499 .. 559.1895 cents 22.93956 cents 37.44887 cents 11: 580.4221 .. 619.5779 cents 39.15577 cents 21.23266 cents 12: 640.8105 .. 663.7501 cents 22.93955 cents 21.23266 cents 13: 701.1990 .. 724.1385 cents 22.93956 cents 37.44887 cents 14: 752.0945 .. 775.0341 cents 22.93956 cents 27.95600 cents 15: 796.2667 .. 835.4225 cents 39.15578 cents 21.23265 cents 16: 856.6552 .. 895.8109 cents 39.15577 cents 21.23265 cents 17: 917.0436 .. 939.9832 cents 22.93956 cents 21.23266 cents 18: 967.9392 .. 990.8787 cents 22.93955 cents 27.95600 cents 19: 1012.1114 .. 1051.2671 cents 39.15578 cents 21.23266 cents 20: 1072.4998 .. 1111.6556 cents 39.15577 cents 21.23265 cents 21: 1132.8882 .. 1155.8278 cents 22.93956 cents 21.23266 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 44.17221 cents, class 1 Average step (divided formal octave): 54.5455 cents Largest one step interval : 67.11177 cents Average / Smallest step : 1.234836 Largest / Average step : 1.230382 Largest / Smallest step : 1.519321 Median interval of one step : 60.38843 cents, amount: 7 Most common interval of one step : 44.17222 cents, amount: 10 Least squares average step : 54.97947 cents, oct.: 1209.54842 cents Scale is strictly proper Step pattern alph. order: ABCCBACCBABCCBACCBACBC Step pattern size order : LMSSMLSSMLMSSMLSSMLSMS Scale is a Constant Structure, by a margin of 21.23265 cents Scale diversity : 1.314918 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.476936 Number of different interval sizes : 74 = 3.52381 / class Number of one step interval sizes : 3 Highest interval variety : 5 Mean interval variety : 3.52381 = 74/21 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 6.72333 cents Most common intervals : 492.07769 cents & inv., amount: 19 Most common triad is 0.0 492.078 707.922 cents, amount: 16 Number of recognisable fifths : 20, average 707.5862 cents Scale contains two identical conjunct "tetrachords" of 10 notes Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 9 = 40.9091% Limited inverse transpositions with margin 39.1558 cents: 19 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
22: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.1923 c. M: 19.5779 c. 31: 2 1 1 2 1 2 1 1 2 1 2 1 1 2 2 1 1 1 2 1 2 1 N D3 SD: 10.3678 c. M: 17.2540 c. 33: 2 2 1 1 2 1 2 1 2 1 2 1 1 2 2 1 1 2 2 1 2 1 N SD: 10.3372 c. M:-17.9543 c. 34: 2 2 1 1 2 2 1 1 2 2 2 1 1 2 2 1 1 2 2 1 2 1 P D3 SD: 7.2904 c. M:-15.7162 c. 35: 2 2 1 1 2 2 1 2 1 2 2 1 2 1 2 2 1 2 2 1 2 1 P D3 SD: 9.3040 c. M:-14.0250 c. 39: 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 P M ME SD: 7.2609 c. M:-13.4030 c. 42: 2 2 2 2 2 2 2 1 2 3 2 1 2 2 2 2 1 2 3 1 2 2 P D3 SD: 8.7655 c. M: 13.2145 c. 43: 2 3 1 2 2 2 2 1 3 2 2 2 1 3 2 2 1 2 3 1 2 2 P SD: 8.4558 c. M:-13.4285 c. 44: 2 3 1 2 2 3 1 2 2 3 2 1 2 2 3 1 2 2 3 1 2 2 P T3 SD: 7.6784 c. M:-13.5378 c. 46: 3 2 2 1 3 2 2 2 2 2 3 1 2 2 3 2 1 3 2 2 2 2 P SD: 7.9920 c. M:-11.7890 c. 47: 3 2 2 1 3 2 2 2 2 3 2 2 2 2 3 1 2 3 2 2 2 2 P SD: 6.8085 c. M: 11.5893 c. 49: 3 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 2 2 3 2 2 2 SP M ME SD: 5.0262 c. M:-9.1271 c. 56: 3 3 2 2 3 3 2 2 3 3 3 2 2 3 3 2 2 3 3 2 3 2 SP D3 SD: 1.7603 c. M:-3.1178 c. 105: 6 5 4 4 5 6 4 4 5 6 5 4 4 5 6 4 4 5 6 4 5 4 SP SD: 1.4485 c. M:-2.5965 c. 139: 8 7 5 5 7 8 5 5 7 8 7 5 5 7 8 5 5 7 8 5 7 5 SP SD: 1.2293 c. M:-2.0048 c. 161: 9 8 6 6 8 9 6 6 8 9 8 6 6 8 9 6 6 8 9 6 8 6 SP SD: 0.4410 c. M: 0.9443 c. 217: 12 11 8 8 11 12 8 8 11 12 11 8 8 11 12 8 8 11 12 8 11 8 SP SD: 0.3682 c. M: 0.7523 c. 356: 20 18 13 13 18 20 13 13 18 20 18 13 13 18 20 13 13 18 20 13 18 13 SP SD: 0.3154 c. M:-0.6468 c. 378: 21 19 14 14 19 21 14 14 19 21 19 14 14 19 21 14 14 19 21 14 19 14 SP SD: 0.3032 c. M: 0.5303 c. 461: 26 23 17 17 23 26 17 17 23 26 23 17 17 23 26 17 17 23 26 17 23 17 SP SD: 0.2851 c. M:-0.5672 c. 517: 29 26 19 19 26 29 19 19 26 29 26 19 19 26 29 19 19 26 29 19 26 19 SP SD: 0.1114 c. M:-0.1996 c. 678: 38 34 25 25 34 38 25 25 34 38 34 25 25 34 38 25 25 34 38 25 34 25 SP SD: 0.0945 c. M:-0.1691 c. 734: 41 37 27 27 37 41 27 27 37 41 37 27 27 37 41 27 27 37 41 27 37 27 SP SD: 0.0474 c. M: 0.0818 c. 1251: 70 63 46 46 63 70 46 46 63 70 63 46 46 63 70 46 46 63 70 46 63 46 SP SD: 0.0413 c. M:-0.0864 c. 1412: 79 71 52 52 71 79 52 52 71 79 71 52 52 71 79 52 52 71 79 52 71 52 SP SD: 0.0214 c. M:-0.0388 c. 2146: 120 108 79 79 108 120 79 79 108 120 108 79 79 108 120 79 79 108 120 79 108 79 SP SD: 0.0054 c. M: 0.0102 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.9837 cents 3 .. 6 match: 3 H SD: 2.5452 cents 4 .. 8 match: 4 H SD: 4.1235 cents 5 .. 10 match: 5 H SD: 10.7744 cents 6 .. 12 match: 6 H SD: 2.2681 cents 7 .. 14 match: 7 H SD: 4.4198 cents 8 .. 16 match: 8 H SD: 2.9420 cents 9 .. 18 match: 9 H SD: 2.8668 cents 10 .. 20 match: 10 H SD: 6.1354 cents 11 .. 22 match: 11 H SD: 5.2920 cents 12 .. 24 match: 12 H SD: 4.1098 cents 13 .. 26 match: 13 H SD: 4.4068 cents 14 .. 28 match: 14 H SD: 4.0312 cents 15 .. 30 match: 14 S SD: 4.8495 cents 16 .. 32 match: 16 H SD: 3.4063 cents 17 .. 34 match: 17 H SD: 4.4496 cents 18 .. 36 match: 18 H SD: 2.5193 cents 19 .. 38 match: 18 S SD: 3.7458 cents 20 .. 40 match: 19 SD: 3.8966 cents 21 .. 42 match: 20 SD: 2.8969 cents 22 .. 44 match: 20 SD: 3.4489 cents 23 .. 46 match: 21 SD: 2.8600 cents 24 .. 48 match: 21 SD: 2.1460 cents 25 .. 50 match: 21 SD: 3.1176 cents 26 .. 52 match: 20 SD: 2.8793 cents 27 .. 54 match: 22 SD: 2.5662 cents 28 .. 56 match: 22 SD: 2.1735 cents 30 .. 60 match: 21 SD: 2.3971 cents 33 .. 66 match: 21 SD: 2.6741 cents 34 .. 68 match: 22 SD: 2.5748 cents 35 .. 70 match: 22 SD: 2.2983 cents 36 .. 72 match: 22 SD: 1.9211 cents 39 .. 78 match: 22 SD: 1.7861 cents 40 .. 80 match: 22 SD: 1.7443 cents 45 .. 90 match: 22 SD: 1.5343 cents 47 .. 94 match: 22 SD: 1.4242 cents 51 .. 102 match: 22 SD: 1.3517 cents 52 .. 104 match: 22 SD: 1.2836 cents 60 .. 120 match: 22 SD: 1.1306 cents 67 .. 134 match: 22 SD: 1.0547 cents 68 .. 136 match: 22 SD: 0.8000 cents 77 .. 154 match: 22 SD: 0.6830 cents 95 .. 190 match: 22 SD: 0.6610 cents 103 .. 206 match: 22 SD: 0.5958 cents 105 .. 210 match: 22 SD: 0.5677 cents 127 .. 254 match: 22 SD: 0.4715 cents 128 .. 256 match: 22 SD: 0.4589 cents 144 .. 288 match: 22 SD: 0.4562 cents 145 .. 290 match: 22 SD: 0.3997 cents 156 .. 312 match: 22 SD: 0.3866 cents 172 .. 344 match: 22 SD: 0.3801 cents 174 .. 348 match: 22 SD: 0.3453 cents 195 .. 390 match: 22 SD: 0.3180 cents 204 .. 408 match: 22 SD: 0.3109 cents 210 .. 420 match: 22 SD: 0.3105 cents 219 .. 438 match: 22 SD: 0.2919 cents 220 .. 440 match: 22 SD: 0.2872 cents 231 .. 462 match: 22 SD: 0.2625 cents 247 .. 494 match: 22 SD: 0.2453 cents 272 .. 544 match: 22 SD: 0.2355 cents 278 .. 556 match: 22 SD: 0.2149 cents 279 .. 558 match: 22 SD: 0.2007 cents 323 .. 646 match: 22 SD: 0.1969 cents 325 .. 650 match: 22 SD: 0.1962 cents 328 .. 656 match: 22 SD: 0.1923 cents 346 .. 692 match: 22 SD: 0.1825 cents 353 .. 706 match: 22 SD: 0.1691 cents 383 .. 766 match: 22 SD: 0.1592 cents 406 .. 812 match: 22 SD: 0.1467 cents 430 .. 860 match: 22 SD: 0.1376 cents 451 .. 902 match: 22 SD: 0.1279 cents 498 .. 996 match: 22 SD: 0.1122 cents 578 .. 1156 match: 22 SD: 0.1121 cents