Friday, February 25, 2022

Counting Music in Circles

Why is Strawberry Fields Forever tuned some place between A and Bb? The story is fairly well-known that John had recorded a slightly slower take in A, and a slightly faster take in Bb. By changing the playback speed of the two clips just a bit (slowing the faster recording and speeding up the slower recording), they ended up being able to use sections from both takes in the final version of the song... in the key of neither A nor Bb, but some place in between.

Was John sensing some connection between the tempo of the song and the root note? Could it be that John already knew how to count music in circles?

In my video The Beatles and the Big Wave I talked about how some songs seem to have everything - from the tempo, to the feel, perhaps even to the key the song is in - all feel perfectly aligned, with the musicians melding together as one. For the times I've personally been lucky enough to play in an ensemble where we all locked together in a Big Wave, there is something a bit mystical, or even something spiritual about that feeling. In Magical Mystery Tour, we saw the Beatles dressed up as wizards in a circle, who Come Together as one to work their magic. If there is only one wave function for the universe, then this coming together is not an illusion but a recognition of an eternal truth - and Schrodinger's lifelong fascination with the connections between the quantum world he was helping to discover and the ancient mystical realm of the Vedanta and the Upanishads makes good sense. It's also why emotions like joy and fear and love move through us all like waves: after all, Schrodinger insisted that "all is waves".

The idea of using our hands to count music in circles occurred to me last month, and I've shown a part of this idea in a few of my most recent YouTube videos. So far I've not been able to find this concept promoted elsewhere, but it certainly seems simple enough: perhaps this is another example of Plato's "anamnesis" - knowledge we are all born knowing, forget as children, then educate ourselves to remember. Please comment if you know where this counting technique has been promoted before.

Most of us, if we're counting along with 4/4 time on our fingers, will hit beat one with our thumb, beat two with our pointer finger, and so on, repeating the pattern with each bar. Next time you're listening to a song, try counting each alternate bar starting with the pinky. This then moves the second beat to your ring finger, so the cycle then repeats starting with the thumb again.

If you do this with both hands starting on the thumb, you end up with a pattern that moves outward in the first four, and inward on the second four. For me, this already starts to make me more aware of the longer structures in the music. It also allows me to visualize that I am describing a circle, where the first four beats move along the top of the circle, and the second four move back to the start along the bottom of the circle. 

 "All is waves", with virtually everything in the universe observing Maxwell's infinitely scalable field equations. Isn't it interesting that all you need to make a wave is a rotating circle? In my video "The Wave and the Circumpunct" I mentioned this idea - the Circumpunct, or "circled dot" has been used through the ages to represent the universe, God, enlightenment, and much more. In my mind this means it could also represent what Max Tegmark called the Ultimate Ensemble, or Gevin Giorbran called the Omniverse, or I've described as the Tenth Dimension in its unobserved state. Thinking of the enfolded whole as a single thing has its uses, but as I've often remarked, it's also a little boring. Add some rotation, and things get much more interesting.

A rotating point on the circumference of a circle creates a sine wave (and the cosine wave, at 90 degrees to what we're seeing here). Faster rotations create higher frequencies, while bigger circles create waves with greater amplitude. In a number of my videos I have superimposed this animation on to the bottom third of my project's rotating helix animation, because this animation could be thought to be representing how rotations in the x, y, and z axis combine to create the 3D world we see around us. And the principle of the Fourier transform tells us that no matter how complex a wave may be, it can be broken down into component parts of sine waves of different amplitude and frequency. Like the sine and cosine, electricity and magnetism are also at right angles to each other, creating the 4D world of spacetime that we are observing. But we still need to add an additional dimension to that to get to Everett's Many Worlds.

In some of my videos I've talked about "the universe as a song": if "all is waves", then the universe we are observing in spacetime is like a recording. The recording is always there, ready to be played, and "before" and "after" the song is really the same thing: Kip Thorne calls it "The Bulk". The Bulk is the "everything else" that our universe is not. In my blog entry "Time in Either Direction" I quoted physicist Sean Carroll writing for Scientific American, in which he said this: "The universe began empty and will end up empty--the appearance of stars and galaxies is a temporary deviation from its usual equilibrium conditions". Thinking of the universe from its beginning to its end as the turning of a wheel through one single revolution, with the start and end at the same position, is a fanciful way of holding this idea in our minds.

Later in the article he adds this: "According to the rules of quantum mechanics, the total number of microstates in a system never changes." The quantum wave function, defined at the fifth dimension using 3D space, 4D time and 5D imaginary time in its calculation, describes these potential microstates. The 4D "world tube" (as Kip Thorne refers to it) of the universe we are observing, represents from its beginning to its end one unique subset of all those possible microstates.  

In the same way, any song represents a unique subset of all the possible ways that waves can be combined to create music. And if we think of a single piece of music as the turning of a big wheel through a single revolution, we end up with the same idea: "before" and "after" the song is a return to the same state, an underlying symmetry where this particular song is not playing. 

From there, we can break our song into its component sections as smaller wheels rotating around the circumference of the big wheel. And each of those can be broken down into even smaller wheels representing phrases, breaths, beats, subdivisions to the beat, vibrato speed, and so on. I have proposed that in some cases we can continue this fractal subdivision even to the root frequency of the song. 

This principal of subdivision down to a root frequency is an extension of a trick I was taught long ago. It's much easier to play at an even tempo if you are mentally subdividing the beat: if you are playing quarter notes at a walking tempo, then just counting 1, 2, 3, 4 is okay, but feeling the pulse of the eighth notes between each of those quarters will tighten up your timing: 1 and 2 and 3 and 4 and. Counting the sixteenths will tend to make your timing even tighter: 1-e-and-a-2-e-and-a-3-e-and-a-4-e-and-a. If everybody is locked together, then a player can mentally subdivide the beat to whatever resolution feels comfortable to them, and often it is the nuances that are introduced by notes that adhere to these much finer resolutions that give a piece of music its unique qualities, its cultural identity, its style. Feeling the faster subdivisions as a "buzz" rather than individual events is where we start to make the transition to pitch from rhythm.

In the 1980s I composed some music in "ten tone equal temperament", or 10-TET (yes, my fascination with "ten" goes back a long way). Some of those pieces also divided the bars into ten beats, and one of my favourites had a lopsided swing feel created by a repeating 3-followed-by-2 pattern. Certainly, there's no reason for us to lock ourselves into 4/4 time and "1-e-and-a-2-e-and-a" as we explore the idea of counting music in circles! Triplets, different swing feels, polyrhythms, and so on are just different ways of dividing up the circumference of a circle, or laying one circle upon another.

I've seen Ringo Starr remark that "Come Together" is his favourite Beatles song. I have an intuitive feeling that this is a song where the key, the tempo, and the groove are all perfectly aligned. Next time you hear that recording, try counting along with it using this two- handed circular counting technique: see if it helps you to feel how Ringo, and everyone else in the band, might have been counting their music in circles.

Enjoy the journey!


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