Page 80 - AC-2-4

Arts & Communication Composition based on singing gestures

graphemes subsequently evolved into the current symbols, 2. Geometry of gestures
which abstract the pneumatic thread into discrete dot
symbols. As Theodor Wiesengrund Adorno said in 1946, Following the methodology described by Mazzola and
4
“Correspondingly the task of the interpreter would be to Andreatta we display the diagram of gesture geometry.
consider the notes until they are transformed into original To define the geometric concept of gestures, one of the
manuscripts under the insistent eye of the observer; authors (Mazzola) refers to two mathematical structures:
a digraph (directed graph) and a topological space. A
5
however not as images of the author’s emotion – they are digraph consists of three parts: arrows (A), vertices (V),
also such, but only accidentally – but as the seismographic and a map (P), which are used as connections between
curves, which the body has left to the music in its gestural vertices.
vibrations.” 1, p. 315 Therefore, apart from the influence of
personal subjective factors, the creation of gestures must P(a) = [h(a), t(a)] (I)
also be evidenced by objective logic.
Where h (a) and t (a) represent the head and tail of
Traditional composers add their own unique gestures
when performing. However, this kind of creation arrows, respectively, which are graphically shown in
Figure 1.
still involves excessive subjective thinking concerns,
including the structure of music design, harmony, A topological space is the second concept to define
counterpoint, etc. Hence, what would the acoustics be like a gesture. For a topological space Z, in each point z ∈
i
if the composition depended entirely on the performer’s Z, there exists a collection of subsets W ⊆ Z, the open
gesture? This idea has been well expanded by some free neighborhoods of z . For two neighborhoods of z ,
i
i
jazz musicians, and some publications focusing on this their intersections should also be a neighborhood of
music creation model have been published. However, z . Next, we define open sets, Q ⊆ Z, subsets of Z which
2
i
this idea has rarely been demonstrated in freely are neighborhoods for each of their elements z ∈ Q. The
i
composed works by singers. spatial diagraph Z* of a topological space Z is the digraph,
whose arrows are the continuous functions x: [0, → Z from
1
Singers are the only musicians who barely use other the unit interval [0, of real numbers into Z. The vertices
1
instruments to express music. They add many personal of Z* are the points of Z, which are the head and tail x(1)
styles and choices when performing, and this musical and x(0) of the arrows x. Morphisms e between diagraphs
creation mode is very personal and subjective. In fact, are defined when two digraphs (R and P) are co-present: e:
most of the time, being fastidious with every note when R → P defines a pair of maps e : V → V , and e : A → A .
R
v
R
P
P
A
creating music is the least of the singers’ concern, because Such an operation maps the heads and tails of the arrows
music creation is influenced by mood or acquired to their images.
experiences. It closely resembles the concept of a behavior,
which is the result of the interaction of innate cognitive With the foregoing concepts, a gesture n can be defined:
patterns and learned reactive habits. Most of the time, It is a morphism n: R → Z*. R and Z* are called the skeleton
it is this symbiotic relationship that helps singers make and body of a gesture (see the sketch in Figure 2). It shows
3
choices of musical creativity. However, in music as a a musical gesture whose body consists of curves in the
whole, the melody created by the singer’s choice can only keyboard space with coordinate pitch, position, over the
appear in the improvisational score as a single melodic keyboard, and time.
line. Gesture morphisms are the key elements that relate
This article extends the basic geometric model of gestures together. If n: R → Z* and x: P → K* are two gestures,
the performer’s gestures and uses the four-dimensional
hypercube of music ontology (introduced and explained in
section 4) to perform a reverse deduction, demonstrating
the basic logical thinking mode of the singer’s creation
of music through free singing. The goals of this article
are: (1) to prove that there is an objective logic in the
emotional gestures of performers, such as singers, when
they freely create works; (2) to reversely deduce the logical
pattern of gestures formed by musicians through the four-
dimensional structure of music ontology; and (3) to discuss
the impact of singing gestures on “free composition” and Figure 1. A directed graph consisting of three vertices connected by four
its possible future prospects. arrows. Image created Yuwen Sun

Volume 2 Issue 4 (2024) 2 doi: 10.36922/ac.2625