Logarithmic intonation: Difference between revisions
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The simplest [[subgroup]] of logarithmic intonation is ln(2).ln(3), but this is a [[nonoctave]] system–if the octave is desired, the simplest subgroup is ln(2).ln(4) which contains the octave as ln(4)/ln(2) and can be rewritten as 2.ln(4). The subgroup ln(2).ln(3).ln(4) or equivalently 2.ln(3).ln(4) can be viewed as analogous to the [[5-limit]] of just intonation. [[Regular temperament]]s can be defined with these subgroups as they can with prime subgroups. The interval ln(2) itself is a descending wide tritone of -635 cents, with it's octave-equivalent ln(4) being a narrow tritone of 565 cents that can be approximated by [[25/18]] and [[18/13]]. | The simplest [[subgroup]] of logarithmic intonation is ln(2).ln(3), but this is a [[nonoctave]] system–if the octave is desired, the simplest subgroup is ln(2).ln(4) which contains the octave as ln(4)/ln(2) and can be rewritten as 2.ln(4). The subgroup ln(2).ln(3).ln(4) or equivalently 2.ln(3).ln(4) can be viewed as analogous to the [[5-limit]] of just intonation. [[Regular temperament]]s can be defined with these subgroups as they can with prime subgroups. The interval ln(2) itself is a descending wide tritone of -635 cents, with it's octave-equivalent ln(4) being a narrow tritone of 565 cents that can be approximated by [[25/18]] and [[18/13]]. | ||
== See also == | |||
* [[Logharmonic series]] | |||
[[Category:Method]] | [[Category:Method]] | ||