One Little Explorer

My exploration of music.

Category: Philosophy

Hearing Music – Impression and Projection

Charles Baxter – Young Girl Leaning on a Stone Ledge

Something I’ve often thought about is how the analysis of music relates to the way in which we experience music and its constituent elements. Particularly I’m interested in the extent that certain, arguably, inaudible structures can be said to exist. Even more so I find fascinating those elements of music that while not initially apparent reveal themselves with either familiarity or close study.

Few uninitiated listeners could hope to hear, for example, each distinct voice in a complex polyphonic passage of music, but with training one learns to differentiate voices with relative ease. Now we would all agree that the music does in fact consist of multiple, essentially solo melodies sounded simultaneously. This phenomenon becomes more nuanced as we consider more opaque musical structures such as the permutations of a tone row, which range from relatively easy to perceive transformations such as augmentation, diminution and transposition to more extreme transformations, such as suppletion and the arranging of elements vertically rather than horizontally, which often result in a permutation that seems entirely distinct from the original.

There is often debate over whether these processes are in fact audible, principally, it seems, because audibility is considered a prerequisite to being worthy of study. I think that the relationship between how we hear music and analysis can be made clearer using, for arguments sake, the idea of a musical ‘structure’.

What is a musical structure?

For the purposes of this post I will define a musical structure as some sort of relationship between one discrete musical element or group of elements with another in a certain musical dimension. So a structure can be a harmony, the simultaneous sounding of two or more notes; a melody, two or more notes played in sequence; a rhythm, two or more notes played at a certain time interval; or the organisation of different timbres/tone colours. These are but a few of the more fundamental structures that can be said to exist in music, all of them are easily audible and rarely ambiguous.

Ambiguity is created when elements can be interpreted as part of more than one structure. As structures become more complex, usually involving a combination of fundamental structures in some form, they become less audible and the potential for ambiguity is increased.

What it is to be ‘audible’?

To be audible is essentially just to be among the simpler, direct structures. Complex structures will always have more simple intervening structures, where there are enough of these, of certain complexity, our ability to perceive the underlying structure is diminished, eventually to the point that we are oblivious too them.

However sometimes we are able to turn our attention away from the surface structures and perceive the deeper structures in the same way that one may decipher a code by selectively reading words from a text.

Are the structures inherently audible in music or projected by analysis upon it?

Subtle aural structures may not always impress themselves upon the listener but may rather be projected by the listener onto the music. Nonetheless I think that generally analysis serves to bring what already exists in the music into focus.

While music is primarily experienced through sound, there are other mediums through which to appreciate it much as one appreciates a painting through is aesthetic beauty, narrative, symbolism, emotional impact and historical context among a myriad of other factors while it remains a primarily visual meaning. It is conceivable that in music and in visual art that these modes of appreciation are not wholly communicated through the artwork itself but also by secondary, associated artefacts, such as scores, programs, critiques and the lexicon of previously defined gestures which are easily accidentally employed i.e. a subtle cross in a painting may not always be an allusion to Christ and more pertinently, music similarities do not necessarily correlate with semantic ones.

This type of speculation could go on indefinitely. Perhaps it is more convenient to consider the sound element of a work is the only part that can be properly called music and everything else becomes part of a subordinate, though inextricable, non-music artwork. Even if this is done, we are brought back to the question of what constitutes audibility.

Does this add and explanatory power? Or allow a more precise definition of music?

It is relatively easy to see the significance of structures, inaudible though they may be, that add semantic content to a piece of music. What is less obvious is whether inaudible structures such as the forms of self imitation already described, which add no obvious semantic or otherwise content, are valuable. Personally I feel there is beauty in these structures, even if I don’t experience it aurally. If this is the case then clearly it is no longer necessary for them to add content, but in what sense are they music. These structures may not be perceived aurally but nonetheless they do manifest as sound.


How imperfect is sound? Part One.

Pierre Auguste Renoir – Gabrielle and Jean

Note or noise?

Take a heap of sand. Now, take one grain away, is it still a heap? Of course. But what if we continued to do this until there was only one grain of sand left? Would it be a heap? Our intuition tells us no, but this seems to be the logical conclusion of our reasoning.

This dilemma is commonly know as the Sorites Paradox. You might wonder why I’m talking about this in a post about sound. To answer that I first need to say a little about the nature of sound, specifically, the relationship between pitch and timbre.

A pitch is a single frequency, for example, the note A is generally placed at 440 hertz (cycles per a second). We perceive these cycles as sound. However, in all but the most controlled environments we will never hear a pure sine wave. In addition to the loudest (usually) and most perceptible frequency, known as the fundamental, there are a series of mathematically related overtones. It is the relative amplitudes (volume) of these overtones that give a sound its unique ‘colour’ usually referred to as timbre. For example, the same frequency played on a violin, will emphasise a different set of overtones to those that would be emphasised if it were played on a guitar.

Now, back to the paradox. In sounds such as those I have described about, the overtones themselves are sine waves (some overtones may have their own series of overtones, but this is not important for our purposes). Based on this fact, theoretically any sound can be broken down as the sum of a set of sine waves at varying amplitudes. Now we can rephrase the paradox in terms of sound.

Take a sine wave of a specific frequency. Add an overtone (another sine wave), is it still a note? Yes. Add another. Is it still a note? Of course. Eventually, we will have summed up so many sine waves that the sound we have constructed is equally loud across all frequencies. This is the very definition of noise.

When, then, does a note become noise? It seems there is no satisfactory answer, but the paradox in itself has some interesting implications.

It seems odd now, to me at least, to speak of ‘right notes’ and ‘wrong notes’. But what it also shows is that pitch and timbre, so rigorously separated ideas in western music, in reality are inextricable from each other. This correlation between pitch and harmony has been explored by some modern composers, such as Olivier Messiaen, who have used harmony to generate timbres, as well as other composers who have used the overtone series as the basis for their melodies.