Riot at the Rite (Stravinsky’s The Rite of Spring)

Stravinsky’s masterpiece “The Rite of Spring” may be the most revolutionary piece of orchestral music ever written. It was the year 1913, and the manager of the famous ballet company “Ballets Russes”, Sergei Diaghilev, comissioned a new ballet from a then virtually unknown composer: Igor Stravinsky. This was his third ballet for the Ballets Russes, the first two being “The Firebird” (1910) and “Petrushka” (1911).

The Rite of Spring is about a pagan ritual, in which a virgin girl dances herself to death as a sacrifice to the goddess of Spring. The first thing that strikes us when we listen to this piece is its rawness and its earthiness, unlike any other piece of music ever before or since. Stravinsky perfectly encapsulates the sounds and the textures of primitive creatures and lands, while maintaining an utter and total control of orchestral technique while still being able to innovative musical elements such as new harmonies (plychords, chords composed by 5ths and 4ths, etc.), melodies, instrumentation and rythm. Indeed Stravinsky himself said “I had a dream, a fleeting vision of a pagan rite, in which a young girl dances herself to death”, “I was not guided by any specific (compositional) system. It is what I hear, and I write what I hear”.

Indeed, Stravinsky’s great work sounded so revolutionary and so avant-garde to the general public in 1913 that during its premiere, there was a riot in the concert hall. Fortunately, Stravinsky’s work was quickly acknowledged as a work of genius, and is still regarded as so to this day.

In this example, we can hear the whole string section (violins, violas, cellos and double-basses) playing a polychord (a chord composed of two different chords), composed of an E major chord and an E flat Major chord, and the accents are reinforced by a huge horn section consisting of 8 french horns. This chord is repeated a total of 59 times throughout this section.

Beethoven’s Pastoral Symphony & Nature

We are now going to talk about Beethoven’s 6th symphony, the Pastoral symphony. It is widely regarded as one of the greatest pieces of the orchestral repertoire, and certainly one of the most played.

This was written in 1808, during one of the most difficult periods in Beeythoven’s life. By this time he was completely deaf and had seriously considered suicide. He was saved, however, by his passion for music and for nature, and often enjoyed long walks across the forests in the outskirts of Vienna.

The Pastoral symphony is one of a handful of works by Beethoven containing explicit programatic content, i.e. a piece of music that is intrisically connected to a extra-musical content, and in the example of this particualr movement, it depicts a walk in a forest, which precedes a storm (3rd movement). This depicts a walk across the forest, similar to the walks Beethoven often enjoyed. The first thing that is noticeable about this piece is the smooth, peaceful melody, which ineviatbly transmits the sensation of being surrounded by nature.

 

In the example above, we can hear the imitation of bird sounds: a nightingale, depicted by a flute, a quail, depicted by an oboe, and lastly, a cuckoo, depicted by a clarinet:

In conclusion, Beethoven’s 6th symphony is a perfect example of how music can (and indeed often does) depict the most diverse situations and moods, and can really take us to other places, sometimes unknown.

Superposition of Quantum States and Qubits

In quantum mechanics, the probabilistic replaces the deterministic. This means that, for instance, an electron can’t be in a well defined position. This is due to a small uncertainty regarding its speed and its position, which means that an electron can actually be in two places at once, pop in and out of existence, and teleport instantly from a place to another, amongst other strange phoenomena. We then stop talking about well defined states and enter the realm of probability, and about the superpositions of those same states, which are described in the Schrödinger equations.

In classical computing, an electrical impulse can either and exclusively represent a 0 or a 1, which are differentiated by their respective voltage (low voltage represents a 0, and a high voltage represents a 1). In quantum computing, however, since we can not know the state of a quantum object until we observe it, then what will happen is a superposition of all the possible states. If we attribute, for instance, the spin of an electron to a bit (spin up=1, spin down=0), we can not know its definite spin, and thus a superposition of all possible spins is created. The bit that is generated is called a quantum bit, or a “qubit”.

Let us now compare the computational power of classical computers and of quantum computers: If we take two bits, each one can only have the value of either 0 or 1. The possible combinations are, therefore, 00, 01, 10 and 11. If we take two electrons, since their spin can correspond to both 0 and 1 at the same time, the number of possible combinations is exponentially larger than the number of bits allowed by classical computing. This then implies a far greater computational power than even our best super computers are capable of.

There is, however, a problem with quantum computing: Even though multiple quantum states can coexist, when observed, only one of those states can be shown. What a quantum computer then does is choose the combination of qubits that best fits the goal of the user. For instance, when running a simulation, a quantum computer is capable of testing all the possible combinations at once, but only one of those combinations is showed. This shows us the immense power of quantum computers relative to classical computers which can only test one combination at a time.

Basic Concepts of Quantum Computing

Most phoenomenon we experience in our everyday lives, if not all, are governed by classical mechanics: from astronomical phonemonons, like sunsests or eclypses, to the mechanics of eletrical devices such as a television or a microwave oven. This is due to the fact that we live in a macro-world, and thus, are not aware of the laws that govern the dimensions of the atomic or even of the subatomic: the laws of the quantum world.

A classical computer (like the one you’re most likely reading this article with), works with basis on classical physics. This means that it generates an electrical current, whose voltage defines if that same current represents a 0 or a 1. That impulse is then conducted through a series of logic gates, and throught various combinations of countles impulses, the result is then shown on the display of the computer. We conclude, therefore, that at a physical level, the behaviour of the computer is well defined by electromagnetic phoenomenon, which are thoroughly explained by the Maxwell equations.

In the beginning of the 20th century, however, there was a revolution in physics: the quantum revolution. Through the efforts of people such as Max Planck, Erwin Schrödinger, Werner Heisenber, Niels Bohr, Louis de Broglie and Paul Dirac, we are now aware of some of the rules that govern the quantum world, such as non-localisation, superposition of quantum states, quantum entanglement and quantum fluctuations.

When these laws are applied to computation, we find that we obtain computational power that is exponentially greater than that which classical computing allows. It is how these phoenomenon work and how they can be applied to computation that we are going to explore in this page.

Introduction to this page

This webpage consists of two separate topics: Quantum computing and music (mostly classical). The reason why I chose two topics so far apart is because I am both an engineering student and a classically trained musician, and so I share a passion for both music and science. My posts will, therefore, be related to both topics: some of them regarding quantum computing, some of them regarding classical music.

My main goal with the music related part of my page is to present the “classical” world to the general public, free of any sort of bias there might be torwards classical music, and, if possible to bring people into the wonderful world that is classical music. I will also do brief and simple introductions to music theory so that all of you can capture some nuances and subtleties of some of the pieces I will share with you, otherwise undeteclable.

Overall, I hope you all become drawn into the world of classical music and that you free yourselves of some of the preconceived notions you might have about this genre. But above all, I hope you all have fun.

 

Regarding quantum computing, my main goal is to intruduce people to this concept, for the most part unknwon. However, I also intend to learn something myself, because, as I have said, I’m still a student and there’s a lot about this topic I’m still to discover.

I will introduce the basic concepts of quantum computing as simply as I can, an some of the concepts may be hard to grasp. I also intend to share some breakthroughs there might be in this area, as it’s still quite recent.

Perfect Harmony – Dmitri Shostakovich’s fugue in A major

In this post we’ll be discussing fugue by Shostakovich which consists of nothing but perfect harmony. First of all a fugue is a complicated musical form which we’ll not be talking about today. It may, however, appear in this web page when we discuss form.

  • First of all, what is harmony? Harmony is very simply the superposition of two or more notes together (for example, playing the notes C, E, and G (Do, Mi, Sol) at the same time). Now, in the study of harmony there are two groups: consonances and dissonances. Consonances are usually thought of as notes that sound good when they’re put together, and dissonances are usually thought of as notes that sound bad when put together.

The piece we’re going to be talking about relies only on perfectly consonant harmony, i.e. perfect major and perfect minor chords. Major and minor chords are groups of three notes put together, a third above each other. This means that if we take the diatonic scale: C, D, E, F, G, A, B (american notation) or Do, Re, Mi, Fa, Sol, La, Si  (british notation), in order to obtain a perfect chord, we have to take every other note until we have three notes, and thus a perfect chord. e.g., in order to make a C (Do) major chord, we take Do (C), skip Re (D), Mi (E), skip Fa (F), Sol (G), thus making our perfect chord Do, Mi, Sol (C, E, G). For Mi (E) minor, we start with Mi (E), skip Fa (F), Sol (G), skip La (A), Si (B), thus making our perfect chord Mi, Sol, Si (E, G, B). We will not be discussing the difference between major and minor chords.

 

  • Dmitri Shostakovich (1906-1975) was one of the leading figures of 2oth century music worldwide.  Living under the crushing dictatorial regime of Stalin, his music is notorious for its immense use of dissonance in order to represent the agony and oppression he felt on a daily basis (listen to his Symphonies nºs 5 and 10 and his string quartets nº8 and 15). In this piece, however, he makes use only of perfect consonance. The reason why is virtually unknown, although, in my opinion, it’s a symbol of hope, as if the consonance here represents a beacon of light in the middle of darkness.