What is the meaning of ET and EDO, and are they interchangeable?
ET: Equal Temperament
EDO: Equal Divisions of the Octave
In practice, yes they are interchangeable. For example, 12-ET and 12-EDO both refer to the exact same tuning which has 12 equal notes per octave. But there is a slight difference in their meaning.
12-ET suggests that the tuning is a temperament, i.e. it tempers some other interval, usually a just interval. 12-ET tempers 81/80, the syntonic comma, and other intervals.
12-EDO suggests that an octave has been divided into 12 equal parts, but otherwise doesn’t imply that tempering is of importance.
Some people will even say ET for 12-ET, 19-ET and 31-ET, while using EDO for 8-EDO, 13-EDO and others. Perhaps because 8-EDO and 13-EDO are not thought of as temperaments, whereas 12-ET, 19-ET and 31-ET are all useful meantone temperaments.
Personally, I always use EDO in my own thinking and private communication with other microtonalists, but will use TET or ET when I need to be understood by a larger, mixed audience.
To complicate things further, some people use ED2 or ED2/1 synonymously with EDO, because the octave is equal to the ratio 2/1. The good thing about this format is that we can generalise it for other scales that divide some interval into equal parts (e.g. EDphi, ED3/2, ED4). I welcome the move to this kind of generalised terminology that helps us describe more tunings with less words.
The world of xenharmonic jargon is often difficult to navigate. Once you get your head around it, you can forget about the tuning theory politics and remember that the important part is to make inspiring and enjoyable music!
For what it may be worth…
I seem to recall that it was Dan Stearns who coined the term EDO for equal divisions of 2/1, but I’ve long ago adopted ED2, ED3, ED4, etc., to indicate Equal Divisions of N-Harmonic, which serves to cover the continuum beyond the typical 2/1 bounding repeat interval. For example, among the many interesting equal divisions of harmonic 3, the Bohlen-Pierce tuning, is a member of the ED3 family, and specifically ED3-13.
It’s a useful and compact naming convention and is used in the factory microtuning library in the new IVOR2 VSTi for all of the equal divisions of harmonic intervals.
I agree that it’s important to not get mired in the various schools of jargon in this field of artistic endeavor, but it’s often useful to adopt these kinds of broadly applicable terms for easily discussing huge families of microtunings. To each their own though.
Indeed, the first time I heard of EDO was from Dan himself, back on the Xenharmonic ning website. I’m sure he came up with it quite a while before that.
The naming scheme in IVOR2’s microtuning library is very logical, as the tunings nicely group together when sorted alphanumerically. I hope this convention could gain more popularity!
I was thinking of this like EDO means it can be either just intonation or equal temperament, but TET specifies that it is equal temperament. Maybe I’m wrong, but this makes sense to me. I also suggest that 10JI2 could be used to say 10 divisions of an octave with just intonation.