Tuesday, 21 March 2017


Relating pitch and rhythm - P.M. Davies



Relationships require a great deal of work to function well, and this is equally true for music as life in general. Recently our blog discussed the "pure work" notion where every component contributes to the potency of the final composition, a perfect marriage. This blog considers some relationships between pitch and rhythm and how the relationship changed in the 20th century.

Ascribing prescribed rhythmic values to a row of pitches is a process of association, they are two separate designs fused into a statement that we regard or perceive as one. Extending the process to include dynamics, timbre or positions in space creates an exotic world of possibilities, these possibilities are so wide that their relationships require a blog all of their own, here we shall restrict ourselves (for the time being) to those arising from melody and rhythm.

While working on Peter Maxwell Davies's "Ave Maris Stella" as a student the first features that became a point of focus for me were the triadic characteristics of the melody, equal phrasing and a rhythmic design associated with the melody.

The opening line played by the cello as pitch classes (C = 0) forms
1, 5, 0, 4, 11, 8, 9, 6, 2
and the associated rhythmic values
1,6, 2, 7, 3, 8, 4, 9, 2

Rhythmic and melodic associations were not new to "Ave Maris Stella", one can hear lengthy melodic lines being conjoined with prescribed rhythms in early works like the organ fantasia “O Magnum Mysterium”. With "Ave Maris Stella" the rhythmic design is varied through a further association of the pitch material with an organizing system arising from a 9x9 magic square. In the first instance one could take these events as rotations and transpositions of the opening line. As a student I was interested by the results that arose from these associations, but I was equally concerned by the question of why such a pairing was made. As a student I found it sufficient to note that the design was numerically simple yet elegant, later I appreciated that such a design was essential to aid clarity when the treatment, particularly contrapuntal treatment became complex.



The rhythms of a magic square worked in wool (Gill Hughes c.1995)


The use of the square when applied to rhythm offers the possibilities of equal and balanced phrasing, those who are familiar with magic squares will understand their feature of consistency in various methods of progressing through the grid. A quick word of warning to those reaching out for their tablets to Google the topic, the grids can throw up a large number of relationships which are interesting from the composer's point of view but the results can also be banal, of course that's true of number based systems in general. For Davies the equal lengths are particularly useful in bring his musical argument to a climax point where lines of different rhythmic durations conclude at the end of a movement. Of course this is possible without the use of a magic square, processes of augmentation and diminution to articulate the form of the work occur in several styles, periods and locations around the world.

When the music is purely linear and contrapuntal how does the composer anticipate the vertical harmony? If only one pitch was used this could make an interesting textural exercise, similarly with a small number of pitches, say the minor third stack, C, E flat, G flat, A. I have used variations on this approach in my own fractal art cycle, and if so inclined one can judge the worth of the exercise at:



We could extend the discussion to familiar constructs like the pentatonic or whole tone scale; perhaps readers would like to explore the possibilities for restricted harmony in the context of association with a magic square. The greater the number of pitches the more care is required to prevent the music becoming harmonically “messy”. In "Ave Maris Stella" the pitch motion and interval structure is very distinct, it (once again) demonstrates a balancing act between simplicity and complexity.

The only movement of Ave Maris Stella on You Tube is the sixth,
https://www.youtube.com/watch?v=uMpAex0-a4Y

primarily a marimba solo, with the later addition of drones and harmonics to build a climax into the seventh movement. Where the square dominates the order and structure of the other movements the construction here is less rigorous. This is not to say that the influence of the square cannot be heard, but the association with the rhythmic values give way to cascades of repeated and accelerating values to achieve a propulsion towards the seventh section. One can relate the phrases used to create the momentum to the square, but in keeping with characteristic writing for the marimba we have phrases repeated in different octaves, octave leaps on the same pitch, wedges of notes expanding outwards, and a number of diatonic runs, even at one point a whole tone collection. Listen out for the C' E F A B D figure which repeats several times in different guises, this is a reordered subset of the opening line.


The whole section has a sense of improvisation and freedom as the various methods of repetition create a sense of musical space.  "Ave Maris Stella" includes freely played figures, in the first movement where the cello plays through fixed values the alto flute plays decorative material (pitches drawn from the square), these form collections of events rhythmically showing accelerando and rit. decorations to the main theme.


One may question whether a greater degree of chance occurs in the vertical harmony when adhering to the strict rhythm and pitch formula of the square. This is particularly so when lengthy lines of triplets, quintuplets etc. are used as a counterpoint to the main line in works like "Stone Litany". In that work there are abundant harmonic references to the minor third, as in the final section with wineglasses tuned to C, E flat and played continuously. Careful listening reveals a number of devices that emphasize the association of the melody with tonal references in "Stone Litany". It seems that the composer is ensuring that the complex array of chords resulting from the counterpoint are underpinned by a foundation that is noticeable through repetition and texture.

The rhythmic character of music in the tonal period drew regularly on dance which originates with the action of human movement. Webern in his lectures (discussed in earlier blogs) makes a great play of the natural evolution of the 12 note system, yet he makes little reference to rhythmic matters in his lectures. Schoenberg however does focus on the rhythms of earlier dance forms, a characteristic which met with criticism from Boulez. How does Schoenberg ‘square the circle’ of relating dance music which depends on tonality and harmonic rhythm to 12 note music? He makes use of a number of associations with the earlier dance forms, accents, anacrusis, phrasing (12 note set per bar) etc. Of course thinking of the 12 note set as producing harmonic rhythm produces very different results in Schoenberg’s work to that of Baroque music. Nurtan and I have been discussing the question of the function of harmonic rhythm outside the tonal system, he condenses the argument to “it requires tweeking”. I agree.

Dance rhythms can be used as a section of parody for dramatic purposes or act as a psychological frame, often used to create nostalgic responses or imply historic associations. Such thinking is not new, all of these elements are present in "Der Rosenkavalier". If you want to explore the associations discussed above why not listen to Thomas Ades Three Mazurkas?  

Three Mazurkas for Piano, Op, 27:



This blog briefly set out to consider relationships in music, whether they are between musical parameters or stylistic pairings.  This blog has restricted itself to the constraints imposed by Western music notation where we have become accustomed to certain types of association. Will contemporary music return to physical movements as the model for rhythm? Where it does, as in the music of Philip Glass and John Adams, the tonic and gravity of tonality is restored. In Peter Maxwell Davies's case tonality became an issue for his critics, it may be that his insights suggested that dance, a powerful influence on his work, requires it, and the price of its use worth paying.

In our next blogs we will explore further the aspect of flexibility; at the present time Nurtan is exploring mathematical systems of generating randomness and the musical quality of the results while I am placing my focus on the various degrees of freedom found in electronic music of the 50’s and 60’s.