Threes all the way down
Most popular music comes grouped in powers of two. What if music came in powers of three? Could you dance three-to-the-floor and freestyle 27 bars in nonuplets?
⮕ Listen ⬅
In this music, you’re hearing threes on all scales of the waveform- the timbre, the melody, the harmony, the rhythm, the riffs, and the composition.
How it’s made
People count in base 10.
Your computer uses base 2.
Trinary computers use base 3.
All the calculations in its microprocessor are based on three-valued logic, sometimes represented as (false, maybe, true) or (0, 1, 2). Bits becomes trits, bytes becomes trytes.
Trytebeats
A trytebeat is a program for a trinary (aka ternary) computer that generates music. It’s a function with time as input, amplitude as output. The function mangles time using a bunch of arbitrary tritwise operators, creating all these crazily dense patterns of threes.
The programs are short and beautiful. They could fit in a tweet:
(t*((tθ(((t>>10)+2)%3%2)*2)>>6))&(t&(tθ2)>>5)%81
That’s it. The code seems tiny, yet it blossoms emergent sonic-visual complexity.
I increment t on a loop to generate the waveform, at a sample rate 3402 Hz. The output is a sequence of amplitudes. We can listen to it, or look at it:
I can also visualize these values by mapping each tryte-amplitude value with brightness, and drawing them pixel-by-pixel.
I can then use these as walls of a triangular tunnel
Trippy af. Watch this one animated to the music.
Trytes
Bytes have 256 different states (8 bits). Some implementations of trytes use 27 states (3 trits). I chose to use trytes with 81 states (4 trits) because it seemed to just sound better.
Tritwise Syntax
To make these videos, I needed to build a tritwise operator emulator in python, and it needed a programming syntax.
I learned more about tritwise operators by reading this article.
There are many more possible tritwise operators than bitwise. Some tritwise ops have bitwise cousins that are loosely equivalent (e.g. |, &) and for these I borrowed their symbols. (Fun fact: AND is basically MIN and OR is basically MAX.) I also came up new operators and gave them new symbols in my syntax (e.g. ≡, θ). For example, θ rotates the value of each trit (2 goes to 0, 0 goes to 1, 1 goes to 2).
Ternary vs Trinary
I like saying trinary better. No remorse.
Future Computers?
Trinary chips have special properties. Compared to binary, trinary has a more efficient radix economy.
With the advent of mass-produced binary components for computers, ternary computers have diminished in significance. However, Donald Knuth argues that they will be brought back into development in the future to take advantage of ternary logic’s elegance and efficiency — from Wikipedia
The Soviets used to experiment with computers like these. Maybe you can help me locate one and we can run trytebeats on them natively.
Bytebeats
Bytebeats are the older ancestor of Trytebeats. They are programs of bitwise operators that generate music for typical binary computers. They were popularized by Viznut in 2011 with a series of videos. Today people run Bytebeat competitions and post on /r/bytebeat. You can compose your own using this web tool.
Info For Collectors
If you’re an NFT collector, read on.
Patrons of Dadabots, thank you 🙏 Revenue from auctions funds our scientific research and invention of new forms of music synthesis.
This foundation video series represents the birth of Trytebeats.
First collectors from this series can claim an animated lenticular print of their Trytebeat which will be shipped at no cost. They look like these! Just get in touch. 🥳
This is the second series by Dadabots of generative music NFTs made from tiny programs. The first was Bytebeats on Artblocks, sold out July 2021.
In the future, once we successfully build a real-time trytebeat emulator in javascript for the browser, there will be a followup series (possibly on Artblocks) of interactive NFTs, where people can actually play with the generator. Collectors from this series will be airdropped a free NFT from the followup series (a snapshot will be taken on a particular day). 🎉
Thank You
Hi, we’re Dadabots. We also develop audio synthesis based on neural networks and quantum circuits, and get in trouble for deep fakes.
Stay tuned for more.
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