Tonal Preliminaries

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The usual diatonic system is “dyadic,” for it privileges two intervals, the perfect octave and fifth; the usual harmonic system is “triadic,” for it privileges, in addition, the major and minor thirds (Sect. 9.1). The dyadic and triadic privileged intervals support, respectively, a dyadic/triadic notion of “consonance.” Every consonance other than the perfect prime has a unique “root,” such that, if the root is also the lower note, the consonance is “stable.” Section 9.2 studies the non-diatonic subset of the “cluster” (the set of all notes that may be received relative to the diatonic core, reduced to their register-zero representatives). It is shown that the subset consists of two length-five segments of the line of fifths, extending the seven-element core at either end to form a line-of-fifths segment totaling 17 elements exactly.

Original languageEnglish
Title of host publicationComputational Music Science
PublisherSpringer Nature
Number of pages9
StatePublished - 2013

Publication series

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

Bibliographical note

Publisher Copyright:
© 2013, Springer-Verlag Berlin Heidelberg.


  • Consonant Triads
  • Harmonic System
  • Lowest Note
  • Minor Thirds
  • Perfect Octave


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