Editing Polytonality (section)

==Polytonality and polychords==

Polytonality requires the presentation of simultaneous key-centers. The term "[[polychord]]" describes chords that can be constructed by superimposing multiple familiar tonal sonorities. For example, familiar ninth, eleventh, and thirteenth chords can be built from or decomposed into separate chords:

[[File:Thirteenth-polychord.PNG|thumb|upright=1.2|center|Separate chords within an extended chord{{sfn|Marquis|1964|loc={{Page needed|date=October 2010}}}}[[File:Thirteenth-polychord.mid]]]]

Thus polychords do not necessarily suggest polytonality, but they may not be explained as a single tertian chord. The [[Petrushka chord]] is an example of a polychord.{{sfn|Ellenberger|2005|loc=20}} This is the norm in jazz, for example, which makes frequent use of "extended" and polychordal harmonies without any intended suggestion of "multiple keys."{{Citation needed|date=August 2015}}

===Polyvalency===
The following passage, taken from [[Ludwig van Beethoven|Beethoven]]'s [[Piano Sonata No.&nbsp;26 (Beethoven)|Piano Sonata in E{{music|flat}}, Op.&nbsp;81a (''Les Adieux'')]], suggests clashes between tonic and dominant harmonies in the same key.{{sfn|Marquis|1964|loc={{Page needed|date=November 2010}}}}

[[File:Bitonality in Beethoven.PNG|thumb|upright=1.8|center|Polyvalency suggested in Beethoven{{sfn|Marquis|1964|loc={{Page needed|date=October 2010}}}}[[File:Bitonality in Beethoven.mid]]]]

Leeuw points to Beethoven's use of the clash between tonic and dominant, such as in his [[Symphony No. 3 (Beethoven)|Third Symphony]], as polyvalency rather than bitonality, with polyvalency being, "the telescoping of diverse functions that should really occur ''in succession'' to one another".{{sfn|Leeuw|2005|loc=87}}

[[File:Polyvalency in Beethoven.png|thumb|upright=1.8|center|Polyvalency in Beethoven{{sfn|Leeuw|2005|loc=88}}[[File:Polyvalency in Beethoven.mid]]]]
[[File:Polyvalency in Stravinsky's Mass.png|thumb|upright=1.8|center|Polyvalency in Stravinsky's ''[[Mass (Stravinsky)|Mass]]''{{harv|Leeuw|2005|loc=88}}[[File:Polyvalency in Stravinsky.mid]]]]

===Polymodality===
Passages of music, such as [[Francis Poulenc|Poulenc]]'s ''[[Trois mouvements perpétuels]]'', I., may be misinterpreted as polytonal rather than polymodal. In this case, two scales{{Clarify|date=November 2014|reason=Which two scales? If they have a common tonic, are they not just different modal interpretations of the same scale?}} are recognizable but are assimilated through the common tonic (B{{Music|flat}}).{{sfn|Vincent|1951|loc=272}}

===Polyscalarity===

Polyscalarity is defined as "the simultaneous use of musical objects ''which clearly suggest different source-collections''.{{sfn|Tymoczko|2002|loc=83}} Specifically about Stravinsky's music, Tymoczko uses the term polyscalarity out of deference to terminological sensibilities.{{sfn|Tymoczko|2002|loc=85}} In other words, the term is meant to avoid any implication that the listener can perceive two keys at once. Though Tymoczko believes that polytonality is perceivable, he believes polyscalarity is better suited to describe Stravinsky's music. This term is also used as a response to Van den Toorn's analysis against polytonality. Van den Toorn, in an attempt to dismiss polytonal analysis used a monoscalar approach to analyze the music with the [[octatonic scale]]. However, Tymoczko states that this was problematic in that it does not resolve all instances of multiple interactions between scales and chords. Moreover, Tymoczko quotes Stravinsky's claim that the music of ''[[Petrouchka]]''{{'}}s second tableau was conceived "in two keys".{{sfn|Tymoczko|2002|loc=85}} Polyscalarity is then a term encompassing multiscalar superimpositions and cases which give a different explanation than the octatonic scale.