Irvian mode: Difference between revisions
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'''Irvian mode''' is the mode of the [[maximal evenness]] scale where the notes are symmetrically arranged. | '''Irvian mode''' is the mode of the [[maximal evenness]] scale where the notes are symmetrically arranged. | ||
The term was proposed in 2021 by Eliora, and it is named after a calendar designer Irvin Bromberg, whose Sym454 calendar's leap year patterns are arranged in the same way. | The term was proposed in 2021 by [[Eliora]], and it is named after a calendar designer Irvin Bromberg, whose Sym454 calendar's leap year patterns are arranged in the same way. | ||
==History== | ==History== | ||
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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> | ''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. | 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. | ||
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and so on. | and so on. | ||
== See also == | |||
* [[Maximal evenness]] | |||
* [[Concoctic]] - a scale where ''U'' is equal to ''L'' | |||
== External links == | == External links == | ||
* [http://individual.utoronto.ca/kalendis/leap/52-293-sym454-leap-years.htm 52/293 Symmetry454 Leap Years] | * [http://individual.utoronto.ca/kalendis/leap/52-293-sym454-leap-years.htm 52/293 Symmetry454 Leap Years] | ||
* [http://individual.utoronto.ca/kalendis/leap/index.htm#slc Solar Calendar Leap Rules - subsection Symmetrical Leap Cycles] | * [http://individual.utoronto.ca/kalendis/leap/index.htm#slc Solar Calendar Leap Rules - subsection Symmetrical Leap Cycles] | ||
[[Category:Scale | [[Category:Scale]] | ||