GPDO: Difference between revisions

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A '''GPDO'''~~{{idiosyncratic}}~~ (geometric pitch division of the [[octave]]) or '''EDQ'''{{idiosyncratic}} (equal division of the quatave) is a type of octave-repeating [[~~scale~~]] obtained by taking a segment from a [[GPS|geometric pitch sequence]]. ~~The~~ k-th step of n-GPDO is ~~equal to~~ 22k/n-1 ~~times the root frequency~~. The underlying GPS is a geometric series of pitches starting at [[2/1]] (1200{{cent}}) 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.

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 22''k''/''n'' - 1. The underlying GPS is a geometric series of pitches starting at [[2/1]] (1200{{cent}}) 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 [[IFDO]]s.

== Individual pages for GPDOs ==

* [[~~1gpdo~~]]

* 1gpdo (equivalent to [[1edo]])

* [[2gpdo]]

* [[3gpdo]]

* [[4gpdo]]

* [[5gpdo]]

[[Category:Lists of scales]]

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-A '''GPDO'''{{idiosyncratic}} (geometric pitch division of the [[octave]]) or '''EDQ'''{{idiosyncratic}} (equal division of the quatave) is a type of octave-repeating [[scale]] obtained by taking a segment from a [[GPS|geometric pitch sequence]]. The k-th step of n-GPDO is equal to 2<sup>2<sup>k/n</sup>-1</sup> times the root frequency. 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.
+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 ==
-* [[1gpdo]]
+* 1gpdo (equivalent to [[1edo]])
 * [[2gpdo]]
 * [[3gpdo]]
+* [[4gpdo]]
+* [[5gpdo]]
 [[Category:Lists of scales]]
 {{stub}}