Dear reader, thank you for visiting the blog, and happy new year! This is an update post, letting you know what I have been up to in the last few months.

**A note about Berlin**

I spent a very enjoyable five weeks in December 2016 to January 2017 visiting Oslo, Munich and Berlin, meeting up with friends, walking around town, enjoyable good food, seeing some concerts, and just in general appreciating being in those cities.

Fortunately I was not in Berlin when the terrorist attack at Breitscheidplatz happened on the evening of 19 December. But being in Germany nonetheless, there was still the feeling of a numbed shock when something hits “too close to home”. This was exactly like the hostage crisis at the Lindt café in Sydney back in December 2014 (in fact, I remember that day I had wanted to go to the library at the Conservatorium of Music, which would have brought me dangerously close to the situation). Returning to Germany: on the evening of 19 December I was enjoying a concert at the Gasteig in Munich, where the violinist Renaud Capuçon performed wonderfully the Mendelssohn Concerto with the Academy of St-Martin-in-the-Fields. After the concert, I turned on my phone to browse the news as I travelled on the U-Bahn, and then immediately learnt of the situation in Berlin. It is difficult to find the right words to say, but I have found something which I believe is appropriate. If you walk around the Mall of Berlin on Leipziger Platz — which is near Potsdamer Platz, where there are remnants of the Berlin wall — you will find gold plaques on the floors with quotes from famous people. One such quote is the following from a speech given by Barack Obama in 2008:

(Image from German Wikipedia). The original English is: “People of the world — look at Berlin, where a wall came down, a continent came together, and history proved that there is no challenge too great for a world that stands as one.” This quote captures quite well one of the many reasons I admire the city of Berlin. A note about the use of language here: I think it’s rather neat that *to stand as one* is encapsulated in the single verb *zusammenstehen*!

**Some notes about composition**

Admittedly I have been lazy in regards to writing music. However, I have recently produced a Christmas-themed composition: the *Intermezzo festivo*, which was performed in a concert at the Vigeland Museum, Oslo, on 8 January this year. You can enjoy a “studio” recording of the piece here (more information in the video description):

After the Rhapsody No. 2 for solo violin, I’ve actually felt a bit stuck when it comes to writing new music. The main problem is that a Rhapsody is a freely-structured piece, which is fine for a solo work. I am sure I could write in a similar style for other instruments, but I am unwilling to proceed this way, as I have ambitions to write works on a larger scale, and also I am in principle against doing the same thing over again just because it is convenient and easy. In particular, I remain firmly focused on my goal to produce a piano trio someday, and although I have made concrete plans for the work and even started sketching some things out, I have yet to find the ‘right’ connections between the ideas floating around in my mind to build the work. In short, the problem is one about structure, form, and how the music progresses.

I am proud of my *Intermezzo, *as it represents something new in my approach, despite being written in a mostly classical harmonic language. I think it is a step in the right direction to solving the problem I have outlined above. I have actively tried to emulate the variation techniques found in the chamber music of Beethoven and Brahms for a while now, but with this new piece I feel that I have begun to grasp the essence of it, rather than merely imitating my favourite pieces. Listen to this excerpt (12:56 to 14:50 in the attached Youtube link) from the second movement of Beethoven’s Op. 127 quartet, for example, to see where I got inspiration for the *poco scherzando* section in my piece (and when you’re done, you might as well listen to the whole of Op. 127, because it’s such a masterpiece). The key idea is that the variations do not adhere to the structure of the theme as the piece progresses. The theme is seen as a flexible entity, perhaps like a piece of soft clay which I am free to mold as I see fit.

As early as the first variation, I start to deviate from the harmonies of the theme, and towards the end, the harmony has a life of its own. What prevents the variations from falling apart completely is the motivic integrity. It may seem trivial, but I am particularly pleased with bars 92-94, where I subtly bring back material from the very opening in order to close* *the greatly expanded variation beginning at bar 73. It is this kind of ‘long-range’ thinking that I need, if I am to write more ambitious works. This is also an example of re-contextualisation and re-harmonisation — the same melodic material is seen in a different light, or can be made to play another role (such as using the opening motif as a closing motif), by using different underlying harmonies. In contrast, my Christmas variations for piano from 2014 sound academic and student-like compared to the *Intermezzo*. While there are some nice figurations in that piece, overall there is nothing interesting structurally, and each variation follows the theme almost exactly in harmony.

**A mathematical remark**

I am quite certain that my studies in mathematics have influenced my approach to writing music. I do not like the idea of using rigid mathematical structures or algorithms to create the piece (call me conservative, but I think music should be developed primarily according to musical processes!), but there are nevertheless interesting and useful analogies. A mathematical concept that has occupied my thoughts frequently during the previous semester is the **group homomorphism** (studied in any introductory algebra course). It is not the place to go into details, but here is a rough idea. A **group** is a set of mathematical objects (numbers, functions, symmetries of a geometrical figure, etc.) equipped with an operation, and some simple rules that describe how to combine elements from the set using that operation. An easy example is the set of integers with the operation of addition. A **homomorphism **between two groups, say G and H, is a **map** (a mathematical rule) that connects the groups while *preserving their structure*. In layman’s terms, this means that performing the group operation of G is “analogous” to performing the group operation of H, and a homomorphism is any rule which can facilitate this “analogy”. Here is an example to aid the intuition. You will probably recall from high school the following rule involving logarithms: log (xy) = log x + log y, where x and y are any positive real numbers. Once again, I won’t go into details, but this can be understood in terms of a homomorphism (in this case, the logarithm function). The important thing to notice is that there is addition on one side, and multiplication on the other. In more complex examples, it could well be the case that a certain operation in a group G is tricky to compute, but a homomorphism between G and another group H could be constructed so that the tricky operation in G becomes “analogous” to an easier operation in H. We can do a lot more than merely computation though! Homomorphisms give us deeper insight into the mathematical objects being studied, and crucially provide a way of studying how they relate to one another. (Note to self: here’s a topic for a future Diversion in Mathematics blogpost…)

Why should this be an attractive idea to a composer? My answer is the term *structure preserving, *which has a natural interpretation in music. The composer can apply elaborate transformations to a particular motif or theme but still retain the same fundamental (musical) structure of that motif. In music as well as in mathematics, there is an essential desire to seek meaningful relationships between apparently different phenomena. This can be achieved via homomorphisms in abstract algebra, and via the principles of variation and motivic development in music composition. I like being able to connect together ideas which may be completely different on the surface, but nonetheless share a common deeper structure. Such transformations may be applied to a single musical phrase (motivic development) or indeed entire sections of a piece (which is what generally happens in variation forms).

**An update regarding focal dystonia**

I purposefully did not take my violin on my recent travels in Norway and Germany. It was the first time I had been overseas without my violin! I must say that it was a welcome change, as I was able to relax and simply have a good time. There is also a psychological factor: every previous trip to Europe I had done was due to performances or professional development courses. As I would inevitably visit concert halls, see concerts, and meet up with musician friends and colleagues, I did not want to be reminded of something I used to do, but could not do now.

Back home, I have begun to practise again, and the improvements are noticeable. Having had time to de-stress and look at the problem with a refreshed mind, the left hand is behaving better and better, and I can actually feel the coordination slowly being restored. Most reassuringly, the *sound *I am able to make has progressed from, well, utterly crap to decent. The left hand is now stable enough so that I can practise vibrato exercises effectively. Overall the results are promising, and I look forward to building upon these developments in my practice.

For string players and teachers living in Australia, I would like to announce that I have contributed a short article for Stringendo magazine, which will appear in the April issue. If you have already read my posts on focal dystonia on this blog, then you will know most of what I have to say, but the article is much more concise, and I do not ramble about my personal life as much, so it is more useful to students and teachers (which is the whole point).

Finally, here is an inspirational article which was sent to me from my violin teacher Ole Bøhn, about the oboist Alex Klein, who suffered severely from focal dystonia for many years. He has made a stellar comeback, playing once again in the Chicago Symphony Orchestra!

http://www.chicagomag.com/Chicago-Magazine/February-2017/Oboe-Alex-Klein/

As always, thank you for reading. I appreciate all the messages of encouragement I receive via Facebook, and also via the occasional email. I am determined to write more regularly here from now on, as it seems to hold interest for many people, and it will also help to focus and elaborate my thoughts about practising violin, composing music, or doing maths!