Notating planar temperaments

Has any thought been given to this?

Gene Ward Smith wrote:
> Has any thought been given to this?

In most typical cases, you could notate them as 5-limit JI with your favorite system of notation (HEWM, Sagittal, or whatever). If you're tempering out 225/224, for instance, you'd represent 7/4 as 225/128.

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> Gene Ward Smith wrote:
> > Has any thought been given to this?
>
> In most typical cases, you could notate them as 5-limit JI with your
> favorite system of notation (HEWM, Sagittal, or whatever).

Not always by any means, but in most cases at least you can notate it
using only primes; for instance for breed (2401/2400 planar) you can
use 2401/800 in place of 3, and then notate it in terms of 2, 5, and
7. I think you are right and this sort of thing is what should be done
when possible. That won't work with commas like 3125/3087, however.
That could be notated with 2, 3, and 25/21, since this does lead to a
rational version, with (25/21)^3 = 3125/3087 * 5/3 being the basic
reduction.

Gene Ward Smith wrote:
> --- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:
> >>Gene Ward Smith wrote:
>>
>>>Has any thought been given to this?
>>
>>In most typical cases, you could notate them as 5-limit JI with your >>favorite system of notation (HEWM, Sagittal, or whatever). > > > Not always by any means, but in most cases at least you can notate it
> using only primes; for instance for breed (2401/2400 planar) you can
> use 2401/800 in place of 3, and then notate it in terms of 2, 5, and
> 7. I think you are right and this sort of thing is what should be done
> when possible. That won't work with commas like 3125/3087, however.
> That could be notated with 2, 3, and 25/21, since this does lead to a
> rational version, with (25/21)^3 = 3125/3087 * 5/3 being the basic
> reduction.

That's a good point, but if you're tempering out 3125/3087 (the BP major diesis), you're probably working with a BP scale, and if that's the case, you won't care much about the 2 factor and you can treat it as a linear temperament.

In any case, most uses for planar temperaments that I've come across involve tempering out a comma to improve the near-consonant intervals of a specific just scale. So I haven't thought much about other uses for planar temperaments.

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@I...> wrote:

> That's a good point, but if you're tempering out 3125/3087 (the BP
major
> diesis), you're probably working with a BP scale, and if that's the
> case, you won't care much about the 2 factor and you can treat it as a
> linear temperament.

The BP scale is a rather bizarre construct, so I don't know why this
conclusion holds, and in any case I could just as well have said
686/675 planar for my example. Of course most of the time if you
temper out 3125/3087 you are not in a planar temperament situation at
all, and instead are in garibaldi or 53-et or something of that sort;
in that case notation would be dead easy.

> In any case, most uses for planar temperaments that I've come across
> involve tempering out a comma to improve the near-consonant
intervals of
> a specific just scale. So I haven't thought much about other uses for
> planar temperaments.

One use is simply to freely make use of it, in the way one freely uses
JI. Another possible use is for notation systems.