{"id":483,"date":"2018-09-22T13:38:05","date_gmt":"2018-09-22T13:38:05","guid":{"rendered":"http:\/\/andrew-may.com\/blog\/?p=483"},"modified":"2018-09-22T13:38:05","modified_gmt":"2018-09-22T13:38:05","slug":"algorithmic-beatles","status":"publish","type":"post","link":"https:\/\/andrew-may.com\/blog\/2018\/09\/algorithmic-beatles\/","title":{"rendered":"Algorithmic Beatles"},"content":{"rendered":"

\"Markov<\/a><\/p>\n

When Eric Morecambe mangled Grieg\u2019s Piano Concerto on a TV special in 1971, he insisted he was \u201cplaying all the right notes, but not necessarily in the right order\u201d. That\u2019s a valid point, because there aren\u2019t that many different notes on a piano and the only thing that distinguishes one tune from another is the order in which you play them.<\/p>\n

To a mathematician or computer programmer the situation is crying out for quantitative analysis. The diagram above shows the \u201ctransition matrix\u201d for one specific Beatles tune (using the MIDI standard where middle C is C5). It\u2019s clear there\u2019s a lot of order here. One thing that jumps out is that there\u2019s only one \u201cblack\u201d note, G#5, and it\u2019s always followed by A5. In fact A5 is a very popular note, cropping up after no fewer than 8 different pitches. On the other hand, G#5 itself is very rare, only ever coming after D6, and then only 6% of the time.<\/p>\n

As well as analysing the original tune, this allows us to write a new tune of our own using the same transition matrix. The result (as the aforementioned mathematicians and computer programmers will recognize) is a first-order Markov chain. Producing an algorithm of this type from scratch would be rather tedious (as indeed the initial analysis would be), but fortunately there\u2019s some free software called OpenMusic<\/a> which includes built-in Markov functions that make the process much simpler.<\/p>\n

Of course, there\u2019s more to a tune than the pitch of the notes \u2013 there\u2019s the duration of a note too. But that can be analysed and reproduced by exactly the same method. I experimented with an algorithmic composition of my own, based on the Beatles song analysed above. As a first step, I used the OpenMusic Markov functions to generate a series of tune-fragments for both the \u201cright hand\u201d and \u201cleft hand\u201d of the piano. Then, to give the composition some structure, I arranged the fragments in a rough approximation to classical sonata form.<\/p>\n

I won\u2019t say what the original song was, because I want to see if anyone can guess it. As a hint, I\u2019ve inserted a brief quotation from the original at the mid-point of the piece. Here it is on YouTube:<\/p>\n