Research output: Chapter in Book/Report/Conference proceedingChapter


This chapter deals with the central issue of modulation between two given tonalities. It involves explicit models of tonalities, of cadences and—even more crucial—of the transition process from one tonality to its successor. The present model involves the analogy to elementary particle physics: Modulation is viewed as a ‘force interactionș between two ‘tonality particles’ which is mediated by a ‘modulation quantum’. The model allows for a complete calculation of fundamental degrees of modulation in congruence with Arnold Schönbergs harmony [948]. The model is realized for diatonic tonalities in 12-tempered and just tuning. It has been extended to all 7-element scales in 12-tempered tuning and to a number of scales in just tuning. The 12-tempered extension reveals a privileged position of the diatonic scale with regard to this modulation theory. We conclude the chapter with a discussion of the basic role of modulation models and their application to optimize harmonic paths in the sense of Section 27.2.

Original languageEnglish (US)
Title of host publicationComputational Music Science
PublisherSpringer Nature
Number of pages24
StatePublished - 2017

Publication series

NameComputational Music Science
ISSN (Print)1868-0305
ISSN (Electronic)1868-0313

Bibliographical note

Publisher Copyright:
© 2017, Springer International Publishing AG, part of Springer Nature.


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