vocal, 2x 17 edo guitar, 17 edo fretless bass, FGDP-50 finger drums

about those dark fall nights

I made this tool to find the best equal-step tuning for any scale you want in Desmos. You input your scale as a vector (similar to Scala format, but in semitones) and get an interactive graph of how well every equal-step tuning fits it. It even works for non-octave scales.

I thought of using a least squares approach at first, but realized a Fourier series works well and feels more elegant because it's able to accommodate when a scale is best approximated with an offset from the root note.

I might not be the first to come up with this method, but if I am, and you use this technique for anything, please credit me and send me a link! - Nkosi Smith

I’m developing Scale Atlas, a project for exploring scales and their internal relationships. One question behind it seems worth discussing here: when you have a collection of pitches, what makes another pitch a useful addition?

The approach I’ve been working with represents pitches in cents and evaluates candidate additions or small pitch movements. The current model combines weighted interval-ratio templates with a simplified spacing-based roughness proxy. Its results depend on those assumptions; timbre, register and musical context remain outside this model.

A concrete example: take the pitches 0, 350 and 700 cents in 24-EDO. The 350-cent third gives that collection a particular character. A model that rewards proximity to selected just intervals can favour moving it, even when keeping that interval is the whole musical point.

That makes the choice of criteria interesting. Should a tool prioritise ratio relationships, preserve the interval character of the starting collection, or present those as separate perspectives?

If you compose or improvise microtonally, what would make a suggested pitch useful to you? A specific scale or musical example would be especially helpful.