Conceptual and cultural disclaimer

It's quite hard to describe the organisational systems of Western classical music without in some way tacitly evoking a series of assumptions based on a musical education. I'm going to try as much as possible in this introductory section not to assume this, not merely because there may be 'gaps' in your knowledge of these musical 'fundamentals' (read, often, 'adopted axioms'). In fact, trying not to assume them is actually conceptually helpful for seeing a) the interest in how the music of some composers/artists/performers challenges these assumptions, and b) the extent to which a lot of this stuff is really just a semi-arbitrary system, a sort of rule-based communication akin, aside (crucially) from the lack of semantic content, to the rules of a language.

Pitched and unpitched sounds

In a general sense in Western music, sounds tend be divided into 'pitched' and 'unpitched' sounds. This is in a sense an arbitrary division because it's really a sliding scale. But we probably most of us have an instinctive grasp of the difference. A scientific explanation of this phenomenon is that all sounds can be described as being made up of partials – that is, that using Fourier analysis any sound wave can be described as a combination of different sine waves of different frequencies and amplitudes. 'More pitched sounds' have a high proportion of waves whose frequencies are in simple mathematical ratios to one another (1:2, 1:3, 2:3 etc. etc.); whereas 'less pitched sounds' have a higher proportion of 'enharmonic' frequencies with no simple mathematical relationship between them. Therefore in a sense the 'most pitched' sound is the simple sine wave; the 'least pitched' is white noise. In between there is a sliding scale between e.g. the sound of a snare drum or a hi-hat cymbal (quite unpitched but with some pitch content), via timpani (more pitch content), various pitched instruments like trumpet, cello, guitar etc. (still more pitch content) to instruments like flute and vibraphone that are very 'pure' and whose sound waves most resemble the sine wave. The particular wave shape, or, put another way, the particular combination of and relative strength of the sine waves that an instrument or voice's distinctive soundwave can be analysed into, determine the sound colour or timbre of the instrument or voice.

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Western's music focus on the organisation of pitched sounds

As previously mentioned, in the Western classical tradition we assume and enforce a sharp division between pitched and unpitched sounds. There is a whole musical period in the canon (excluding some French music like Rameau and occasional ceremonial works like Handel's Music for the Royal Fireworks) where unpitched sounds not only are not of primary importance, but do not feature at all. Even for the Rameau and Handel examples, the role of the unpitched elements is not notated but rather it is left to the performers to improvise. In general the central focus of Western classical music has always been the organisation of pitched material, and the exploration of the rules and rationales of the organisation and flow of that material - in dialogue with certain kinds of formal structures, which themselves are more or less entirely determined by how they describe complicated pitch relationships. This is radically different from, for example, the historical focus of Indian classical music or of the historic Ashanti court music of modern-day Ghana.

It is the task of the following articles to give some systematic insight into these sometimes quite dauntingly ramified structures through looking at some specific examples from the canon which are mainly familiar to you.

First, however, a few words about the most basic principles of Western pitch organisation.

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The octave

In the Western classical tradition, individual tones of a pitched instrument are tuned in a scale of 12 pitches (A, B, C, D, E, F, G and their sharp/flat alterations) in an octave. An octave is defined by the frequencies of the two tones an octave apart: the frequencies of tones an octave apart are in a 1:2 ratio – it is the most consonant interval possible, i.e. the frequencies of the tones cause the minimum disruption to each others' wave shapes and as a result the combination of the sounds sounds 'relaxed' rather than 'tense' and dissonant.

As a result the octave is often and in various cultures used as the base division of pitch organisation (not necessarily through calculation but rather through instinct - see below). In fact in Western classical music the octave is in some contexts barely considered an interval, i.e. the same 'pitch class' (A, G, Bb etc.) in different octaves is not always considered a 'different note' in any structurally important way. In other words, doubling a note at the octave is often perceived/considered as a change in timbre rather than in harmony because the notes are so consonant together that the change in sound cannot be of any structural significance. You can hear musical examples to the left and right.

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The chromatic scale as one of many possible ways of dividing the octave

As mentioned, in Western music the octave is divided into twelve steps, which we call the chromatic scale. At other times and other places the octave has been divided into greater or fewer steps (for example, thirty-one equal tones in some Renaissance music - see the video to the left, or the very different double system of slendro (five unequal tones) and pelog (seven unequal tones) in Javanese Gamelan). But in the Western classical tradition, we understand all pitches as being part of this chromatic system – if a note is between the frequency of two of these notes, it is an out-of-tune version of one or other of them. At this point I won't elaborate on the historical and scientific basis for how the twelve-tone octave was arrived at and why it is quite a robust system. Most Western listeners don't even perceive it as in any way a non-trivial axiom.

The tonal system; music being “in a key”

However it is not until the early part of the twentieth century when Western music began to use all twelve tones of the octave in a free and relatively constant fashion, in what is called atonal music. Rather, Western Classical music before this time is primarily tonal. This means that at any given moment the music is in fact primarily based not on twelve equal pitches, but rather on an unequal division of the octave into seven pitches, which all have a more or less consonant relationship with a single tonic pitch around which they are organised. Partially because of the science of the way that these notes are spaced and partially by acculturation, we naturally hear the tonic pitch of a piece of Western music as its natural point of rest, and the other notes of the scale (for that is what these seven notes together comprise) as points of greater or lesser tension, depending on the scale degree (which note in the scale is being played, with the tonic considered the first note) and the context.

When there is a clear hierarchy of this kind where we can hear or sense where the note of resolution would naturally fall, the music is said to be in a key, and that key is named after its tonic. For example, “in the key of A”.

The piano is organised, for whatever reason, around the key of C. Any white note on the piano is a scale degree in the key of C. You can experiment with the 'gravitational pull' of the tonic by sitting at the piano and playing (& ideally singing along with!) a series of random notes (ideally slowly, so that your ear has time to hear them as pitches). You may well find that your improvised melody does not feel concluded until you strike the key of C, (which is the note placed on the keyboard just below and to the left of two black notes together).
 

Major and minor

There is one additional thing to note about the tonal system, and that is the existence of the minor keys, or the minor mode (for now these two compound terms can be considered more or less equivalent).

The minor mode is a slightly different organisation of tones around the tonic, an organisation that is asymmetrically shaped in a slightly different way, and as a result sounds quite different from the one previously mentioned, which is the major key (or major mode). The minor mode is also based on a scale of seven notes. You can hear this scale by playing the white notes of the piano starting on A (which is the white note between and below the second and third of the group of three black notes). However, the tonic of the minor mode is a bit less stable than the major tonic (otherwise the 'random melody' exercise we discussed at the end of the previous section would usually end up with us choosing A as the natural point of rest rather than C). As a result, two notes of the seven in the minor mode are frequently altered to organise the tonal structure more definitively around the tonic, in certain contexts. As a result the minor keys are in a sense systems of nine pitches rather than seven; or perhaps better they are still systems of seven pitches, two of which have often-used alternatives.

Modulation; related keys

We've discussed, and experienced by listening and experimenting, the phenomenon of music being in a key and the gravitational pull of the tonic. But it is possible to escape the gravitational field of a key. By introducing notes that are not within the seven-note system of one key, the centre of gravity of a piece of music can be forced to change from one tonic to another. This is called modulation. Usually a modulation is achieved from one key to another that shares many pitches with it. These are called related keys. Western classical structures are very intimately tied up with systems of modulations to related keys.

The tonic key; the role of the tonic key

When a piece of music is listed as being in a key (e.g. Beethoven's Symphony No.1 in C major), it does not mean that the whole piece is in C major from first note to last. When we have a large piece of this kind it will contain many modulations and visit many different keys.

Instead what the note “in C major” means is that, just as how when we play music within a key it is hierarchically organised around its tonic, there is a system of modulation in place across the whole piece whereby all the keys are organised more or less closely around the home key (in this case of C major).

Just as one note in the scale is referred to as the tonic of that key, when a whole piece is structured around one key, that key is referred to as the tonic key, or – more often – simply, the tonic. Pieces of Western classical music almost always always begin in the tonic, and they almost always return to it at their conclusions.

Structurally-important keys; symmetry of micro and macro in tonal structures

Keys that share many pitches with the tonic key, i.e. its most closely related keys, tend to assume crucial importance in the structures typical of Western classical music. Because of the way that the asymmetrical seven-note scale is organised, the tonics of these related keys also often assume importance in music within a key as scale degrees within it (e.g. G major is one of C major's most closely-related keys; the note G and its related chords are also a particularly important within musical passages in C major). Thus the tonal system by which a short passage of music is organised is often reflected by the large structures of which that passage of music forms a part. This fact is crucial for the way that large-scale tonal structures are constructed, explored and exploited by Western classical composers, for part of why they can be intellectually and emotionally satisfying, and why they can communicate coherence even on very large scales.

The task of these articles

As I mentioned, the task of the following articles is to introduce and explain the typical forms of classical works without resorting to the ability to play an instrument, technical aural skills, or the ability to read musical notation. In a sense the articles will require music theory, indeed in a sense they constitute music theory; they will use fundamental terms that have been covered in this initial introduction, terms like modulation, tonic, related keys etc.; and they will introduce further technical terms as the forms require them to do so (e.g. exposition, development, recapitulation etc.). My aim, however, is that they will be comprehensible to an intelligent person who has no educational grounding in practical music-making. Further than this, the aim is that the audio examples and elements of theory that are introduced will be sufficient to create an effective synapse between the intellectual and the auditory, and that the insights offered will thus not be bound to the page; rather that the experience of listening to music will be effectively enriched by the understanding of formal structures that the articles hopefully afford.

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Historical and formal purview

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The articles will focus on building up an understanding of the symphonic forms of Classical music - that is to say, the musical forms most in use in symphonies, sonatas, and chamber works during the Classical and Romantic periods of Western music (roughly 1750-1914, though many of the structures we discuss were used by some composers much later than these dates in some form). They will not constitute an historical survey of the development of the forms, rather they will take an intellectually progressive approach, building up from the simplest forms (scherzo, variation form) to the most complex (sonata form) in a completely and unabashedly ahistorical manner, and relying throughout repertoire familiar to you. Further, they will not be concerned with contrapuntal forms like fugue, primarily because I don't have enough expertise on these to explain them with any degree of authority in general, and certainly not with the comfort with the forms that would be required to explain them without resorting to technical language.

 

However, that does not mean we will entirely avoid the Baroque – in fact we will begin our exploration of formal structures by looking at a form that is in very common use in the Baroque period – the binary form, or Baroque dance form.