music is math…

Music is Math(s)

“Sometimes music or art can pull back the curtain for you and reveal the Wizard of Oz, so to speak, busy pushing the levers and pressing buttons. That’s what maths is, the wizard.”

– Boards of Canada, 2002 interview

The days of “maths” as I knew it at school are now, thankfully, several years behind me.  The idea of mathematics as numbers on paper is not one that has ever seemed particularly engaging to me but the idea that everything around us is quantifiable in this form certainly is.

The mathematical nature of music is one that too few fans, and artists, think of as a positive and enriching fact.  If someone goes to the length of experimenting with maths in music it implies a level of thought and detail absent in most verse-chorus pop music, although by no means with automatically superior results.

Doing this could be seen as somewhat self-indulgent and “prog”, and rightly so because it really is quite unnecessary when one accepts that every note itself has a pitch or frequency (e.g. A440), every rhythm produces a repetitive pattern (e.g. 4/4).  Music is, by its very nature, a mathematical process in its creation and reception.

Like music, maths has an inexplicable “understanding” behind it that is separate from the raw data but is nonetheless key to appreciating the end product.  Take, for example, a sequence of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

This is the sequence of Fibonacci numbers in which the sum of the two previous figures produces the next number in the pattern.  We only see this as a pattern because of this “understanding” we have, in the same way as we hear melodic patterns instead of unconnected notes of different pitches.

Fibonacci numbers appear frequently in nature, but this is not evidence of any secret code or divine creator, but more likely a result of the related “golden ratio” being an efficient way for plants to have evolved to store seeds etc. (see this and this for a proper explanation).

A bird is as aware of the musical properties of its “song” as a flower or pinecone is of its mathematically significant patterns (i.e. not at all).  And this is the ultimate link between these systems we have devised; that music and maths exist similarly to bring order and meaning to the world around us, just in different ways.

Anyway, enough maths talk.  Here are a few links to songs on Youtube (open in new tab) with a few interesting points to do with maths (sort of)…

1. Boards of Canada – Music is Math

Like many other BoC tracks, Music is Math displays the wide range of external influences which permeate their musical sound, from maths and science to childhood memories (and a lot of dark, dark stuff in between).

The title is a reference to their idea that “anything beautiful in nature or even manmade is only so because it has reached some sort of mathematical completeness, a kind of working equation in the form of tones and rhythms”, as Marcus Eoin put it in a rare interview.  Quite.

2. The Chemical Brothers – Star Guitar

An excellent song by itself, but check out this making of video for a glimpse inside the inscrutable mind of director Michel Gondry.  A mathematical representation of the song acts as the starting point for his eventual jaw-dropping visual production.  Pure (eccentric) genius.

3. Radiohead – Reckoner

There are very few bands who could successfully use the “golden ratio” in their music without smacking of Floyd-esque overindulgence of the highest degree.  That’s right, 61.8% of the way through the album (at 2:49 in this song) something very special happens as the strings enter and the backing vocals change slightly.

Thom Yorke said in an interview that the album’s focal point on which everything else hangs is this very section but has not admitted it was deliberately placed at this point.  On purpose or not, this is the most beautiful moment of a beautiful album.  The vocals emphasise its importance when they (almost inaudibly) change from singing “Oooh” to “In rainbows”.  Whether or not it was the effect Radiohead wanted, it works perfectly.

P.S. Hope that wasn’t too boring, but in many ways I think maths is the key to fully understanding music and why it affects us.  No Spotify playlist this time due to a lack of BoC and In Rainbows.  Credit must go to this page (and the slightly less academic world of Wikipedia) for teaching me more interesting stuff about maths than school did in 14 years.


2 responses

  1. Your post immediately brought to mind a Japanese composer, Ryoji Ikeda, I am a big fan of. He sites as his inspiration mathematicians, not other musicians. He develops music on mathematical principles. Check this link for an interview with Ryoji Ikeda:

    You have a great collection of music in your blog. Looking forward to exploring the Radiohead song.

    You may also be interested in an earlier post I wrote on string theory:

    September 1, 2009 at 5:57 am

  2. Thanks, loving Ryoji Ikeda. Interesting beats and sounds. Good post on string theory too, all that physics stuff is mind-bendingly interesting.

    September 1, 2009 at 4:25 pm

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