On the Function of Function — Music Theory Online

Claims

1. many-meanings
   Kopp argues that harmonic function has no unitary, universally understood meaning: the term is used for scale-degree identity, for a chord's tendency to progress, for grouping chords with similar behaviour, for the primacy of tonic, dominant and subdominant, and for phrase-based syntax, among other things. Theories by Rameau, Weber and Riemann are all associated with the concept but mean quite different things by it.

   "The concept of harmonic function, far from carrying a unitary and universally understood meaning, has signified many different things to theorists past and present. This essay examines some of the different meanings commonly associated with the term today, as well as aspects of the harmonic theories of Rameau, Weber, and Riemann, all regularly associated with the concept."

   Locator: paragraph: Abstract; 1-2 · Quote language: en
2. rameau-weber-riemann
   Rameau's tonique, dominante and sous-dominante are defined by how chords progress, which he explained by added dissonances. Gottfried Weber, writing in the 1820s, labelled chords with Roman numerals according to their position in a key but had no concept of secondary dominants, so he analysed chromatic passages as rapid modulations. Hugo Riemann, who popularized the term function, treated tonic, dominant and subdominant as the three primary chords of a key and related every diatonic and chromatic chord to one of them, so that chromatic chords could be understood within a single key; his functions describe chords' meanings rather than determining their progressions.

   "Tonique, dominante, and sous-dominante are defined by action -- their relation to the chord which follows. I, ii, iii, etc., are defined by identity -- their relation to a tonic. ... In essence, Weber's theory identifies chords by their participation and position in a key ... But Weber had no concept of secondary/applied dominant ... Consequently, he analyzed stretches of music containing tonicizations of secondary degrees as quick successions of modulations to different keys. ... Hugo Riemann's theory is indisputably a functional one in some sense, since it was he who popularized the term. ... The principal significance of the functional archetypes Tonic, Dominant, and Subdominant is that they are the primary chords of the key, linked by the preeminent interval of the fifth. ... By allowing for the identification of every possible diatonic and chromatic chord with one of the three functional archetypes, Riemann provided a means not otherwise available by which to understand these chords as exercising meaning within a prevailing key ... Ultimately, Riemann's functions inhere as tonal meanings in individual chords; they do not determine action from one to the next."

   Locator: paragraph: 3-11 · Quote language: en