GPDO: Difference between revisions

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An '''EDQ'''{{idiosyncratic}} (equal division of the [[quatave]]) is a type of [[~~GPS~~]] (geometric pitch sequence~~) scale~~. n-~~edq~~ is a geometric series of pitches starting at [[2/1]] (1200{{cent}}) and multiplying the previous pitch by 21/n each time~~. For example~~, ~~[[1edq]] doubles the pitch each time with~~ the ~~sequence of cent values being {1200, 2400, 4800, 9600...} and sequence of ratios being {~~[[2/1]], [[4/1]], ~~[[16/1]]~~, ~~[[256/1]]...}~~. [[~~1/1~~]] ~~is not present within an EDQ scale~~, ~~so another interval (typically [[2/1]]) would be used~~ as ~~the "root". The scale type was first described by~~ [[~~User:CompactStar|CompactStar]] and the name EDQ was coined by [[User:R-4981|R-4981~~]].

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 ~~EDQs~~ ==

* [[~~1edq]]~~

== Individual pages for GPDOs ==

* [[2edq]]

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

* [[3edq]]

* [[2gpdo]]

* [[4edq]]

* [[3gpdo]]

* [[5edq]]

* [[4gpdo]]

* [[6edq]]

* [[5gpdo]]

* [[7edq]]

* [[8edq]]

* [[~~9edq~~]]

* [[~~10edq~~]]

* [[~~11edq~~]]

* [[~~12edq~~]]

[[Category:Lists of scales]]

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-An '''EDQ'''{{idiosyncratic}} (equal division of the [[quatave]]) is a type of [[GPS]] (geometric pitch sequence) scale. n-edq 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. For example, [[1edq]] doubles the pitch each time with the sequence of cent values being {1200, 2400, 4800, 9600...} and sequence of ratios being {[[2/1]], [[4/1]], [[16/1]], [[256/1]]...}. [[1/1]] is not present within an EDQ scale, so another interval (typically [[2/1]]) would be used as the "root". The scale type was first described by [[User:CompactStar|CompactStar]] and the name EDQ was coined by [[User:R-4981|R-4981]].
+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 EDQs ==
-* [[1edq]]
+== Individual pages for GPDOs ==
-* [[2edq]]
+* 1gpdo (equivalent to [[1edo]])
-* [[3edq]]
+* [[2gpdo]]
-* [[4edq]]
+* [[3gpdo]]
-* [[5edq]]
+* [[4gpdo]]
-* [[6edq]]
+* [[5gpdo]]
-* [[7edq]]
-* [[8edq]]
-* [[9edq]]
-* [[10edq]]
-* [[11edq]]
-* [[12edq]]
 [[Category:Lists of scales]]
+{{stub}}