Regions and Standard Modes

  • David Clampitt
  • Thomas Noll
Conference paper

DOI: 10.1007/978-3-642-02394-1_8

Part of the Communications in Computer and Information Science book series (CCIS, volume 38)
Cite this paper as:
Clampitt D., Noll T. (2009) Regions and Standard Modes. In: Chew E., Childs A., Chuan CH. (eds) Mathematics and Computation in Music. MCM 2009. Communications in Computer and Information Science, vol 38. Springer, Berlin, Heidelberg

Abstract

Norman Carey and David Clampitt observed in [4] that each region has two well-formed scales as its prefixes. If one looks at this finding from the viewpoint of word theory, one observes that regions are central words and the two prefixes are their independent periods. More precisely, each region, understood as a word in a two-letter alphabet, contains two distinct prefixes, both of which represent well-formed scales. One period is a special standard word, and the other period is a non-special standard word. Thomas Noll proposed in [13] to generalize the authentic Ionian mode through special standard words. He showed that the property of divider incidence characterizes these words among their conjugates. Thus there are two parallel lines of generalization which can be further enriched by observations from [7], [8], as well as by further combinatorial connections between central and standard words.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • David Clampitt
    • 1
  • Thomas Noll
    • 2
  1. 1.Ohio State University, School of MusicUSA
  2. 2.Escola Superior de Musica de CatalunyaBarcelonaSpain

Personalised recommendations