In percussion theory, just as in music, scale, or chord theory, there are tones, intonations, and intervals – therefore, percussive instruments produce not only tempo and rhythms, but tones (whole and half) as well. These characteristics could be most aptly being described as “harmonic rhythms” and the essential mathematical characteristics of these harmonic rhythms are directly relative to the musical qualities produced by each interval. Because music is essentially comprised of just two elements: harmony and rhythm, these dynamic elements are irrefutably integrated by a universal mathematical structure, which is based on innate harmonic progressions.
Mathematical and Musical Correlation
Illustrative of this mathematical musical correlation are those musical derivations such as Diatonic scales – because these particular style of scales produce sonic occurrences with a high percentage of mathematical sympathy, or consonance. Specific intervals and chords when transposed to tempo produce very stylized patterns which are related with certain societies. Consequently, stylistic qualities of harmonic rhythms can be found in major, minor, diminished, augmented, and perfect intervals.
Harmonic rhythmic patterns contain distinct rhythmic elements of dotted, triplet, polyrhythm, swing, African, and Latin cadences. Different rhythmic styles and patterns which have been correlated with certain ethnic and geographic areas worldwide, have continually been included within the harmonic intervals of the natural harmonic series, and the diatonic scale.
The collective ability to perceive increasingly complex harmonic rhythm patterns in instrumental and vocal timbre appears to be on a similar evolutionary path. This also occurs in increasing complexity as you move up the natural harmonic series by intervals. Just as certain rhythmic patterns appear to have natural downbeats, harmonic intervals and chord combinations have root, or tonic notes. Harmony and rhythm sympathize, sustain, and mutually vitalize each other.
Pitch, Harmony, Rhythm and Tempo
Examining the unified field between pitch, harmony, and rhythm leads to some interesting new theoretical connections.
Harmo-rhythmic relationships exist horizontally in time as linear melodies, vertically in harmonic intervals, internally between the overtones of each individual timbre, and in the combination of all three.
Harmo-rhythmic sympathy increases its internal symmetry. The harmonic rhythms of chords are so fast and complex that their total conscious perception is impossible. Only inaudibly low pitches played at extremely fast tempos would qualify.
The relativity between harmony and rhythm can be represented mathematically by the equation: H/2N=R – (H = Any interval or group of intervals produced by two or more simultaneous pitches; R = A rhythmic repeating pattern or group of patterns; N = The number of octaves necessary to transpose a given example).
The relationship between pitch and tempo can be likewise mathematically represented.
For example, the interval of an octave, A 440 and A 220, with its high denominator, is a simple rhythmic pattern of eighth notes over quarter notes. Each additional note complicates the harmonic rhythm in a proportional dynamic to the color it adds to the harmony of the chord. Smaller intervals with lower common denominators form repeating patterns of longer duration, and vice-versa.
When intonation is imperfect, the rhythm of a harmonic interval becomes a sequence of patterns through which the activity moves in regular cycles each time the phase shift crosses the center axis of the frequencies involved. Some intervals produce a sequence of rhythmic patterns in shifting meters which are similar in dynamic character to the multiple meter sequences performed by traditional drummers in West Africa.
Sympathetic tempo is referred to here as the key to tempo relationship that produces the simplest harmonic rhythms. The connections between each individual pitch and its relative tempo are subject to the perception of rhythmic pulse when interpreted by the listener. Pitch/Pulse Conversion for A 110.
Certain scale temperings, timbre voicings, interval bending, and off-sets produce unusually perfect harmo-rhythms. Bending notes and glissandos equal ritards and accelerandos on the harmo-rhythmic level. The study of harmonic rhythm and its many wide ranging theoretical connections may lead to a better understanding of certain unusual musical occurrences, i.e. : why certain tempos seem to flow more naturally for a given key; why some rhythm/harmony textural combinations produce strikingly beautiful musical symmetry in themselves without regard to specific compositional elements; why slightly out of tune notes actually sound better in certain harmonic contexts; what makes harmonic elements ring, or sustain in varying degrees; why certain harmonic sonorities seem to imply specific rhythms, and sympathize with particular rhythmic styles.