Coming: Octave-specific lattices

The idea is to "look down the pitch axis" at the Tenney lattice.
Distance "into the screen" or "out of the screen" will correspond to
pitch height. The prime intervals 2:1, 3:1, and 5:1, and whatever
other prime:1 intervals you want, at least, will appear with their
correct length, and thus the 'taxicab' length of any interval will
appear correctly as well. I have yet to decide on the angles between
the prime intervals; probably the best choice will vary depending on
which primes you want.

hi paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> The idea is to "look down the pitch axis" at the Tenney
> lattice. Distance "into the screen" or "out of the screen"
> will correspond to pitch height. The prime intervals 2:1,
> 3:1, and 5:1, and whatever other prime:1 intervals you want,
> at least, will appear with their correct length, and thus
> the 'taxicab' length of any interval will appear correctly
> as well. I have yet to decide on the angles between the
> prime intervals; probably the best choice will vary depending
> on which primes you want.

i had this idea a long, long time ago.

not sure if i ever wrote about it here ... i may have also
mentioned it to you when i visited you in 1999, but maybe not.

i'm planning to implement this in my software too.
since the user can already rotate the lattices in
3 dimensions, it would be easy to add this.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi paul,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > The idea is to "look down the pitch axis" at the Tenney
> > lattice. Distance "into the screen" or "out of the screen"
> > will correspond to pitch height. The prime intervals 2:1,
> > 3:1, and 5:1, and whatever other prime:1 intervals you want,
> > at least, will appear with their correct length, and thus
> > the 'taxicab' length of any interval will appear correctly
> > as well. I have yet to decide on the angles between the
> > prime intervals; probably the best choice will vary depending
> > on which primes you want.
>
>
>
> i had this idea a long, long time ago.
>
> not sure if i ever wrote about it here ... i may have also
> mentioned it to you when i visited you in 1999, but maybe not.
>
> i'm planning to implement this in my software too.
> since the user can already rotate the lattices in
> 3 dimensions, it would be easy to add this.
>
>
>
> -monz

I can't wait. I had no idea you were working with the pitch axis and
with the logarithmic lattice-rung lengths that make the
above 'correct length' property hold.

hi paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > hi paul,
> >
> >
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > > The idea is to "look down the pitch axis" at the Tenney
> > > lattice. Distance "into the screen" or "out of the screen"
> > > will correspond to pitch height. The prime intervals 2:1,
> > > 3:1, and 5:1, and whatever other prime:1 intervals you want,
> > > at least, will appear with their correct length, and thus
> > > the 'taxicab' length of any interval will appear correctly
> > > as well. I have yet to decide on the angles between the
> > > prime intervals; probably the best choice will vary depending
> > > on which primes you want.
> >
> >
> >
> > i had this idea a long, long time ago.
> >
> > not sure if i ever wrote about it here ... i may have also
> > mentioned it to you when i visited you in 1999, but maybe not.
> >
> > i'm planning to implement this in my software too.
> > since the user can already rotate the lattices in
> > 3 dimensions, it would be easy to add this.
> >
> >
> >
> > -monz
>
> I can't wait. I had no idea you were working with the
> pitch axis and with the logarithmic lattice-rung lengths
> that make the above 'correct length' property hold.

i can't guarantee that this particular item will appear
in release 1.0 ... we're finished with the tuning and
piano-roll editors for that release now, and are about
to begin working on staff-notation. but as i said, it
seems to me that it would be easy to add.

right now the Tonalsoft software only offers one type
of lattice projection, and it's *not* my "Monzo formula"
(as described on my lattice webpage). Chris wanted to
make all prime-axes as orthogonal as possible ...of course,
this becomes a problem as soon as you pass beyond 3-D.

maybe you should talk to him about implementing this
pitch-axis feature. he would understand the math of it
better than me anyway.

-monz