funCode—Versatile Syntax and Semantics for Functional Harmonic Analysis Labels

Abstract

Traditional harmonic analysis annotations can be represented in a computer model of a piece of music by plain text strings. But whenever automated processing like analysis, comparison or retrieval is intended, a formal definition is helpful. This should cover not only the syntactic structure, but also the semantics, i.e. the intended meaning, and thus adheres to the technique of mathematical remodelling of existing cultural phenomena. The resulting models can serve as a basis for automated processing, but also help to clarify the communication and discussion among humans substantially. This article proposes such a definition in four layers, which address different problems of encoding and communication: (a) relation of symbol sequences to staff positions, (b) combining functions, (c) chord roots, and (d) interval structure and voice leading. Only one of them is specific to functional (Riemannian) theory and can possibly be replaced to represent scale degree theory. The proposal is configurable to different interval specification methods and open to localisation. Syntax and semantics are defined by precise mathematical means, borrowed from computer science, and thus are unambiguously documented.

Modulation Mining—Computer-Aided Exploration of Functional Chord Forms

“…A unique case is e + g + b ♭ + d as D/79+ with root c as dominant to f versus s56+ with root g as subdominant to d, because this re-interpretation does not cause enharmonic change of notation in the foreground (but in the background the coordinates in the Euler net change nevertheless, see Lepper et al (2022a)).…”

“…As discussed in detail in Lepper et al (2022a), different semantics can be assigned to a sequence of labels from a functional labelling system. In most use cases, the author of a labelling sequence intends to apply several different semantics simultaneously, for expressing a combined interpretation.…”

“…The funCode project, which is the larger context of the results presented in this paper, is a first attempt to reexamine the historically defined labels of functional harmonic theory as consistent mathematical objects (Lepper et al 2022a). This is done by applying rigorous techniques from computer science, namely compiler theory, to the semantics S-p.…”

“… 7. The sorting order for normalization of chord components is as follows: first comes 7^ as the ‘lowest in stack’, when the traditional chord structure of ‘thirds above a root’ is imagined. Then follow all other chord components with ascending interval numbers, their modifiers in the order: no modifier, / , …, ‐‐‐ , ‐‐ , ‐ , + , ++ , …, ^ , ^^ , … Such a normalization is not possible when using for concrete analyses, because the sequential order of the code components may describe voice leading, see Lepper et al (2022a).…”

“…It is a matter of mere convenience that the former need not to be written but always sound unless explicitly cancelled or suppressed by a neighbour pitch (by suspension etc.). In the Euler net semantics of (Lepper et al 2022a), this behaviour is configurable. The corresponding definition would be s u p p r e s s = falsefalse{ 7 0.25em 0.25em false^ .1em false↦ 1 , 2 + false↦ 1 , 2 − false↦ 1 , 2 0.25em 0.25em false^ .1em 0.25em false^ .1em false↦ 3 , 4 false↦ 3 , 4 + false↦ 3 , 4 0.25em ^ false↦ 5 , 6 false0 - false↦ 5 , 6 + false↦ 5 falsefalse}.…”