Re: Porcupine notatio

>>>I take Porcupine temperament to be an approximately 163c
>>>generator with primes 3,5,7,11 mapping to -3,-5,6,-4
>>>generators, (11-limit sans 9's). I'd notate the 7 note MOS
>>>as
>>>
>>>A Bv C^ D Ev F^ G
>>>
>>>v and ^ represent both the syntonic comma and the undecimal
>>>diesis and correspond to 1 step of either 15 or 22-tET, and
>>>2-steps of 37-tET.
>>
>>Aha! What does the lattice look like?
>
>Which lattice?

All of it!

-Carl

--- In tuning@y..., Carl Lumma <carl@l...> wrote:
> >Which lattice?
>
> All of it!

Carl,

either you're making a joke here or we have some misunderstanding of
terminology or something. I'm using the word "temperament" here to
refer to a potentially infinite number of notes. I'm guessing you're
referring to a particular size MOS of that temperament. Which one?

Even a finite MOS gives rise to an infinite lattice, but at least it's
periodic and we could draw a few periods to get the idea.

And do you mean a 5-limit, 7-limit, or 11-limit-sans-9s lattice. I'm
not willing to try to draw the latter. Actually, I don't want to draw
any of them.

>>>Which lattice?
>>
>>All of it!
>
> Carl,
>
>either you're making a joke here or we have some
>misunderstanding of terminology or something. I'm
>using the word "temperament" here to refer to a
>potentially infinite number of notes.

Dave,

I'm guessing your notation makes the lattice periodic
with respect to the commas operating on the 7-tone
MOS you've picked. I was asking for one period of this
lattice, which I could construct myself, but maybe others
here could not, so I thought maybe it would be most
appropriate for you to do it. And besides, I might make
a mistake, and that would result in plenty of confusion.

> periodic and we could draw a few periods to get the idea.

One period should do it.

>And do you mean a 5-limit, 7-limit, or 11-limit-sans-9s
>lattice.

5-limit, since we've been discussing and notating porcupine
in terms of 5-limit music, and since they're easiest to draw
and see.

>Actually, I don't want to draw any of them.

In a sense this is equivalent to not drawing them, since if
you drew them you must have wanted to. Internally, though,
it may be that parts of you want to draw them, but not enough
to get you to do it. In this case, I have no desire to sway
you; I've always believed in never doing anything I didn't
want to. And so far, it hasn't knocked me out of the richest
tiny percentile of humans that I was born into, where I had
the luxury of formulating it in the first place, so it can't
be too bad of an idea.

I should really stop skipping dinner.

-Carl