Part One, One: Fibonacci and the Bridge-Time Ratio!!
4*60= 240 (seconds)
240 *0.618 = 148.32
convert all back to min and go to 2:28 and bang! There it is! Holeee Mother F-ing OMG!! Fibonacci was a genius! phi landed right at the bridge!! The Golden Ratio is for f-ing real!!
Part Two: Fibonacci: Not so Fast, Smartypants...
2 is also a Fibonacci number, And I often grab my guitar, eager to play the second note in a chord (in honour of Fibonacci and his contribution to music) on either the chromatic or diatonic scale and for some reason, it sounds incredibly dissonant and 'not so perfect' at all! Oh, sorry, was I just supposed to forget about the 2? I thought it was a Fibonacci number and thus 'Golden'! Gee, no one seemed to forget the one or the three or the five or the eight or even the thirteen, which is usually considered bad luck in North America! But what about the 2? Doesn't a great math-metician-musician like Fibonacci want to be associated with the background music from the movie 'JAWS'? No? Oh, I guess great mathematicians only want to be associated with the really perfect and non-dissonant beautiful inspiring music! Well, I guess that's only natural. If you were a smarty-pants mathematician like Fibonacci you'd want to be compared to an artist that's also another smarty-pants like Mozart or DaVinci or someone like that.
Unfortunately, I also tried the corresponding phi formula on something other than your usual verse/chorus basic musical composition and found results more like the dissonant and imperfect Fibonacci 2: on Bohemian Rhapsody (6min*60=360*0.618=222.48/60=3.708 about 3min,40sec) by Queen the phi-calculated 'ideal place for a bridge' landed me smack in the middle of the operatic section in Bohemian Rhapsody, well past the opening 'I see a little silhouetto of a man' and twenty five seconds away from the really cool guitar part. Basically neither here nor there. I also tried the formula on Stairway to Heaven (8 min = 460sec 460*0.618=296.64/60= 4.94 or about 5min) by Led Zeppelin and the phi calculation placed me just after the 'Spring clean for the May Queen' lyrical part of Stairway where it's rumoured that if you play it backwards, it contains messages from Satan. Maybe phi switched sides from the Divine to the Devil, but basically it landed in no specific place. So the phi formula works perfectly, so long as the song you choose doesn't happen to be a masterpiece. Either that or some musicians really are worshiping the anti-Christ and therefore using a different set of disturbing and non-divine numbers to write their songs.
The Phi formula of where to put the break or bridge in a song is something thought up/calculated/figured-out by a guy named Gary Ewer, who teaches courses on musical composition. I have never taken his course and I don't know how much of a role that the number phi or the Fibonacci sequence plays in his teaching. But there is no organic numbers-math-magic involved or universality of phi in music. The phi calculation works, not because the golden-ratio is so 'golden' but because most pop songs are structured so similarly. Simply put: In a typical verse-chorus rock or pop song, with three verses, it's not unreasonable to assume that the break, or bridge, if there is any, is about 2/3 of the way through. Whether 0.618(phi) or 0.66(2/3) doesn't really matter because It's usually a difference of less than 2 seconds and I would go ahead and give 2 or 3 seconds leeway on either side. Once you change that basic pop-tune structure, however, phi no longer applies. This isn't because you're playing poor quality music, and it isn't because your music is antithetical to the golden ratio or the mathematical harmony of the universe. Simply put, you've changed the structure of the song to something other than the most typical form. Perhaps you're playing a song that has a longer chord progression, say five-chords instead of four or three, or no specific chorus, or no bridge, or perhaps it's arranged in two or four parts instead of the usual three. Or perhaps, you've made a pact with the Devil...
We at Very Us Mumblings don't mean any offense to the great Fibonacci, but if everything in music was simply a matter of arranging a collection of notes, arrangements and bridges in order to fulfill some sort of divine progression or formula or mathematical aesthetic... music would be boring and predictable, much like listening to pop music all day long. It would all have the same structure and style, and would essentially be like hearing the same song over and over. And for some people, that's good enough. Phi, phi, the golden ratio and the Fibonacci numbers, and the 'spiral' that they represent may be pleasing to the eye or the ear and universally appealing to mathematicians and artists alike, but they are not the 'ideal' way to arrange a song. Given time, effort and creativity, I'm sure that a musician could come up with numerous musical pieces based on Fibonacci numbers or phi, but sometimes great music is about breaking with doctrine and formula. So although you can arrange a song according to Fibonacci numbers doesn't mean that you should.
Part two of this blog-entry might be a little dissonant to the ears of a mathematician, but the number 2 is STILL A FIBONACCI, even if papa no like him a no-more!! And if you really like, you can still do things the Fibonacci-way, but there are many other ways to arrange a song!
Part Three: The Half-Time Shuffle: Math applied to music or Fool in the Rain?
Many people, music-lovers, listeners and even musicians themselves have wondered "Why should I learn or listen to that complex song/rhythm/solo? It's too difficult to understand or learn quickly and once you do, it only sounds as difficult and complex as it is to play." It's a question all musicians must face. How much time do you want to spend on learning something... and is it really worth it for the sound that you achieve at the end?
Well, If any kind of rhythm suggests that complexity doesn't necessarily mean that the music is difficult to listen to, disturbing or unnerving, it's the Half-Time Shuffle!!
A complex rhythm that sounds easygoing, simple and fun. It contains eighth notes, sixteenths, triplets, counteracting ghost notes and one big whole-note. It's kind of a shuffle, but not really. What is it? It's the half-time shuffle, a rhythm used in at least three hit songs by Steely Dan, Toto and Led Zeppelin.
And with all this action going on, you wonder how does it not sound busy and aggressive? How can it sound groovy, lighthearted and easygoing? And all I can answer is that it just does... provided it's done right.
In Led Zeppelin's Fool in the Rain, the half-time shuffle switches to a calypso rhythm and then back again. Drummer Jeff Porcaro changes the bass drum to a Bo Diddley beat In the song "Rosanna" by Toto. With allowance for variation of the use of the bass drum and emphasis of the hi-hat, the Half-Time Shuffle is one of the more challenging and yet popular rhythms that drummers want to learn. Variations of this rhythm have been used in hundreds of other songs, and any drummer would be proud to have the Half-Time Shuffle in his or her repertoire of tricks.
Part Five: "Really Odd" Time Signatures:
A song like 'Schism' is meant to unnerve a person, both its' timing and the musical structure of the song as well as the lyrics and the melody of the vocalist. This song is clearly using odd-timings to throw the listener into a mood of strangeness and disturbance.
The real question, then, for musicians is how 'odd' or complex a time signature is possible before it just sounds too weird or disturbing to listen to? And can these strange timings be used for other stuff? Can you write a love song in an odd time? Can you dance to it? It seems unlikely but not impossible. Certainly not every song in an odd timing is an ominous and morose tune. Money by Pink Floyd, though critical, is not unnerving. So how complex can you get without forcing some weird or strange vibrations upon the listener? Perhaps only Bernard Purdie can help us by coming up with yet another amazingly complex but still up-beat kind of groove.
For release Next Week: The Very Us Mumblings Team have their thinking-caps on and are popping the brain-glucose tablets to get ready for the release of Volume 2 of Math-sicians!! Next time, we leave the subject of Time and the Golden Ratio and enter the world of Coding and Frequencies! Samuel Morse and the great Pythagorus and perhaps we'll even unlock the frequency of the Universe!
Volume 2: Morse, Pythagorus and De-coding The Divine Frequency!