Editing Pseudo-octave (section)

{{short description|Musical interval which is not a perfect harmonic}}
{{Listen
| filename = Octave and septimal chromatic semitone on C (ogg).ogg
| title = Pseudo Octave
| description = Pseudo Octave
}}
{{Listen
| filename = Perfect_octave_on_C_(ogg).ogg
| title = Perfect Octave
| description = Perfect Octave
}}{{use dmy dates|date=October 2024}}
[[Image:Octave and septimal chromatic semitone on C.png|thumb|300px|right|Pseudo-octave (2.1:1)]]

In [[music theory]], a '''pseudo-octave''', '''pseudooctave''',<ref name=Mathews>
{{cite journal
 |first1=C. |last1=Roads   |author1-link=Curtis Roads
 |first2=M. |last2=Mathews |author2-link=Max Mathews
 |date=Winter 1980
 |title=Interview with Max Mathews
 |journal=[[Computer Music Journal]]
 |volume=4 |issue=4 |pages=15–22, esp.&nbsp;21
}} <!-- |publisher=The MIT Press --- no publ. for jrnls./mags. -->
</ref>
or '''paradoxical octave'''<ref>
{{cite journal
 |first=Jenő |last=Keuler
 |year=1999
 |title=The paradoxes of octave identities
 |journal=Studia Musicologica Academiae Scientiarum Hungaricae
 |volume=40 |issue=1-3 |pages=211–224, esp.&nbsp;213
}} <!-- |publisher=Akadémiai Kiadó --- no publ. for jrnls./mags. -->
</ref> 
is an [[interval (music)|interval]] whose [[ratio]] of [[frequencies]] is not exactly {{nowrap| 2:1 {{=}} [[octave]]&thinsp;:&thinsp;[[tonic (music)|tonic]] }} expected for perfectly [[harmonic series (music)|harmonic pitches]], but slightly wider or narrower in pitch – for example {{nowrap|1.98:1}}, {{nowrap|2.01:1}}, or even as large as {{nowrap|2.3:1.}}<ref name=Mathews/> The pseudo-octave is never-the-less perceived as if it were equivalent to the conventional 2:1&nbsp;harmonic ratio, and consequently is treated the same: [[pitch (music)|Pitches]] separated by a pseudo-octave appropriate for a given instrument are considered equivalent to each other just as with normal ''"[[pitch class]]es"'' (which are typically explained only in terms of the idealized 2:1&nbsp;octave).