Interval of equivalence: Difference between revisions
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An '''interval of equivalence''' is a musical interval at which pitches are perceived or treated as functionally equivalen, 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]]. | |||
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 | 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 | == 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. | |||
[[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. | |||
== 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]] | * 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]] | ||
== References == | == References == | ||