This present project and my last CD, the three sonatas, could hardly be more contrasted. The sonatas were large scale works, No. 8 lasting almost an hour, whereas Entangled States is comprised of 48 short pieces. 12 are in Middle Order and High Order format. Two realisations of each of these is planned. There are 24 Low Order pieces. If you require clarification regarding my non-prescriptive techniques please go to the introduction to the blog where you will find an explanation.

Why short pieces? Over the years I have gained an increasing respect, tantamount to awe, when, by reading science, I stumble upon simple, elegant mathematical equations which are the distillations of so much innovative thinking and experimentation by hugely intelligent scientists and mathematicians. Some of these are pinned upon my studio door – Einstein, Dirac, Euler, Mandelbrot. I always find them to be quite inspirational.

For quite some time, years, I have had an idea percolating that I might attempt in my own field to emulate this process of distillation however badly. And again, as you saw in my last post, you might recognise links between my interest in science and music. Cosmology with large scale sonatas, quantum science with very short pieces, most lasting barely 2 minutes.

I have previously written many short pieces, most of them having been given away or carelessly lost, misplaced, but never have I written so many, so exclusively with such intensity and focus, and with such a strict self-imposed discipline. Each piece must of necessity be concise. Every note, every phrase must be there for a purpose. An immediacy has to be established. There has to be a clarity of ideas and a clarity of the expression of those ideas. There is an intriguing creative self-imposed limitation in the presentation, a sparseness, almost a brutality in these acts of reductivism. Writing the short pieces ultimately became the art of omission. This is quite the opposite of enjoying the luxury of being able to develop, to discuss and evolve ideas at great length as I did in the sonatas. More than anything I relish the opportunity of being able to extend an initial motif, seeing where this takes me, how many different facets of its character I can discover, giving it the time to reveal its secrets to me.

Also pinned to my laboratory door is a quote from a book entitled “Quantum – A Guide for the Perplexed” by Jim Khalili. He states “The quest for the ultimate truths is always a quest for beauty and simplicity” I agree so completely with that, Jim, and that statement in itself is an example of complexity of thought simply and beautifully expressed.

Unlike “Set for Piano” which was structured tonally, there being a slow graduation from Low Order (predominantly tonal) to High Order (atonal) formats, I have decided not to present the 48 short pieces in any predetermined specific sequence. This ordering becomes one of the responsibilities of the performer. Bear in mind that one of the principles of my non-prescriptive philosophy is to reduce the presence of the composer as one who fixes the parameters. Another is to abnegate, relinquish ownership of the scores once these are in the possession of the performer

The collisions, the juxtapositions, the resulting kaleidoscope made by the contrasting pieces is intended to set up tensions and dynamics when heard in the context of the overall performance. To what extent this will occur is a variable, being totally dependent on both the ordering of the scores by the performer and the manner in which the realisations are articulated.

A date for the recording has been set but more of this in my next post.

on August 30, 2016 at 5:45 pm |Dave CrozierEric,

I think your analogy to mathematical theory is quite apt in that there is so much synergy between maths and music on so many levels.

My background is in maths both at school and university leading on to a long career in computing and I still, to this day, marvel about some of the “proofs of theorem” that are so simple in execution yet so difficult to grasp in concept. As a simple example, take for instance, the proving of a factorial theorem where you generate a formula to add up the product of all the numbers between 1 and ‘n’. The solution of summing a divergent series was well know to the Pythagoreans in the 6th century BC and the numbers are known as triangular numbers:

See:

https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF

for a more visual representation.

The answer is (n*(n+1))/2 which almost any schoolboy will give you as an answer but how many know that there are many, many ways to come to the end result, just as there are many, many ways to come to the end performance in music.

How magical that the solution to the problem becomes instantly obvious once the numbers to be added together in the sequence are shown in a different form i.e instead of depicting 5! as 5*4*3*2*1 we realise that factorial (n+1) is simply factorial (n)* (n+1) where n is greater than 0 and factorial 1 ALWAYS equals 1.

See:

https://en.wikipedia.org/wiki/Factorial

We can now redefine the problem as a triangle for each group of numbers (1+2+3+4) increasing in height, just like a pyramid in fact and similar in some ways to musical notation!! Music and maths definitely do have a special synergy in that the saying “simple is beautiful” was never so true. I leave it to the reader to work out the derivation of the end equation, just as the performer will do with a musical piece.

One other solution used to prove a theorem is using what is known as mathematical induction by which we:

1. Show something works the first time.

2. Assume it works for this time.

3. Show it will work for the next time.

4. Conclude that it works all the time (within certain pre-defined constraints).

Once the mathematical equations are established, there are a multitude of methods that can be used to confirm a formula by looking at the problem from different perspectives, similar to the musician interpreting a work. Many solutions, but one end result – once again as in musical composition.

Maybe you should incorporate these steps to your musical thinking/strategy a little more as I do believe that the concept fits in with your overall objectives, especially any future short pieces.

We always think of beauty in maths as being the simplicity and simplification of difficult concepts. The initial proof of the theorem (musical composition) is invariably difficult whereas the replication of further proofs (musical performance) once the goal has been well defined normally tends to be somewhat easier as well as providing a voyage of discovery to the listener. Composition or “Getting to the initial result” – is hard graft allied to a modicum of luck sometimes as you have no doubt discovered over the years.

There is however, in my humble opinion, one major difference between mathematics and music in that the mathematics always lead back to a common ground i.e the existence of the formula as opposed to the music which simply evolves as it is subject to outside forces (emotions, feelings, surroundings etc.). However, thinking in a different way about a problem often leads to miraculous discoveries – for the musical equivalent read “performances”. Maybe that is the dividing line between the elevation of music from a science to an art form.

Your own personal “base formula” (Eric’s formula) is undoubedly in your own head and consciousness, leaving the various “proofs” to both the player as well as the listener. The two are not so far adrift and appreciation of the end result can often not be quantified easily in words as I am finding out here, so less of my babble!

Meanwhile, I have now listened to the whole collection a number of times, sometimes enjoying certain compositions on differing levels depending on the listening environment and also my own level of concentration, just as i would do when analysing a good mathematical proof!

Keep up the great work and I look forward to more “proof by induction”.

😉

Dave

on September 7, 2016 at 11:17 am |PeterHi Eric,

I read Dave’s comment with great interest! It is fascinating to consider why we believe things to be the case as opposed to not being the case. At risk of being a bore as usual, I am fond of pointing out that the origin of the phrase “to prove” is in the sense of “to test” – as in “the proof of the pudding is in the eating”.

The potential asymmetries or differences in the proving analogy between music and mathematics do not trouble me much – mainly because I believe that in the ultimate explanation of the universe, time is an illusion. Consequently, the only thing that is “real” is that the composition, its derivation, and its multiple performances are related to one another by the laws of physics, and are consequently much more likely to be experienced. Cause and effect emerge only from the “arrow of time”, which arises (for some as yet unexplained reason) in our human brain.

I believe that the relationship between the encoding and the rendering, is the test, and the only reason we perhaps cannot easily perceive its mechanism is that our human memory of the “future” is so hazy and multi-faceted when compared to our memory of the “past” which is perceived as singular and sharp (even though it actually isn’t) by virtue of being constantly redefined and reinforced in the specious present.

Just as with traditional prescriptive music, all of the potential and actual renderings (performances) are in fact already encoded within the piece, and just as a gene is expressed (or not) in its ecological niche, then an n-p meme is expressed in its informational niche, giving rise to a rich variety of outcomes.

( A wonderful explanation of a timeless understanding of the universe is presented in physicist Dr. Julian Barbour’s book “The End Of Time”.

http://www.amazon.co.uk/dp/0753810204 )