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.

Go and listen to a pure chance music concert.

Duration: no less than 15 minutes, no more than an hour.

Effect: refreshment and revelation.

A pure chance concert is free of cost. Seating, or standing room if you prefer, is usually available. Travel is not an issue, but imaginative venues can be found. Pure chance music can be rhythmic and repetitious or arrhythmic and ever changing, or of course a mixture of the two. Try a seaside venue for distinct timbres; voices, often young ones with high frequency screeches panning quickly across the audio field and deep thundering bass tones when water brakes against the shore followed by the percussive rolling of thousands of pebbles.

If that venue is unavailable try a more urban environment, one may discover a complexity of pedestrian footfalls and a wealth of mechanical sounds emerging into the sound field from every direction.

You may be thrilled by an ear shattering climax or be hypnotised by a single rhythmic tone, the joy of the experience is that everything is possible. While there may, or may not, be similarities between performances there can be no formal replay. Recordings of pure chance works are increasingly popular as "field recordings", but you may find these lack the spontaneity of the live event.

Should you worry if you find structure in a pure chance performance? It is difficult to avoid making connections, the mind plays little tricks adding its own references and memories when the attention wanders, but that can happen in any concert. Just refocus. After the event you could discuss the performance with a friend or friends, though listeners of pure chance music often have radically different views about their experience.

Does listening to a pure chance music inform you about music in general? Should it be a course of study in music colleges and universities? All experiments in the philosophy of everyday life will prompt these types of questions, don't expect any academic rewards when you formulate your answer.

Please be aware that some concerts are not of the pure chance nature, if you find yourself in an auditorium with the paraphernalia of amplification, programme notes, scores and stands it is likely that degrees of control are in place. An entrance fee is a certain indicator that you are in the wrong place, just walk a little distance away from the venue and try again.

With thanks to the wonderful world of 101 Experiments in the Philosophy of Everyday Life by Roger-Pol Droit.

Sometimes finding the correct format to express an issue takes longer than collating factual material. So it is when one explores the relationships and differences between "pure music" and what must be its opposite, pure chance. So it is that I offer my thanks to the wonderful world of 101 Experiments in the Philosophy of Everyday Life by Roger-Pol Droit.

Having read through the Webern lectures it was almost inevitable that one had to follow the historical argument through to Boulez and his writings, and almost equally inevitable that the questions arising from pure chance would lead to randomness, indeterminacy and chance. The acid test of how different the outcomes are can be heard by simply comparing works written within a few years of each other

https://www.youtube.com/watch?v=eAjKD12RkEY&t=72s

https://www.youtube.com/watch?v=A5lKCtFfV_o

Have a friend play both for you so you are unaware of the composer, and use the slow movement of the 2nd example at around 8'15".

I have included this image from the I Ching, for those unaware of its history or its use by Cage here are two useful sites:

http://www.iging.com/intro/introduc.htm

An English translation of the introduction given by Richard Wilhelm

https://en.wikipedia.org/wiki/Music_of_Changes

A wiki account of Music of Changes. There is also a PDF file of the fourth book available:

http://academic.brooklyn.cuny.edu/music/dcohen/coremusic/pdf/m-o-c.pdf

I shall give the final word to Nurtan, in a recent exchange of posts we traded ideas on randomness, and put together some musical material to test the ideas. He put forward this view:

Fortunately, we have raised some …very fundamental questions in the musical aesthetics. I
cannot think of a work where the most important note, chord or rhythm is what is expected. In all cases, it is the unusual, unexpected, innovative series of musical utterances that imparts originality and interest in a piece. How do the composers find that? Is it a logical process or a random
process followed by culling out the chaff? Really, John Cage's dice, and other toys are not necessary, the brain is a powerful enough computer to generate a series of random processes and sorting the results out to get the "best " result; or at least what we think as the best for that moment.
Of course there are very conventional rule based, well ordered passages that provide a breathing space for the next emotional utterance. I think this is an important aspect of music - i.e. before you make your listener jump out of his/her seat the composer has to provide a bridge or a respite,
or a repetition of the previous sentence to draw attention to the unusual when it comes. If a composition lays out a root progression according to an accepted pre-existing root progression and composed strictly using a well-recognised or recognisable rhythmic or melodic devices, in my opinion, that would not be a complete composition - it would be just passage work to
prepare for the next leap.

John Cage: “What I do, I do not wish blamed on Zen.”

During the period following the recent blogs on rigour and flexibility Nurtan and I have been discussing randomness, our starting points were different, his a mathematical perspective, mine its historical place in 20^th century music. Inevitably one line of thinking colours and informs the other; this took us to imposing random elements on a plainsong to test out some of our ideas. While all this is fascinating it emphasised that our starting point in recent blogs regarding rigour and flexibility requires further exploration. Even when reduced to a focus on Boulez and Cage it is a wide ranging subject, one every novice composer needs to understand as part of his or her “musical toolbox”. Having written about some of the aesthetic elements of Boulez’s work, and having considered his concept of the “pure” work where reason and rigour are fundamental to the composing process, it is timely to look at some of the ideas behind Cage’s approach, to clarify the essential differences, and similarities between the two, (a matter which should be all the easier as they both wrote a great deal about their artistic intentions).

I used the term random in the introduction and it is one of a number of terms that crop up alongside indeterminacy, aleatoric music and chance-controlled music, all of which can be associated with the term ‘flexibility’.  The three questions that can be examined in the context of a short blog are what effect does the use of flexibility have on a composition, can it coexist with rigorous planning, and does it produce similar or dissimilar musical results?

The opening quotation suggests that Cage understood that relating any artistic endeavour to a philosophy like Zen is going to generate contradictions and debate. Even in his pre-Zen days Cage was pushing the boundaries of traditional approaches to music making. His early music had a mathematical foundation and his interests took him to study with Cowell and Schoenberg, the latter composer reveals to us an element of Cage’s alternative thinking in his often mentioned quotation regarding his pupils:

  "There was one...of course he's not a composer, but he's an inventor—of genius."

There is a clear progression to Cage’s work starting with his interest in the flexibility of events in the work of Ives through to Cowell which later leads to his development of chance-generated music.  This progression could be explored purely in terms of musical consequences without reference to Zen, but if that approach was taken we would miss out on the developing interest in oriental philosophy and its effect on the arts in the latter half of the 20^th century.  Let us consider a few ideas which were influential in providing fertile ground for flexibility in the arts:

The world can be represented as it is, the artist only needs to make “uncoloured” observations.

Occidental thinking views nature as requiring control while oriental thinking places an emphasis on an affinity between man and nature.

Oriental art historically endeavours towards economy and simplicity.

It can be argued that European art and music in particular also aimed at economy, but from the period where music modulated and changed key, greater complexity became inevitable, pushing composers further away from the pull of the tonic. Webern sets out the case in his lectures covered in a previous blog. The affinity between man and nature and uncoloured observation takes us towards a frequently discussed outcome of Buddhist enlightenment, a direct experience of the world. In this state everything is connected (oneness), there is no hierarchy.

Adapting the above ideas to music generates some radical outcomes:

No one sound or event is more significant than any other.

Attempting to control experience (or our experience of music) is valueless, attempting to control everything is impossible. Every action or event we perceive can become music/art, as Cage says:

I saw that all things are related. We don’t have to bring about relationships.

The religious implications of the process of enlightenment are well represented in Cage’s writings, and its thinking is also well represented in the psychedelic sub-culture of the 1960’s and presented by such authors as Aldous Huxley in his “Doors of Perception” .

Music can involve us in “a moment when, awareness of time and space being lost, the multiplicity of elements which make up an individual become integrated and he is one.” (Cage).

The next statement directed at the audience demonstrates a difference in emphasis between Eastern and Western values, the first part could be applicable to both (if we are talking about listening to music) while the second is distinctly oriental:

What is important is to insert the individual into the current, the flux of everything that happens. And to do that, the wall has to be demolished; tastes, memory, and emotions have to be weakened. (Cage).

What is also evident is that such actions come with a cost, one that would be wholly unacceptable to Boulez:

…if we want to use chance operations, then we must accept the results. We have no right to use it if we are determined to criticize the results and to seek a better answer.

The Canadian scholar of Eastern thought Victor Hori makes an interesting observation regarding “Pure Consciousness”, such a state

…without concepts, if there could be such a thing, would be a booming, buzzing confusion, a sensory field of flashes of light, unidentifiable sounds, ambiguous shapes, color patches without significance. This is not the consciousness of the enlightened Zen master.

Whether or not it represents the consciousness of the Zen master, or indeed if this statement is true in every detail confusion is a possible outcome of complete musical freedom, but is Cage’s music “free” of all constraints?

If we take “Cartridge Music” as an example we find that there are a number of restrictions on time (length of events) and timbre. If we listen to the available performances on You Tube we recognise a family resemblance in the performances. Within individual performances we hear the percussive sounds produce regular rhythms and repeats of timbre, there is no doubt that this is organised sound. In the most free of all Cage’s works, 4’.33” we are most familiar with it being performed in a concert hall where specific restrictions are in place to the range of sounds we hear, should the work be performed in the open air, in a factory or garden our perceptions would be changed. It seems that we lean towards placing constraints even when they are not indicated or even implied.

Returning to Cartridge Music the 20 page score contains graphic indicators for the number of performers (maximum 20), each performer is given indicators (points, circles and a stopwatch) which shows the time allocated to events such as pitch and dynamics/amplitude. There is also a scheme to introduce sounds other than through the cartridge made by applying contact microphones. The You Tube video filming a performance makes demonstrates the process clearly:

https://www.youtube.com/watch?v=VaNHAswN2hU

This second link gives a performer’s view, I don’t agree with everything in these notes, but it offers interesting historical viewpoints and relates to the question of rigour and flexibility:

http://www.anothertimbre.com/cartridgemusic.html

One issue arising from Cartridge music is that if a musician was inclined he/she could create a work of the same timbre, impose time and dynamic restrictions etc. and create a rigorous, reproducible composition. Family likeness, no Zen. If the composer was interested in the music having flexibility it would be a simple exercise to share the composition as a MIDI file and permit as many variations in the structure as there are people with the interest to play with it. In truth there is no reason why the given sounds could not form the basis of a “pure” work where each element is accountable and related to a single source.

Of course all these developments are now history, and the Zen thinking is scaffolding that provided a change of direction, a structure creating an empty space that could be filled with whatever a composer desired, and with the advent of sampling “whatever” is the state of play. As in the Biblical statement “Out of the eater came forth meat, and out of the strong came forth sweetness?” we should recognise that rigour and flexibility are, as always with music, two distinct characteristics that permit life and progress.

Composer's toolbox PDF

https://drive.google.com/file/d/0B_EeqYYl3MfMeXpXY1ZSOWI4bVk/view?usp=sharing


Titles include:

Dynamics

Drones

Ostinato

Words and text

Select a brilliant title

Graphic scores a recipe for composition?

Topics covered in the first hundred blogs

Looking for a simple way to locate topics covered in the blogs? As the first hundred blogs cover only four sheets on the Google blogger we have divided the material into four categories: Composers, Music and Psychology, Musical characteristics and Helping Novice composers.

Feedback and suggestions for improving on this format are welcome!

Composers:

Webern – order and flexibility / Webern lectures / Webern, repetition // Messiaen: Et Expecto Resurrectionem Mortuorum //

Lili Boulanger “Pie Jesu” // George Crumb “Vox Balaenae” // Takemitsu “Les Yeux Clos II” / Takemitsu Art v. architecture

The mode of limited transposition // R. V. Williams 6^th symphony // Nielsen 5^th symphony (the simplicity of)

George Sollazzi – overview of style // Jeff Lade – overview of style // Satie “Vexations” / Gnossienne 1 // Frank Bridge Sea Idyll,

Lament and Winter Pastoral / Frank Bridge Piano sonata analysis // British music of the 20^th century (full PDF) / Chopin:  So you want to write ‘beautiful’ music

Beethoven sonata in D (Architecture v. form) // Mozart rhythmic design (piano sonata K.309) / Rhythmic design in Mozart's piano sonata VII K.309 and Beethoven's Op.110

Links to G+ composer’s works (open invitation to add works) / 6 works and links (examples of G+ composer works)

Music and Psychology:

Creativity and aging / Be serious for a minute / Time Travel and music / Laughter / Repetition and brain worm

Music and the incubation period / Creating and experiencing emotional responses / Musical cues

Chunking and musical attention / further questions on attention / Motivation and musical experience /

What motivates you to write music? / Does your music target the right audience? / Deciphering musical codes / Music for meditation?

Why do we derive pleasure from listening? / Why do we listen to difficult music? / Why write difficult music?

Is human ‘messiness’ better than a synthetic performance? / What is wrong with synthetic music performances?

Musical characteristics:

Alternative approaches to rhythm 1 and 2 / Complex rhythms / Verbs of physical action / Relationships (pitch and rhythm)

The curious case of cyclic symmetric octaves / Nurtan Esmen thoughts on polytonality / Climax / Bitonality and Polytonality /

Symmetric scales (link to PDF) / Using 01 and 02 scales / Processes of transformation / Silence is dead…long live silence /

Harmony, sound colour and Beyond / A rose by any other name / Zen and the composer’s voice / Japanese aesthetics 2 / A

sampler of Japanese music / Jack of all trades? The synthesiser / The contest between live and synthetic sounds /

10 popular songs that deserve study / Bells and repetition / Minimal music past and present / The Tao of musical intentions /

Helping novice composers:

First steps in orchestration / Investigation into folksong (full PDF) / Composers tool box: Composition fault finder / The Zen of

Musical Reasoning / Walkthrough “Zen of Musical Reasoning” / Composer’s toolbox – size matters / Composer’s toolbox – How   to find your muse /

Deciphering musical codes / to compose is to be 3 times human / Where to go when I have run out of ideas 1 and 2 /

Parallel 5ths / Invitation, make a recording of this graphic score / the composer’s perspective /

Composer’s toolbox graphic scores / selecting a brilliant title / word and text / ostinato / drones / dynamics

Inspiration / Preparing to write for String Quartet - 10 suggestions / Esmen an immortal love song, incorporating folk music into

a more complicated structure / An investigation of folksongs

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 20^th 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:

https://www.youtube.com/watch?v=X3_GF-zDIlQ&list=PLKjdfGS1edVGFFZKs56s-hLywsr5YMJ2q

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:

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

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.