matzine

Four weeks to-go until submission deadline for the decidedly-winterly matzine#12 issue!
To help set your minds in rich places we [Seán & Stephen] will offer you a weekly fragment from our own investigations, while at the same time building up to the fast approaching 1st december

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Image : The keyboard of the Enharmonic Harmonium of Bosanquet, constructed around 1876, an instrument for playing 53-notes/intervals per octave! Author of drawing is unknown, though sourced from here.

Ever wondered why the keys on a piano are arranged the way they are? Or why singers jump between notes of a song, rather than sliding between them? In preparation for my submission to matzine#12 I found myself wanting to explore music. And in particular, to understand what a “semi-tone” is, or what the term refers to. Well the above Harmonium described by the diagram above is a musicologists attempt at defining infinitely transposable tonal intervals. Simplified: Robert Bosanquet’s answer was to fit 53 micro-tones in the same space our modern day piano has 12 “semi-tones”.

Image : the Enharmonic Harmonium of Bosanquet. This photograph was found on page 49 of Music and Mathematics: From Pythagoras to fractals

It is thought that tonal harmonies were first discovered amongst humans by our hunter-gatherer ancestors, as they sang during work and rituals. The most rudimentary harmony, that of notes separated by an octave [this is mathematically described as the ratio of the frequencies being 2:1, e.g. 440Hz : 220Hz], would have developed so that men and women of different ages could make their collective sound conform, rather than remain disparate, creating tension. Far fetched, though fascinating all  the same. How much of what-we-now-call harmony/consonance and discord/dissonance is cultural conditioning and how much of it is human instinct?

– Seán