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Timothy Summers

musical explorations in performance and computation

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# Timothy Summers

musical explorations in performance and computation

## Sitemaps

- [XML Sitemap](https://www.timsummers.org/sitemap.xml): Contains all public & indexable URLs for this website.

## Posts

- [Blog](https://www.timsummers.org/?page_id=1952)
- [naïve backpropagation, laziness and chord roots](https://www.timsummers.org/?p=1861) - The rolling-down-a-hill of backpropagation with gradient descent has proven enormously powerful. The process of identifying chords in a ternary harmony system is curiously similar, though the loss function is far more naïve and transparent. Instead of using derivatives, the algorithm simply derives the smallest earth-moving distance, at bit level. It's rather prosaic. But what this admin Timothy Summers October 22, 2026
- [scale- and chord-building](https://www.timsummers.org/?p=1789) - One advantage of this ternary system is that a lot of the crazy folds and skips of scales and arpeggios – even in quite advanced tonalities – turn out to be pretty simply algorithmic. Here, for example, is what you get when you take every second bit in the F-to-B group of bits, starting on scale- and chord-building
- [ternary harmonic system in color](https://www.timsummers.org/?p=1743) - Up to now, I've been showing these bit-groups in black and white, like a piano. But doesn't do justice to the differences within the 12-bit bandwidth. An octave makes a sort of spectrum. To begin, here is the circle fifths, visible and audible. This serves as a kind of identity matrix, serving specifically to mark Up to now, I've been showing these bit-groups in black and white, like a piano. But doesn't do justice to the differences within the 12-bit bandwidth. An octave makes a sort of spectrum. To begin, here is the circle fifths, visible and audible. This serves as a kind of identity matrix, serving specifically to mark
- [shepard tones](https://www.timsummers.org/?p=1714) - Just as an experiment, here are a few chord progressions given as shepard tones. I was curious to see/hear how they would affect the perception of voice leading. (The intonation is just: powers of 3, sequential.) C Major: ii-V-I C minor ii-V-i: A harmonic minor ii-V-i: It begins to introduce questions of voice leading and
- [chord progressions](https://www.timsummers.org/?p=1710) - A few simple patterns within the ternary harmony system can yield a surprising wealth of familiar diatonic chord progressions with close to zero computational effort. To keep things simple, I'm going to do just one sequence, reachable with only a bit shift operation. All the major/minor folds of thirds fall naturally into the right place.
- [musical harmony as ternary computing](https://www.timsummers.org/?p=1667) - This is a theory, but it works in practise, and yields surprisingly specific and rich musical results.We know that binary numbers represent the presence or absence of powers of
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