GPDO - Revision history

CompactStar at 02:44, 3 June 2024

2024-06-03T02:44:27Z

← Older revision		Revision as of 02:44, 3 June 2024
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	== Individual pages for GPDOs ==		== Individual pages for GPDOs ==
	* 1gpdo ([[1edo]])		* 1gpdo (equivalent to [[1edo]])
	* [[2gpdo]]		* [[2gpdo]]
	* [[3gpdo]]		* [[3gpdo]]

CompactStar at 02:44, 3 June 2024

2024-06-03T02:44:20Z

← Older revision		Revision as of 02:44, 3 June 2024
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	== Individual pages for GPDOs ==		== Individual pages for GPDOs ==
	* [[~~1gpdo~~]]		* 1gpdo ([[1edo]])
	* [[2gpdo]]		* [[2gpdo]]
	* [[3gpdo]]		* [[3gpdo]]
			* [[4gpdo]]
			* [[5gpdo]]

	[[Category:Lists of scales]]		[[Category:Lists of scales]]

	{{stub}}		{{stub}}

CompactStar at 02:44, 3 June 2024

2024-06-03T02:44:00Z

← Older revision		Revision as of 02:44, 3 June 2024
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	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 [[~~IFDOs~~]].		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 ==

CompactStar at 02:43, 3 June 2024

2024-06-03T02:43:54Z

← Older revision		Revision as of 02:43, 3 June 2024
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	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.		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 [[IFDOs]].

	== Individual pages for GPDOs ==		== Individual pages for GPDOs ==

FloraC: I approve of the term GPDO, making us three; it's also the term that's well connected to other similar objects (-template: idiosyncratic).

2024-06-02T12:08:32Z

I approve of the term GPDO, making us three; it's also the term that's well connected to other similar objects (-template: idiosyncratic).

← Older revision		Revision as of 12:08, 2 June 2024
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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]]. In the first octave, 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.

	== Individual pages for GPDOs ==		== Individual pages for GPDOs ==

CompactStar at 03:20, 2 June 2024

2024-06-02T03:20:25Z

← Older revision		Revision as of 03:20, 2 June 2024
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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'''{{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]]. In the first octave, 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.

	== Individual pages for GPDOs ==		== Individual pages for GPDOs ==

CompactStar at 03:19, 2 June 2024

2024-06-02T03:19:59Z

← Older revision		Revision as of 03:19, 2 June 2024
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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'''{{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.

	== Individual pages for GPDOs ==		== Individual pages for GPDOs ==

CompactStar at 03:19, 2 June 2024

2024-06-02T03:19:50Z

← Older revision		Revision as of 03:19, 2 June 2024
Line 1:		Line 1:
	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'''{{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.

	== Individual pages for GPDOs ==		== Individual pages for GPDOs ==

CompactStar at 03:18, 2 June 2024

2024-06-02T03:18:48Z

← Older revision		Revision as of 03:18, 2 June 2024
Line 1:		Line 1:
	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]] is taken to construct a GPDO.		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.

	== Individual pages for GPDOs ==		== Individual pages for GPDOs ==

CompactStar at 03:17, 2 June 2024

2024-06-02T03:17:29Z

← Older revision		Revision as of 03:17, 2 June 2024
Line 1:		Line 1:
	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 a GPDO is equal to 2<sup>2<sup>1/k</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]] is taken to construct a GPDO.		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]] is taken to construct a GPDO.

	== Individual pages for GPDOs ==		== Individual pages for GPDOs ==