Irvian mode: Difference between revisions

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''K'' = (''C''-1)/2 if ''C'' is odd, can choose between (''C''-1)/2 and ''C''/2 if ''C'' is even</blockquote>

In addition, there's two more numbers in this math - ''U'' and the ''accumulator''. The number corresponds to the [[Mathematics of MOS|generator]] in MOS theory. Bromberg does not provide a name for it, and the reason for this is unknown. Accumulator is the amount of generators for a given note, counting from the tonic.

In addition, there's two more numbers in this math - ''U'' and the ''accumulator''. The ''U'' number corresponds to the [[Mathematics of MOS|generator]] in MOS theory. Bromberg does not provide a name for it, and the reason for this is unknown. Accumulator is the amount of generators for a given note, counting from the tonic.

The current, "canonical" usage of the cycle is that of 52 leap week years in 293 years - year is leap if the remainder of (52 x Year + 146)/293 is less than 52. Musically, this would correspond to a [[33L 19s]] MOS scale of [[293edo]]. 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. The ''U'' of this cycle is equal to 62, and it represends a mode of a [[maximal evenness]] 62\293 scale.

@@ Line 20: / Line 20: @@
 ''K'' = (''C''-1)/2 if ''C'' is odd, can choose between (''C''-1)/2 and ''C''/2 if ''C'' is even</blockquote>
-In addition, there's two more numbers in this math - ''U'' and the ''accumulator''. The number corresponds to the [[Mathematics of MOS|generator]] in MOS theory. Bromberg does not provide a name for it, and the reason for this is unknown. Accumulator is the amount of generators for a given note, counting from the tonic.
+In addition, there's two more numbers in this math - ''U'' and the ''accumulator''. The ''U'' number corresponds to the [[Mathematics of MOS|generator]] in MOS theory. Bromberg does not provide a name for it, and the reason for this is unknown. Accumulator is the amount of generators for a given note, counting from the tonic.
 The current, "canonical" usage of the cycle is that of 52 leap week years in 293 years - year is leap if the remainder of (52 x Year + 146)/293 is less than 52. Musically, this would correspond to a [[33L 19s]] MOS scale of [[293edo]]. 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. The ''U'' of this cycle is equal to 62, and it represends a mode of a [[maximal evenness]] 62\293 scale.