Polyrythm and polymetre in modern jazz

A study of Miles Davis' quintet from the 60s by Peter Vuust

About Peter Vuust

Peter Vuust. Born in 1961. B.Sc. in mathematics with French as a subsidiary subject at Århus University. Preparatory training in music. Teacher at the Rhythmic Centre in Silkeborg since1988, associate professor at the Royal Academy of Music, Århus since 1995. Is a composer and performing musician and has as a bassist played together with a great many Danish and foreign artists, mostly in modern jazz. As a musician, composer and producer he has also made a number of recordings in widely varying genres. Peter Vuust made his début with his own quartet in 1997 on the CD “Travel Light” (Olufsen Records) which in 1998 was followed by The Big View (Storyville), a recording which received considerable acclaim from the critics, with the saxophonist Christian Vuust, the pianist Lars Jansson, the drummer Alex Riel, and the Norwegian percussionist Paolo Vinaccia.


MILES DAVIS’ QUINTET from the middle sixties – with Herbie Hancock, Ron Carter and Tony Williams in the rhythm group – plays the main role in this book, in which the musician and mathematician Peter Vuust pinpoints a complex musical phenomenon which can only be put into words with difficulty but with which most modern jazz musicians are intensely involved. The polyrhythmic structures in jazz – a neglected area in the theory of jazz.

Through the implication of semiotic theories, analyses of the quintet’s recordings as well as interviews with two members of the quintet, Vuust attempts to unveil the rhythmical grammar in the quintet’s communication – and to place polyrhythm in relation to the quintet’s music in the perspective of musical analysis and the history of jazz.

Polyrythythm and polymetric in modern jazz stems from a research project at the Royal Academy of Music, Århus, financed by the Ministry of Culture’s research fund.

The book deals with the occurrence of polyrhythm in modern jazz, illuminated by a study of Miles Davies’ quintet from 1963-68.

The book deals with paradigmatic relationships in connection with the construction of polyrhythmic occurrences, semantic relationships with regard to the intensity of the polyrhythmical occurrences, syntactic relationships where, together with the harmonic and melodic “out”, polyrhythm enters into the construction of the music’s dynamic climax, the placing of polyrhythm in the internal communication of the music and polyrhythm’s chronological placing as a phenomenon in the quintet’s music.

In this account polyrhythmic occurrence is defined as being a part of the music limited by time in which the possibility for perceiving two (or more) simultaneous pulses is induced. The simultaneous pulses are called the basic pulse and counter pulse. A polyrhythmic occurrence gives rise to a state of tension which is resolved when the counter pulse discontinues.

The basic pulse is not necessarily explicitly present in the music in connection with the polyrhythmic occurrence. Therefore it is necessary to distinguish between polyrhythmic occurrences and a definite groove shift (metric modulation). In a groove shift the music changes its rhythmical foundation, precisely as with a harmonic modulation. Subsequently any polyrhythmic occurrences relate to this new basic pulse.

In a polyrhythmic occurrence the basic pulse must as a general rule – seen from both the listener’s and the performer’s point of view – be maintained. Otherwise the tension-creating effect disappears, just as the requirement to maintain the form is made difficult for the performer. In a few cases it is possible to make an exception.

The polyrhythmic occurrences can be divided into three groups: 1) polyrhythmic occurrences which can be notated, 2) polyrhythmic occurrences which can be notated to a certain extent (where the counter pulse can be notated, but where part of the rhythm cannot be notated meaningfully) and 3) polyrhythmic occurrences which cannot be notated.

In connection with the first two groups the counter pulse can be expressed as groupings of the subdivisions of the basic pulse. These two groups can be subdivided further in a number of isometric and non-isometric types68: I) Homometric polyrhythm, II) melodic displacement, III) displaced homometric polyrhythm, IV) change of pulse and V) non-isometric polyrhythm with various time-signatures. As a result of their different constructions these types can be used in various ways and likewise there are small differences in the way they are perceived.

The isometric occurrences are repetitive after every bar, i.e. either all the 1st beats in the basic pulse and the counter pulse fall together or they never fall together. With the non-isometric occurrences there will as a rule be simultaneous 1st beats at regular intervals. The common 1st beats are points of reference between the two pulses.

Polyrhythmical phrases can either be structured purely rhythmically or contain melodic and/or chord structures. The addition of melodic/chordal structure to a polyrhythmic figure helps to decide the metrical nature of the counter-rhythm and with it its type. In many cases the melody is crucial for deciding whether or not there is any polyrhythm at all. In those cases where the experiencing of polyrhythm is induced by the repetition of a rhythmical motive, this will be rhythmically reflected as I) a pattern of changing note-values II) a pattern of accents (e.g. quaver triplets where every fifth one is stressed). The melodic elements in these repetitions are as a rule determined by direction: 1) consistently rising 2) consistently falling, 3) circulating with a return to the same note, 4) circulating with a return to a note-row which moves in a given pattern (often up or down). Both elements can create repeated patterns for themselves separately or, most often, together.

It is necessary to be aware that unequivocal criteria for the segmentation of polyrhythm are virtually impossible to establish. The parts which must be segmented are the polyrhythmic phrase and the motive which is repeated (in cases owing to the repetition of a rhythmic motive). The polyrhythmic phrase can be a part of a longer phrase which does not entirely consist of polyrhythm. When does the phrase begin and end? If the phrase begins with a rest it can in certain cases be difficult to decide whether the phrase begins on the rest or on the first note. The same conditions apply to the motive which is repeated. Another difficulty is that in many cases the motives can be subdivided into sub-motives. The rhythmic motive which is repeated can be short. The addition of melodic structure will on the other hand often cause a repetition to occur on several planes. The segmentation of cases of melodic displacement is furthermore encumbered by a subjective uncertainty.

What effect does polyrhythm have on the listener/musician? The intensity of a polyrhythmic occurrence varies by virtue of the motive which is repeated or displaced, but also by the context into which it is placed. The factors which influence how strongly we perceive a polyrhythmic occurrence are 1) the counter pulse’s general rhythmical character, 2) the counter pulse’s recognizability, 3) the distribution of the counter pulse and basic pulse internally in the orchestra, 4) the duration of the polyrhythmical situation, 5) the inherent ambivalence of the basic groove.

The conflict between periods of music with only one pulse (single pulse) and polyrhythmic passages often has a dramatic effect on the jazz musician’s narrative process, on the music’s drive. By way of comparison the harmonic tonic/dominant relationship is typically a distended row of contradictions possibly contained in each other like Chinese boxes, each of them moderate in effect, where the polyrhythm appears with a violent supremacy for most of the relatively few times it occurs in a solo.

In the melodic/harmonic area there is in jazz music a conflict which corresponds to the rhythmical one, namely the harmonic “in/out” conception. In a given chord a note will either belong to the harmonic “in” or the harmonic “out”, and a harmonic “out” occurrence can create a simultaneous chord structure (or at least tonal structure) which corresponds to what is expected. Just as with the case of polyrhythm, the harmonic foundation does not need to be explicitly present in the music. In the same way a certain number of “out” periods in the music will also typically occur, on the other hand possibly with an effect which is comparable with that of polyrhythm.

Because of this kinship one often sees the rhythmical and harmonic/melodic “out” appear in connection with each other. A polyrhythmic phrase has a tendency to move “out” harmonically, just as the collective effect of a phrase, which is “out” both rhythmically and harmonically/melodically, in many cases is stronger than the individual effects. The following progressive phases reflect a syntactic structure which applies to the more extensive polyrhythmical passages and which includes the elements rhythmic/polyrhythmic, harmonic “in/out” as well as the “out” effect’s gradations of intensity. In individual cases certain of the phases are however omitted.