Interval of equivalence: Difference between revisions

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== 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 ===

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 ==

@@ Line 27: / Line 27: @@
 == 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 ===
 {{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.
+[[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 ==