Music’s two dimensions
Music resembles time. As you know, for the Greeks, time was both chronos (the horizontal dimension of time) and kairos (the moment, or vertical dimension of time).
Similarly, music has two dimensions: harmony (vertical) and counterpoint (horizontal). Harmony is associated with chords and counterpoint, with melody, but they may intersect.
I just looked up the entry harmony in Wikipedia and found a quotation by Carl Dalhaus (remember The Idea of Absolute Music). He also uses the terms vertical and horizontal to differentiate harmony from counterpoint. I may therefore have picked the terms browsing Dalhaus.
It was not that counterpoint was supplanted by harmony (Bach’s tonal counterpoint is surely no less polyphonic than Palestrina’s modal writing) but that an older type both of counterpoint and of vertical technique was succeeded by a newer type. And harmony comprises not only the (‘vertical’) structure of chords but also their (‘horizontal’) movement. Like music as a whole, harmony is a process.vertical to explain the difference between counterpoint and harmony.[i]
For instance, the fugue is a form that is mostly contrapuntal. However, when the voices touch one another, it has to be harmonically acceptable. Consequently, one cannot dissociate fully harmony and counterpoint. There are links. However, in the curriculum, the study of harmony precedes the study of counterpoint.
The Melodic line
With respect to the melodic line, I cannot go into details because I am writing a mere blog. But, it may be useful to know that, generally speaking, the melodic line takes us from chord to chord, but not necessarily in a chordal fashion. The notes may be distributed over the staff (the lines).
The basic chord consists of three notes, the triad: do-mi-sol or four notes, as in the dominant seventh sol-si-ré-fa, or more notes. These notes may be played simultaneously, in chordal fashion, but they may also be played separately (arpeggiated).
In most traditional music: Bach, Haydn, Mozart, Beethoven, etc., the melodic line is eight “measures” long. Just sing Twinkle, twinkle little star or Ah, vous dirais-je, maman. Or sing the choral movement, the Ode to Joy, of Beethoven’s Ninth Symphony.
Fully-deployed, the harmonic progression of the melody consists of chords built on I-IV-VII-III-VIII-II-V-I, or do-fa-si-mi-la-ré-sol-do, but a I-IV-V-I progression is just fine. It depends on the length of the melody and other factors.
In solfège, sight-singing, musicians use the do-ré-mi chain. But in harmony, they use Roman numerals.
Throughout the middle-ages, the Renaissance and the Baroque era (c. 1600 – c. 1750), schools worked on the combination of notes. Nowadays students still learn Rameau (harmony) and Fux (counterpoint). However they do not study the original treatises. They use a textbook.
Western Europe’s fundamental theoretical works are:
- Gradus ad Parnassum (1725), by Johann Joseph Fux (1660 – 13 February 1741)
- Traité de l’harmonie (1722), by Jean-Philippe Rameau (September 25, 1683 – September 12, 1764)
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So, we now know, albeit superficially and in a simplified manner, that harmony is the vertical dimension of music and counterpoint, its horizontal dimension.
What amazes me is that, undergirding sublime music, there should be so much theory. Yet give the barbershop quartet a piece to sing and, if they know the piece, the tune, they just might “harmonize” it very little time, by ear.
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- Mozart: 12 Variations: Ah, vous dirais-je, maman KV 265 (Clara Haskill, piano)
- Beethoven’s Ninth Symphony: An die Freude
- Beethoven’s Ninth Symphony: An die Freude (from The Immortal Beloved, 1994)
Dahlhaus, Carl. Gjerdingen, Robert O. trans. (1990). Studies in the Origin of Harmonic Tonality, p. 141. Princeton University Press.