Actually, there is – I’d never noticed it before:
May, the height of spring, is my absolute favorite time of year (not necessarily because I was born in May), and that would be symmetrically balanced by... well, unfortunately November is not one of my favorite times of the year: to be true, it should be October. While I like seeing the structure of trees once the brilliantly colored leaves of October have fallen and now need to be raked, the month of November is a month I can otherwise take or leave.Let’s see, the Golden Section of the year would fall in... Mid-August! And the next dividing point would be – May! Which would be mirrored by – yes, October!
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But I can’t really carry it beyond that, working in February to be the next logical point. Hmmm... so it becomes fairly arbitrary, doesn’t it? Starting the year in January is pretty arbitrary, too, since the man-made calendar we now use (different from the ones the Romans used) has nothing to do with the actual cycle of the seasons or the lunar month, if you determine a month by the rising of the full moon. Is that how Nature marks its months? Certainly nothing in Nature will tell us January 1st is the New Year, but I digress...Yet it’s really no more arbitrary than saying music moves in 8-bar phrases, the standard structural unit of Classical Music. If the 12 notes of the chromatic scale relate to the 12 months of the year, symmetrical patterns develop:
If you choose the mid-point of this series of notes, you’d have two parallel units (1-6 = 7-12) but creating an interval that, since medieval times, has been called “The Devil in Music,” the tritone. Can’t have that!If you follow through with this pattern – comparable to form evolving from multiples of 2: 4+4 = 8 - then a parallel pitch symmetry would be based on dividing the scale in half and then in half again. This gives us C - E-flat (or D-sharp) - F-sharp - A, a diminished 7th chord. We are trained, after how many centuries of traditional diatonic harmony, to hear this as “dissonant” or “unsettled,” a chord that needs to resolve.
If we divide the 12 pitches by taking every 4th note, you would get C - E - G-sharp which is an augmented triad and equally ambiguous in its traditional harmonic function (or lack of it, which is what attracted Debussy to it in the first place).
If we divide the scale according to the Golden Section, we would get C to G which subdivides at E and A. This creates a C Major Triad – aaahhhhh – and A, which could be the pop-style added-6th harmony which is actually not a dissonance (it doesn’t need to resolve) and which also points up the relation of C Major to its logical relative minor, A Minor (different modes sharing the same key signature).
So why not apply the Golden Section to phrase lengths and formal structure, too? Can’t we have 3+2 measure units where an 8-measure phrase that subdivides into 5+3 measure units? Try that in your Theory 101 class and see how far you get.
The traditional tonal scheme of the Classical Era tells us that the logical chord progression is I - IV - V - I – the tonic chord moves to its dominant through the subdominant: in other words, major chords built on C, F and G resolving back to C. That can translate into a key scheme as well: if you’re in C Major, you can most easily modulate to the dominant, G, or (next in importance) to the subdominant F. A C Major symphony could have a second movement in G or F: that was logical. You could also go to the relative minor, A Minor, and that would be okay, too. Not to forget the parallel minor, C Minor and its relative major, E-flat Major. But when Beethoven and Schubert started going to, say, E Major – a “distant” key in the scheme of things – this was considered bold and questions like “can they do that?” were heard across the land...
When theorists began codifying certain rules of music in the 18th Century, symmetry of form was one of the hall-marks of the Classical Era. This would be typical of the Apollonian Mindset, which was disrupted by the messiness of those ‘composing under-the-influence’ when Dionysos, the icon of the Romantic Era, became the leading psychological figure of the 19th Century.
It would be too cut and dried if it actually worked that way, since Mozart could slip in a 10-bar phrase once in a while and be called daring and there are many composers in the 19th Century who were much more classically-oriented than the going approach to then-contemporary music. The best and most creative composers could get beyond these rigid ideas of a system to create music we can appreciate without being conscious of the rules they’re breaking.
Anyway, I was just thinking of patterns and their logic. It amuses me to be building the structure of my musical language on patterns determined by the Golden Section (or the Fibonacci Series) and then turning around and building a ‘tonal’ scheme out of the symmetrical halving of the scale – if I have a tonal center, C, its dominant-relationship would be F-sharp; E-flat and A would be its secondary relationships. So in a way, I’m being just as illogical as the old traditional tonal system of the 18th Century.
The reason I’d done that – again, fairly arbitrarily – focused more on finding some kind of equivalent rather than just being petulant. If it’s the opposite (the antithesis), then I can find some other thesis to create a synthesis.
By applying some of these structural ideas to writing prose, the temptation would be to think too rigidly – all structure seems rigid, anyway. If I were writing poetry, I might look into the idea of balancing the number of syllables – poetic feet – according to the Fibonacci series. At this point, I haven’t really looked at my prose style (such as it is) to see what its natural rhythms and internal designs may be. I know many times I will choose a particular word over another or place, for some reason, a sub-clause here as opposed to there because I find the rhythm more interesting, a little embellishment of a straight-forward clunking rhythm that becomes too predictable.
It’s the balance and forward momentum of the form that intrigues me: Beethoven did it all the time in his music, using shorter and shorter subdivisions as he approached the climax of a phrase or movement. The tempo doesn’t change but our sense of it does: the days, that arbitrary division into 24 hours, aren’t getting shorter, but our perception of it is because the sun sets earlier, now.
In the past couple of days, in between headaches, back-aches and dealing with the hernii – not to mention referee-ing the Cats versus the Kittens – I’ve been applying some of these thoughts to the novel-in-waiting, “Echoes in and out of Time.” In a previous post, I described how I came up with a 100-block grid and mapped out the different segments of the novel’s various “echoes” (the novel is, in fact, a series of echoes). Not wanting to have, like, 100 short chapters, the process now is how to group them into larger units.
Like the structure I’d used for the quartet and the symphony, there will be five “parts” (each the equivalent of a movement) in an overall arch-form: Part One will be balanced by Part Five, and Parts Two and Four will be balanced around the large central Part Three. But rather than dividing the 100 units equally into Five Parts of 20 each, I’ve divided things along Fibonacci lines:
Interestingly, the number of episodes in each Part will be in a Fibonacci relationship with its parallel part (and Part III will equal Parts I + V).From that, the first part becomes a “sonata form,” the equivalent of a traditional symphony or sonata first movement, but divided along similar lines. The “Exposition” is the standard introduction of thematic material – not just the characters, since my two “themes” revolve around the personal life and the various creative issues that define the Narrator.
The five episodes of “Theme 1" introduce the narrator, his mentor, his wife and his parents (this further breaks the episodic structure down fibonacciously to 3 + 2). Theme 2 consists of four episodes focusing on “creative issues” – the narrator’s epiphany when he hears his first piece of music by the composer who will become his teacher and mentor; his wife’s spontaneous approach to being a performer; a new character, the mentor’s stylistic rival at the university where they both teach; climaxing with the narrator’s doubts about his own creative voice (his lack of spontaneity, the dichotomy between his mentor and his mentor’s rival).Having established this inner conflict, the next batch of episodes constitutes a Development Section – kind of a free-form approach, musically – which takes elements of this thematic material and creates something dramatic out of it, ending with a climactic segment about the Writer’s Block that is frustrating the narrator’s life and, he discovers, his mentor’s. (While this divides into 2+2, they’re balanced by the number of words in each episode.)
All of this, Episodes 1-14 so far, takes place in about 24,000 words (maybe 50 pages or so) – because I’d also gone through the whole 100 blocks and figured out, according to the structure, how many words (approximately) would be “allocated” for each episode, keeping things within a certain fibonaccic symmetry but also maintaining the inevitable natural rhythm as it moves toward the end.
But at the moment, we’re trying to see how many kittens can dance on the top of a desk, so I’ll leave it at that for today...
Dr. Dick
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