Space and the composer's toolbox

Using nothing as a composing tool took on a new importance in 1952 when Cage composed 4.33”. Over the years it received a lot of discussion regarding the nature of silence but less on the notion of the space it creates, the space we perceive individually and collectively when we “hear” the music, or perhaps we should say engage with the musical intention. Before making use of musical space in music the composer must consider what type of space to use and how it influences the content we apply onto that space. Astronomers have used the following phrase as a definition of space:

Nothing as undifferentiated potential

What we need to consider is the use and transformation of that potential within nothing and the effect of nothing on its content.

Using space as a characteristic of a composition or art work is not new, what has changed is the degree of space that we are willing to accept into our field of expectation. I have recently reread Hardy’s “The Return of the Native” (1878) and now appreciate the role of Egdon Heath in a new light. Previously I took Egdon Heath to be a character in its own right, in the way the local inhabitants react and interact with the landscape.  Now I regard it more as space in which the events are permitted to occur, and as space to provide time for the development of the novel. Every art work in every medium requires time to develop, in discussing architecture later we will see that there is an instant response followed by a movement through time where we review our perceptions of the forms. An immediate response to a canvas similarly alters as we examine different aspects of the space used, even before we begin to consider symbolic meanings, associations or cross references.

If one listens and examines the proportions of the rondo of Beethoven's Pastoral sonata (D major), the repetitions differ by small quantities, a bar or two, the music is breathing more deeply to accommodate the harmonic changes and respond to the musical drama. Regular 16 bar sections occur in the Rondo, e.g. at the beginning and in the preparation for the final piu allegro, but Beethoven prefers flexibility.  This expansion and contraction is the composer building with space, and it is this that makes the examination of formal structures fascinating not the naming of parts.

 

In the hands of the performer this musical space is worked on with the result that no two performances are ever the same, sometimes we forget how differently performers differ in terms of the space they use. Those of us who enjoy listening to Gould may be more aware of this; I am reading through Murakami’s conversations with Ozawa and the discussions on Beethoven’s piano concertos return time and again to the matter of musical space in Gould’s interpretations.

There are types of music in which the use of space is very regular and rigorously used. Recently the New Music Hub on G+ hosted a discussion about Morton Feldman's music for bass clarinet and percussion; in that work there are successive repetitions of a fluctuating quaver pulse into which the musical content is placed.

3/8  3/4  7/8  2/4  3/8  2/4  3/8  3/4  2/2  3/4  9/8  2/4  3/8  10/4

The 10/4 bar is a resting bar for the clarinet but the percussion either plays in that bar of is permitted to vibrate over the length of the bar so it is less active space not empty space (not that such a concept can occur in a concert hall). We may think in this case of musical space as a mould, nothing new in that, though as implied above after Cage's 4.33" the varieties of moulds have expanded dramatically.

Our style of musical education often leads us to the view that musical form is a Lego-like structure of blocks added together to create a shape, held in the space of performance time or on the pages of a score. For some styles of music this is appropriate but as music developed processes of thematic (and rhythmic) transformation formal constructions could vary between rigorous and distinct to flexible, with dramatic or subtle changes, as heard in the Feldman bass clarinet work. It is true that Feldman's music on paper can be read as being contained within large block units but musically the listener has to be particularly aware of small textural alterations and the use of transposition to perceive such changes. Did Feldman expect such attention from his audience? These blogs have touched many times on the nature of attention and how the composer can aid the pathway through musical time. Going back to Egdon Heath Hardy makes us aware that it is a bleak environment and then colours it with many detailed descriptions of its unique plants and insects, the big and the small create a dynamic force in the writing. My instinct tells me that there are several different aesthetic values at play in Feldman’s use of musical space; it may be that he is offering us an opportunity to hear music in a variety of contexts, to offer us the opportunity to repeatedly consider music as it undergoes small scale changes, to have the space to evaluate our own changing responses, to gauge the altering responses of the audience. When I walk through a cathedral I am aware of the stone, designs and spaces as well as the content, but unless I enter the building with the intention of undergoing some change of my own awareness then I am not fulfilling the intention of the space. Here is Feldman his preferred term is scale, but essentially it is space:

"My whole generation was hung up on the 20- to 25-minute piece. It was our clock. We all got to know it, and how to handle it. As soon as you leave the 20- to 25-minute piece behind, in a one-movement work, different problems arise. Up to one hour you think about form, but after an hour and a half it's scale. Form is easy: just the division of things into parts. But scale is another matter."

 

Returning to the block view of music in space let us consider one composer’s development of its use post 1950; there are many examples of Maxwell Davies's music where he provides distinctive character changes between sections, all of which share thematic and rhythmic material arising from a single source. His method is to create a continuum of micro variants of his source. In figurative terms the blocks are shattered, kaleidoscopic, but in essence the pathway is clear enough. Urban design has indoctrinated us into thinking of pathways as a linear design, if you have time read “The Old Ways: A Journey on Foot” by Robert Macfarlane to understand how awareness of markers can link spaces together, and how small and unobtrusive these can be for those attuned to the landscape.

Is there a guide for composers that helps determine the time or space allocated to a composition? Some types of music are associated with given lengths, the popular song had a three minute format and that still holds for a large number of songs produced for the mass market. Composers writing film music can be required to work second by second. Setting a text is more flexible, but questions of continuity and poetic constructions may influence the composer. Many time constraints are a matter of audience expectation, a 25 minute hymn in the middle of a service would not be acceptable in most Welsh chapels, but a 25 minute qawwali song would be acceptable in a concert hall, yet both serve the same general purpose. Classical Indian music has conventions that match the time of day, hour by hour, but as with improvisation in general the ability to captivate the audience is key. Contemporary composers often make demands of the audiences with improvisations that exceed conventional time limits as with the texts of “Aus Den Sieben Tagen”; this link provides a large amount of information that may promote further thoughts on the micro and macro us of time in a composition:

http://stockhausenspace.blogspot.co.uk/2015/03/aus-den-sieben-tagen.html#Anchor%2013

Is expectation our only guide? Do composers work in a more purposeful way with time? On You Tube there is a conversation with the composer Enno Poppe where he discusses his cello piece “Zwölf”, he describes the music as a succession of miniatures, lasting three seconds, four seconds, five seconds and so on.

https://www.youtube.com/watch?v=g6AwV_yYKxY&t=224s

Making progressive numerical patterns is one method of providing the listener with a musical pathway through music, expansions and contractions of figures in time have been commonplace throughout musical history for this very reason, though not in the way Poppe employs expansion.

Poppe also refers at one point to the musical symbolism of the number 12 and makes a claim that without its “mythical” value “12 tone technique would not have been so influential without this aspect”. However one responds to such a statement there is no doubt that number symbolism has played a significant part in music and art over the centuries. As these blogs are concerned with music of the 20^th century onwards less will be made of the issue than it deserves, but some points need to be made as they have influenced at least the aesthetics held by composers in approaching space and time in music.

During the medieval period proportion played a significant role in architecture, Platonic ideas were adapted into Christian buildings and number symbolism can be found in many diverse places. An easy to read article dealing with proportion and light can be read at:

http://www.iep.utm.edu/m-aesthe/

(windows at Chartres)

The following passage regarding the sketchbooks of Villard de Honnecourt makes correlations between music and stone:

The proportions of Villard’s Cistercian church designed ad quadratum that is, one proportions are derived from the square which used to determine the dimensions of the entire structure.
The proportions of Villard's Cistercian church correspond to the Boethian sequence of proportions. Nor were his discussions merely theoretical since there is evidence that these plans were employed by Cistercians in the construction of their churches. According to Villard's canons, the length of the cathedrals nave is in the ratio of 2:3 to the transept. This relationship may be considered in the proportion of a fifth in musical terms or a sesquialter in mathematical vocabulary. The ratio of 1:2 (duplex), or the octave, occurs between the side aisles and the nave. We find the same relationship between the length and width of the transept and interior elevation. The ratio of 4:3 of the nave to a choir is a sesquitertial relationship or the musical fourth. 5:4 relationship of the side aisles taken as a unit and the nave is a third or sesquiquartan. The crossing, liturgically and aesthetically the center of the church, is based on the ratio of unison, the mathematical unity, the most perfect of consonances and the foundation for all number.

Whether these descriptions were accurately translated into buildings or not it reveals the intention and more importantly awareness of the potential of space in design. Architecture has certainly made use of the power of proportions, particularly in the use of the golden section. This reaches into musical history via sonata form and Mozart, and remains with us in  post 1950’s music. A balanced view on Mozart and the golden section may be read at:

http://www.americanscientist.org/issues/pub/did-mozart-use-the-golden-section

and more food for thought regarding Bartok and Webern at:

http://solomonsmusic.net/diss7.htm

One final example before we return to musical space, this time relating to poetry:

The arithmology of poetry seems … musically inspired. The significant numbers that scholars have found in Dante and Spenser, for instance, are all governed by unmusical principles, such as Christian number symbolism or the Kabbalah. On the other hand, we could take the fourteen-line sonnet as an example of harmonic construction of the most perfect kind. The so-called "octave" of the first eight lines, divided into two quatrains, exemplifies the musical interval of an octave (proportion or 2:1), while the closing "sestet" of six lines relates to it in the proportion of a perfect fourth (8:6 or 4:3). Moreover, each line is an iambic pentameter of five beats, concluded by a pause or rest of one beat. However much rubato is used in an expressive reading, the underlying meter is triple, like a slow 3/2. This may be somewhat elementary mathematics, but so are the perfect consonances and meters that are the basis of all music. A case such as this illustrates the effectiveness of harmonic proportions when applied to other media.

Can pitch selection determine the way space is used in music? Webern comes to mind with his condensed and highly symmetrical constructs. Symmetry defines space and does so in several different ways, previous blogs have touched on symmetrical scales and modes of limited transposition. These create compositions often characterized by a quality of timelessness, Holst and Bax have used them for formal contrast (back to Egdon Heath again) while Vaughan Williams creates a masterpiece of its use in the last movement of the 6^th symphony.

Having touched on some aspects of space in music perhaps one should ask at which end of the composing process should one begin? Is it best to consider the scale of one’s music first and then fill in the content or play with the material you chose to develop and permit it to occupy space which may or may not display proportions, symmetries or even number symbolism? For many composers the question does not arise, models are in place for their designs. There is undoubtedly something that pleases in proportional design whether it is experienced walking through Chartres cathedral, perhaps making one’s way through its maze, or listening to the process that generates the climax at the “golden” moment in the ultra-romantic “Ein Heldenleben” (R. Strauss). Having touched on Beethoven in this blog it is well to realise that his sketchbooks often contain verbal comments as indicators of the processes to be worked, there are blank bars, spaces to be realised later or other musical shorthand reminders, all of which imply that the shape of the music was well established even if the details still required work.

Changing hierarchies.

Over the past few weeks Nurtan and I have been looking at the musical equivalent of supervenience, or at least something very close to it. If you are new to the term:

In philosophy, supervenience is an ontological relation that is used to describe cases where the upper-level properties of a system are determined by its lower level properties.

Nurtan’s use of mathematics to refine some of the issues has been interesting, as has the process of turning the observations into a set of statements in plain English. The discussion has generated a large number of e-mails and involved other composers and linguists; it may be a while before the results form into a blog.

In the meantime, as a side issue, we came to thinking about order. Surely this term would be much easier to deal with, it is something we are all familiar with; however, it has a degree of flexibility that requires comment.

The synonyms and phrases that may be substituted for order which are of interest to a musician could include arrangement or sequence, proper condition, (where proper = appropriate or strict), function, method, system, procedure, instruction, and action towards some end.

There is room for discussion here with the terms appropriate and strict, indeed it has been a major part of the previous discussions regarding flexibility and rigour. To develop, and introduce some fresh thoughts, let us take a rejuvenated view of a frequently discussed element of order in music, hierarchy. We have made several references to hierarchy following the blog on the Webern lectures, with tonic-dominant and overtone series considerations at the fore. Because traditional harmony remains the preferred method of teaching music in schools we are conditioned into thinking of the leading note moving to the tonic, what form strong and weak chord formations and order as simple formal structures ABA, AABB and so on. To quibble one might argue that the leading note could just as easily move to the dominant or mediant, but quibble I will because it shows preference, such as with the use, or restriction on the use of the augmented fourth in Renaissance times. It is a significant factor to composers that preference as hierarchy is central to post 1950’s music. It can be argued that music provides its reference point for a central “tone” by its own context, as with the minor dyad of C and E flat in Peter Maxwell Davies’s “Stone Litany”. The presence of reference points like this is to guide the listener through the musical argument and help retain the structure of the music. The hierarchy is established through duration, placement of tones at significant points within a phrase, the use of a drone, metric stresses, i.e. hierarchy is in the recurrence of detail. The more listeners are familiar with these details in one work the greater the ease in mapping the skill onto other compositions, in simple terms, we get used to listening that way.

Memory plays a significant part in musical hierarchy, what we recall with greatest ease takes on greater or greatest significance and that which we struggle to recall is regarded less well or disregarded. The popular song with its hooks makes this self-evident. Chunking material is a recognised way of assisting recall. Returning to hierarchy by specific content, we come to recognise order by the structuring of material into familiar groups, e.g. modes of limited transposition, symmetrical formations, which then cluster into larger groups by devices like canon, passacaglia contained within augmented and diminished rhythmic values or repeated cycles of rhythm. Messiaen's Et exspecto resurrectionem mortuorum is an excellent example of this approach. Psychologists refer to the memory constructs as displaying “psychological distance”, strong or weak depending on their intrusion on our conscious recall. It reminds me of the joke, “What is the difference between a drummer and a drum machine”? “You only need to hammer the rhythm into a drum machine once”.

On a more serious level we must understand that hierarchy is not only a system of order in music, but an integral part of the process of learning, recognising and feeling secure about the work we engage with. One may consider that disrupting the hierarchy could become a means to achieving the shock element which also has its place in art and music. Musical changes (e.g. in melodic outlines) are more easily identified in familiar hierarchical constructs. This is a given state of affairs with tonal music (at this time in history with those familiar with art music), so we recognise and find a pathway through the evolution of motifs in Mahler’s first movement of the 8^th symphony, but might struggle should alterations to the regular and highly organised melody occur in Maxwell Davies’s “Ave Maris Stella”.

Preference is a blessing and a curse in music, one way which it shows itself is the way certain musical features dominate the aural landscape. Let us take the common triad, seventh chords and the diminished chord as examples. They are so familiar that they become a “landscape” feature in post 1950’s music. They perform as a focus point even whether or not the composer has not set out for them to have additional significance. They can take on a psychological identity. I set out with that purpose when writing an oboe and piano work which included three chords from Holst’s “Egdon Heath”.

 https://www.youtube.com/watch?v=Y90QWfdIGsQ

Some composers have endeavoured to avoid the use of such chords because of their disruptive qualities particularly in serial music, and this extends to other tonal characters like the use (or non-use) of the octave, whose character has altered from being one of articulating strength to one of disrupting structural integrity. One still needs to consider carefully whether this is structure or preference.

When considering order some (rather radical people) may be tempted to question the value of order as a necessary component of music. In a work like “Cartridge Music” we have a clear understanding of its content but not its internal order. There are indications for the performers to follow but the listener would not be or need to be aware of these when executed. On a personal level this doesn’t make the music less appealing, indeed performances of the music draw an audience, some people wish to engage with the work, and even use a recording which is a form of ordering, because it preserves the events in a fixed state. Reordering most music would destroy its integrity, but some works are designed to randomise order, this happens in Lutosławski’s later works where he avoids the synchronisation of internal events. What we do experience as a shared factor in pre-50’s art music, Lutosławski late works and Cage’s “Cartridge Music” is homogeneity, a sense that the internal contents belong together. Given that hierarchy can be an operating system on any content is it this quality that we search for when we listen to music?

When we approach a piece of music most of us have pre-conceived ideas of its form and content, for some listeners the joy of music is in having these met or partly met, and for others it is in breaking away from prescription. For those who write music and create art the process of innovation (on some level) is essential to developing a recognisable style; popularity depends on balancing innovation and finding consensus. It may be that the consensus leads to a musical school of thought or is shown in the mass purchasing of a new popular song, the numbers are only significant when, or if, we consider the financial outcome. We have discussed in previous blogs the power bred by consensus groups and the degree of vitriol they can generate, that is the most negative aspect of unanimity. These days it is much easier for innovators to reach out to an audience, in my opinion the proliferation of such music can only be good for the listener, who is hopefully discriminating enough to search out valuable contributions while remaining in control of the off button.
Are we to take pre-conception as a required condition to recognising order? If you have time look up expectation states theory and make up your own mind on the matter.

Perhaps we should remind ourselves that art is like a playground, a place where regulation exists but feels best when we deceive ourselves that we are free of constraint.