Interval of equivalence - Revision history

FloraC: + fix interwiki

2026-04-13T09:25:56Z

+ fix interwiki

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	{{~~interwiki~~		{{Interwiki
	\| en = ~~Equave~~		\| en = Interval of equivalence
	\| de = Äquivalenzintervall		\| de = Äquivalenzintervall
	\| es =		\| es =

Inthar at 01:41, 13 April 2026

2026-04-13T01:41:48Z

← Older revision		Revision as of 01:41, 13 April 2026
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	{{interwiki		{{interwiki
	\| en = Equave		\| en = Equave
	\| de = ~~Äquave~~		\| de = Äquivalenzintervall
	\| es =		\| es =
	\| ja =		\| ja =

FloraC: Fix internal style. There's no reason every sentence should start with a newline

2025-05-21T10:59:13Z

Fix internal style. There's no reason every sentence should start with a newline

← Older revision		Revision as of 10:59, 21 May 2025
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	An '''interval of equivalence''' is a musical interval at which pitches are perceived or treated as functionally equivalent, despite their different absolute frequencies.		An '''interval of equivalence''' is a musical interval at which pitches are perceived or treated as functionally equivalent, despite their different absolute frequencies. When an interval is established as the equivalence interval, all pitches separated by one or more instances of this interval are considered members of the same [[pitch class]].
	When an interval is established as the equivalence interval, all pitches separated by one or more instances of this interval are considered members of the same [[pitch class]].

	In a [[periodic scale]], the interval of equivalence is typically the same as the [[period]] or a multiple thereof.		In a [[periodic scale]], the interval of equivalence is typically the same as the [[period]] or a multiple thereof. Almost all [[Musical notation\|notation systems]] give equivalent pitches the same name.
	Almost all [[Musical notation\|notation systems]] give equivalent pitches the same name.

	== Octave equivalence ==		== Octave equivalence ==
	The octave ([[2/1]]) is the most common interval of equivalence.		The octave ([[2/1]]) is the most common interval of equivalence. Tones separated by an octave are perceived as essentially the same. This equivalence is so strong that in most musical notation systems, notes separated by octaves share the same name. For the same reason, most [[scale]]s repeat at the octave.
	Tones separated by an octave are perceived as essentially the same.
	This equivalence is so strong that in most musical notation systems, notes separated by octaves share the same name.
	For the same reason, most [[scale]]s repeat at the octave.

	The physical basis for octave equivalence is believed to be caused by the [[harmonic series\|harmonic structure]] of periodic sounds.		The physical basis for octave equivalence is believed to be caused by the [[harmonic series\|harmonic structure]] of periodic sounds. When a tone with frequency ''f'' is played, it typically produces [[overtone]]s at 2''f'', 3''f'', 4''f'', etc. The first overtone (2''f'') is an octave above the fundamental, creating a consistent pattern in many natural sounds. This harmonic relationship may contribute to the perceptual significance of the octave in human hearing.
	When a tone with frequency ''f'' is played, it typically produces [[overtone]]s at 2''f'', 3''f'', 4''f'', etc.
	The first overtone (2''f'') is an octave above the fundamental, creating a consistent pattern in many natural sounds.
	This harmonic relationship may contribute to the perceptual significance of the octave in human hearing.

	The perception of octave equivalence appears to have both biological and cultural components.		The perception of octave equivalence appears to have both biological and cultural components. Studies have shown that various non-human animals, including rhesus monkeys and rats, experience octave equivalence to a certain extent.<ref>Hoeschele M. [https://doi.org/10.3819/CCBR.2017.120002 ''Animal Pitch Perception: Melodies and Harmonies'']. Comp Cogn Behav Rev. 2017</ref> However, the degree of octave equivalence perception varies across cultures, particularly in those with non-Western musical traditions.<ref>Jacoby, Nori et al. [https://doi.org/10.1016/j.cub.2019.08.020 ''Universal and Non-universal Features of Musical Pitch Perception Revealed by Singing'']. Current Biology, 2019.</ref>
	Studies have shown that various non-human animals, including rhesus monkeys and rats, experience octave equivalence to a certain extent.<ref>Hoeschele M. [https://doi.org/10.3819/CCBR.2017.120002 ''Animal Pitch Perception: Melodies and Harmonies'']. Comp Cogn Behav Rev. 2017</ref>
	However, the degree of octave equivalence perception varies across cultures, particularly in those with non-Western musical traditions.<ref>Jacoby, Nori et al. [https://doi.org/10.1016/j.cub.2019.08.020 ''Universal and Non-universal Features of Musical Pitch Perception Revealed by Singing'']. Current Biology, 2019.</ref>

	== Non-octave equivalence ==		== Non-octave equivalence ==

FloraC: /* Non-octave equivalence */ equave should not exclude octave

2025-05-21T10:57:15Z

Non-octave equivalence: equave should not exclude octave

← Older revision		Revision as of 10:57, 21 May 2025
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	== Non-octave equivalence ==		== Non-octave equivalence ==
	When the interval of equivalence is ~~specifically not an~~ octave, it is called the '''equave''' (a portmanteau of "equivalence" and "octave") or '''formal octave'''<ref>Op de Coul M. ''Scala help'' https://www.huygens-fokker.org/scala/help.htm</ref>.		When the interval of equivalence is allowed to be a non-octave interval, it is called the '''equave''' (a portmanteau of "equivalence" and "octave") or '''formal octave'''<ref>Op de Coul M. ''Scala help'' https://www.huygens-fokker.org/scala/help.htm</ref>. While the octave is the predominant interval of equivalence in most musical traditions, alternative equivalence intervals have been explored. A famous example is the [[tritave]] in [[Bohlen–Pierce]] and related systems.
	While the octave is the predominant interval of equivalence in most musical traditions, alternative equivalence intervals have been explored.
	A famous example is the [[tritave]] in [[Bohlen–Pierce]] and related systems.

	=== Pseudo-octave ===		=== Pseudo-octave ===
	{{Wikipedia\|Pseudo-octave}}		{{Wikipedia\|Pseudo-octave}}

	A '''pseudo-octave''' is an interval that is not exactly [[2/1]], but close enough to still be treated as an octave.		A '''pseudo-octave''' is an interval that is not exactly [[2/1]], but close enough to still be treated as an octave.

	[[Stretched tuning\|Stretched or compressed tunings]] may be said to have pseudo-octaves, as do many non-octave scales.		[[Stretched tuning\|Stretched or compressed tunings]] may be said to have pseudo-octaves, as do many non-octave scales. For example, the [[Carlos Beta]] scale has a pseudo-octave of 1212.8{{c}} at 19 steps.
	For example, the [[Carlos Beta]] scale has a pseudo-octave of 1212.8{{c}} at 19 steps.

	== Examples ==		== Examples ==

Fredg999: Undoing last two edits (the term "formal octave" is not limited to Scala, other software programs and other people also use it)

2025-05-01T04:18:52Z

Undoing last two edits (the term "formal octave" is not limited to Scala, other software programs and other people also use it)

← Older revision		Revision as of 04:18, 1 May 2025
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	== Non-octave equivalence ==		== Non-octave equivalence ==
	When the interval of equivalence is specifically not an octave, it is called the '''equave''' (a portmanteau of "equivalence" and "octave")~~. The app Scala refers to this as a~~ '''formal octave'''<ref>Op de Coul M. ''Scala help'' https://www.huygens-fokker.org/scala/help.htm</ref>.		When the interval of equivalence is specifically not an octave, it is called the '''equave''' (a portmanteau of "equivalence" and "octave") or '''formal octave'''<ref>Op de Coul M. ''Scala help'' https://www.huygens-fokker.org/scala/help.htm</ref>.
	While the octave is the predominant interval of equivalence in most musical traditions, alternative equivalence intervals have been explored.		While the octave is the predominant interval of equivalence in most musical traditions, alternative equivalence intervals have been explored.
	A famous example is the [[tritave]] in [[Bohlen–Pierce]] and related systems.		A famous example is the [[tritave]] in [[Bohlen–Pierce]] and related systems.

VectorGraphics: formatting

2025-05-01T03:38:08Z

formatting

← Older revision		Revision as of 03:38, 1 May 2025
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	== Non-octave equivalence ==		== Non-octave equivalence ==
	When the interval of equivalence is specifically not an octave, it is called the '''equave''' (a portmanteau of "equivalence" and "octave"). (The app Scala refers to this as a '''formal octave'''<ref>Op de Coul M. ''Scala help'' https://www.huygens-fokker.org/scala/help.htm</ref>).		When the interval of equivalence is specifically not an octave, it is called the '''equave''' (a portmanteau of "equivalence" and "octave"). The app Scala refers to this as a '''formal octave'''<ref>Op de Coul M. ''Scala help'' https://www.huygens-fokker.org/scala/help.htm</ref>.
	While the octave is the predominant interval of equivalence in most musical traditions, alternative equivalence intervals have been explored.		While the octave is the predominant interval of equivalence in most musical traditions, alternative equivalence intervals have been explored.
	A famous example is the [[tritave]] in [[Bohlen–Pierce]] and related systems.		A famous example is the [[tritave]] in [[Bohlen–Pierce]] and related systems.

VectorGraphics: Deformalization

2025-05-01T03:37:53Z

Deformalization

← Older revision		Revision as of 03:37, 1 May 2025
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	== Non-octave equivalence ==		== Non-octave equivalence ==
	When the interval of equivalence is specifically not an octave, it is called the '''equave''' (a portmanteau of "equivalence" and "octave") or '''formal octave'''<ref>Op de Coul M. ''Scala help'' https://www.huygens-fokker.org/scala/help.htm</ref>.		When the interval of equivalence is specifically not an octave, it is called the '''equave''' (a portmanteau of "equivalence" and "octave"). (The app Scala refers to this as a '''formal octave'''<ref>Op de Coul M. ''Scala help'' https://www.huygens-fokker.org/scala/help.htm</ref>).
	While the octave is the predominant interval of equivalence in most musical traditions, alternative equivalence intervals have been explored.		While the octave is the predominant interval of equivalence in most musical traditions, alternative equivalence intervals have been explored.
	A famous example is the [[tritave]] in [[Bohlen–Pierce]] and related systems.		A famous example is the [[tritave]] in [[Bohlen–Pierce]] and related systems.

Fredg999: Fix typo

2025-04-30T21:50:43Z

Fix typo

← Older revision		Revision as of 21:50, 30 April 2025
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	\| ja =		\| ja =
	}}		}}
	An '''interval of equivalence''' is a musical interval at which pitches are perceived or treated as functionally ~~equivalen~~, despite their different absolute frequencies.		An '''interval of equivalence''' is a musical interval at which pitches are perceived or treated as functionally equivalent, despite their different absolute frequencies.
	When an interval is established as the equivalence interval, all pitches separated by one or more instances of this interval are considered members of the same [[pitch class]].		When an interval is established as the equivalence interval, all pitches separated by one or more instances of this interval are considered members of the same [[pitch class]].

Sintel: Add short blurb about physical basis (trying to be careful about wording)

2025-04-30T19:17:44Z

Add short blurb about physical basis (trying to be careful about wording)

← Older revision		Revision as of 19:17, 30 April 2025
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	This equivalence is so strong that in most musical notation systems, notes separated by octaves share the same name.		This equivalence is so strong that in most musical notation systems, notes separated by octaves share the same name.
	For the same reason, most [[scale]]s repeat at the octave.		For the same reason, most [[scale]]s repeat at the octave.

			The physical basis for octave equivalence is believed to be caused by the [[harmonic series\|harmonic structure]] of periodic sounds.
			When a tone with frequency ''f'' is played, it typically produces [[overtone]]s at 2''f'', 3''f'', 4''f'', etc.
			The first overtone (2''f'') is an octave above the fundamental, creating a consistent pattern in many natural sounds.
			This harmonic relationship may contribute to the perceptual significance of the octave in human hearing.

	The perception of octave equivalence appears to have both biological and cultural components.		The perception of octave equivalence appears to have both biological and cultural components.

Sintel: Major rewrite

2025-04-30T19:15:51Z

Major rewrite

← Older revision		Revision as of 19:15, 30 April 2025
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	\| ja =		\| ja =
	}}		}}
	~~{{Wikipedia\|Pseudo-octave}}~~		An '''interval of equivalence''' is a musical interval at which pitches are perceived or treated as functionally equivalen, despite their different absolute frequencies.
	~~The '''equave''' (/ˈiːkwɪv/ ''EE-kwiv'' or /ˈiːkwəv/ ''EE-kwəv''), also called~~ '''interval of equivalence'''~~, '''equivalence~~ interval''', '''formal octave'''<ref>Op de Coul, E.F. [https://www.huygens-fokker.org/scala/help.htm Scala help.]</ref><ref group="note" name=":0"/>or '''pseudo-octave'''<ref>[https://help.ableton.com/hc/en-us/articles/10998372840220-ASCL-Specification ASCL Specification]. Ableton.</ref><ref group="note" name=":0">The terms ''formal octave'' and ''pseudo-octave'' are ~~often used specifically to designate a [[stretched tuning\|stretched~~ or ~~compressed octave]]~~, ~~but they may more generally designate any kind of equave~~.~~</ref>,~~ is the interval ~~such that~~ pitches separated by it are considered ~~psychoacoustically or formally [[equivalent]] and are elements~~ of the same [[pitch class]].		When an interval is established as the equivalence interval, all pitches separated by one or more instances of this interval are considered members of the same [[pitch class]].

	If a [[periodic scale]] ~~has an equave~~, the ~~equave~~ is typically the same as the [[period]] or a multiple thereof.		In a [[periodic scale]], the interval of equivalence is typically the same as the [[period]] or a multiple thereof.
			Almost all [[Musical notation\|notation systems]] give equivalent pitches the same name.

	== Octave equivalence ==		== Octave equivalence ==
	The octave is ~~usually called~~ the ~~'''~~interval of equivalence~~''', because tones~~ separated by ~~this interval~~ are perceived as ~~having~~ the same ~~[[pitch class]] despite their different absolute pitches~~. This equivalence is so strong that in most musical notation systems, notes separated by octaves share the same name. For the same reason, most [[scale]]s repeat at the octave.		The octave ([[2/1]]) is the most common interval of equivalence.
			Tones separated by an octave are perceived as essentially the same.
			This equivalence is so strong that in most musical notation systems, notes separated by octaves share the same name.
			For the same reason, most [[scale]]s repeat at the octave.

	The perception of octave equivalence appears to have both biological and cultural components.		The perception of octave equivalence appears to have both biological and cultural components.
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	However, the degree of octave equivalence perception varies across cultures, particularly in those with non-Western musical traditions.<ref>Jacoby, Nori et al. [https://doi.org/10.1016/j.cub.2019.08.020 ''Universal and Non-universal Features of Musical Pitch Perception Revealed by Singing'']. Current Biology, 2019.</ref>		However, the degree of octave equivalence perception varies across cultures, particularly in those with non-Western musical traditions.<ref>Jacoby, Nori et al. [https://doi.org/10.1016/j.cub.2019.08.020 ''Universal and Non-universal Features of Musical Pitch Perception Revealed by Singing'']. Current Biology, 2019.</ref>

	When a ~~different~~ interval ~~(such as~~ the [[tritave]]) is ~~used as the~~ interval ~~of equivalence, it~~ is ~~referred to as an~~ [[~~equave~~]] ~~or "formal~~ octave".		== Non-octave equivalence ==
			When the interval of equivalence is specifically not an octave, it is called the '''equave''' (a portmanteau of "equivalence" and "octave") or '''formal octave'''<ref>Op de Coul M. ''Scala help'' https://www.huygens-fokker.org/scala/help.htm</ref>.
			While the octave is the predominant interval of equivalence in most musical traditions, alternative equivalence intervals have been explored.
			A famous example is the [[tritave]] in [[Bohlen–Pierce]] and related systems.

			=== Pseudo-octave ===
			{{Wikipedia\|Pseudo-octave}}
			A '''pseudo-octave''' is an interval that is not exactly [[2/1]], but close enough to still be treated as an octave.

	~~== Etymology ==~~		[[Stretched tuning\|Stretched or compressed tunings]] may be said to have pseudo-octaves, as do many non-octave scales.
	~~The term ''equave'' was coined by~~ [[~~User:Inthar~~\|~~Inthar~~]]. ~~It is~~ a ~~portmanteau~~ of ~~''equivalence'' and ''octave''~~.		For example, the [[Carlos Beta]] scale has a pseudo-octave of 1212.8{{c}} at 19 steps.

	== Examples ==		== Examples ==
	* In octave-repeating scales, the equave is typically [[2/1]].		* In octave-repeating scales, the equave is typically [[2/1]].
	* In [[Bohlen–Pierce]], the equave may be taken as [[3/1]].		* In [[Bohlen–Pierce]], the equave may be taken as [[3/1]].
	* In [[edf]]s, the equave may be taken as [[3/2]] or less commonly [[9/4]].		* In an [[edf\|equal division of the fifth]], the equave may be taken as a [[3/2\|perfect fifth]] or less commonly a [[9/4\|major ninth]].

	== See also ==		== See also ==
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	* [[Stretched tuning]]		* [[Stretched tuning]]
	* [[Equave limit]]		* [[Equave limit]]

	~~== Notes ==~~
	~~<references group="note"/>~~

	== References ==		== References ==