One Little Explorer

My exploration of music.

Category: Music

The Mirage of Talent and How to Overcome It.

Pierre-Auguste Renoir - The Swing

Pierre-Auguste Renoir – The Swing

One of the most frustrating things that I regularly encounter is clearly intelligent people demeaning themselves. One of the most tragic is seeing clearly intelligent children told they are not good at something. In The Geography of Thought Richard Nesbit highlights the particularly western perception that people have certain fixed attributes and competencies whether they be sociability, musicality, writing ability, mathematics or any number of other things. This is for the most part just wrong. Many fail to appreciate the degree to which people able to change themselves; our personalities and aptitudes are constantly developing. Once we acknowledge that we are inherently changeable we are able to see that what is more important than talent is just plain work. No one wakes up one day able to play piano, solve differential calculus equations or paint, or write poetry. People are able to do these things because they devote a huge amount of time and effort to them. It’s horrendously unfair to attribute these achievements merely to talent.

As someone with eclectic interests, a principle that I live my life by is that with some effort I can generally achieve a reasonable degree of proficiency in most things. This is how, after struggling through mathematics in high school and generally considering myself of at best average ability, I was able to complete two university courses in pure mathematics with relative success.

So what turned things around? I think I owe a large part of my success to my father’s ceaseless, to the point of being infuriating, insistence that I was good at maths despite my bad results in school. At the time I thought of a number of reasons why he would say this. Principally I thought he was just assuming that because he was good at maths that I would be too. Whatever the reason, he said it enough that even though I achieved mediocre results in school I eventually believed him.

In addition to giving me the confidence to attempt mathematics at a later stage this forced me to locate the reason for my poor results somewhere other than an innate lack of talent. And there was only one thing to blame, really. I was lazy. From then on I had the belief that I was probably okay at maths as long as I applied myself.  Still I held this belief for almost two years before I did anything about it.

A semester before I started studying mathematics again I took a course in introductory logic under the philosophy department. It was a difficult course but I assumed that I would do well because I “knew” I was good at philosophy. As it turned out, I did excel, but at the same time I realised that what I was doing was essentially mathematics. And I loved it. The surprise of finding hidden contradictions and unexpected but irrefutable conclusions from seemingly innocuous premises was intoxicating. I realised this by approaching the subject with confidence and positive belief. This is what finally prompted me to take up mathematics for the first time since high school.

Now I don’t want to give the impression that it was smooth sailing from there on out, because it certainly wasn’t. I wasn’t able to pick a course out of nowhere, in a field that was for the most part foreign to me, and succeed just because I was “clever”. Truth be told the first course I took in Discrete mathematics (not discreet) was worth 3 out of 24 credit points for the semester and it probably took up about half of my time. I remember spending a disproportionately large number of hours on an assignment that was only worth 5% of my total mark for the course only to get 2/5 for it. That was definitely discouraging but I found consolation in the fact that I had lost one mark out of sheer carelessness (I had erroneously written in my last line of working that 2^8 equals 64) and I persevered to pass the course comfortably.

Even now I don’t see myself as particularly exceptional in mathematics but I’m also aware that the people I am comparing myself to have spent an inordinately greater amount of time and effort on the subject than I have. Two semesters at university is really not that much. Nevertheless this was a life changing experience, I had turned what I considered a great weakness into a strength, and now I’m able to help others achieve the same thing.

The benefits of this experience reach far beyond proficiency in mathematics. Since then I’ve never limited myself to anything. Just this year I’ve taken up piano and learning German, both of which I am now competent in to a degree that I honestly never expected. Learning a foreign language especially was something that I had given up on in high school after lacklustre experiences in German and Japanese (which were mostly my fault).

Having said all this, I do not wish to imply that a struggling student struggles simply because she does not try hard enough. Effort directed towards the wrong area is practically useless. Often it is harder to determine where and how effort should be applied than to spend hours aimlessly slaving over a text-book. The point is that for the majority of students a lack of talent is not what is holding them back, and the more that they believe that it is, the more they allow themselves to be lazy. But this is a good thing! It’s easy to address. Hard work and a positive attitude may seem like tired advice to give but it is inevitably overlooked.

I also don’t want to lead anyone to believe that it is necessary to set ones goals at the same level as I do. I set my goals at the level I do because I know what motivations me. I know that I’m not discouraged by striving for things which I’m unsure of whether I can achieve. But I also know that there are many people for whom this is not the case. Indeed some people are more productive with sequential easily achievable goals. To set a highly challenging goal at the outset would paralyse them. Despite this, what I do want to get across is that most students are capable of far more than they believe or are told, and for this reason they should set their goals accordingly, even if it is just a little higher. If we work towards being fearless of failure, soon it becomes clear that the higher we set our goals, the more we allow ourselves to achieve, regardless of whether we reach our goal or not.

It would be naive to assert that talent doesn’t exist. But by definition, it’s innate and unchangeable, so it’s useless to concern ourselves with it. We are much better of focussing on what we can achieve, which for most of us is a very great deal. Even for those who might be called talented, they didn’t get to where they are by talent alone. Setting challenging goals and positively pursuing them is the best way to become more competent, regardless of talent.

More infomation:

Norman Doidge – The Brain That Changes Itself

Richard Nesbit – The Geography of Thought

Judy Willis – Learning to Love Math


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.

Stop and Hear the Music

José Julio de Souza Pinto – In the Fields

I am currently working on a quite difficult post about how the analysis of music relates to the way in which we hear it. It is taking a lot of time and effort so I thought I should post something small in the meantime. Every now and then even the most scholarly of us need a break from erudition. So I ask you and myself, to reminisce about why we do “it all”, to stop and hear the music:

Und morgen wird die Sonne wieder scheinen
und auf dem Wege, den ich gehen werde,
wird uns, die Glücklichen sie wieder einen
inmitten dieser sonnenatmenden Erde…
und zu dem Strand, dem weiten, wogenblauen,
werden wir still und langsam niedersteigen,
stumm werden wir uns in die Augen schauen,
und auf uns sinkt des Glückes stummes Schweigen…

The Return of the Amateur Musician

Berthe Morisot – Eugene Manet and His Daughter in the Garden

Yesterday I had a long conversation with my friend, also a music student, about music. Specifically we considered the fact that some classically trained performers feel they have the right to an audience. We both agreed that while we desired them to have audiences, it is nonetheless the performers’, and musicians’ in general, responsibility to ensure attendances.

We dismayed the diminishing financial success of concerts and lamented that fewer and fewer people had had the opportunity to experience our art. Which led us to ask, what could musicians do to publicise themselves? It is an often asked question but the answers given are generally short sighted, tending to aim directly at increasing revenue from performances and music sales. There are issues to address in these areas but I don’t think that they are the most important.

I think foremost that an appreciation of music, particularly classical music, is born out of familiarity and education. Few people grow up hearing classical music, so it’s not surprising that as adults they have little interest in attending concerts.

Of those who do experience classical music from a young age many have their first encounter with music through learning an instrument. Unfortunately, many resent it. Why is this? I think it boils down to a lack of empowerment. Some don’t want to play music in the first place leading inevitably to an antagonistic relationship with music, or at least some style of music. Those that are motivated to learn music find that they are often expected to follow lesson structures and practice regimes dictated wholly, or partly, by teachers and parents.

So why is empowerment important? I think that students who feel that they are in control of their experience are more likely to have a continued passion for music. Conversely I think students whose entire experience of music has been outwardly imposed upon them are likely to abandon music as that scaffold of routine and regimentation is inevitably withdrawn.

I think the solution in part is to encourage music making which is spontaneous and self instigated. Most people don’t become professional musicians, so why should music education be geared solely towards this end? Without the pressure to be of or towards elite standard, amateur musicians can enjoy themselves more readily and be less concerned by playing for other people, especially friends and family.

This is ultimately where my friend and I saw a dire need: the return of the amateur musician; where amateur didn’t mean non-skilled but merely non-paid. With more amateur musicianship and more outgoing amateur musicians I think I music culture will begin to recover from what has been over a century of declining audiences.

Finally, I’d love to hear your opinions/observations on this issue. So comment below!

Multidisciplinary Musicology – Science, Philosophy and Subjectivity in Music

Edouard Manet -The Railroad

Since my second year studying music at university I have had it in the back of my mind that I would like to follow some sort of academic career. At that time I had a plethora of interests – I still do – that I could have chosen follow but no single one seemed satisfactory in itself. I didn’t want to be a musicologist, a philosopher, a historian or follow any other academic specialisation. So the thought lay there in the back of my mind as I let my studies be determined solely by whim.

I am now in my third year and only now are my aspirations beginning to coalesce. I’ve been inspired greatly by a number of authors such as Douglas Hofstadter (author of Gödel, Escher, Bach) and Jarrod Diamond (author of Guns, Germs and Steel) who have succeeded in synthesising many usually dispersed fields of academia to create valuable and exciting new insights. Hofstadter combined Mathematics, Physics, Literature, Computer Science and Neuroscience to meditate on the nature of intelligence while Diamond employed Linguistics, Molecular Biology, History and Botany to answer the question  “Why did Europe conquer the rest of the world and not the other way around?” I found both these expositions in the realm of hybrid academia highly engaging and convincing.

After encountering these works I found myself wondering “Why doesn’t this happen more?” Surely there are incredible things to be discovered by challenging academics to interact with each other outside their own and closely related disciplines. I decided, perhaps not surprisingly, that I would like to take an analogous approach to studying music.

While I am not deeply entrenched in the academic culture of musicians, I am in contact with it frequently. My general impression is that musicians are extremely academically introverted, to the point that many performers are reluctant to study harmony and other, as they see them, extraneous subjects. Musicologists are rarely as extreme but, compared to their counterparts in fields such as History, English, Political Economics and to an extent Philosophy (philosophers are also somewhat prone to suffer this blinkered academic vision) they are less inclined to apply the insights and techniques of other fields to their own work.  One caveat, these observations are of course not without exception and I have encountered very interesting work by both musicians working with other disciplines and other scholars enlisting the advice of musicians. Nonetheless, I think that these observations are at least to an extent accurate and certainly enough to prompt a new methodology.

The approach I would like to take to studying music is a multifaceted one. Essentially I would like to incorporate additional, robust methods of analysis drawn from mathematics and the sciences, to compliment, not replace traditional analysis. I think these new types of analysis (new, at least, to the field of musicology. The techniques involved are not extremely advanced.) Will provide increased analytical power, especially, I speculate, when applied to music where the traditional methods of analysis break down, for example in non-tonal and non-western music. Additionally I think working with a better understanding how music affects the listener is of great philosophical and analytical interest. There are also the syntactical and semantic elements of music which have been studied in depth by musicologists but could no less be bolstered by an injection of interdisciplinary steroids. Already I have listed too many possible approaches to take all at once but this is a testament to the number of new syntheses to be made.

I don’t believe that the lack of interest in extending the bounds of musicology is solely due to benign neglect. Indeed I think many musicians do not see music as something to be studied at all. They play music, they hear music, it is beautiful, what else is needed? This reminds me of a fable I vaguely recall in which scientists, or some similarly investigative class of people, destroy something beautiful by the mere act of trying to understand it. Music has long had a connection with the divine and with that association the implication that it is something that cannot be understood by humankind. This view is pervasive today, in countless variations. Of course, religious musicians commonly incorporate music into their faith but even in this increasingly secular society many musicians, and listeners for that matter, who have little or no religious inclination cling to the idea that music is ethereal or divine and separate from the rest of the world just as Plato thought over two thousand years ago manifesting in his famous concept of the ‘Music of the Spheres’. I simply do not believe this. I love music like nothing else, and I take immense pleasure in playing music, and I feel privileged to experience it, but I don’t think that it lies on a higher plane to anything else. It just is. And I think that this is more than enough for it to be. And thus it is by no means untouchable.

If it is enough for music just to be then why study it? Personally, I feel that I enjoy music more the more I understand it; I know others like this and I know some who are not. The more we study music the better we as a society can understand it and enjoy it. Most importantly and understanding and explanation of why music is beautiful (if it is possible) leads to an understanding of why it is important for it to be preserved, fostered and made accessible to everyone. Also if music is studied from a broad spectrum of fields of thought as I have suggested, not only will the process of studying itself encourage us to make exciting discoveries, I am confident that we will learn something profound about ourselves.

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.