Digital Sound & Music: Concepts, Applications, & Science, Chapter 3, last updated 6/25/2013
Figure 3.23 Transposition from key of C major to E major and C minor
3.1.6 Musical Composition
18.104.22.168 Historical Context
For as far back in history as we can see, we find evidence that human beings have made music.
We know this from ancient drawings of lutes and harps, Biblical references to David playing the
lyre for King Saul, and the Greek philosopher Pythagoras’s calculation of harmonic intervals.
The history of music and musical styles is a fascinating evolution of classical forms, prescriptive
styles, breaks from tradition, and individual creativity. An important thread woven through this
evolution is the mathematical basis of music and its relationship with beauty.
century BC, the Greek philosopher Pythagoras recognized the mathematical
basis of harmony, noting how the sound of a plucked string changes in proportion to the length
of the string. However, harmony was not the dominant element of music composition as it
developed through the Middle Ages. The chanting of medieval monks consisted of a single
strand of notes, rather unmelodic, with no instrumental accompaniment and, by modern
standards, a free-form rhythm. Madrigals of the Middle Ages were composed of single solo
lines with simple instrumental accompaniment. In the Baroque period, multiple strands became
interwoven in a style called polyphony, exemplified in the fugues, canons, and contrapuntal
compositions of Johann Sebastian Bach. Although we have come to think of harmony as an
essential element of music, its music-theoretic development and its central position in music
composition didn’t begin in earnest until the
century, spurred by Jean-Philippe Rameau’s
Treatise on Harmony.
In this chapter, we emphasize the importance of harmony in musical composition because
it is an essential feature of modern Western music. However, we acknowledge that perceptions
of what is musical vary from era to era and culture to culture, and we can give only a small part
of the picture here. We encourage the reader to explore other references on the subject of music
history and theory for a more complete picture.
An understanding of melody and harmony in Western music composition begins with intervals.
An interval is the distance between two notes, measured by the number of lettered notes it
contains. If the notes are played at the same time, the interval is a harmonic interval. If the