Ploidacot: Difference between revisions

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The '''ploidacot''' system is a classification of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] based on how a temperament divides the intervals of [[Pythagorean tuning]]. Ploidacots are written as ''m''-ploid ''s''-sheared ''n''-cot, with ''m''- and ''n''- often replaced by greek numeral prefixes, such as mono-, di-, tri-, etc. (and ''m''-ploid omitted entirely if the [[2/1|octave]] is not split), and "''s''-sheared" replaced by a greek letter, such as alpha-, beta-, etc. (or omitted entirely if ''s'' = 0).

To put it simply; if your temperament can divide its 3/2 interval into N steps, it can be called an N-cot tuning.

The "ploid" number of a temperament refers to how many equal parts, or "ploids" (known as [[period]]s in [[regular temperament theory]]), the octave is divided into, and the "cot" number refers to how many [[generator]] steps of the temperament, or "cots", is needed to reach the third harmonic. Cots are generally presumed to reach 3/2 in a nonnegative number of generators. Temperaments where 3/2 is a whole number of ploids are written as ''acot''. However, stacking ''n'' cots sometimes doesn't reach 3/2, but instead an interval ''s'' ploids above 3/2. There are infinitely many possible values of ''s'', but for the sake of ploidacot, ''s'' takes its residue modulo ''n'' (which is the same for all possible cots), and is an integer between 0 and ''n'' - 1 inclusive.

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 The '''ploidacot''' system is a classification of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] based on how a temperament divides the intervals of [[Pythagorean tuning]]. Ploidacots are written as ''m''-ploid ''s''-sheared ''n''-cot, with ''m''- and ''n''- often replaced by greek numeral prefixes, such as mono-, di-, tri-, etc. (and ''m''-ploid omitted entirely if the [[2/1|octave]] is not split), and "''s''-sheared" replaced by a greek letter, such as alpha-, beta-, etc. (or omitted entirely if ''s'' = 0).
+To put it simply; if your temperament can divide its 3/2 interval into N steps, it can be called an N-cot tuning.
 The "ploid" number of a temperament refers to how many equal parts, or "ploids" (known as [[period]]s in [[regular temperament theory]]), the octave is divided into, and the "cot" number refers to how many [[generator]] steps of the temperament, or "cots", is needed to reach the third harmonic. Cots are generally presumed to reach 3/2 in a nonnegative number of generators. Temperaments where 3/2 is a whole number of ploids are written as ''acot''. However, stacking ''n'' cots sometimes doesn't reach 3/2, but instead an interval ''s'' ploids above 3/2. There are infinitely many possible values of ''s'', but for the sake of ploidacot, ''s'' takes its residue modulo ''n'' (which is the same for all possible cots), and is an integer between 0 and ''n'' - 1 inclusive.