Re: Keeper of the FAQ: EDO

Joseph Pehrson wrote:

> My understanding is that the difference is like in a court of law...
> and hangs, believe it or not, on the INTENT... (!!) In other words,
> if somebody was looking for APPROXIMATIONS of just intervals, one is
> dealing with a TET. If one INTENTIONALLY wanted a system that divided
> up the octave with NO REGARD for any pure intervals, and wanted the
> resulting sounds, one is dealing with an EDO.
>
> It's pretty much "humbug," isn't it.... I wonder if it should have a
> prominent place in the FAQ, or not at all. Besides, as Dan Stearns
> quickly pointed out, EDO doesn't do too very well for scales that have
> no octaves! (Like Bohlen-Pierce, of course...)

Gary and Joe,

As far as I ever knew, there was never any difference of definition between t-ET and EDO except
that the latter is more explicit.

The usefulness of the term EDO is that it does distinguish Equal Divisions of the Octave from Equal
Divisions of anything else. If the Bohlen-Pierce scale didn't have a formal name, what would you
call it? 13 t-ET? It is, you know. "13 tone equal temperament" could mean steps of virtually any
size at all, depending what IoE (interval of equivalence) was being equally divided 13 times.
Since the octave is by far the most common IoE, the term EDO clarifies the meaning, distinguishing
it from divisions of some other interval, such as the 3:1 of Bohlen-Pierce's 13 ED 3:1. So if a
non-octave IoE is being used for an ET, you simply replace the "O" with it.

Most of the time it's not necessary to be so precise; most of us tend to assume octave equivalence
most of the time. But now and again the subject of non-octave IoEs comes up and then things get
confusing if you don't have some simple way of distinguishing between them. That's why I have
tried to consistently use EDO instead of t-ET any time the context doesn't already make it clear.

BTW, EDO should include stretched octaves, IMO. (That's kind of a funny sentence, isn't it?) Any
interval near enough to 2:1 to be heard, and to function, as an octave should be counted as an
octave for purposes of classifying ETs, right?

and wacth that dang speling and capitalzation, would ya?!! :)

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

--- In tuning@y..., "David J. Finnamore" <daeron@b...> wrote:

/tuning/topicId_19452.html#19452

Thanks, David, for your response concerning the EDO, TET offensive...

Frankly, my impression was not so much that EDO was to be used in a
"clarification" of the octave over the TETs, which is actually an
excellent point you are making, but, rather that a "subjective"
quality was being called into play -- whether the creator of the
scale had a "temperament" in mind rather than just an equal division
of a frequency span...

Anybody else get that impression as well??
_________ _____ ___ _
Joseph Pehrson