Editing Twelve-tone technique (section)

===Cross partition===<!--[[Cross-partition]] redirects directly here.-->
[[File:Aggregate Von Heute auf Morgen.png|thumb|Aggregates spanning several local set forms in Schoenberg's ''[[Von heute auf morgen]]''.<ref>Haimo 1990, 13.</ref>]]
{{See also|Derived row#Partition and mosaic}}

A ''cross partition'' is an often monophonic or homophonic technique which, "arranges the pitch classes of an aggregate (or a row) into a rectangular design", in which the vertical columns (harmonies) of the rectangle are derived from the adjacent segments of the row and the horizontal columns (melodies) are not (and thus may contain non-adjacencies).<ref>Alegant 2010, 20.</ref>

For example, the layout of all possible 'even' cross partitions is as follows:<ref name="Alegant 21">Alegant 2010, 21.</ref>
:{|
|style="width:30px;"|6<sup>2</sup>
|style="width:30px;"|4<sup>3</sup>
|style="width:30px;"|3<sup>4</sup>
|style="width:30px;"|2<sup>6</sup>
|-
|**||***||****||******
|-
|**||***||****||******
|-
|**||***||****
|-
|**||***
|-
|**
|-
|**
|}

One possible realization out of many for the ''order numbers'' of the 3<sup>4</sup> cross partition, and one variation of that, are:<ref name="Alegant 21"/>
 0 3 6 9 0 5 6 e
 1 4 7 t 2 3 7 t
 2 5 8 e 1 4 8 9

Thus if one's tone row was 0 e 7 4 2 9 3 8 t 1 5 6, one's cross partitions from above would be:
 0 4 3 1 0 9 3 6
 e 2 8 5 7 4 8 5
 7 9 t 6 e 2 t 1

Cross partitions are used in Schoenberg's [[Zwei Klavierstücke (Schoenberg)|Op. 33a ''Klavierstück'']] and also by [[Alban Berg|Berg]] but [[Luigi Dallapiccola|Dallapicolla]] used them more than any other composer.<ref>Alegant 2010, 22, 24.</ref>