Eigenmonzo: Difference between revisions

Revision as of 15:29, 17 June 2021

An eigenmonzo is a just intonation interval that, when tempered in a given tuning of a given temperament, remains justly tuned.

For example, [0 0 1⟩ is an eigenmonzo in quarter-comma meantone. This is a fancy way of saying that 5:4 is justly tuned in quarter-comma meantone.

For any pure-octave temperament tuning, [1⟩, aka 2:1, is an eigenmonzo.

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-An '''eigenmonzo''' is (the monzo representation of) a JI interval that is rendered exactly in a concrete tuning of a temperament.
+An '''eigenmonzo''' is a just intonation interval that, when tempered in a given tuning of a given temperament, remains justly tuned.
-For example, in quarter-comma meantone, the generator is 5^(1/4), so the eigenmonzo here is {{monzo|0 0 1}}. For any pure-octave temperament tuning, {{monzo|1}}, aka 2/1, is an eigenmonzo.
+For example, {{monzo|0 0 1}} is an eigenmonzo in quarter-comma meantone. This is a fancy way of saying that 5:4 is justly tuned in quarter-comma meantone.
+For any pure-octave temperament tuning, {{monzo|1}}, aka 2:1, is an eigenmonzo.
 == See also ==