Editing Polytonality (section)

==Challenges==

Some music theorists, including [[Milton Babbitt]] and [[Paul Hindemith]] have questioned whether polytonality is a useful or meaningful notion or "viable auditory possibility".{{sfn|Baker|1993|loc=35}} Babbitt called polytonality a "self-contradictory expression which, if it is to possess any meaning at all, can only be used as a label to designate a certain degree of expansion of the individual elements of a well-defined harmonic or [[voice leading|voice-leading]] unit".{{sfn|Babbitt|1949|loc=380}} Other theorists to question or reject polytonality include [[Allen Forte]] and [[Benjamin Boretz]], who hold that the notion involves logical incoherence.{{sfn|Tymoczko|2002|loc=84}}

Other theorists, such as [[Dmitri Tymoczko]], respond that the notion of "tonality" is a psychological, not a logical notion.{{sfn|Tymoczko|2002|loc=84}} Furthermore, Tymoczko argues that two separate key-areas can, at least at a rudimentary level, be heard at the same time: for example, when listening to two different pieces played by two different instruments in two areas of a room.{{sfn|Tymoczko|2002|loc=84}}

===Octatonicism===

Some critics of the notion of polytonality, such as Pieter van den Toorn, argue that the octatonic scale accounts in concrete pitch-relational terms for the qualities of "clashing", "opposition", "stasis", "polarity", and "superimposition" found in Stravinsky's music and, far from negating them, explains these qualities on a deeper level.{{sfn|Van den Toorn and Tymoczko|2003|loc=179}} For example, the passage from ''Petrushka'', cited above, uses only notes drawn from the C octatonic collection C–C{{music|#}}–D{{music|#}}–E–F{{music|#}}–G–A–A{{music|#}}.