# The Center of Math Blog

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## Friday, January 13, 2017

### Friday The 13th, Math and Music.

Friday the 13th is perhaps the single most superstition inducing date. Weather you are from China or Italy where 13 is considered a lucky number, or from America where pop-culture has developed Friday the 13th into a paranoia and horror ridden day. Indeed, Friday the 13th ranks up there with Halloween and Valentines Day (invisible fairies shooting you with magic arrows… no thanks!) as one of the spookiest days you and I will live through.
In the spirit of horror and tingly sensations running down your spine, it is important to appreciate, or at lease inspect one of the most bone-chilling ballads of our time: John Carpenter’s Halloween Theme.

John Carpenter is one of the early experimenters of synthesizers and digital interfaces in music, and this horrifying song features both analogue and digital elements. Surprisingly enough, the reason both elements are so readily accessible to composers like John Carpenter is because of math!
Let’s go way back in time, before computers and before the widespread use of mathematical techniques to calculate approximations of irrational numbers: the year is 1600. At about this time, music theorists are on the verge of normalizing the octave into a neatly partitioned scale; and in ten years Simon Stevin will draft a report postulating the 12th root of two to be the frequency ratio between two semitones. It will be another 20 years after Stevin’s postulate until the French mathematician Marin Mersenne will calculate the 12th root of two (even before logarithms were used for such calculations!), giving the octave a rigorous tuning standard. This development gave professional composers access to an easy system in which they could change keys freely (the Halloween Theme is in the spookiest key of them all: D), as well as allowing music to spread rapidly since tuning an instrument could now be done in a systematic way. All thanks to math!
 The octave split into a nice geometric partition.
Fast-forward to the 1970’s, electronic music is on the rise, but still very decentralized, it will be 1983 when Dave Smith and Chet Wood pioneer a musical instrument digital interface (MIDI) that will allow synthesizers to ‘talk’ to each other (MIDI uses an 8bit format, which increased the resolution of pitch and other sound synthesis parameters {like volume, panning, frequency oscillation} to 128, but I am getting ahead of myself here). Sadly, the year is 1978, and John Carpenter is composing the Halloween theme without the use of MIDI, relying on circuitry (and a fair amount of under-the-surface math) alone to produce chilling electronic sounds.
Because of innovations in math, music broke free of the stigma that only professionals could create pieces; so next time you hear a song on the radio, thank mathematics for those sweet vibrations.