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.

'Questa Fanciulla Amor.'.. Francesco Landini's magnificent mediaeval masterpiece

Francesco Landini, composer, musician, and instrument maker.

My latest offering is not my creation at all, but that of superstar Francesco Landini (1325-1397). I've been a flag-waving Landini fan for decades, and in particular of this piece, so I wanted to share it. It's a pity that my computerized rendition uses vocalise instead of real words, but the lyrics are in Italian anyway. The music is disarmingly simple, but the haunting melancholic melody lingers with you after the show. In fact, historical anecdote has it that the original 13th century audiences were so emotionally overcome by this song that 'their hearts burst out of their chests'.

Get some good wrap-around headphones or a decent sound system, and click the orange Play button:



If you would like to follow the 3 pages of the score, here it is, along with the lyrics. Scroll through as the music plays:

   Questa Fanciulla Amor (3-part Ballata by Francesco Landini) by Peter Gore-Symes

The music is categorized as a Ballata, derived from the Italian verb 'ballare', to dance, and is also a form of Italian poetry in the form AbbaAbbaA (my version is but an abbreviated sample). But even though it has its ancestry in dance music, I feel it should not be performed too fast, as many on Youtube like to do. True, many dances have evolved over the centuries - the stately Sarabande, for example, used to be a rollickingly fast folk dance in its early incarnations, as did the Waltz before it became so sylized. In Landini's work, however, the delicious little passing notes in the accompaniment can offer moments of yearning dissonance, yet most performers gallop recklessly over them without giving one's ear the time to savour. Sure, any music can be sped up to become dance music, but in this case that would be to mask the essential melancholy and brooding at the heart of the lyrics. Imagine the Beatles performing their song 'Yesterday' in a fast country rock style.

Instrumentation was not specified in Landini's score, as was often the case in those times. I have chosen viols to accompany the voice, as well as a lute. There was no lute indicated in Landini's score, but it was common practice for a lutenist (or a harpist) to join in, mostly doubling the lines of the viols. It helped the ear to pick out the viols' lines, much in the same way that an artist might etch the edges of objects with a line of black or white. Given the relaxed attitude to instrumentation in Landini's day, it would even be ok to perform the music with lute alone to accompany the voice, but a piano?  Nope - that would cross the red line. Violin/cello can replace the viols in modern performance, but tend to be much brighter and have a stronger 'attack' due to the greater bow-hair tension. Maybe bring out the mute?

I have added musica ficta in the manner of the day. These are accidentals which were not written in Landini's score, but which he knew the performers would insert according to commonly understood practices of the time. Why bother writing them in if you know your performers will do it anyway?  However, those once-common understandings have long since disappeared down the black sinkhole of Time, so in this day and age we the un-tutored are in danger of believing literally in what we see on the music page before us. Oh, the deadly traps for trusting young players of early music.