some thoughts on an alternative definition of ETs

PROPOSING AN ALTERNATIVE DEFINITION OF EQUAL TEMPERAMENT:

I'd like to propose a different interpretation of the term "equal
temperament", one that's perhaps more in line with contemporary
microtonal practice.

I've always been somewhat of a pantheist when it comes to tuning
systems, and as such I've never felt much of a want to acknowledge a
specific tuning hierarchy. Of course I'm aware that one of the chief
advantages of Just Intonation is its relationship to the human
auditory system. But music is not tuning, and it's my belief that
other contextually relevant factors shouldn't be ignored. For
example, is it not true that our ancient ancestors cut holes in
flutes based not only on how they sounded but also on how well they
fit the hole-cutter's hands? If so, then one only need extrapolate a
bit to realize that it's probably misleading to assume that tuning is
simply a byproduct of human physiology... perhaps blind obedience
intermeshes with context-specific circumstances to produce a multi-
tiered model too nebulous to properly consider? The only sure bet is
that no one can say for sure (even those who do).

It's my personal opinion that the tuning community's use of the term
equal temperament is, generally speaking, an outmoded one. It's the
21st century, and when it comes to tuning systems the only limits are
our technology, our tastes, and our imaginations. But for the moment,
I'll attempt to put aesthetics and ideologies to the side and I'll do
my best to sheath my opinions.

One of the recurrent debates regarding the term equal temperament is
how does one align it with obstinate tunings such as 11, 13 and 20;
equal tunings that are generally used with little regard for whatever
rational tuning they might be said to approximate. In the past I used
the acronym E.D.O. in an attempt to philosophically
differentiate "equidistant divisions of the octave" from the T in ET—
temperament. Unfortunately, as I became interested in more and more
exotic tunings (specifically equal tunings that forego the octave as
their means of periodicity), EDO was not quite generalized enough,
and the augmented alternatives seemed too cumbersome for my tastes...
if nothing else, an acronym should be sexy and somewhat self-
perpetuating!

The solution I'm presently considering came about as a result of
realizing that if one were to bend n-overtone series and n-undertone
series towards each other, then one could arrive at a rational series
that closely approximates the corresponding n-equal temperament:

http://tunesmithy.netfirms.com/japplets/uo_non_oct_scale_tree.htm

So my proposal would simply be to allow the term equal temperament to
encompass the idea that n-equal temperaments are at their most basic
assumption a sort of generalized mean—i.e., temperament—of their
corresponding n-overtone series and n-undertone series.

Hopefully this sort of a paradigm shift could help dislodge ET from
the superannuated confines of 12-tone equal temperament as well as
generalize periodicity as it relates to ETs. And if I could be so
bold as to intentionally reintroduce my personal ideology and
aesthetics into the argument, then it would be my sincere hope that
this process might also place generalized ETs firmly in the
over/under context of series thereby liberating them of years of Just-
centric suspicion.

Tvoj oddany rojko

--- In tuning@yahoogroups.com, "daniel_anthony_stearns"
<daniel_anthony_stearns@y...> wrote:

> It's my personal opinion that the tuning community's use of the
term
> equal temperament is, generally speaking, an outmoded one.

Some of us use et to mean something which has an enforced
consistency, becuase it uses a single "val", or mapping of primes to
steps of the et.

> The solution I'm presently considering came about as a result of
> realizing that if one were to bend n-overtone series and n-
undertone
> series towards each other, then one could arrive at a rational
series
> that closely approximates the corresponding n-equal temperament:
>
> http://tunesmithy.netfirms.com/japplets/uo_non_oct_scale_tree.htm
>
> So my proposal would simply be to allow the term equal temperament
to
> encompass the idea that n-equal temperaments are at their most
basic
> assumption a sort of generalized mean—i.e., temperament—of their
> corresponding n-overtone series and n-undertone series.

I don't know what this means or how to use the web page, but it
sounds interesting. Can you expand on it?

This is pretty straightforward:
http://tunesmithy.netfirms.com/japplets/uo.htm

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "daniel_anthony_stearns"
> <daniel_anthony_stearns@y...> wrote:
>
> > It's my personal opinion that the tuning community's use of the
> term
> > equal temperament is, generally speaking, an outmoded one.
>
> Some of us use et to mean something which has an enforced
> consistency, becuase it uses a single "val", or mapping of primes
to
> steps of the et.
>
> > The solution I'm presently considering came about as a result of
> > realizing that if one were to bend n-overtone series and n-
> undertone
> > series towards each other, then one could arrive at a rational
> series
> > that closely approximates the corresponding n-equal temperament:
> >
> > http://tunesmithy.netfirms.com/japplets/uo_non_oct_scale_tree.htm
> >
> > So my proposal would simply be to allow the term equal
temperament
> to
> > encompass the idea that n-equal temperaments are at their most
> basic
> > assumption a sort of generalized mean—i.e., temperament—of their
> > corresponding n-overtone series and n-undertone series.
>
> I don't know what this means or how to use the web page, but it
> sounds interesting. Can you expand on it?

Actually, this is the link I meant to put up in the first post:
http://tunesmithy.netfirms.com/japplets/uo_non_oct.htm

--- In tuning@yahoogroups.com, "daniel_anthony_stearns"
<daniel_anthony_stearns@y...> wrote:
> This is pretty straightforward:
> http://tunesmithy.netfirms.com/japplets/uo.htm
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "daniel_anthony_stearns"
> > <daniel_anthony_stearns@y...> wrote:
> >
> > > It's my personal opinion that the tuning community's use of the
> > term
> > > equal temperament is, generally speaking, an outmoded one.
> >
> > Some of us use et to mean something which has an enforced
> > consistency, becuase it uses a single "val", or mapping of primes
> to
> > steps of the et.
> >
> > > The solution I'm presently considering came about as a result
of
> > > realizing that if one were to bend n-overtone series and n-
> > undertone
> > > series towards each other, then one could arrive at a rational
> > series
> > > that closely approximates the corresponding n-equal temperament:
> > >
> > >
http://tunesmithy.netfirms.com/japplets/uo_non_oct_scale_tree.htm
> > >
> > > So my proposal would simply be to allow the term equal
> temperament
> > to
> > > encompass the idea that n-equal temperaments are at their most
> > basic
> > > assumption a sort of generalized mean—i.e., temperament—of
their
> > > corresponding n-overtone series and n-undertone series.
> >
> > I don't know what this means or how to use the web page, but it
> > sounds interesting. Can you expand on it?

Gene wrote:
>I don't know what this means or how to use the web page, but it
>sounds interesting. Can you expand on it?

There's another bit of info about Dan's under/over scales in Scala,
under "HELP HARMONIC". If you try the command, you'll get the
idea.

Manuel