# Xenharmonic

## Third-Tone Tunings

After a bit of exploration into quarter-tones I thought I'd add to my collection of EDO-based 12-note tunings by exploring third-tones, which split the gap between (say) C and D into three equal parts rather than the usual two. The EDO made entirely of this interval is 18-EDO, which we can think of as three equally-spaced whole-tone scales.

## Semi-Regular Quarter-Tone Scales

In *Manual of Quarter-Tone Harmony*, Wyshnegradsky describes a "semi-regular" scale as a scale that divides the octave into equal parts, then divides each of those in the same way. Quarter tones are very practical on an unmodified guitar (using a slide), at least for melodies, and they can be coaxed out of many other instruments too so this may be a bit more friendly than the 30-EDO stuff I've been playing with over the last year. In this post we explore the 12-note semi-regular scales that form nicely symmetrical ways to impose a subset of 24-EDO onto a standard keyboard.

## Highly Symmetrical 12-Note Scales from 30-EDO

...in which I sift through 1,073,741,824 possibilities to find 12 interesting ones for the good of humanity. Results and some Scala tuning files inside.

## 30-EDO Ideas

Dividing the octave into 30 notes is an interesting proposition in part because 30 has the factors 2, 3 and 5, which means it contains a few smaller EDOs. In particular, it has three copies of 10-EDO that sit inside it like the three augmented triads (3-EDO) in standard tuning, and I've been working a lot with 10-EDO lately. But 30 notes is a lot to deal with, and far too many for me to play on a single keyboard. So in this post I muse about some ways to split 30-EDO up into more manageable parcels.

## All the Pentatonics in 10EDO

In 12EDO, the most interesting scales are (I think) the ones that use about half the notes: 5-, 6- and 7-note scales. In 10EDO, then, it makes sense to look at 5-note scales at least, and perhaps those with 4 and 6 notes. Today we'll look at all the available pentatonics in 10EDO and some relationships between them.

## The Scheerbart Tunings

I'm currently working on a project involving mixing 10-EDO with symmetrical structures in 12-EDO. I thought it might be instructive for me to look at tunings that mix pitches from these two. The project is inspired by visionary modernist Paul Scheerbart so I've decided to call them Scheerbart Tunings. Free synthesizer (sort of) inside!

## Some Chords from 10 EDO

10 EDO divides the octave into ten equal parts instead of the usual twelve. We may as well number these notes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. This is a pretty tuning that doesn't take too much getting used to. Let's create some harmony out of it.

## 9-EDO: Three Augmented Triads in Perfect Symmetry

I've recently acquired a basic synth setup with a view to exploring some non-standard tunings. This is something I've messed with in the past and used for "colour" but never really got deeply into, but that's about to change.