IFDO: Difference between revisions
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An '''IDO''' ('''inverse-arithmetic division of the octave''') or '''ELDO''' (''' | An '''IDO''' ('''inverse-arithmetic division of the octave''') or '''ELDO''' ('''equal length division of the octave''') is a [[period]]ic [[tuning system]] which divides the [[octave]] [[equal length division|inverse-arithmetically]] rather than logarithmically, which means it is divided proportional to the length of a string to be divided. All IDOs are subsets of [[just intonation]]. | ||
== Formula == | |||
Within each period of ''n''-ido, the [[frequency ratio]] ''c'' of the ''k''-th step is | |||
<math>\displaystyle c = (2n)/(2n - k)</math> | |||
== Individual pages for IDOs == | == Individual pages for IDOs == | ||
* [[2ido]] | * [[2ido]] | ||
* [[3ido]] | * [[3ido]] | ||
== See also == | == See also == | ||
* [[EDL]] – equal division of length, a similar concept | * [[EDL]] – equal division of length, a similar concept | ||
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* [[EDO]] – equal division of the octave | * [[EDO]] – equal division of the octave | ||
[[Category:IDO]] | [[Category:IDO]] | ||
[[Category:Just intonation]] | [[Category:Just intonation]] | ||
Revision as of 03:18, 22 March 2023
An IDO (inverse-arithmetic division of the octave) or ELDO (equal length division of the octave) is a periodic tuning system which divides the octave inverse-arithmetically rather than logarithmically, which means it is divided proportional to the length of a string to be divided. All IDOs are subsets of just intonation.
Formula
Within each period of n-ido, the frequency ratio c of the k-th step is
[math]\displaystyle{ \displaystyle c = (2n)/(2n - k) }[/math]