Nature and Artifice in Structure

[This is a continuation of the last post ‘Experiencing Function’. I do welcome comments and responses on what I’ve written, especially since many of those who usually read what I write actually study music or are practitioners.]

In the last post, I suggested that the experience of function in music is the experience of live possibilities as governed by a set of rules, the rules of harmony. I promised to discuss two further related questions, namely: (1) How do these rules make the possibilities salient to us? and (2) What is the status of these rules: are they merely formal constructs or are they somehow natural or innate? I then try to extend some of these findings to two other areas: logic and narrativity.

Convention in Structure

Strictly speaking, the rules of the harmony are but a set of rules, a formal structure: they dictate to us the function of the various notes and chords. How does a formal structure enliven certain possibilities for us? There is a fairly straightforward way in which this is possible — this is by actually learning the structure deliberately or by some kind of social pressure. Consider the rules of chess. Each of the pieces can only move in certain ways, the knight moves in an L-shape, the bishop moves diagonally and so on. If I observe a game of chess before I learn the rules the game would make no sense to me. Without understanding the legitimate moves, I would not understand why the pawn may not simply go off and knock the king off his rocker. It is only as I learn the rules of the game, deliberately or gradually by observing others, that I observe the game as a series of live possibilities. Only certain moves are legitimate, are ‘live’. A game would be played beautifully by a player only if he manages to artfully navigate his pieces according to the formal rules.

Using chess as an example would seem to suggest that in some sense the rules of harmony are conventional. I think this is true to some extent. Consider another larger scale formal structure in music that is somewhat based on the rules of harmony, the fabled sonata form. The sonata form governs not micro chord progressions but the various parts of certain pieces of music — it is somewhat based on the rules of harmony, however, specifically on the primacy of the tonic. (Very roughly, a sonata form always begins and ends in the initial key, throughout the music passes through other keys and passes through an stormy section known as the development where both harmony and melody are developed and extended in various ways, with the harmony tensely anticipating the return of the initial key. Think of it as some kind of musical home-coming story) The sonata form must be learnt in order to be appreciated — without it, the sonata would barely make any cohesive sense, or would be enjoyed as simply discrete sections of music. In fact, the very genius of many composers lies not in their adherence but in their transcendence of the sonata form — presupposing it but subverting it in various ways to electrifying psychological effect. This effect, however, is only felt by the discerning listener, one who has been led by convention to expect certain possibilities and is pleasantly surprised to find them subverted. This conventionality is more evident in the larger formal structure than in the rules of harmony itself, though I believe it is also present there to some degree.

[I digress here and have to add: here is wherein I believe the very definition of art music and pop music lie. Art music always has a form, but the genius of composers lie in their both presupposing and transcending the form at the same time. To simply re-use the form would be lazy, creating some pastiche as most of popular music does. To cast off form completely would result in mere noise: like one who plays chess and then decides that the pawn can move like a queen or that the game can continue when the king is dead. Some contemporary music falls into this category, some others do something more interesting: they contrive a new formal structure and play around in it, I discuss this possibility in a bit.]

The Experience of Natural Structures

Nonetheless, this cannot be the entire picture. There is a sense in which the formal structure is not merely learned but in some sense discovered. The rules of harmony are not laid down completely arbitrarily as say the rules of chess or checkers are. Instead, they purport to describe something we naturally or instinctively experience. Presumably, even before the rules of harmony were formalised, people already had a natural sense of harmony, they felt that certain notes in certain contexts tended to go well together resulting in the formalisation of various modes and scales. Furthermore, the specific kind of experience generated in the experience of function is a lot more rich than that of one who anticipates a myriad of possibilities of chess moves, they are imbued, to borrow a visual metaphor, with a number of colours. It is not merely that the dominant chord anticipates the tonic, but that this movement or anticipation generates a specific phenomenological experience, one that feels like a kind of closure — ditto for the various other kinds of progressions. Therefore, while it is true to say that there is some element of conventionality in music, at bottom there is a certain sense in which the rules of harmony are formalised subsequent to their being experienced as such.

Talk of the naturalness of the rules of harmony, especially as formulated by the old white men of the western classical tradition is sometimes met with accusations of western hegemony. There may be some truth to this suggestion — I concede that that there is some conventionality in play here. Yet I think it would be fantastic to suggest that the entire system is an artifice. Even in other musical traditions (of which I have only a passing acquaintance), the interplay between the tonic and dominant notes in a mode is still a prominent feature. An fruitful consideration here would be to examine formal musical structures that are really invented artifices. One finds such a trend in much of modern music: Schoenberg is such a case. He turns his back on the normal harmonic structure of the classical tradition, but interestingly he does not cast structure off completely; instead, he contrives a new one — what is called the 12-tone technique or serialism. I don’t pretend to understand or appreciate the system fully, but in each iteration of the system there are certain rules that govern the music. Have a listen to one such example below:

What strikes the untrained listener is probably how confusing it all sounds. One does not know what to expect and the notes that come out seem random. They are not in fact random but are the product of following a different set of rules from the ones which we are used to. This suggests that the expectations are in some sense unnatural — they are not the ones we are naturally led to expect.

Now, it might be suggested that the reason why it sounds in this manner despite there being a structure could be due to the fact that unlike the classical rules of harmony, Schoenberg’s system has not yet achieved the privilege of having hegemonic status. If one is sufficiently familiar with its rules and after it has been more widely adopted, perhaps we would come to experience its possibilities as live in the same manner we do the usual rules of harmony. Perhaps, according to the possibly apocryphal quote of Schoenberg, “milkmen would whistle his tunes”.

Let me suggest three responses to this. Firstly, I think there is some truth to the fact that more acquaintance with Schoenberg’s system would allow one to better experience his music. I have been in concerts with more careful listeners who are able to discern the structure and intentions of such esoteric composers. Perhaps the learned and discerning listener experiencing this is like one who experiences live possibilities in a game of chess after having mastered the rules — the moves are now live to him because they have been learned. Secondly, despite this, I do think that there is a manifest difference in the experience of the live possibilities as a result of learning purely formal rules and the corresponding experience when the possibilities are given naturally. The natural possibilities, in the first place, do not have to be learnt — and they carry with them distinct phenomenological qualities, the closure, anticipation etc. that I have been gesturing at. The experience or pleasure that one derives from experiencing the learned possibilities might feel more ‘intellectual’, for lack of a better word. This might suggest why Schoenberg’s prediction about the milkmen have yet to come true.

Thirdly, while I do think that there is a natural innate set of possibilities, I do not think that they necessarily have been completely represented in our current systems of harmony, not least those expressed in the western tradition. There might be new harmonic possibilities that are naturally coherent to us but that we have yet to formulate and composers may be able to grasp these somewhat intuitively. Indeed in Schoenberg’s music, one sometimes catches a whisk of such moments when the music seems to convey something — perhaps it is him as a composer intuitively mapping out some natural harmonic possibility while studiously avoiding some of the hackneyed ones. This is purely speculative of course, but the diversity of harmonic systems in various cultures ought give us some humility into thinking that the set of harmonic rules formulated in the West represent the only natural set.

Dependence and Transcendence

Let me step outside this seemingly neutral analysis of the issue here and make a normative suggestion that I have hinted at already. I believe that the task of the artist is to work within the natural set of possibilities and to transcend them at the same time. This calls for some humility — to step completely outside the natural set of possibilities would result in utter cacophony, mere sound. Nonetheless, while we should not too quickly cast off the ancient harmonic forms, it calls for boldness in that we must not assume that all the harmonic possibilities have been discovered or that artists should simply parrot the music of old. And I mention this again, but art must both presuppose and transcend its form, it must be intelligible and fresh, it must be ancient and new. Thus, there must be room for some sort of artifice in art — and yet the artifice must be in some ways rooted in nature. The sonata form for example, is somewhat based on the harmonic system; it is possible that the larger forms created by other composers may be rooted in natural possibilities as well, grasped somewhat intuitively. A lot more can be said here, and indeed many more qualifications need to be made, but I hope the general direction is sufficiently clear.

There is therefore an interesting interplay between nature and artifice in creating art. And in some ways the very task reflects our ontological status before God: as a created being, we are dependent on him and the natural possibilities he offers us — they are rich and wonderful, to step outside them is a kind of hubris. And yet as image bearers of God, we mimic in a dependent way his creative acts: as he creates new things, so do we out of the materials that he has offered us — such is our task, we must not shirk it or be lazy. We must sing to God ancient truths in a new song. (Psalm 33, 96 et. al.)

Some Extensions: Logic and Narrativity

In this last section I very briefly sketch two areas in which similar phenomenon seem to occur and in which a similar analysis might be extended. My familiarity with these topics is even more sketchy and so I dare not say much.

Firstly, the experience of logical inferences appear to be similar to music. There is a canon of logical rules in the West, the fountainhead of which is Aristotle’s syllogisms, that appear to some today as nothing but a bunch of formal rules and mere convention. And then there is a proliferation of new formal systems of para-consistent logics from the contemporary era, and some from non-western traditions. Certainly the task of logic is not the same as that of art, (on my naive view, its main task should be but aiming at the truth), but I wonder if one can, by reflecting on one’s experience of the various rules of inference, distinguish the natural rules from the merely conventional ones. When I encounter the usual logical rules and move from one proposition to another by logical inference, there is a certain phenomenological experience that I have, when I try to do the same with the non-standard logics, a more jarring experience occurs. I dare not say more.

A second area in which a fruitful connection might be made is with the area of narrativity. Let me consider this first in relation to the field of historical writing, with which I am somewhat more familiar. Historiographers such as Hayden White have noted that in writing history, historians are compelled to adopt one of various generic plot structures such as romance, comedy, tragedy, epic etc. And he notes that this structure seems to float above the facts of history, in the sense that historians can agree about the facts of the case but that they still disagree about how specifically to ‘emplot’ the case. For example, the French revolution has been variously narrated as a story of progress, of tragic decline and of comedy. The decision to make of which facts are relevant and which areas of history to focus on are all governed by the narrative structure, but the structure itself seems to be independent of the facts. Most importantly, the narrative structure provides coherence to the events, attempts to evade it by simply dictating all that has happened result in one feeling as though the historical events have not been explained.

Once again, the status of these narrative structures come into question — are they purely artificial? Were they the result of simply taking the familiar plot forms of the old myths and tales and re-using them for other purposes? Yet from where did the writers and tellers of those tales pluck out these forms in the first place? Surely, the narrative forms must firstly have been experienced before they were formalised. The way we experience history and past events, or perhaps the way we understanding them in the first place is through these structures which are somehow inherent in the way we experience the world. Furthermore the inescapability of these narrative structures parallels the fact that to step outside the natural rules of harmony in music is to lead to incomprehensibility. These are somehow natural structures that we come to experience before they are formalised. There have been narratives before there were narrativists.

Simply because a certain structure is not merely formal but natural in some sense does not yet fully answer the question about how a narrative structure is related to truth. Still, some kind of objectivity may be purchased because if we concede that the natural forms are to be privileged, it provides a heavy constraint on historical writing. Given that there are indeed a set of natural structures, we cannot simply formulate any kind of structure we want with which to explain historical events. These structures have constraints of their own, although there is some leeway on how one might emplot an event: not everything can be a tragedy or comedy, at least not in the same way. However, to answer the question about the relation of historical narrative to truth or historical reality is a far more difficult task.

Here is my intuition of a Christian response to the problem: given that God stands as the ontological ground of the world and that God is personal, it is possible that he understands historical events in a narrative fashion as well. A narrative is true or objective insofar as it corresponds to the narrative that God experiences or fashions in the world. The variety of possible emplotments is no barrier to this formulation: there is no reason why God should not experience or fashion events such that they could be understood under various narrative frameworks. The history of salvation (or if you like, Heilsgeschichte) in fact is understood under various narrative forms in Scripture, it has been described variously as a romance (the pursuit of God’s people), epic (the victory of the serpent-crusher, the coming of the kingdom of God) and perhaps even comedy (John Frame mentions this in connection to Psalm 2:4, I’m half convinced).

I’m sure more connections can be made with narrativity as it is found in literary texts, though I am less familiar with this. The proliferation of new narrative forms in literature mirrors the proliferation of new harmonic forms in music: both the result of a studious avoidance of the ancient forms. Some of these new forms may in fact reflect natural experiences that the ancient systems may have yet formalised: the streams-of-consciousness style of writing may fall into this category. Yet others who are far more experimental or who try to cast off narrative structure completely again fall into incomprehensibility. Once again there is a similar interplay between nature and artifice.

Experiencing Function

[This was initially conceived as a fun post for me to write down my amateurish quasi-psychological/phenomenological musings. Somehow my thoughts became more serious as I continued write to the extent that it seems best to extend my thinking into two posts. Note that some of what is written may require some musical background. Also, I often post my entire writing on Facebook for people who find clicking on links a tiresome task (like myself) — I am not doing that this time because there are pictures and embedded audio which won’t appear on Facebook.]

What I wish to do in this post and the next is to put down some of my thoughts on the experience of music — it’s really an effort to put down some reflections that I have had for quite a while. Much of what I mention may appear painfully obvious to anyone who has had some musical training. Yet I think a closer introspection into our experience of music will prove fruitful in elucidating an interesting aspect of such experience. Specifically, I want to examine how we experience function in music and suggest that the phenomena of function is not in fact a sound. In other words we do not strictly speaking ‘hear’ function. Following this, I want to make some speculative suggestions on how the experience of function might be explained and, I hope, fruitfully extend it to other analogous areas of experience.

Isolating the Experience

To understand what I mean by function, let me try to describe and isolate the specific phenomenology that I am thinking of. By doing so, I hope to show that the experience of function is not a auditory experience, in other words, experiencing function in music is not hearing something. What does it mean to hear something? According to prevailing scientific opinion, the experience of sound is the result of sound waves entering the ear. Depending on the wave, its frequency, amplitude, and form (I think this is the word), what we hear varies — frequency determines the pitch of the sound (whether it is high or low), amplitude its volume (whether it is loud or soft) and form its timbre (e.g. a middle C played on a piano sounds different from a middle C played on a violin). There is a parallel here with visual experience — what we see is dependent on the light waves that enter our eye. Depending on the frequency of the wave, we see variations in colours, depending on its amplitude, we see variations in intensity — a combination of the two gives us the notion of various hues of colours.

Notice, however, that in the experience of music we also experience what musicians call harmony, which is the result of a progression of a cluster of notes (a chord). There are certain rules guiding this progression, some of which are tastefully transgressed at times but often still presupposed. These are the rules of musical harmony. In this framework, each piece of music revolves around a primary note, known as the tonic (or pitch-centre) and will be governed by a certain mode (thus we say that a piece is in A major, C minor and so on) — every note and chord will have a specific function once the tonic and mode are determined (i.e. its key). Note that the function of each note is not a product of its corresponding sound wave (a C still sounds like a C in whatever context) but is determined by its context, namely the key.

So far, this sounds like simply restating in a complex manner what everyone has learnt in Grade 5 theory. Yet I think this experience is actually fairly mysterious. One notices the strangeness when one reflects on the context-dependence on this phenomenon. In other words, the fact that the harmony or function that we experience of the same notes change when its harmonic context changes. Now, that certain experiences are context-dependent is nothing particularly novel. Our visual experience is also commonly susceptible to context dependence — take the famous checker shadow illusion as seen below. The two squares, A and B, are in fact of the same shade of grey, but the context has altered our perception of the shade such that one appears lighter than the other. (google ‘wiki checker shadow’ to see proof that they are indeed the same shade) However, consider what exactly the context alters in our experience of the two squares: it is the very hue or shade of the colour itself i.e. the visual experience, the very sight of the squares. However, the alteration of our experience of the same note or chord in a different context is emphatically not an alteration of the auditory experience — we still experience the exact same pitch, timbre, volume (assuming the latter two are kept constant) — something else, something that isn’t a sound, changes.


Let me say a bit more to isolate this experience for you. This part will require some acquaintance with music. Think about the C Major chord (the notes C, E, G played simultaneously). In the key of C major, this chord is the tonic chord, whereas in the key of F major, it is the dominant chord. The chord sounds the same in both situations, and yet is experienced differently: the appearance of the C major chord in the C major key is experienced (especially at the end of a perfect cadence) with some kind of closure to it or perhaps stability (one struggles to describe such things in words), in the F major key however, the chord is experienced as causing some tension or as generating anticipation. However, especially if you have perfect pitch, you will be able to tell that they are the same old notes.

Consider a different example: the experience of melodic intervals. (This relates more to the context dependence in the experience of specific notes rather than chords). In the key of B major, the notes B and D# are described as in the interval of a major third, whereas in the key of C minor, the same notes, B and Eb (enharmonic of D#, i.e. the same note on the keyboard or whatever) are described as in the interval of a diminished 4th. Few actually know that the change in the description of the intervals are really to mark a change in function. The interval in the context of B major will sound pleasant, whereas the very same interval in the context of C minor will sound gaping and jarring. If you don’t believe me, try it out yourself: play a B major scale (five sharps in case you forgot) and then play B followed by D# and then play a C minor scale (three flats) followed by the same notes. (cf. Beethoven’s last sonata, first movement, where I got the example from). [Alternatively, play the example below. The relevant notes are the last two notes of each phrase, the rest help to set the context, B major first and then C minor] Notice that the two notes sound the same, you should be able to recognise this if you follow the example, but at the same time they are experienced very differently.


Function as the Experience of Live Possibilities

Hopefully I have helped you to locate what exactly I mean by the experience of function and have convinced you that it is not heard (it does not correspond to auditory experience, since the notes or chords are heard as having the same pitch etc.) but somehow experienced. What then is this experience? Here is my suggestion as to what that experience is: the experience of function is in some sense the experience of a set of live possibilities.

What do I mean by live possibilities here? Let me take a step back and talk about live possibilities in general. [The thought here is drawn from McCulloch’s Using Sartre pp. 35-36 though with some modification.] What does it mean to say that some x is possible? There are many senses of possibility at play. Of the broadest scope is perhaps logical possibility, where some x is logically possible as long as it is not a contradiction. And so consider the scenario where I will soon be suddenly transported to the moon and find that there is a nice summer resort there — the scenario is fantastic, but there is nothing logically inconsistent with this scenario, it is logically possible. There is also epistemic possibility, where some scenario x is epistemically possible if it is consistent with what I currently know — the above scenario would be epistemically impossible in this case. But neither of these are relevant here, what we want is live possibility. But what is it for some possibility x to be a live possibility? It is hard to describe, but that possibility x must be a salient possibility for me. This is not the same as epistemic possibility — there could be a range of possibilities that are consistent with what I know but only a number of them could be salient to me. For example, say I wake up one day and find that my parents are not in their room. It may well be consistent with what I know, after considering all the evidence I have, that they may have been kidnaped, but this is not a possibility salient to me. What is salient is the possibility that they left early and are already out etc. This is a live possibility for me.

What determines what the live possibilities are? Perhaps desire or expectation or something else, whatever makes those possibilities salient. What about our musical case? Here I suggest that the salient possibilities are in fact determined by its musical context, namely its pitch-centre and mode, i.e. its key. Each key has a formal structure (the rules of harmony) that mark out the permissible moves that are available after each note or chord, the harmony can only resolve in certain ways and only certain notes are made available. Of course, this formal structure is often subverted, but even in its subversion the very structure is still presupposed. My proposal is thus that what one experiences when one experiences function is in some sense the spectre of live possibilities as governed by the rules of harmony.

Our exploration might still feel somewhat incomplete at the stage. Given that the experience of function is the experience of live possibilities as governed by a set of rules, the rules of harmony, further questions arise. How do these rules make the possibilities salient to us? What exactly are these rules: are they merely formal constructs or are they somehow natural or innate? I think these two questions are related, in a subsequent post, I provide some speculation regarding these questions and try to extend it to other areas of thought.

The Commensurability of Incommensurable Sensations

[This is a fun post because I want to write down something I found philosophically interesting]

In this essay, I want to show that time is the reason why certain sensations which are incommensurable appear commensurable in some way to us.

I started thinking about this when my girlfriend mentioned to me that the tea which she got tasted sharper than usual. Wait a minute, sharp is a term referring to a physical quality corresponding to our sense of touch. Whereas the quality she was picking up was a quality of taste. The two sensations are clearly incommensurable – yet, something didn’t feel right. It is possible that the word ‘sharp’ might just be used incidentally to describe these two qualities which had nothing to do with each other, but intuitively the two ‘sharp’ sensations had something in common, they appeared commensurable in some sense. One possible linguistic program that could be undertaken to strengthen this is to do a survey to see if the word ‘sharp’ in various other languages are used to describe both the taste of sharpness as well as the touch sensation of sharpness — this seems to be the case for mandarin, we describe certain foods as 尖. (at least I think we do, my mandarin is quite bad and this could just be a singaporean thing where we use a literal translation of another language in our vocabulary to stand for the thing in the original language)

How do we make sense of this apparent commensurability? There is another sensory realm where such physical or ‘touch’ descriptions also frequently apply. This is when we describe auditory sensations, or sounds. I just pick one example which I think will illuminate how a relationship with time connects two sensations that are incommensurable. Sometimes music can be described as broad, the Italian term Allargando is often used for this direction. Broadness, however, is clearly a physical conception and has nothing to do with sound at all. The reason the two are connected is because we usually have a spatial conception of time. We conceive of the music as stretched out across temporal space (note the spatial metaphor already) and we imagine rhythm as a series of patterns in that stretched out space. The rhythm is broad when the interval between each imagined pattern becomes larger. This allows us to connect and use the term ‘broad’ for both the auditory and spatial sensation. This usage is not incidental, but there is a real connection between the two.

Applying this to the case of ‘sharp’ we see that something similar is going on as well. The touch sensation ‘sharp’ is usually a burst of (painful) sensation i.e. a substantial quantity of sensation over a short time. Similarly the tastes that we describe as sharp are also the result of a burst of taste, again a substantial quantity of sensation over a short time. It is the connection to time that connects these two qualities in our head and allows as to call them by the same name ‘sharp’. My guess is that when we consider other qualities that appear incommensurable but have some kind of connection that is revealed by our linguistic usage, some sort of temporal connection is also present. As Kant noted, time is one of the forms of our sensibility and structures all of our experience including phenomenologically diverse and incommensurable ones, and yet by being the one form that binds them all, it also links them all and allows us to compare them. As indeed we do through our linguistic usage of certain words for multiple sense modalities.