Editing Tone row (section)

==Nonstandard tone rows==
[[File:Pierre Boulez - Second Piano Sonata series.png|thumb|upright=2|[[Pierre Boulez]]'s ''Second Piano Sonata'' series consists of three cells: A) an ascending [[perfect fifth]] followed by a [[tritone]] and a [[perfect fourth]], B) a descending perfect fifth followed by an ascending major second and a descending [[augmented fifth]], and B1) B [[inversion (music)|inverted]].{{sfn|Leeuw|2005|loc=166}}[[File:Pierre Boulez - Second Piano Sonata series.mid]]]]
[[File:Stravinsky - In memoriam Dylan Thomas five-tone row.png|thumb|upright=1.5|Prime form of five-note tone row from [[Igor Stravinsky]]'s ''In memoriam Dylan Thomas''.{{sfn|Whittall|2008|loc=127}}[[File:Stravinsky - In memoriam Dylan Thomas five-tone row.mid]]]]

Schoenberg specified many strict rules and desirable guidelines for the construction of tone rows such as number of notes and intervals to avoid. Tone rows that depart from these guidelines include the above tone row from Berg's Violin Concerto which contains triads and tonal emphasis, and the tone row below from [[Luciano Berio]]'s ''[[Nones (Berio)|Nones]]'' which contains a repeated note making it a 'thirteen-tone row':

[[File:Berio - Nones thirteen-tone row.png|thumb|center|upright=2|Thirteen-note tone row from [[Luciano Berio]]'s ''[[Nones (Berio)|Nones]]'',{{sfn|Whittall|2008|loc=195}} symmetrical about the central tone with one note (D) repeated.[[File:Berio - Nones thirteen-tone row.mid]]]]

[[Igor Stravinsky]] used a five-tone row, chromatically filling out the space of a major third centered tonally on C (C–E), in one of his early serial compositions, ''In memoriam Dylan Thomas''.

In his twelve-tone practice, Stravinsky preferred the inverse-retrograde (IR) to the retrograde-inverse (RI),<ref>Claudio Spies, "Notes on Stravinsky's ''Abraham and Isaac''", ''[[Perspectives of New Music]]'' 3, no. 2 (Spring–Summer 1965): 104–126, citation on 118.</ref><ref>Joseph N. Strauss, "Stravinsky's Serial 'Mistakes{{'"}}, ''[[The Journal of Musicology]]'' 17, no. 2 (Spring 1999): 231–271, citation on 242.</ref><ref name="Whittall 139">{{harvnb|Whittall|2008|loc=139}}</ref> as for example in his ''[[Requiem Canticles]]'':

[[File:Stravinsky - Requiem Canticles basic row forms.png|thumb|center|upright=2|Basic row forms from Stravinsky's ''Requiem Canticles'':<ref name="Whittall 139"/> P R I IR]]

[[File:Stockhausen - Klavierstücke I-IV 2 series.png|thumb|upright=1.5|Unordered sets from the second of Stockhausen's ''[[Klavierstücke (Stockhausen)#Klavierstücke I–IV: from point to group composition|Klavierstücke I–IV]]'' which "retained only the rudiments of the 12-note series".<ref name="Leeuw176">{{harvnb|Leeuw|2005|pp=176–177}}</ref>[[File:Stockhausen - Klavierstücke I-IV 2 series.mid]]]]
[[File:Stockhausen - Klavierstücke I-IV 3 series.png|thumb|upright=1.5|Unordered sets from the third of Stockhausen's ''Klavierstücke'' I–IV<ref name="Leeuw176"/>[[File:Stockhausen - Klavierstücke I-IV 3 series.mid]]]]

[[Ben Johnston (composer)|Ben Johnston]] uses a "just tone row" (see [[just intonation]]) in works including String Quartets Nos. 6 and 7. Each permutation contains a just chromatic scale, however, transformations (transposition and inversion) produce pitches outside of the primary row form, as already occurs in the inversion of P0. The pitches of each hexachord are drawn from different [[Otonality and Utonality|otonality]] or utonality on A+ utonality, C otonality and utonality, and E{{music|b}}- otonality, outlining a [[diminished triad]].

[[File:Ben Johnston String Quartet No. 7, mov. 2 just tone row.png|thumb|center|upright=2|Primary forms of the just tone row from [[Ben Johnston (composer)|Ben Johnston]]'s ''String Quartet No. 7'', mov. 2<ref>[[John Fonville]], "Ben Johnston's Extended Just Intonation: A Guide for Interpreters", ''[[Perspectives of New Music]]'' 29, no. 2 (Summer 1991): 106–137, citation on 127.</ref>[[File:Ben Johnston String Quartet No. 7, mov. 2 just tone row.mid]] and hexachords.[[File:Ben Johnston String Quartet No. 7, mov. 2 just tone row chords.mid]]]]