GPDO: Difference between revisions
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A '''GPDO'' | A '''GPDO''' ('''geometric pitch division of the octave''') or '''EDQ'''{{idiosyncratic}} (equal division of the [[quatave]]) is a type of [[octave]]-[[period|repeating]] [[tuning system]] obtained by taking a segment from a [[GPS|geometric pitch sequence]]. In the first octave, the [[frequency ratio]] of the ''k''-th step of ''n''-GPDO is 2<sup>2<sup>''k''/''n''</sup> - 1</sup>. The underlying GPS is a geometric series of pitches starting at [[2/1]] (1200{{cent}}) and multiplying the previous pitch by 2<sup>1/''n''</sup> each time, and the segment from [[2/1]] to [[4/1]], spanning one octave, is taken to construct a GPDO. GPDOs are close approximations of modes of the [[subharmonic series]], also known as [[IFDO]]s. | ||
== Individual pages for GPDOs == | == Individual pages for GPDOs == | ||
* [[ | * 1gpdo (equivalent to [[1edo]]) | ||
* [[2gpdo]] | * [[2gpdo]] | ||
* [[3gpdo]] | * [[3gpdo]] | ||
* [[4gpdo]] | |||
* [[5gpdo]] | |||
[[Category:Lists of scales]] | [[Category:Lists of scales]] | ||
{{stub}} | {{stub}} | ||
Latest revision as of 02:44, 3 June 2024
A GPDO (geometric pitch division of the octave) or EDQ[idiosyncratic term] (equal division of the quatave) is a type of octave-repeating tuning system obtained by taking a segment from a geometric pitch sequence. In the first octave, the frequency ratio of the k-th step of n-GPDO is 22k/n - 1. The underlying GPS is a geometric series of pitches starting at 2/1 (1200 ¢) and multiplying the previous pitch by 21/n each time, and the segment from 2/1 to 4/1, spanning one octave, is taken to construct a GPDO. GPDOs are close approximations of modes of the subharmonic series, also known as IFDOs.
Individual pages for GPDOs
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