need definition of "brat"

Gene or whomever,

can i please get a good, complete definition
(with examples) of "brat", for the Tuning Dictionary?

thanks.

i've decided to create a page about Wendell
well-temperaments. this is the incipient version:
http://sonic-arts.org/dict/wendell.htm

... i'm having trouble following much of the thread,
but i hope to be able to expand this into a nice
comprehensive page about this interesting category
of tunings.

-monz

--- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:
> Gene or whomever,
>
>
> can i please get a good, complete definition
> (with examples) of "brat", for the Tuning Dictionary?

For a major triad in close root position, let f be the ratio of the
fifth to the root, and t the ratio of the major third to the root.
Then the beat ratio, or brat is

brat = (6t - 5f)/(4t - 5)

If t = 5/4, so that major thirds are pure, the brat is considered to
be infinity, rather than undefined, unless the minor thirds are pure
also, in which case we have a JI triad and the brat is undefined.

For any tuning system with uniform fifths and major thirds, the brat
for the system is the brat for any one of the major triads of the
system. For example, for 12-equal the brat is

(6 2^(1/3) - 5 2^(7/12))/(4 2^(1/3) - 5) = 1.713299...

> i've decided to create a page about Wendell
> well-temperaments. this is the incipient version:
> http://sonic-arts.org/dict/wendell.htm

Why not a page about the more general concept of well temperaments
with synchronized beating? Unless that's what you meant...

>Why not a page about the more general concept of well temperaments
>with synchronized beating? Unless that's what you meant...

Yes; I for one have no idea why I the Maj3rd/Min3rd ratio should
be so important, how to parse the Scala output Paul and Manuel
have been posting, how Paul's approach compares to Bob's/Gene's,
etc.

-Carl