The research is constructed to test the applicability of the harmonic perspective of rhythm as a paradigm for understanding rhythmically complex, relatively unfamiliar, non-Western music. This theory is not new but is not mentioned as such in academic literature, therefore a description follows.
Metre in music is normally taken as the constant by which all other temporal phenomena are measured. If a piece of music is said to be in ‘three’ or ‘four’, this implies that there is a constant pulsation which is delineated into the appropriate grouping of three or four. This grouping is usually based on a clear repetitive cycle inherent in the repetitions or phrases of the music. However, many of the musics of the world, notably those of the African Diaspora, suggest or clearly demonstrate several concurrent metric cycles within the same span of time.
In order to expand the traditional, Western European-based system of conceiving and conceptualizing metre, this study will investigate the potential of a harmonic conception of metre. That is, the normal time span during which the basic elements or patterns of accentuation[1] of the music repeat—what would have been counted in the above discussion as ‘three’ or ‘four’—will now be taken as ‘one’. This ‘one’, regardless of its relative duration, will be counted as the fundamental frequency. Other, ‘harmonic’ frequencies (which by definition are integer multiples of the fundamental)[2] will be generated from this fundamental frequency. Thus, along with the fundamental repetitive time span, other cycles or concurrent metres of two, three, four, five, six, seven, eight, nine, and so on, will be recognized as potentially important for the analysis and aesthetic mastery of the piece in question.
The Harmonic Perspective of Rhythm in Western Notation. Notice the time signature.
Although several of these metric cycles are uncommon in the music of Africa and the West, they are not unheard of. What is different about the harmonic perspective, however, is that several or all of the cycles are considered at the same time. We do not limit ourselves to playing in two and subdivisions of two, or seven and subdivisions of seven. Two, seven, three, five and the rest are all heard, felt, and available as material for improvisation or composition.
Sweet Resonance.
A physical phenomenon that illustrates this perspective is that of the harmonic series with regard to pitch. When a pitch is sounded by setting a resonant material in rapid, vibratory motion by striking, plucking, or blowing across it the lowest note produced is the called the fundamental note. This is the note by which we determine the pitch name of the sound produced. Making up the sound we hear with that fundamental, however, are a theoretically large number of other pitches created by vibrations at other, higher frequencies. These other, higher pitches are often referred to as ‘harmonics’ or ‘upper partials.’ Thus, when the one note is sounded, other frequencies of varying intensity are also set in motion. These pitches are all sounding at the same time. All the pitches of a musical scale can be derived this way, as demonstrated by Pythagoras. Furthermore, it is the balance of relative intensities of these harmonics that creates the different timbres of different sound sources[3]. This phenomenon, if slowed considerably[4], is the harmonic perspective of rhythm: Many frequencies happening concurrently and thus, interacting.
At much faster vibratory frequencies, we hear pitch, at slower frequencies, rhythm. In the words of Stephen Jay:
…I have observed that harmony (pitch) and rhythm are really the same “thing”, happening at two radically different speeds. They are aspects of each other. Harmony can be converted into rhythm and vice versa, and the special features that make each of them work as music, are translated analogously between their respective domains. The two seemingly diverse elements are really an occurrence of the same physical phenomenon, follow identical mathematical rules of consonance, and coincide in the effect of specific characteristics, across the range of their musical activity. (Jay)
With this brief introduction, I will proceed to other important considerations before returning to the subject in more detail in, “The Harmonic Perspective of Rhythm Revisited” (page 84)
Much of the literature on non-Western (and particularly African) music suggests that the accent pattern usually taught as part-and-parcel of the Western concept of metre is not applicable outside the music of Western Europe, therefore advocating that the idea of metre be left out of the discussion. I would argue that the underlying concept of accentuation is what should be reserved for those musics to which it is appropriate, in particular those in which the aesthetic locus is melody rather than rhythm. In rhythmic music such as that of the African Diaspora and India, the beat structures (or several concurrent ones, in the view of this study) around which the music is organized are most clearly delineated and understood as marking cycles of repetition, not patterns of accentuation. ↑
For a definition and related information, see (“Harmonic” 2017) ↑
This is why two instruments such as trumpet and violin sound different, even when playing the ‘same’ note. ↑
For example, ‘middle C’ has a fundamental of 262 Hz, or 15,720 vibrations per minute. Divided by 500, the frequency becomes 31.4 vibrations, or beats, per minute (bpm). This is a rather slow for music, but two beats to the metric cycle would be counted at 62.8 bpm, somewhere between Largo and Adagio. Three beats are counted at about 94 bpm, and so on. ↑
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