In order to properly express the ideas of the visualization of harmony, I must articulate the scaffolding in
which the theory of mapping is built upon. One aspect of the mapping of chords and scales is an idea taken from
structural linguistics; and how this concept of representation aligns with some of the aforementioned composers.
For Schenker, “... structural linguistics is perhaps most prominently represented, for it is clear that the modern
notion of leveled structures in language corresponds in a remarkable way to Schenker's concept of musical
organization (Schenker, 2001, xx.).” As a linguist, I try to organize my musical thoughts in the manner of a sign
as expressed by Saussure (Saussure, 2016).
As expressed by Saussure, a sign is a linguistic phenomenon that has two parts: the signified and the
signifier. For the sign, the sound image, or tangible occurrence, is called the signifier while the concept, or idea,
is the signified (Saussure, 2016). In music, the signifier would be the aural, temporal existence of a piece; as the
written music operates more as the signified. This conceptual practice, the signified aspect of music, is the basis
of music theory as described by Schenker in the previous paragraph. The performance of a piece of music is the
signifier, or temporal and aural, phenomenon in music. This is very similar to spoken language (signifier) and the
written word (signified); no matter the language or script.While this one-to-one correspondence can yield insight
into the theory of music, I argue that mathematical phenomena have more of a one-to-one correspondence, or
cardinality, with music and music theory in both the aural, temporal and theoretical aspects of music.
For instance, if one were to take a ‘structural linguistics’ approach to write for a particular instrument, then
certain aspects of that practice must be taken into account: the technique of the instrument; the historical
development of the instrument through music; the current practice of the instrument; and a mapping of that
which creates sound. In order to limit the harmonic phenomena that occurs with chordal or scalar instruments, I
will use the snare drum to show these musical and compositional ideas.
(insert link to snare drum studies)
(insert video of snare drumming compositions from the recital)