Update post (July 2019)

It seems that every time I return to write something on this blog, it’s about how infrequently I write (and that I’m awfully sorry, and I promise to write more, but it never happens). I see three main reasons for this:

  • I am now in a masters program in the School of Mathematics at the University of Sydney! My honours year went quite well overall, and my supervisor was happy to take me as a postgraduate research student.
  • Since March, I have also been working casually for Matrix Education, a private tutoring company that is well-known in particular for its HSC preparation courses.

From the two reasons listed above, you can appreciate that most of my time is spent doing mathematics in some way — reading articles and learning new theory for my research project, working on exercises from textbooks, or preparing tutorials and classes. The third reason is really a blend of two:

  • My own laziness coupled with a lack of direction about this blog.

This update post will explain this last point further.

calvinhobbes-peck

Continue reading

On the importance of chamber music

On 19 and 20 January, I had the pleasure of teaching at the Zhang Violin Summer School for young violinists (AMEB grade 3 to A.Mus equivalent). This was a 4-day intensive course, where students received training in preparing solo repertoire and chamber music, as well as Dalcroze eurhythmics. I was invited to take chamber music lessons, a task that I gladly accepted. There was quite a wide range of ages: the youngest students were in years 1 and 2, while the eldest ones were senior school students. As a result, there was a similar range of experience in chamber music. Teaching at the summer school has reinforced my belief of the high importance of chamber music in music education, and in this blogpost I would like to share some of my thoughts on the subject.

First of all, I remark that it is a happy coincidence that the summer school was held at Barker College, where I was a former student. It was at Barker that I first experienced playing chamber music — specifically, the string quartet. As it turned out, I played string quartets throughout my entire education at Barker College, and it was one of the most important factors in my development as a musician — not only as a performer, but also as a composer! The main point that I will emphasise is this: playing chamber music makes great demands on the musicians involved, in technical aspects (i.e. the physical part of instrumental playing) as well as conceptual (i.e. intellectual understanding of the music). These demands are quite different from those encountered in solo playing, and furthermore, I will try to argue that chamber music should play a significant role in a student’s musical development.

Continue reading

Composer’s Notebook #7: Variations for wind quintet

This blogpost is a short commentary on my new quintet for winds. Click here for the Youtube video.

The Variations were not my first attempt to write for wind instruments, but it is my first finished work for winds. (I had previously attempted solo pieces for oboe and bassoon, and “sonata”-like pieces for oboe and piano. I did not think any of these could have been successful, and so I have discarded all such fragments). The piece bears the subtitle Small Steps and Giant Leaps, primarily because the foundation of the whole piece is the main theme of John Coltrane’s famous piece Giant Steps. The subtitle also plays on Neil Armstrong’s famous words “One small step for man, one giant leap for mankind.” One could interpret this as representative of the fact that the quintet is my first completed work for winds, and hence it represents an important new step in my compositional development. At the risk of disappointing music analysts, the real reason is much more mundane. I think it is simply a rather cool title. If one has to interpret it, then I can offer the following suggestion: I tend to write melodic lines with large jumps, while the Giant Steps theme heavily features steps of major and minor thirds. It is the combination of these steps and leaps that characterise much of the material in this piece.

On the concept of ‘variation’

If you take a look at my Youtube channel, you will find other attempts at variation form. Perhaps the best one preceding the wind quintet is the Intermezzo festivo for string quartet. However, that piece follows the classical variation form more closely than the wind quintet, at least initially. (The piece transitions into a freer form halfway through). In the quintet, the Giant Steps theme does not appear until the very end of the work. This is in opposition to the classical form, where one hears the theme at the beginning, and then follow the variations. In this sense, even Arnold Schoenberg’s Variations for Orchestra (Op. 31) is classical, although the ways in which he varies the theme are of course more intricate and abstract than what is generally encountered in pre-20th century works. How, then, is my quintet a set of variations? Although the score is divided into sections which may indeed be identified with particular variations, it is not obvious (or at least it is not supposed to be obvious) how they are variations of a theme, which is not explicitly stated until the end anyway. Here, the word ‘variation’ conveys a much more general principle, which I think is similar to the term developing variation, often used in connection with Brahms. Another term I like is thematische Arbeit, or ‘thematic working’, which is often attributed to Joseph Haydn. I think the second term is more flexible, and hence easier to appropriate into a modern context. The general recipe is to start with a basic idea (the simpler the better), and see how much can be generated from it. Then introduce some embellishments, pertubations, variations — this produces a new but related idea. Now consider variations of this second idea, and so on. Of course, this process can happen in a nonlinear way. Moreover, the basic idea need not be a melodic fragment (although this is often a natural choice), but it can be something rather abstract. In my quintet, the basic idea, or Ursatz (a gross misuse of a term from Schenkerian analysis), consists of the following pair of elements:

quintet-ursatz

The chord is comprised of the opening bass notes, while the second element is first five notes of the melody in Giant Steps. Observe that both elements coincidentally contain five notes, which is perfect for a quintet. An important secondary idea is the following voice-leading pattern, also featuring extensively in the melodic line of Giant Steps:

quintet-secondary

These two ideas comprise the essence of my wind quintet. I noted above that my use of the term Ursatz is a gross misrepresentation. In Schenkerian analysis, the Ursatz is supposed to be the fundamental structure of the entire piece — to put it facetiously, this means that “all of classical music is essentially the chord progression I-V-I.” However, in my current compositional process, the basic idea only needs to affect the ‘surface’ of the piece, and it does not necessarily determine the large-scale structure. (Controlloing large-scale structure remains one of my greatest challenges — you will notice that all the pieces I have written so far are quite short). The fact that the elements presented above do affect the large-scale structure of the wind quintet is the reason for the title Variations. These three elements are collectively the ‘theme’ of the composition.

Remarks on the structure

I will offer some comments on the structure of the quintet that may be helpful for both players and listeners. It is easily observed that each variation features one of the instruments of the quintet. The order of appearance is: flute, clarinet, oboe, horn, bassoon. After these five variations, there is a fugal variation, which leads into the coda, where the Giant Steps theme is finally present. The way the variations are organised suggests an embedded multi-movement structure. One possible partition of the piece into movements is as follows:

  • 1st movement: introduction, flute variation, clarinet variation (“Scherzo”)
  • 2nd movement: oboe variation (“Adagio”), horn variation, bassoon variation (“Cadenza”)
  • 3rd movement (Finale): fugue, Giant Steps coda

Notice also that the bassoon “cadenza” recalls material from the introduction (namely, the staggered chord-building entries).

Update post (June 2018)

calvinhobbes-almost-started

Hey, I almost forgot I have a blog! (Since I’m paying for the site hosting, why not make more use of it).

This post will simply be an update, to let the readers of this blog (the number of which is non-zero) know what I am currently doing. It will be a random assortment of thoughts and comments. Right now, I am busy preparing for the semester 1 exams in the Pure Mathematics Honours program at the University of Sydney, but it is nice to take a break from study and write something here. Needless to say, it has been a very challenging semester, but also quite a rewarding one. Mathematics honours students are required to take a total of 6 courses throughout the honours year, as well as prepare a thesis. Many (?) people opt to take 4 of the 6 courses in the first semester, with the intention that more time can be devoted to the preparation of the thesis in second semester. But naturally, this means that one undertakes a lot of coursework in first semester (4 honours level courses at the same time is no joking matter), and as I am prone to procrastination, the time management has been especially challenging. Fortunately, I get along well with my thesis supervisor — who is conveniently also the honours coordinator this year — and he has been understanding and supportive during the periods when I had many assessments to submit and had not worked on the honours project!

Continue reading

Composer’s Notebook #6: Bowing and Articulation in Violin Playing

GENERAL UPDATE:

At the beginning of the year, I promised that I would try to write more regularly. This has clearly not been achieved! In my defence, studying mathematics full-time requires much dedication, patience, and practice — not unlike learning a musical instrument. But now I have time to write since I have completed my semester 1 exams.

(Main article is below)


Continue reading

Diversions in Mathematics #2: Hilbert’s Hotel

In this instalment, I introduce the concept of infinity in a simple and (hopefully) entertaining way, which puts into practice the counting concepts introduced in the previous Diversion. In fact, Hilbert‘s infinite hotel was one of the ‘stories’ that got me seriously interested in mathematics in the first place, and so it is a pleasure to share it here. This is a very well-known piece of story-driven mathematics. I hope that experienced mathematicians who happen to come across this blog do not tire of hearing (reading) it again, and that they see the value in telling the story to the general public.

Just before we start: I assume knowledge of the definitions and notations introduced in the previous instalment, namely, the very basics of set theory.

Continue reading