equal is not well (was: A single notation...)

hi Joel and Joe,

> From: "Joel Rodrigues" <jdrodrigues@Phreaker.net>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, November 26, 2002 5:57 AM
> Subject: [tuning] Re: A single notation system for any tuning
>

>
> Coincidentally, I was about to post a quote from Plato that I
> came across in a paper entitled, 'A MATHEMATICA NOTEBOOK ABOUT
> ANCIENT GREEK MUSIC AND MATHEMATICS', by Luigi Borzacchini and
> Domenico Minunni (Dept. of Mathematics, University of Bari,
> Italy)
>
<http://math.unipa.it/~grim/SiBorzacchini.PDF>
>
>
> 'And Plato shared the opinion of the musicologist Damon that:
> �For a change to a new type of music is something to beware of
> as a hazard of all our
> fortunes. For the modes of music are never disturbed without
> unsettling of the most
> fundamental political and social conventions� (Respublica 424c).'
>
>
> The paper is not without it's flaws though, for one there is the
> cringe-inducing equation of 'well-tempered' with
> 'equal-tempered'.

it's good that you know and point out the difference ...
there are a *lot* of papers in the tuning literature which
make that fallacious equation.

based on my research, it seems to me that in fact it was
standard practice to do so for almost the entire 20th century.

it was only in the late 1980s that most writers on tuning
began using "well-tempered" to refer specifically to the
12-tone irregular circulating temperaments. i believe
(but could be mistaken) that in the German-speaking areas
where these temperaments were popular, they went by the
name of "equal-beating" temperaments ... or at least, i
think some of them did.

-monz

--- In tuning@y..., "monz" <monz@a...> wrote:
>
> i believe
> (but could be mistaken) that in the German-speaking areas
> where these temperaments were popular, they went by the
> name of "equal-beating" temperaments ... or at least, i
> think some of them did.

"equal-beating" refers to a class of temperaments, some of which are
well-tempered, and some of which aren't -- specifically, those which
were tuned by setting certain beat rates equal to one another. for
example, smith's 5/18-comma meantone tuning (well, not exactly, but
at least it approximated 5/18-comma to a ridiculous number of decimal
places) is derived by making the perfect fifth and the major sixth,
constructed above any given pitch, have the same rate of beating.