Bohlen–Pierce scale - Revision history

Fredg999 category edits: Categories

2025-07-31T15:43:40Z

ArrowHead294: Undid revision 188013 by ArrowHead294 (talk)

2025-03-24T12:01:29Z

Undid revision 188013 by ArrowHead294 (talk)

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	== Variations ==		== Variations ==
	=== Triple ~~Bohlen%E2%80%93Pierce~~ ===		=== Triple Bohlen–Pierce ===
	Proposed by [[Paul Erlich]] is [[39edt]], also known as the ''Triple Bohlen–Pierce scale''. It adds to 13edt accurate approximations to the 11th and 13th harmonics ([[11/9]] and [[13/9]]) and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen–Pierce scale interlocking three times with calm-sounding quarter-tones, and for various JI modulations.		Proposed by [[Paul Erlich]] is [[39edt]], also known as the ''Triple Bohlen–Pierce scale''. It adds to 13edt accurate approximations to the 11th and 13th harmonics ([[11/9]] and [[13/9]]) and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen–Pierce scale interlocking three times with calm-sounding quarter-tones, and for various JI modulations.

ArrowHead294: /* Triple Bohlen–Pierce */

2025-03-24T12:01:15Z

Triple Bohlen–Pierce

← Older revision		Revision as of 12:01, 24 March 2025
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	== Variations ==		== Variations ==
	=== Triple ~~Bohlen–Pierce~~ ===		=== Triple Bohlen%E2%80%93Pierce ===
	Proposed by [[Paul Erlich]] is [[39edt]], also known as the ''Triple Bohlen–Pierce scale''. It adds to 13edt accurate approximations to the 11th and 13th harmonics ([[11/9]] and [[13/9]]) and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen–Pierce scale interlocking three times with calm-sounding quarter-tones, and for various JI modulations.		Proposed by [[Paul Erlich]] is [[39edt]], also known as the ''Triple Bohlen–Pierce scale''. It adds to 13edt accurate approximations to the 11th and 13th harmonics ([[11/9]] and [[13/9]]) and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen–Pierce scale interlocking three times with calm-sounding quarter-tones, and for various JI modulations.

ArrowHead294: Replace entities with characters

2025-03-10T13:13:55Z

Replace entities with characters

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	[[File:Sword_BP_guitars.jpg\|thumb\|300px]]		[[File:Sword_BP_guitars.jpg\|thumb\|300px]]

	The '''~~Bohlen–Pierce~~ scale''' ('''BP''') is a 13-tone [[macrotonal]] [[nonoctave]] [[scale]] designed to emphasize odd-number intervals and chords, such as the 3:5:7:9 tetrad. It was first described as a 7-limit [[just intonation]] scale and as an [[equal-step tuning\|equal temperament]], [[13edt\|13 equal divisions of the tritave]]. The [[tritave]] (3/1) usually replaces the [[octave]] in the role of the [[equave]], such that intervals a tritave apart are considered [[equivalent]].		The '''Bohlen–Pierce scale''' ('''BP''') is a 13-tone [[macrotonal]] [[nonoctave]] [[scale]] designed to emphasize odd-number intervals and chords, such as the 3:5:7:9 tetrad. It was first described as a 7-limit [[just intonation]] scale and as an [[equal-step tuning\|equal temperament]], [[13edt\|13 equal divisions of the tritave]]. The [[tritave]] (3/1) usually replaces the [[octave]] in the role of the [[equave]], such that intervals a tritave apart are considered [[equivalent]].

	It is closely related to the rank two temperament [[Sensamagic clan #Bohpier\|bohpier]]. It is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 [[Just intonation subgroup\|subgroup]]. However, it can be extended to the 3.5.7.11/4 subgroup, especially when considering 13edt instead of the JI version. This extension is controversial because of the presence of 2 in the denominator of 11/4, but the interval is present in the sense that 3^(12\13) provides an approximation to it. Chords of ~~Bohlen–Pierce~~, from this extended perspective, may be found listed on the page [[chords of bohpier]].		It is closely related to the rank two temperament [[Sensamagic clan #Bohpier\|bohpier]]. It is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 [[Just intonation subgroup\|subgroup]]. However, it can be extended to the 3.5.7.11/4 subgroup, especially when considering 13edt instead of the JI version. This extension is controversial because of the presence of 2 in the denominator of 11/4, but the interval is present in the sense that 3^(12\13) provides an approximation to it. Chords of Bohlen–Pierce, from this extended perspective, may be found listed on the page [[chords of bohpier]].

	~~Bohlen–Pierce~~ was discovered independently by [[Heinz Bohlen]], [[John Pierce]], [[Kees van Prooijen]], and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.; but not necessarily 4:11, 5:6, 6:7, etc.		Bohlen–Pierce was discovered independently by [[Heinz Bohlen]], [[John Pierce]], [[Kees van Prooijen]], and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.; but not necessarily 4:11, 5:6, 6:7, etc.

	== Theory ==		== Theory ==
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	== Variations ==		== Variations ==
	=== Triple Bohlen–Pierce ===		=== Triple Bohlen–Pierce ===
	Proposed by [[Paul Erlich]] is [[39edt]], also known as the ''Triple Bohlen–Pierce scale''. It adds to 13edt accurate approximations to the 11th and 13th harmonics ([[11/9]] and [[13/9]]) and can be used in a variety of ways, for both just intonation chords and harmonies, as standard ~~Bohlen–Pierce~~ scale interlocking three times with calm-sounding quarter-tones, and for various JI modulations.		Proposed by [[Paul Erlich]] is [[39edt]], also known as the ''Triple Bohlen–Pierce scale''. It adds to 13edt accurate approximations to the 11th and 13th harmonics ([[11/9]] and [[13/9]]) and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen–Pierce scale interlocking three times with calm-sounding quarter-tones, and for various JI modulations.

	== Regular temperament properties ==		== Regular temperament properties ==
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	== Music ==		== Music ==
	{{Main\| ~~Bohlen–Pierce~~ scale/Music }}		{{Main\| Bohlen–Pierce scale/Music }}
	{{Catrel\|Bohlen-Pierce tracks}}		{{Catrel\|Bohlen-Pierce tracks}}

	== See also ==		== See also ==
	* [[Catalog of 3.5.7 subgroup rank two temperaments]]		* [[Catalog of 3.5.7 subgroup rank two temperaments]]
	* [[Lumatone mapping for ~~Bohlen-Pierce~~]]		* [[Lumatone mapping for Bohlen–Pierce]]

	== Further reading ==		== Further reading ==

ArrowHead294: /* Variations */

2025-03-10T13:13:08Z

Variations

← Older revision		Revision as of 13:13, 10 March 2025
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	== Variations ==		== Variations ==
	=== Triple ~~Bohlen–Pierce~~ ===		=== Triple Bohlen–Pierce ===
	Proposed by [[Paul Erlich]], is ~~39EDT~~, also known as the [[Triple ~~BP\|Triple Bohlen–Pierce~~ scale]]. It ~~approximates additional odd~~ harmonics and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen–Pierce scale interlocking three times with calm-sounding quarter-tones, and for various JI modulations.		Proposed by [[Paul Erlich]] is [[39edt]], also known as the ''Triple Bohlen–Pierce scale''. It adds to 13edt accurate approximations to the 11th and 13th harmonics ([[11/9]] and [[13/9]]) and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen–Pierce scale interlocking three times with calm-sounding quarter-tones, and for various JI modulations.

	== Regular temperament properties ==		== Regular temperament properties ==

ArrowHead294 at 13:03, 10 March 2025

2025-03-10T13:03:43Z

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	* [http://ziaspace.com/_academic/BP/ Bohlen-Pierce Scale Research] by [[Elaine Walker]]		* [http://ziaspace.com/_academic/BP/ Bohlen-Pierce Scale Research] by [[Elaine Walker]]

	[[Category:~~Bohlen-Pierce~~\| ]] <!-- main article -->		[[Category:Bohlen–Pierce\| ]] <!-- main article -->
	[[Category:13-tone scales]]		[[Category:13-tone scales]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

ArrowHead294: /* Triple Bohlen–Pierce */

2024-12-09T18:36:16Z

Triple Bohlen–Pierce

← Older revision		Revision as of 18:36, 9 December 2024
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	== Variations ==		== Variations ==
	=== Triple Bohlen–Pierce ===		=== Triple Bohlen–Pierce ===
	Proposed by [[Paul Erlich]], is the [[Triple BP\|Triple Bohlen–Pierce ~~Scale~~]]~~, or 39th root of 3~~. It approximates additional odd harmonics and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen-Pierce scale interlocking three times with calm sounding quarter-tones, and for various JI modulations.		Proposed by [[Paul Erlich]], is 39EDT, also known as the [[Triple BP\|Triple Bohlen–Pierce scale]]. It approximates additional odd harmonics and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen–Pierce scale interlocking three times with calm-sounding quarter-tones, and for various JI modulations.

	== Regular temperament properties ==		== Regular temperament properties ==

ArrowHead294: /* Theory */

2024-11-20T16:18:11Z

Theory

← Older revision		Revision as of 16:18, 20 November 2024
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	== Theory ==		== Theory ==
	* [[Relationship between ~~Bohlen-Pierce~~ and octave-ful temperaments]]		* [[Relationship between Bohlen–Pierce and octave-ful temperaments]]

	=== Lambda scale ===		=== Lambda scale ===

ArrowHead294 at 14:33, 20 November 2024

2024-11-20T14:33:03Z

← Older revision		Revision as of 14:33, 20 November 2024
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	\|de = Bohlen-Pierce		\|de = Bohlen-Pierce
	}}		}}
	{{Wikipedia~~\|Bohlen-Pierce scale~~}}		{{Wikipedia}}
	[[File:vaisvil-BP-guitar-052-crop.jpg\|thumb\|x00px\|Chris Vaisvil's BP electric guitar. [http://chrisvaisvil.com/the-bohlen-pierce-epiphone-roadie-guitar/ Music from this guitar.]]]		[[File:vaisvil-BP-guitar-052-crop.jpg\|thumb\|x00px\|Chris Vaisvil's BP electric guitar. [http://chrisvaisvil.com/the-bohlen-pierce-epiphone-roadie-guitar/ Music from this guitar.]]]
	[[File:Sword_BP_guitars.jpg\|thumb\|300px]]		[[File:Sword_BP_guitars.jpg\|thumb\|300px]]

	The '''Bohlen-Pierce scale''' ('''BP''') is a 13-tone [[macrotonal]] [[nonoctave]] [[scale]] designed to emphasize odd-number intervals and chords, such as the 3:5:7:9 tetrad. It was first described as a 7-limit [[just intonation]] scale and as an [[equal-step tuning\|equal temperament]], [[13edt\|13 equal divisions of the tritave]]. The [[tritave]] (3/1) usually replaces the [[octave]] in the role of the [[equave]], such that intervals a tritave apart are considered [[~~Equivalence\|~~equivalent]].		The '''Bohlen–Pierce scale''' ('''BP''') is a 13-tone [[macrotonal]] [[nonoctave]] [[scale]] designed to emphasize odd-number intervals and chords, such as the 3:5:7:9 tetrad. It was first described as a 7-limit [[just intonation]] scale and as an [[equal-step tuning\|equal temperament]], [[13edt\|13 equal divisions of the tritave]]. The [[tritave]] (3/1) usually replaces the [[octave]] in the role of the [[equave]], such that intervals a tritave apart are considered [[equivalent]].

	It is closely related to the rank two temperament [[Sensamagic clan #Bohpier\|bohpier]]. It is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 [[Just intonation subgroup\|subgroup]]. However, it can be extended to the 3.5.7.11/4 subgroup, especially when considering 13edt instead of the JI version. This extension is controversial because of the presence of 2 in the denominator of 11/4, but the interval is present in the sense that 3^(12\13) provides an approximation to it. Chords of Bohlen-Pierce, from this extended perspective, may be found listed on the page [[chords of bohpier]].		It is closely related to the rank two temperament [[Sensamagic clan #Bohpier\|bohpier]]. It is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 [[Just intonation subgroup\|subgroup]]. However, it can be extended to the 3.5.7.11/4 subgroup, especially when considering 13edt instead of the JI version. This extension is controversial because of the presence of 2 in the denominator of 11/4, but the interval is present in the sense that 3^(12\13) provides an approximation to it. Chords of Bohlen–Pierce, from this extended perspective, may be found listed on the page [[chords of bohpier]].

	Bohlen-Pierce was discovered independently by [[Heinz Bohlen]], [[John Pierce]], [[Kees van Prooijen]], and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.; but not necessarily 4:11, 5:6, 6:7, etc.		Bohlen–Pierce was discovered independently by [[Heinz Bohlen]], [[John Pierce]], [[Kees van Prooijen]], and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.; but not necessarily 4:11, 5:6, 6:7, etc.

	== Theory ==		== Theory ==
	* [[Relationship between Bohlen-Pierce and octave-ful temperaments]]		* [[Relationship between Bohlen-Pierce and octave-ful temperaments]]

	=== Lambda scale ===		=== Lambda scale ===
	{{Main\|4L 5s (~~tritave~~-equivalent)}}		{{Main\|4L 5s (3/1-equivalent)}}

	== Intervals ==		== Intervals ==
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	== Variations ==		== Variations ==
			=== Triple Bohlen–Pierce ===
	=== Triple Bohlen-Pierce ===		Proposed by [[Paul Erlich]], is the [[Triple BP\|Triple Bohlen–Pierce Scale]], or 39th root of 3. It approximates additional odd harmonics and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen-Pierce scale interlocking three times with calm sounding quarter-tones, and for various JI modulations.
	Proposed by [[Paul Erlich]], is the [[Triple BP\|Triple Bohlen-Pierce Scale]], or 39th root of 3. It approximates additional odd harmonics and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen-Pierce scale interlocking three times with calm sounding quarter-tones, and for various JI modulations.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 39:		Line 39:

	== Music ==		== Music ==
	{{Main\| Bohlen-Pierce scale/Music }}		{{Main\| Bohlen–Pierce scale/Music }}
	{{Catrel\|Bohlen-Pierce tracks}}		{{Catrel\|Bohlen-Pierce tracks}}

ArrowHead294: ArrowHead294 moved page Bohlen-Pierce scale to Bohlen–Pierce scale: Per wikipedia:MOS:ENDASH

2024-11-20T14:31:00Z

ArrowHead294 moved page Bohlen-Pierce scale to Bohlen–Pierce scale: Per wikipedia:MOS:ENDASH

← Older revision	Revision as of 14:31, 20 November 2024
(No difference)

← Older revision		Revision as of 15:43, 31 July 2025
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	[[Category:Bohlen–Pierce\| ]] <!-- main article -->		[[Category:Bohlen–Pierce\| ]] <!-- main article -->
	[[Category:13-tone scales]]		[[Category:13-tone scales]]
	~~[[Category:Edonoi]]~~
	~~[[Category:Edt]]~~
	[[Category:Guitar]]		[[Category:Guitar]]
	[[Category:Macrotonal]]		[[Category:Macrotonal]]