While there are many composers to cite in the explanation of modern harmony, I’ve chosen the following composers and theorists: Johann Kirnberger, Heinrich Schenker, Arnold Schoenberg, and Jeff Hellmer. Each composer offers a slightly different take on the ideas surrounding composition and the harmonic tools used to create compositions. However different they are in concept and practice, the selected scholars have overlap in some of their ideas. One of the common tropes is the development of the composition practice through the development of motifs, or motivic development. In my practice for composition, there are a few main components to the development of motifs: ear training, daily scalar practice, motivic development through improvisation, and the study of works by other composers.
For Schenker, he stated on page 18 of his book on Harmony: “For genius, the gift of improvisation and long-range hearing, is requisite for greater time spans (Schenker, 1954)” This backs up the idea of a daily scalar and chordal chromatic practice as a form of compositional development (ear training). Without the gift, or practice, or improvisation; there is not another tool to enable a composer to take a simple motif and develop a symphony, or series of works. In order to understand the process of ear training, one must come into the realization of the arrangements of musical ideas. As Schenker said on page 25, “[…] any sound is composed of an infinite sum of over-tones (Schenker, 1954).” This concept of over-tones can be traced back to the practice of the Pythagoreans, more specifically, through the work of Barbara Hero (Hero, 1975). The Pythagorean Lambdoma is one example of the use of note combinations which create overtones. This Pythagorean concept is the basis of the visual mapping of chords and scales. With the Pythagorean Table as an aside, motivic development is a basis for many composers and theorists.
Here are some quotes from selected Theorists on the concept of motivic development:
“The motif […] is a primordial and intrinsic association of ideas (Schenker, 1954).”
“The motive should produce unity, relationship, coherence, logic, comprehensive lift, and fluency. […] basic motive is often considered the germ of the idea […] smallest common multiple […] greatest common factor (Schoenberg, 1967, pg 8).”
“It is better to be indulgent with his awkwardness, even his gross errors, as long as necessary than to mislead him as to the true nature of his task and to let him kill time with an absurd activity. [If the process of developing motifs and harmonic sequences to solve a modulation example is used] to create a situation where the artist would be able to improvise freely [is a practice to be used to develop as a composer] (Schoenberg, 1967).”
“[composition is] compromise between nature and art; [for] repetition thus is the basis of music as an art (Schenker, 1954).”
These quotes from various writings illustrate the importance of the development of works through motifs. Once this concept of motivic development is practiced, one can understand the use of the visualization of chords and scales, along with the application of some of mathematical components that have been introduced by the Pythagoreans.
Works Cited
Hero, B. (1975). Paintings Based on Relative Pitch in Music. Leonardo, 8(1), 13–19.
https://doi.org/10.2307/1573182
Schenker, H., Jonas, O., & Borgese, E. M. (1954). Harmony. University of Chicago Press.
Schoenberg, A., & Strang, G. (1967). Fundamentals of musical composition. St. Martin’s Press.