Regions and Standard Modes
- 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
Norman Carey and David Clampitt observed in  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  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 , , as well as by further combinatorial connections between central and standard words.
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