I did an interview for Miranda Sawyer on BBC Radio 6 for her forthcoming series which will include a programme about maths and music. I did a radio series about maths and music for The Essay on BBC Radio 3 some years ago which you can listen to here
That series was mostly concerned with my love of classic music. So I was interested to find out about good examples of maths in popular music. Radiohead, Bjork, Gorillaz all have good examples of interesting time signatures and mixtures of beats which give an unsettling feel of not quite knowing where the beat is. For example: Radiohead 15 Step is in 10/8, Gorollaz 5/4 does what it says on the tin...moves between 5 and 4 beats per bar in an unsettling way, Bjork's Crystalline is in 17/8 (I think Messiaen would have enjoyed that!).
But I was intrigued to know about other examples. So who better to ask than my twitter followers. Below are some of their replies. I thought it worth sticking them here because it's hard sometimes for everyone to see all the interesting responses. It's also worth checking out the wiki entry
which is full of good examples of songs with interesting rhythms and metres.
One of the most striking examples was Tool's Lateralus
which uses the Fibonacci Series via @SalisburyHill Reminded me of my post on fibs
Here are some of the replies I had from twitter:
Jon Saunders @fygaro146 the Birdie Song is based on fractals. However hard you listen it remains just as annoying as it was before.
Paul O'Hagan @pmohagan Golden Brown by Stranglers has that extra beat in the instrumental. Think it goes 6/8 to 7/8 v. effective
MaST@EdgeHill @EdgeHill_MaST @RobertSmyth Golden Brown by Stranglers is in 13/4 time
Richard Hopkins @dadhopdog Golden Brown by the Stranglers is in 3 time but sticks in a 4 beat bar on the 4th bar between verses.
Julian Peace @JulianPeace1 As mentioned, Lateralus by Tool varies from 9/8 - 8/8 - 7/8. 987 being the 16th Fibonaci number.
Julian Peace @JulianPeace1 Lateralus by Tool is worth looking at. It's all rather clever...
Paul Firth @TedInCanada Check out the information online about tool, particularly the album lateralus. fibonnaci rhythms! Tool's Lateralus uses Fibonacci Series via @SalisburyHill@msmirandasawyer Check out http://www.youtube.com/watch?v=wS7CZIJVxFY …and http://findingmoonshine.blogspot.co.uk/2010/07/twitter-fibs.html …
Damian Armitage @iAxiom78 All You Need is Love, by the Beatles swap between 3/4 and 4/4. Some think it's 7/8 but its not
Damian Armitage @iAxiom78 Excuse my language but "Bastard" by Ben Folds mixes it up; 3/2, 3/4, 4/4, 5/4, 6/4 & 7/4.
Stuart @20Hotels Jeff Buckley’s “So Real” moves from 4/4 to 6/8 to 2/4 in space of a few bars. Quite unnerving. Cream “White Room” opens 5/4
Brett Callacher @bcbluesy Jacobs Ladder by Rush alternates 5/4 6/4 and 6/8 7/8. Results in a really ominous feel.
Brett Callacher @bcbluesy also intro: this song was originally done in 1968 but we are going to do it 4/4 so you can clap along.
Geoff Smith @GeoffBath "Strawberry Fields Forever" is all over the shop.
Robert Smyth @RobertSmyth two faves: tessellate by Alt J, and Dodecahedron by Beth Jeans Houghton
Michael Sheen @SheenNotHeard And the overture to Class's Akhnaten uses the same phrase but in 1/4 notes, then 16th notes, then 32 notes
Michael Sheen @SheenNotHeard More popularly, Kashmir by Led Zep: the riff is 3/4 or 6/8, and the drums 4/4. Black Dog is similar.
Michael Sheen @SheenNotHeard Math rock and metal acts like Meshuggah will play a riff in 17/8 etc over a 4/4 drum so the accent shifts
Eddie Rumkee @eddrumkee Penguin Cafe Orchestra's Perpetuum Mobile has 15 beat phrases.
Mike Pitt @mhpitt Serenade by Derek Bourgeois. Cuts from 11/8 (3323) to 13/8 and 7/8 etc. Wedding march for his wife...http://www.windrep.org/Serenade_(Bourgeois) …
Mike Pitt @mhpitt I assume you've got Brubeck on the list...
Leighton Pritchard @widdowquinn Not time sig, but 'phasing' may also be of interest: e.g. http://en.wikipedia.org/wiki/Piano_Phase … and http://en.wikipedia.org/wiki/Clapping_Music …
EP @Phonosexual Conlon Nancarrow even experimented with using irrational and even transcendental musical proportions!
EP @Phonosexual Blackened, by Metallica also goes through a range of time signatures.
EP @Phonosexual Soft Machine also play a lot with time signatures. And Debussy allegedly used measures the length of Fionacci numbers.
EP @Phonosexual Lobachevsky, by Tom Lehrer! Frank Zappa's Little House I Used To Live In also has am interesting time sig.
Tariq Desai @tariqDesai Also, interesting thing about the Gorillaz song is the 20-beat phrasing; 20 being LCM of 5 and 4.
Tariq Desai @tariqDesai Pink Floyd's Money is interesting: 7/4 over melody but 4/4 over the guitar solo; illusion of speeding up.
Tariq Desai @tariqDesai Outkast's Hey Ya features a queer combination of 4/4 and 2/4 bars.
RespectMyCrest @RespectMyCrest @msmirandasawyer money changes sigs as Gilmore couldn't do a solo in original sig, unlike the saxophonist
Dave Brown @youldave http://en.m.wikipedia.org/wiki/Xenochrony
David Gower @Gowerly Skimbleshanks (from cats) starts in 13/8 and Gershwin's Chichester Psalms changes time whenever it wants
hooperdave @hooperdave Wikipedia claims Meheeco by Sky is 8/8 and 7/8. I'm sure they've done one in 3/4 and 4/4 or arguably 15/4
Jon Dickenson @Newtonfrisky Didn't 'Money' by Pink Floyd do 7/8 or 7/4 with 4/4 or something? It does sound a bit odd?!
Peter Jeal @redziller http://www.youtube.com/watch?v=dIuDwESKjZc … Second part (from ~ 7mins) 4s & 3s classic Edgar Froese
Si Prentice @Mr_fermion Under a Glass Moon by Dream Theater, it's all over the show.
John Wilson @JohnWilson14 Try Radiohead's Pyramid Song - 7/8 time or something? - But you mean songs that interchange time sigs?
Laura Fearn @oulaura Some sections of Radiohead's Paranoid Android are in 7/8 timing in contrast to the general 4/4
Steve Skipper @SteveSkipper Nine Inch Nails March of the Pigs http://en.m.wikipedia.org/wiki/March_of_the_Pigs#section_1 … plus @trent_reznor had an interest in maths
Stephen J Henstridge @HenstridgeSJ I think "Money" (Pink Floyd) used a combination of 7/4 & 4/4
Alabaster Crippens @AlabasterC Outkast's Hey ya is probably the biggest pop hit of recent years to be so off kilter.
Alabaster Crippens @AlabasterC Blue Rondo alla Turk, 15 Steps, Money, Hey Ya!, two differently time signatured versions of Morning Bell.
davidjwbailey @davidjwbailey so many: for starters Foo fighters have intros in 7/4, and Genesis messed about with rhythm endlessly
Helen Ferguson @HelenFerguson5 love plus one by Haircut 100. What's the total?
Jane Bromley @jmbromley I like "New Math" composed and sung by Tom Lehrer.
Chris Marshall @oxbow_lakes American Pi: apparently it's 4
Helen Ferguson @HelenFerguson5 Senses Working Overtime by XTC. All together now 1, 2, 3, 4, 5 etc
Mark Fletcher @mdfletcher I am the Walrus: I = he as you = he therefore you = me and we are all together
FrankH @2FrankH Mathematic by Cherry Ghost
Jim Spinner @Vim_Fuego I believe when Queen recorded We Will Rock You @DrBrianMay used delay times that were prime numbers on the intro.
Raymond Vander Metal @MetalJudge Obvious - Karma Police "arrest this man he talks in maths" Radiohead
Matt Foster @matt_j_foster Quasimoto - Microphone Mathematics (which samples De La Soul) or The Pointer Sisters - Pinball Number Count
andy hilton @iamandyhilton The amazing Kate Bush and Pi
Johnny Daukes @jdaukes Violent Femmes 'Add it up...'
Richard Hopkins @dadhopdog I've always loved the five beat rhythm of Take Five or the seven beat rhythm of Sabine-Gould's Gabriel song
Alfred Walker @donawalf Bobby Darin's multiplication.
Dz3k0 @JamesDafydd Calculus rhapsody on youtube.
Jerry Roche @JerryRoche no. 6 on this article might be what you're looking for: http://www.cracked.com/article_18896_10-mind-blowing-easter-eggs-hidden-in-famous-albums.html … #biglink
david kelner @davidkelner The album A Grounding In Numbers by Van Der Graaf Generator has a track called 5533 among other mathematical delights
Jenny Jacoby @pixiecake obviously, three is the magic number. Even with the sums as lyrics I don't remember the three times table.
Cheesy winner Bruno Mars U can count on me like 1 2 3 I'll be there. And I can count on u like 4 3 2 U'll be there
Michael Seaton @mikeo_s Tom Lehrer's New Math and Lovachevsky - arithmetic method vs. results and mathematical plagiarism. :)
Malcolm Chalmers @UrsaMal Jonathan Coulton - Mandelbrot Set. Contains a (slightly adapted) version of the entire formula.
Phil Marsh @Hey_Marshy anything by Joy Division
Justified Left @justified_left Big Audio Dynamite: E=mc2http://www.youtube.com/watch?v=wRyZyrnVsFA …
Paul O'Hagan @pmohagan 2 4 6 8 Motorway. (2 times table for the keen eyed).
Lorna @LornaRedpath Inchworm with Danny Kaye - maths isn't just for the classroom! http://www.youtube.com/watch?v=fXi3bjKowJU …
Joel Tibbitts @TibbittsJoel It has to be Three is the magic number by Bob Dorough.Kate Bush's song Pi about pi is also good.
sam wollaston @samwollaston Hit Me With Your Logarithm Stick by Ian Dury #bbcradio6 #MathsMusic
Robert Smyth @RobertSmyth The whole Bjork's Biophilia album. One is 17/4.
Louise Brown @LouiseBrown definitely @applesinstereo. Robert did a whole episode of Relatively Prime on it @Samuel_Hansen
James Fowkes @fowkc check out Klein four "finite simple group of order two" http://m.youtube.com/watch?v=UTby_e4-Rhg&desktop_uri=%2Fwatch%3Fv%3DUTby_e4-Rhg&gl=GB …
Norman Dunbar @NormanDunbar One and One is One by Medicine Head? I think they got it wrong!
Oliver Prior @InfraredPanda Most time signature changes in a song for some ~(relaxing) Sunday listening: http://www.progarchives.com/forum/forum_posts.asp?TID=69410 …