Notation for multiple mappings

Let's say you want to play around in 60-equal. Now, with one mapping,
60-equal supports magic and compton temperament, whereas with another
it supports porcupine and blackwood temperament, and with another it
supports progression. How can we ever keep this straight? Will we be
bound to one val until the end of time? Will we remain enslaved to our
own limitations? Or will we just write that we are in the

2.3.3b.5.5c.5cc

subgroup?

Sincerely,
The Riddler

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

> Will we remain enslaved to our
> own limitations? Or will we just write that we are in the
>
> 2.3.3b.5.5c.5cc
>
> subgroup?

I suspect doing that would enslave you to massive confusion. The best val in the 5 and 7 limits is clearly the patent val, so why not just say so? If you want to use other mappings, or go wild inconsistently, feel free. What's the big deal?

Since you are such a fan of 5n edos, I wonder what you think of the 5&60 temperament tempering out 245/243 and 16807/16384?

On Thu, May 12, 2011 at 1:06 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Will we remain enslaved to our
> > own limitations? Or will we just write that we are in the
> >
> > 2.3.3b.5.5c.5cc
> >
> > subgroup?
>
> I suspect doing that would enslave you to massive confusion. The best val in the 5 and 7 limits is clearly the patent val, so why not just say so? If you want to use other mappings, or go wild inconsistently, feel free. What's the big deal?

This way seems like it makes more sense than the 2.3.other
three.5.other 5.other other 5 subgroup.

> Since you are such a fan of 5n edos, I wonder what you think of the 5&60 temperament tempering out 245/243 and 16807/16384?

I'm a fan. I think it's a temperament that demands that you getting
away from its MOS's and just compose with the general structure of the
tempered-lattice in mind. There's lots of neat things you can do with
the concept of (8/7)^5 ~ 2/1 without having to think in terms of
60-note MOS's and all that.

-Mike

On Thu, May 12, 2011 at 1:51 PM, Mike Battaglia <battaglia01@gmail.com> wrote:
>
> I'm a fan. I think it's a temperament that demands that you getting
> away from its MOS's and just compose with the general structure of the
> tempered-lattice in mind. There's lots of neat things you can do with
> the concept of (8/7)^5 ~ 2/1 without having to think in terms of
> 60-note MOS's and all that.

Although I will say that I don't know how in the heck 60-equal tempers
out 250/243 if it has the fifth of 12-equal and 12-equal does'nt
temper out 250/243. Some things remain a mystery, I guess.

-Mike

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

> Although I will say that I don't know how in the heck 60-equal tempers
> out 250/243 if it has the fifth of 12-equal and 12-equal does'nt
> temper out 250/243. Some things remain a mystery, I guess.

You can't temper out 250/243 using the fifth of 12-equal. You can use the 15-equal mapping contortedly.

On Fri, May 13, 2011 at 12:56 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Although I will say that I don't know how in the heck 60-equal tempers
> > out 250/243 if it has the fifth of 12-equal and 12-equal does'nt
> > temper out 250/243. Some things remain a mystery, I guess.
>
> You can't temper out 250/243 using the fifth of 12-equal. You can use the 15-equal mapping contortedly.

Do you mean 256/243? I thought that 250/243 meant the schismatic major
third became 6/5, and if we're using the 5-equal fifth that means 9/8
and 6/5 get equated, which isn't a temperament I feel like you'd
recommend.

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, May 13, 2011 at 12:56 PM, genewardsmith
> <genewardsmith@...> wrote:
> >
> > --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > Although I will say that I don't know how in the heck 60-equal tempers
> > > out 250/243 if it has the fifth of 12-equal and 12-equal does'nt
> > > temper out 250/243. Some things remain a mystery, I guess.
> >
> > You can't temper out 250/243 using the fifth of 12-equal. You can use the 15-equal mapping contortedly.
>
> Do you mean 256/243?

No, you said 250/243. Using the fifth of 12-equal gives a val of
<60 95 t| for whatever value of t makes 250/243 go away; that we can find from <60 95 t|1 -5 3> = 3t-415 = 0, so that t = 138 1/3. It's the 1/3 that does you in.

On Fri, May 13, 2011 at 1:37 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> > >
> > > You can't temper out 250/243 using the fifth of 12-equal. You can use the 15-equal mapping contortedly.
> >
> > Do you mean 256/243?
>
> No, you said 250/243. Using the fifth of 12-equal gives a val of
> <60 95 t| for whatever value of t makes 250/243 go away; that we can find from <60 95 t|1 -5 3> = 3t-415 = 0, so that t = 138 1/3. It's the 1/3 that does you in.

Sorry, I meant 245/243. Your original message was

> Since you are such a fan of 5n edos, I wonder what you think of the 5&60 temperament
> tempering out 245/243 and 16807/16384?

I don't see how 60-equal can temper out 245/243 if the fifth of
12-equal is used, since I thought 245/243 vanishing meant that the
schismatic major third was equated with 6/5.

-Mike

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

> I don't see how 60-equal can temper out 245/243 if the fifth of
> 12-equal is used, since I thought 245/243 vanishing meant that the
> schismatic major third was equated with 6/5.

Since this isn't want it means, no problem. Two 9/7s and a 6/5 make up an octave.

On Fri, May 13, 2011 at 5:19 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I don't see how 60-equal can temper out 245/243 if the fifth of
> > 12-equal is used, since I thought 245/243 vanishing meant that the
> > schismatic major third was equated with 6/5.
>
> Since this isn't want it means, no problem. Two 9/7s and a 6/5 make up an octave.

Oh. I thought 245/243 was 5-limit superpyth for some reason, and what
I said above is 5-limit superpyth. Whoops.

-Mike