tET vs. EDO (or was that e?...)

Apologies for responding late to this one - I just found
TD 449...

> [Dan Stearns, TD 449.24]
>
>>> [Joe Monzo:]
>>> A side note: those who have looked at my webpage of this
>>> will see that I've changed 'tET' to 'EDO' in every case.
>>> I did that because Woolhouse specifically states that the
>>> 'octave' is always to be a 1:2 ratio.
>>
>> [Paul Erlich:]
>> Seems to me like 'tET' would be better then, since 'tET's
>> always assume a 1:2 octave, at least around here (where we
>> discuss such things as 27.35-tET).
>
> [Dan]
> Just thought that I'd add that I originally started using EDO
> (equally divided octave) because I was personally dissatisfied
> with how the "T" in "ET" was historically and (lacking a better
> term) politically tied to twelve-tone equal temperament (or
> twelve-tone equal temperament specifically, and tempering in
> general)... the "T" in "ET" had a lot of baggage that didn't
> always seem to be a good match for what I was trying to say or
> do... equally divided octave just seemed to me to be a better
> overall fit: more specific, more neutral... and while I tend
> to agree with Paul that it really is pretty clear that "tET's
> always assume a 1:2 octave" (and I use "e" as both a less
> cumbersome abbreviation of EDO and as an assumption of the "O"
> in EDO), I also think that if "27.35-tET" really is supposed
> to be saying a 3/2 divided into 16 equal parts -- or something
> else as specific as that -- then some easy to decipher shorthand
> that says just that would be preferable... perhaps something
> like (2:3 / 16)e, though I really haven't given it a lot of
> thought... I guess I'd say that the ideal (for me) 'equal tag'
> would be one that is flexible (so as to cover exceptions, like
> the octave assumption for instance), specific (so as to bypass
> the accumulation of rounding errors and whatnot), and easy to
> decipher (so it can be quickly memorized and internalized).

While I generally go along with the maxim 'If it ain't broke,
don't fix it', in the case of definitions of terms I really
think there's no excuse for unclearness. Not even the law
of inertia should allow us to continue using a term just
because it's already accepted, when there are much better
solutions.

In this case, I think Dan's argument that ET can mean an
equal division of *any* interval is absolutely a good one,
and the qualification of how many degrees that scale has
still provides no information to an 'outsider' as to what
is the basic interval being divided.

His idea of '(2:3 / 16)e' is basically a good one, one
that I think is far better than 27.35-EDO or 27.35e
(altho that too gives a different perspective on the
tuning).

But if we're going to get *that* cryptic, why not just use
for the name the mathematical notation which provides a
completely lucid description of what's going on?
(3/2)^(16/16). I hereby nominate this kind of notation
to describe any equal-temperament of any interval.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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