IFDO: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Cmloegcmluin (talk | contribs)
add link
Clarify, expand on formula, link style (no bolded links)
Line 1: Line 1:
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]] inverse-arithmetically, which means proportional to the length of a string to be divided. The a-th interval in b-IDO is equal to (2b)/(2b-a). All IDOs are subsets of [[just intonation]].
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
Line 8: Line 15:
* [[EDO]] – equal division of the octave
* [[EDO]] – equal division of the octave


[[Category:Stub]]
[[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]

Individual pages for IDOs

See also

  • EDL – equal division of length, a similar concept
  • ADO – arithmetic division of the octave
  • EDO – equal division of the octave