Jump to ContentJump to Main Navigation
Generalized Musical Intervals and Transformations$
Users without a subscription are not able to see the full content.

David Lewin

Print publication date: 2007

Print ISBN-13: 9780195317138

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780195317138.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 10 December 2019

Transformation Graphs and Networks (1): Intervals and Transpositions

Transformation Graphs and Networks (1): Intervals and Transpositions

Chapter:
(p.157) 7 Transformation Graphs and Networks (1): Intervals and Transpositions
Source:
Generalized Musical Intervals and Transformations
Author(s):

David Lewin

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195317138.003.0007

Instead of starting with a Generalized Interval System (GIS) and deriving certain characteristic transformations therefrom, it is possible to start with a family of characteristic transformations on a musical space and derive a GIS structure therefrom. That is, instead of regarding the i-arrow as a measurement of extension between points s and t observed passively “out there” in a Cartesian res extensa, one can regard the situation actively, like a singer, player, or composer, thinking: “I am at s; what characteristic transformation do I perform in order to arrive at t?” This chapter explores this conceptual interrelation between interval-as-extension and transposition-as-characteristic-motion-through-space. After developing the mathematics that shows a logical equivalence between GIS structures and certain structures of transformations on spaces, the work proceeds by example. Passages from Schoenberg, Wagner, Brahms, and Beethoven indicate how suggestive it can be to consider networks of “intervals” and networks of “transpositions” (modulations and so forth) as various aspects of the same basic phenomenon.

Keywords:   Generalized Interval System, music theory, musical spaces, interval, transposition

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .