MODwakalixes?

Consider the following pitch set:

{1/1 9/8 6/5 4/3 3/2 5/3 15/8 2/1}

This set has the interesting property that it tempers down, in
meantone, to the symmetrical MODMOS of LsLLLLs. But, it also tempers
down, in mavila, to the symmetrical MODMOS of ssLsLss. It tempers down
to a dicot MOS and doesn't temper down to anything in porcupine.

Now let's change that 5/3 to 27/16:

{1/1 9/8 6/5 4/3 3/2 27/16 15/8 2/1}

Now we get something that tempers down in meantone to the symmetrical
MODMOS of LsLLLLs. And also, it tempers down in dicot to the
symmetrical MODMOS of LssLLss, which I'll term the "rastic" MODMOS for
4L3s. Now it's mavila that tempers this down to an MOS.

Now we'll go back to 5/3, and also change the 15/8 to 16/9:

{1/1 9/8 6/5 4/3 3/2 5/3 16/9 2/1}

Now we get something that tempers down in meantone to a MOS. In
mavila, it tempers down to the symmetrical MODMOS. In dicot, it
tempers down to the symmetrical rastic MODMOS again.

Anyone know what's going on here? The one-alteration symmetrical
MODMOS's of temperaments are usually pretty awesome. Are there any
MODwakalixes which temper down to the symmetrical MODMOS in 3 ways?

-Mike

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

> Anyone know what's going on here? The one-alteration symmetrical
> MODMOS's of temperaments are usually pretty awesome. Are there any
> MODwakalixes which temper down to the symmetrical MODMOS in 3 ways?

What is your definition of "the" symmetrical MODMOS?

I'm talking about the one-alteration MODMOS in which the generator chain
looks like this:

# ##### #

So for meantone, dorian #7 gets you to one mode of this; dorian b2 gets you
to another. For porcupine, 6|0 #7 is one mode of this MODMOS, 6|0 b3 is
another.

It's noteworthy for the reason that it requires only one alteration to get
to, and is reachable in two ways, meaning it'll probably turn up a lot.

We should probably have a name for this, since it's not the only
symmetrical MODMOS in town.

-Mike

On Mar 30, 2012, at 12:25 PM, genewardsmith <genewardsmith@sbcglobal.net>
wrote:

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

> Anyone know what's going on here? The one-alteration symmetrical
> MODMOS's of temperaments are usually pretty awesome. Are there any
> MODwakalixes which temper down to the symmetrical MODMOS in 3 ways?

What is your definition of "the" symmetrical MODMOS?

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

> It's noteworthy for the reason that it requires only one alteration to get
> to, and is reachable in two ways, meaning it'll probably turn up a lot.

I've certainly seen it a lot.

> We should probably have a name for this, since it's not the only
> symmetrical MODMOS in town.

Is the name to be a one-off or part of a systematic naming scheme for MODMOS shapes?

--- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> Is the name to be a one-off or part of a systematic naming scheme for MODMOS shapes?

Here's a thought: an ordinary MOS is an N MMOS, which in standard form has generators running from 0 to N-1. An N+1 MMOS has generators 0, 2, 3, ... N-1 N+1, and is your symmeric MODMOS. N+2 is 0,1,3,...N-1 N+2, and so forth. N+1+3 would be 0, 2, 4, ..., N-1, N+1, N+3. N;N+1 would be a 1/2 octave period MMOS, and so forth.

On Fri, Mar 30, 2012 at 1:49 PM, genewardsmith <genewardsmith@sbcglobal.net>
wrote:
>
> --- In tuning-math@yahoogroups.com, "genewardsmith" <genewardsmith@...>
> wrote:
>
> > Is the name to be a one-off or part of a systematic naming scheme for
> > MODMOS shapes?
>
> Here's a thought: an ordinary MOS is an N MMOS, which in standard form has
> generators running from 0 to N-1. An N+1 MMOS has generators 0, 2, 3, ...
> N-1 N+1, and is your symmeric MODMOS. N+2 is 0,1,3,...N-1 N+2, and so forth.
> N+1+3 would be 0, 2, 4, ..., N-1, N+1, N+3. N;N+1 would be a 1/2 octave
> period MMOS, and so forth.

Is MMOS just short for MODMOS?

I like this terminology a lot; it's basically what I was thinking of
(although I was going to use something like #1g, for sharp the first
step in the generator chain, but I like just using + better).

Are we saying that harmonic minor and harmonic major are both 7+2
MMOS? If not, then the trouble is that we need to be able to
distinguish between generators.

I'm not sure I get the N;N+1 thing, can you explain?

-Mike

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

> Is MMOS just short for MODMOS?

Yes, but with the idea that if we need a special term for things designated by this sort of notation that might work.

> Are we saying that harmonic minor and harmonic major are both 7+2
> MMOS? If not, then the trouble is that we need to be able to
> distinguish between generators.

No; harmonic minor is 7+2, but harmonic major is 7+1+2.

> I'm not sure I get the N;N+1 thing, can you explain?

Forget about it. I was thinking of notating things like ssLss sLsss in pajara, but that won't work.

On Fri, Mar 30, 2012 at 3:14 PM, genewardsmith <genewardsmith@sbcglobal.net>
wrote:
>
> > Are we saying that harmonic minor and harmonic major are both 7+2
> > MMOS? If not, then the trouble is that we need to be able to
> > distinguish between generators.
>
> No; harmonic minor is 7+2, but harmonic major is 7+1+2.

That implies a canonical choice of generator. Is it going to be the
chroma-positive one?

-Mike

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

> That implies a canonical choice of generator. Is it going to be the
> chroma-positive one?

Since that's what modal UDP uses, it seems to make the most sense.