music is math…

Archive for April, 2009

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.


Best of the 80s, anyone?

No, don’t worry!  This isn’t a blog about how we can now fully appreciate the true genius of Duran Duran, thus justifying the recent wave of pointless synth-laden imitations and “cool” t-shirts advertising the fact that one was born in (and therefore probably quite unaware of) the decade in question.

The 80s have understandably left a sour taste in the mouths of music lovers across the world and many a record collection reflects this.  The prolific mainstream rock scene so iconic of the 60s and 70s was giving way to something new.  Almost three decades on and popular music still bears the scars that resulted in the rise of consumerist culture and the valuation of what was fast and shiny over what was personal or meaningful.  I mean, could there have been any X-Factor or American Idol nonsense in the without it?

However, our planet is a mercifully large and diverse one in which it is possible to find all sorts of interesting places and people to whom George Michael’s ‘Faith’ is not considered a relevant or worthy contribution to civilised society.  To many the 80s were just another decade, or even a creative influence, as this list attempts to prove…

1. Paul Simon – Diamonds on the Soles of her Shoes

Taken from the excellent ‘Graceland’, this track demonstrates the album’s fusion of South African and western pop music.  The ensuing controversy over the album promoting apartheid South Africa sets it firmly within the context of the period (that and the liberal use of slapped fretless bass) but actually endures to this day as an example of the quality of African music and the benefits of crossing racial divides.

In terms of pop music and Africa, the 80s is unfortunately remembered more for “Do They Know it’s Christmas?” which, despite raising phenomenal amounts of money, is in reality a completely unlistenable and patronising piece of music.  If they inflict another version of this rubbish on us in the future, I suggest giving a fiver to Oxfam and buying something like ‘Graceland’ instead.

2. The Smiths – There is a Light That Never Goes Out

Civil unrest, Thatcherism and society’s newfound love of hairspray must not exactly have made it a hopeful age for those of a bookish, romantic disposition.  Fortunately, Morrissey and Marr came together in 1982 to produce songs that sum up the frustrations felt by many in dreary, deprived towns in the north of England.

The combination of wry, articulate lyrics and a very British jangly guitar sound was the ideal antidote for a working class alienated by the money grabbing, cocaine fuelled, linen lined excesses of 80s culture.  In this 1986 classic, Morrissey reminds us of the simple, yet fragile, pleasures of love in life against a gritty urban landscape of busy roads and dark underpasses.

3. A Guy Called Gerald – Voodoo Ray

Something a little different now.  The development of house music in 1980s Chicago is one the decade’s most overlooked gifts.  This 1988 acid house classic from English producer Gerald Simpson shows the influence of disco and the true potential of synthesisers.  The electronic era had arrived and dance music would never be the same again.

4. Eric B. & Rakim – I Ain’t No Joke

Part of hip hop’s “golden age”, this duo represent the 80s real musical success story.  The fresh and innovative sound of old school hip hop evolved and from the second half of the decade artists such as Eric B. & Rakim, A Tribe Called Quest and Public Enemy led the way in creating an unforgettable musical era.

This opener to the album ‘Paid in Full’ is vintage “golden age”, cutting up an old soul sample over an 808 breakbeat.  The only other element is some typically boastful (but positive) rhymes and there you have a simple but classic tune, made the way rap music should be.

5. Tenor Saw – Ring the Alarm

Like hip hop in New York, Jamaica continued to produce amazing music with the rise of dancehall.  Electronic instruments began to be incorporated into “riddims” and a new style of “ragga” vocals emerged.  Dancehall stayed true to the soundystem culture of Jamaica as well as drawing on modern global influences to produce a unique and infectious sound. 

As with hip hop, we in the west regrettably overlook Jamaica in our judgement of 80s music too often.  Obviously, the conclusion one comes to is that it can’t all have been that bad then.  The death or decline of several musical icons and the shift in the sound of pop and dance music did the decade no favours.  Every decade has produced obscene amounts of worthless musical contributions but got away with it because it rarely fits into a perceived decline in society in general.

So, the next time someone disrespects the 80s with a grossly generalised statement (as people often do), tell them they are in fact wrong.  Not only that, but to be dismissive of everything the period has to offer is to also be unaware of some truly great music.

P.S. Check out the first of what will hopefully be many Spotify playlists here to listen to all these tunes (and some bonus selections) in one place.  Couldn’t find “Voodoo Ray” on there though.  Damn you Spotify!