Irvic scale: Difference between revisions
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C = number of years per cycle | C = number of years per cycle | ||
K = (C-1)/2 if odd, can choose between (C-1)/2 and C/2 if even</blockquote>The current, "canonical" usage of the cycle is that of 52 leap week years in 293 years - year is leap if (52 x Year + 146)/293 is less than 52. Musically, this would correspond to a [[33L 19s|33L 19]]<nowiki/>s MOS scale. In addition, if the remainder of the leap year is less than the count of long intervals in the MOS, the next year will be in a long interval, otherwise in a short interval. For example here, this means if remainder is less than 33, next leap year (or key) will be 6 years later (6 steps above), otherwise 5 years later. | K = (C-1)/2 if odd, can choose between (C-1)/2 and C/2 if even</blockquote>The current, "canonical" usage of the cycle is that of 52 leap week years in 293 years - year is leap if (52 x Year + 146)/293 is less than 52. Musically, this would correspond to a [[33L 19s|33L 19]]<nowiki/>s MOS scale. In addition, if the remainder of the leap year is less than the count of long intervals in the MOS, the next year will be in a long interval, otherwise in a short interval. For example here, this means if remainder is less than 33, next leap year (or key) will be 6 years later (6 steps above), otherwise 5 years later. | ||
Even-length symmetrical cycles with an irreducible (that is odd) number of years per cycle have a feature where they aren't 100% symmetrical - two middle years follow a pattern of non-leap - leap. If the K is chosen as (C-1)/2 instead of C/2, the sequence will be leap, nonleap. | Even-length symmetrical cycles with an irreducible (that is odd) number of years per cycle have a feature where they aren't 100% symmetrical - two middle years follow a pattern of non-leap - leap. If the K is chosen as (C-1)/2 instead of C/2, the sequence will be leap, nonleap. | ||
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L L s L L L s L L s | L L s L L L s L L s | ||
[[Maqam|Maqamic]] alternative | [[Maqam|Maqamic]] alternative as listed on the 17edo page: | ||
0-2-4-6-7-9-11-12-14-16-17 | 0-2-4-6-7-9-11-12-14-16-17 | ||