Kite Giedraitis's thoughts on enharmonic unisons

Here's a sentence you don't see much, with or without the "12edo":

Any 12edo note or interval can be respelled enharmonically by adding a diminished 2nd to it or subtracting one from it.

I may possibly be the first person to say that. I doubt it, but it's possible. Someone might have said it about the diesis, but that's different. The diesis is not a conventional interval with a quality and a degree.

Respelling notes enharmonically is an important skill for a musician to develop. You'd think describing exactly how to do it would be common knowledge. Here's why I think it isn't.

The process of internalizing the structure of 12edo and becoming proficient in its interval arithmetic takes a while. It usually happens as a result of playing a physical instrument, hearing the sounds, and associating them with note names and interval names.

Once you've found your way around the keyboard or fretboard or whatever, and you need to respell a G augmented chord as a B chord, you're not thinking "hmm, G minus a minor 2nd is F#, so G minus a diminished 2nd must be Fx, so the chord's fifth must be Fx". No, because you learned long ago that F# is just below G and a sharp raises you one key or fret or whatever. In other words, years of practice means you can "let your fingers do the thinking".

So why would anyone care about enharmonic unisons? Is it just pointless theory lagging far behind actual practice?

If all one ever plays in is 12do, yes, it's largely useless information. Because first you learn all the major, minor and perfect intervals, and you use them in multiple keys. At some point you learn about the obvious augmented and diminished intervals, the sharp 4, the sharp 5 and the flat 5. Maybe the diminished 7th. By the time you're finally ready to learn about something as esoteric as the diminished 2nd, you've already figured out how the 7 names apply to the 12 notes.

But what if you're a microtonalist? What if you like to explore many different edos and temperaments? What if you want to understand the structure of one without spending a long time playing it on an instrument? Learning the EUs of an edo or temperament can provide a shortcut. Especially since many EUs are not nearly as esoteric as the diminished 2nd. For example, 15edo has a minor 2nd EU.

Another use for EUs is navigating very large edos. Anything larger than what will fit on a lumatone is very difficult to get under your fingers. It may even be too large to picture all the notes between C and D in your mind.

Also, if you're a notation designer, EUs are essential. I absolutely couldn't have written the notation guide for rank-2 pergens without using EUs.

A final use: I have a hunch writers of microtonal software will find edo EUs very useful.