Editing Lulu (opera) (section)

====Serialism====
[[Tetrachord|Cell z]] (also one of the basic cells in Bartók's [[String Quartet No. 4 (Bartók)|String Quartet No. 4]]) is the basic cell of ''Lulu'' and generates [[trope (music)#20th-century music|trope]] I:{{sfn|Perle|1977|loc=[https://books.google.com/books?id=Vw3IeMkt8KAC&pg=PA12 p.&nbsp;12]}}

[[File:Berg's Lulu trope I.png|thumb|center|400px|The two non-identical forms of trope I, each generated from all even or odd forms of cell z]]

Although some of ''Lulu'' is freely composed, Berg also makes use of Schoenberg's [[twelve-tone technique]]. Rather than using one [[tone row]] for the entire work, however, he gives each character his or her own tone row, meaning that the tone rows act rather like the [[leitmotif]]s in [[Richard Wagner]]'s operas.

[[File:Berg - Lulu basic tone row.png|thumb|center|400px|Berg's ''Lulu'' basic tone row{{sfn|Whittall|2008|loc=p.&nbsp;81}} on C]]

From this one tone row, Berg derives tone rows for many of the characters. For example, the tone row associated with Lulu herself is: F, G, A{{music|flat}}, B{{music|flat}}, C, D, F{{music|sharp}}, D{{music|sharp}}, E, A, B, C{{music|sharp}}. This row is constructed by extracting one note (F) from the basic row's first trichord, then taking the next note (G) from the basic row's second trichord, then taking the third note (A{{music|flat}}) from the basic row's third trichord, and so on, cycling through the basic row three times.

[[File:Berg - Lulu Alwa tone row.png|thumb|center|400px|Berg's ''Lulu'' Alwa tone row{{sfn|Whittall|2008|loc=p.&nbsp;81}} on C]]

The tone row associated with Alwa is arrived at by repeating the basic tone row over and over and taking every seventh note;
[[File:Berg - Lulu, derivation of Alwa from basic series.png|thumb|400px|center|Derivation of Alwa series from basic series by taking every seventh note from repetitions of the basic series.{{sfn|Pople|1991|loc=p.&nbsp;22}}]]
this results in the following tone row: B{{music|flat}}, F{{music|sharp}}, E{{music|flat}}, G{{music|sharp}}, F, B, E, D, A, C, C{{music|sharp}}, G

[[File:Berg - Lulu Dr Schön tone row.png|thumb|center|400px|Berg's ''Lulu'' Dr. Schön tone row{{sfn|Whittall|2008|loc=p.&nbsp;81}} on C]]

Similarly, the tone row associated with Dr. Schön is arrived at by repeating the basic tone row (as in the previous example) and taking the first note, missing one note, taking the next, missing two, taking the next, missing three, taking the next, missing three, taking the next, missing two, taking the next, missing one, taking the next, missing one, taking the next, missing two, taking the next, and so on; this results in the following tone row: B{{music|flat}}, E{{music|flat}}, G, G{{music|sharp}}, D, F, E, A, B, C, F{{music|sharp}}, C{{music|sharp}}

[[File:Berg - Lulu Schoolboy tone row.png|thumb|center|400px|Berg's ''Lulu'' Schoolboy tone row{{sfn|Whittall|2008|loc=p.&nbsp;81}} on C]]<!-- Any analysis for the tone row of Der Gymnasiast? -->