Thursday, 11 February 2016

Fibonacci's Private Fantasy in C major

Oh no, I've dabbled again with those addictive Fibonacci numbers. Get yourself some good wraparound headphones or connect to a decent sound system, crank up the volume, and click the orange play button:

Like my earlier piece Fibonacci's Rabbits, its form and content are based on a musical expression of the number series, in terms of pitch (where the unit is the semitone) and also in terms of time. In the first example below, the unit of time is the 32nd note, and the pitches each rise by the corresponding number of semitones:
Technically, the Fibonacci series can be understood to begin with zero  (viz, 0+1=1, 1+1=2, 1+2=3, 2+3=5, etc), so by rights I ought to have started my music with a very brief silence. But as silence theoretically precedes the beginning of every piece of music (except in supermarkets, of course), I decided that this was just an academic w*nk and no-one except me would notice its shocking absence.

As with 'Fibonacci's Rabbits', the climax of the piece comes at the golden mean - as you'd expect - and I'm sure you'll detect the sudden aggressive change in mood just after the half-way mark at 1' 15". It effectively cleaves the piece into two unequal sections (AB) the B being shorter than the A in the proportion of the golden mean (0.618). To account for this shorter time-span, the underlying bass figure is consequently slightly speeded up in the B section, but still retains its Fibonacci ratios, of course. This B section, besides being announced by the aggressively louder instrumentation, is tempered and made somehow more familiar and 'gentle' by use of the diatonic C-major scale in the upper instruments (the numerical 1st, 2nd, 3rd, 5th, 8th, 13th, and 21st notes of the scale, ie, c d e g c' a'' g'''. This generates an entirely different harmonic feel by comparison with the A section, even though the original Fibonacci-derived bass continues to the end, complete with its naughty G-sharp, and finds itself at odds with the major scale environment. Parallel universes, multiple existences.

Overall, the music is clearly C-centric, ie pivoting around the pitch-class C as the epicentre of its sound universe. Given the pitches in the Natural Overtone Series (closely related to the Fibonacci series), the triad of C-major therefore cannot help but be prominent. But there is that unrepentant G-sharp to spice things up a little and introduce some delightful (and badly-needed) irrationality. Several bars before the climax, there is a somewhat 'brittle and quiet' sounding region where the harmony swings vaguely towards G, the V chord, although it is deliberately ambiguous with that  G-sharp lurking in the bass. This is reminiscent of the old classical 'Development' section, and is even introduced by a subtle V/V applied dominant.  So in fact, the piece is extremely traditional in its overall tripartite XYX form, redolent of the eighteenth-century Enlightenment. Nothing new to see here, Mr Mozart, move along now. But hey, what the hell... listen anyway. You might even like the noise it makes.

Confused? You should be. The form of the piece is deliberately ambiguous, with a 2-section format superimposed over a 3-section format (Note that 2 and 3 themselves are Fibonacci numbers). The 2-part AB aspect derives from the golden mean of Nature, as revealed by the great mathemagician Fibonacci,  and the 3-part XYX aspect derives from Nurture, the artifice of human creation. (Some might argue that the 3-part form should be labelled XYZ, given that the last part is so considerably less chromatic than the first. Whatever, my thesis is still valid:- whatever you want to call them, there are still 3 sections. Making art ambiguous is not yet illegal in Australia - (well, at least not until Snot Morrison's inevitable coup dumping Malcolm Turnbull).

Instrumentation: a variety of synthesizers and handbells, as per Sibelius 7.2 software. This time there is no score - maybe until someone asks for one.

Mrs Fibonacci Baked a Pie.

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