Quick clarification about brats

The "brat" term refers to the ratio, in a major triad of a certain
tuning, between the minor third and a major third.

As in, for C-E-G in say some meantone temperament, the "brat" is going
to be the beat frequency, in Hz, between the E-G dyad divided by the
beat frequency, in Hz, between the C-E dyad.

So the C-G dyad is left out of the equation entirely, except can be
calculated indirectly by working some algebra with the above.

Right?

Sincerely,
A brat

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> So the C-G dyad is left out of the equation entirely, except can be
> calculated indirectly by working some algebra with the above.
>
> Right?

Right. If b = EG/CE, then CE/CG = 5/(3-2b) and CG/EG = (3-2b)/(5b) with a bunch more along the same lines. Minor beat ratios depend on the value of the fifth, and correspond to major brats in systems with nearly pure fifths very well.

So would the same terminology apply to tetrads then? So say for a detuned
4:5:6:7 tetrad, the brat would be 7/6:6/5:5/4...?

So let's say that the ~6:7 beats at 2 Hz, the ~5:6 beats at 3 Hz, and the
~4:5 beats at 4 Hz. Would the whole thing be said to have a brat of 2:3:4?

AKA, it would generate a polyrhythm that's a mixture of "hot cup of tea" and
"pass the goddamn ketchup"
(or whatever your favorite variant thereof would be)

?

The reason I'm asking is because the 55-equal representation of
2:3:5:7:9:11:13 is amazing, and I wonder if "brats" are somehow involved.

-Mike

On Wed, May 19, 2010 at 2:24 AM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > So the C-G dyad is left out of the equation entirely, except can be
> > calculated indirectly by working some algebra with the above.
> >
> > Right?
>
> Right. If b = EG/CE, then CE/CG = 5/(3-2b) and CG/EG = (3-2b)/(5b) with a
bunch more along the same lines. Minor beat ratios depend on the value of
the fifth, and correspond to major brats in systems with nearly pure fifths
very well.

> The reason I'm asking is because the 55-equal representation of
> 2:3:5:7:9:11:13 is amazing, and I wonder if "brats" are somehow involved.
>
> -Mike

To add to this, it's more amazing than the 43-equal version, despite
that the 43-equal one is far more in tune, particularly with the
ratios of 7 and 13. The 55-equal one just sounds like a thick meaty
slab of goodness, whereas the 43-equal one is sort of lifeless and
dull in comparison. I think it has something to do with the way it's
beating -- maybe.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> The "brat" term refers to the ratio, in a major triad of a
> certain tuning, between the minor third and a major third.
>
> As in, for C-E-G in say some meantone temperament, the "brat"
> is going to be the beat frequency, in Hz, between the E-G dyad
> divided by the beat frequency, in Hz, between the C-E dyad.
>
> So the C-G dyad is left out of the equation entirely, except
> can be calculated indirectly by working some algebra with
> the above.
>
> Right?
>
> Sincerely,
> A brat

I would hardly say the fifth is left out of the equation, because
the fifth is in the equation

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

and moreover, when the fifth is 3:2, the brat is always 3/2.

-Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> So would the same terminology apply to tetrads then? So say for a detuned
> 4:5:6:7 tetrad, the brat would be 7/6:6/5:5/4...?

It's not as easy to get a tetrad to beat in synch, but I showed how to do it in marvel temperament here recently in painful detail.

> The reason I'm asking is because the 55-equal representation of
> 2:3:5:7:9:11:13 is amazing, and I wonder if "brats" are somehow involved.

Maybe you just like meantone and mohajira a whole lot?

On Wed, May 19, 2010 at 5:34 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > So would the same terminology apply to tetrads then? So say for a detuned
> > 4:5:6:7 tetrad, the brat would be 7/6:6/5:5/4...?
>
> It's not as easy to get a tetrad to beat in synch, but I showed how to do it in marvel temperament here recently in painful detail.

I missed that, I'll have to go back and read.

> > The reason I'm asking is because the 55-equal representation of
> > 2:3:5:7:9:11:13 is amazing, and I wonder if "brats" are somehow involved.
>
> Maybe you just like meantone and mohajira a whole lot?

I only like meantone because most of my favorite chord progressions
turn out to be comma pumps otherwise.

A quick search for mohajira on the tonalsoft encyclopedia and the
xenharmonic wiki turned up... not much. A quick search for it on the
tuning list archives reveals that it is a possibly 13-limit
temperament that has something to do with neutral thirds, and that you
aren't very happy when people use 24-tet as a form of mohajira tuning.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> The reason I'm asking is because the 55-equal representation of
> 2:3:5:7:9:11:13 is amazing, and I wonder if "brats" are somehow involved.

What modality of 55-equal are you using? Surely there are different regular temperaments for example which would embrace one or the other of the two different possible 11/8s in 55, and 11/9 in 55 is closer than either possible 11/8, etc. Or are you using "pick the nearest approximation"? You'd have to define these things before calculating proportional beat rates.

-Cameron Bobro

On Wed, May 19, 2010 at 6:02 AM, cameron <misterbobro@...> wrote:

>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > The reason I'm asking is because the 55-equal representation of
> > 2:3:5:7:9:11:13 is amazing, and I wonder if "brats" are somehow involved.
>
> What modality of 55-equal are you using? Surely there are different regular temperaments for example which would embrace one or the other of the two different possible 11/8s in 55, and 11/9 in 55 is closer than either possible 11/8, etc. Or are you using "pick the nearest approximation"? You'd have to define these things before calculating proportional beat rates.
>
> -Cameron Bobro

Yeah, the nearest approximation. I wasn't thinking in terms of any
rank-2 system, but just playing static chords and listening to them.
I've mapped 7/4 as 44 steps, 11/8 as 25 steps, and 13/8 as 38 steps
(although 13/8 could also be said to be 39 steps, it just sounds
better as 38 for some reason).