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Posted by on Nov 5, 2012 in Background, Just Intonation | 0 comments

Beauty is Truth

It’s probably Keats’ most famous pair of lines:

‘Beauty is truth, truth beauty,—that is all
Ye know on earth, and all ye need to know.’

I believe he’s right on the money. I think that when we experience beauty, it’s because we have seen a little deeper into the nature of things.

This seems especially true of mathematical beauty. I had a college friend who found math exquisitely beautiful. He bought a blackboard for his room, and stayed up until all hours, glorying in the work. Elegance, simplicity (but not too much!),  and beauty are important guidelines to the rightness of a solution or direction of research. A sense of beauty guides the scientist as well as the artist. I’m really familiar with this from my engineering career.

So there is the nugget of my own epiphany:

The beauty of music is the beauty of mathematics, perceived in real time.

We see this in its visual manifestations all the time. The curve of the cables of the Golden Gate Bridge, the pattern of seeds in the sunflower, the rings of Saturn — all clear manifestations of the way the universe works, that can be described by math, and that we find beautiful.

Music presents a pure, distilled form of this: beauty created by small, whole numbers and their relationships to each other.

Next: Notes and Intervals

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Posted by on Nov 4, 2012 in Background, Just Intonation | 0 comments

Pythagoras’ Epiphany

Pythagoras was a Greek philosopher who lived about a century before Athens’ golden age. Some time before 530 BC, he had an epiphany. He had been investigating vibrating strings, and found that when you cut the length of the string in half, the note it makes is an octave higher.

Sound is vibration. When one sound is vibrating twice as fast as another, it still sounds the same in some crucial way. The pitch is higher, or lower, but somehow we perceive it as having the same essential character. A C note, multiplied or divided by two as many times as you like, still sounds like a C.

Here are all eight C’s on the piano. They are different in pitch, but all have the same character. Eight Cs

Pythagoras also found that when you shorten the string to a third of its original length, it vibrates three times as fast. The note this creates is different in character from the C. Today it is called a perfect fifth. If you’re in the key of C (that is, if the full string sounds a C), this note will be a G.

This observation led him to what must have been a terrific epiphany — math, particularly number, is at the heart of all things. I sometimes envy those early Greek thinkers — what joy, to come across something basic for the first time!

But you know, everyone, everywhere, has lived in modern times. A thousand years after Pythagoras, Galileo was the first to find out that the Milky Way is made of stars. Can you imagine how he felt? And we are still on the cutting edge — civilization is in its infancy. Future generations will envy us our discoveries while smiling at their primitiveness. “A keyboard, how quaint!”

Pythagoras’ epiphany still has merit. Cosmologists have imagined many alternate universes, with different basic physical constants and laws, curved space, more dimensions — but it’s pretty tough to imagine a universe without number. I believe the integers — 1, 2, 3 and so on, are the most basic things we know about for sure.

Pythagoras actually founded a religion based on this insight. The inner circle were called the mathematikoi, and they lived a monastic life of study. The order had many rules, including a ban on eating beans. Perhaps they worked in close quarters. They also had a rule against picking something up when you dropped it. Cluttered, close quarters! But they found out a lot about math.

Next: Beauty is Truth

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Posted by on Oct 28, 2012 in Just Intonation, Recordings, The Lattice | 9 comments

Flying Dream on YouTube

This may have been the most intense art project of my life. Some time early in 2012, I got it into my head to create a stop-motion animation of my song Flying Dream, moving in harmonic space. I’ve spent the past five months working like crazy on it. The song is carefully arranged using the lattice of fifths and thirds, sung and played in just intonation, and animated using colored lenses, rice paper and a flashlight.

If it doesn’t play smoothly, don’t hesitate to lower the resolution. It survives scaling well, and the timing is crucial.

This video encompasses almost everything I’ve learned in the past couple of years. I will be writing much more about it. Meanwhile, here are a couple of external links about the basic subjects:

just intonation

lattice (music)

Next: Back Story

 

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Posted by on Oct 28, 2012 in Background, Just Intonation | 0 comments

Untempered Music

For almost two years now, I’ve been exploring the nature of music almost full-time. I threw out everything I knew, started with the most basic thing I could think of, the number 1, the origin of the musical universe, and worked my way from there.

My explorations quickly led to the underpinnings of musical harmony, the natural notes that can be expressed as ratios of small whole numbers. These are the notes people generally played and sang, before twelve-tone equal temperament (12ET) came along. 12ET is a clever tuning system, a collection of 12 notes that are slightly retuned from the natural ones, mathematically fudged so that you can play fixed-pitch instruments in any key, and change keys without retuning.

Before 2011, I’d never seriously questioned those 12 notes. They are “The Notes,” after all. They’re the ones on the piano, and they’re what your guitar tuner tunes to. They’re right, right? Well, not really. In the past two years, I have met and made friends with a whole color palette of new, untempered notes, no two alike, each with its own function and personality. In the process, I’ve discovered new ways of thinking about and visualizing music that have greatly increased my enjoyment of it. I have even made friends with equal temperament again, after a long journey away. This website will tell about the journey. Welcome!

Gary Garrett

Next: Flying Dream on YouTube

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