A “mode” (Sect. 10.1) consists of a core-like, seven-element segment of the line of fifths; a consonant subset of the core termed the “nucleus” (assumed to contain a maximal number of elements); and a message-like sequence of notes termed the “score.” The root of the nucleus is termed “final.” In a “dyadic mode” the nucleus is dyadically consonant, and is therefore an open fifth; in a “triadic mode” the nucleus is triadically consonant, and is therefore a major or minor triad. A “key” (respectively, “semi-key”) is a mode, the nucleus of which (a privileged proper subset thereof) forms a minimal number of dissonances relative to the non-nucleus core elements. It is shown that a semi-key is not “Lydian”; moreover, a triadic key is “Ionian” or “Aeolian.” Section 10.2 is a theory of modal communication. The theory is “context dependent” since, in effect, contextual cues that allow the final of the “transmitted mode” to be mapped into the final of the “received mode,” are assumed to exist. Section 10.3 studies the “scale-degree” function by which cluster elements are represented in terms of their intervallic relation to the final. A distinction is drawn between “first-order” and “second-order” chromatic degrees, where a first-order degree is a primary interval or the augmented fourth. A mode is “robust” if the elements of its score, represented as degrees, are diatonic or first-order chromatic (Sect. 10.4). It is shown that robust modal communication satisfies not only the Communication Principle, but via a coherence-like algorithm, the Economical Principle as well. Finally, Sect. 10.5 introduces the notions of “congruent” and “standard” modes. Standard modes display no more than five flats or six sharps in their “accidental index” (known as the “key signature” in the case of keys).
|Title of host publication||Computational Music Science|
|Number of pages||22|
|State||Published - 2013|
|Name||Computational Music Science|
Bibliographical notePublisher Copyright:
© 2013, Springer-Verlag Berlin Heidelberg.
- Economical Principle
- Modal Communication
- Receive Message
- Receive Mode
- Standard Mode