Invariance properties of Schoenberg's tone row system

Fill, James Allen; Izenman, Alan Julian

doi:10.1017/s0334270000002368

Search citation statements

Order By: Relevance

Paper Sections

Select...

Gs(s)=(gs(s)2k-s Kl )=(G U G 2 G Kl 2k-s Kl )1

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1980

Publication Types

Select...

Article1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this case, e 2 = 2 2I2~1 = 1. There are (2)(2 2-1 ) = 4 canonical Rl-invariant four-tone rows; that is, b 2 = 4, which is the coefficient of x 2 in x/(l -2x) 2 .…”

Section: Gs(s)=(gs(s)2k-s Kl )=(G U G 2 G Kl 2k-s Kl )mentioning

confidence: 99%

See 1 more Smart Citation

The structure of RI-invariant tweleve-tone rows

Fill

Izenman²

1980

J. Aust. Math. Soc. Series B, Appl. Math

Self Cite

View full text Add to dashboard Cite

This paper presents an efficient method for generating the class of all twelvetone rows which are transpositions of their own retrograde-inversions. It is shown here that the members of this class can be obtained from a subclass of those rows whose first six notes are ascending and whose first note is C. The number of twelve-tone rows in this subclass is 192, and a complete listing is given in an appendix to this paper. The theory as developed here can be applied to tone rows having any even number of notes. 402[2]Rl-invariant twelve-tone rows 403

show abstract

“…In this case, e 2 = 2 2I2~1 = 1. There are (2)(2 2-1 ) = 4 canonical Rl-invariant four-tone rows; that is, b 2 = 4, which is the coefficient of x 2 in x/(l -2x) 2 .…”

Section: Gs(s)=(gs(s)2k-s Kl )=(G U G 2 G Kl 2k-s Kl )mentioning

confidence: 99%

“…The algorithm is extremely efficient and can be readily extended to the generation of Rl-invariant tone rows possessing a given even number of notes. The reader may also be interested in the companion paper [2].…”

Section: Introductionmentioning

confidence: 99%