Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Overture: Some Issues Facing the Contemporary American Composer
- Part One Essays on Composers
- Part Two Talks on My Music
- Part Three Essays on Criticism and Aesthetics
- A Some Serial Music Terms
- B Set-Class Table
- C Hexachordal Combinatoriality
- D Two-Row Combinatoriality
- Notes
- Bibliography
- Index
D - Two-Row Combinatoriality
Published online by Cambridge University Press: 17 February 2023
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Overture: Some Issues Facing the Contemporary American Composer
- Part One Essays on Composers
- Part Two Talks on My Music
- Part Three Essays on Criticism and Aesthetics
- A Some Serial Music Terms
- B Set-Class Table
- C Hexachordal Combinatoriality
- D Two-Row Combinatoriality
- Notes
- Bibliography
- Index
Summary
The begin set of a row P is the note set formed by taking the first n notes of P; the end set of P the note set formed by taking the last n notes of P; the set of notes not in the begin set or end set is the midset of P.
There are two cases of this kind of combinatoriality:
Case 1. The begin set remains the same under some transformation X. Then the row P will produce combinatoriality with the row RXP.
Case 2. The end set under some transformation X is the same as the begin set.
Then the row P will produce combinatoriality with the row XP. Hexachordal combinatoriality is just a special case of 2-row combinatoriality where the begin set and end set are hexachords (so the midset is empty). Note also that X can be any one-to-one and onto pitch-class transformation whatsoever.
If a row has a begin set that satisfies case 1 under TmI, and case 2 under two transformations, Tn and TpI, then the row is all-combinatorial. The set-classes that fulfill these requirements are the 2-row all-combinatorial source-sets. We know that there are 6 hexachordal source-sets; there are also 5 dyadic, 5 trichordal, 14 tetrachordal, and 9 pentachordal all-combinatorial source-sets.
- Type
- Chapter
- Information
- The Whistling BlackbirdEssays and Talks on New Music, pp. 368Publisher: Boydell & BrewerPrint publication year: 2010