Historically, 'consonance' and 'dissonance' refer to five distinct concepts, not one unified notion

Sethares identifies five historical Consonance-Dissonance Concepts (CDCs): CDC-1 (melodic consonance — small intervals are dissonant in melody, large intervals are consonant), CDC-2 (polyphonic consonance — intervals that blend vs. clash in early polyphony), CDC-3 (contrapuntal consonance — Renaissance rules of which intervals may begin/end phrases), CDC-4 (functional consonance — tonal harmony’s resolution tendency, e.g., tritone resolves), and CDC-5 (psychoacoustic/sensory consonance — roughness from beating partials, Helmholtz/Plomp-Levelt). These five concepts often conflict: a minor seventh is functionally dissonant (CDC-4) but has low sensory dissonance (CDC-5). Much confusion in music theory arises from conflating them. The book primarily uses CDC-5 because it can be quantified and measured.

Examples

The tritone (augmented fourth) is CDC-4 dissonant (it demands resolution in tonal harmony) but its CDC-5 sensory dissonance depends entirely on the timbre — with pure sine waves it has low sensory dissonance at many tunings. Gregorian chant treats the fifth as highly consonant (CDC-3) but parallel fifths are forbidden in later counterpoint (also CDC-3, different context).

Assessment

For each of the following, state which CDC is most relevant: (a) a guitarist avoiding parallel fifths in a chord progression, (b) a physicist measuring the roughness of a major third, (c) an early medieval singer finding that a fourth is a ‘perfect consonance.’ Explain why conflating these concepts causes confusion.