TOP history

Paul, could you tell us something about when and how you discovered
TOP? I'd like to add some history to my top page.

> Paul, could you tell us something about when and how you
> discovered TOP? I'd like to add some history to my top page.

Well you can see from my recent post that Dave was pretty
close for fixed scales.

Also of excerpts from the list in 1999 may be of interest,
forthcoming in a forthcoming post of mine.

-Carl

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> Paul, could you tell us something about when and how you discovered
> TOP? I'd like to add some history to my top page.

It's exactly what I've been pleading to you guys to help me figure
out last year and probably even earlier, except without octave-
equivalence. The idea was to temper out commas uniformly over their
length in the lattice, to see what error function this was optimal
with respect to, and to then apply this same error function to
optimize temperaments with more than one comma. The posts asking
about this can be found in the archives here.

When I made that 'waterfall' plot, I thought about replacing the
former 'octave-equivalent' quantities, that Gene called 'heuristics',
with their octave-specific versions in the Tenney lattice. Sometime
shortly after that, and after I posted an example of the kind of
tempering that makes the new 'heuristics' exact, I was at home and
grasped that there was no 'limit' to the set of intervals satisfying
the particular error function, minimax tenney-weighted error, that
was being optimized here.

Paul Erlich wrote:

> It's exactly what I've been pleading to you guys to help me figure > out last year and probably even earlier, except without octave-
> equivalence. The idea was to temper out commas uniformly over their > length in the lattice, to see what error function this was optimal > with respect to, and to then apply this same error function to > optimize temperaments with more than one comma. The posts asking > about this can be found in the archives here.

Was it? Oh. Well, I found this thread:

/tuning-math/message/2857

The new thing is the concept of weighted minimax.

Graham

--- In tuning-math@yahoogroups.com, Graham Breed <graham@m...> wrote:
> Paul Erlich wrote:
>
> > It's exactly what I've been pleading to you guys to help me
figure
> > out last year and probably even earlier, except without octave-
> > equivalence. The idea was to temper out commas uniformly over
their
> > length in the lattice, to see what error function this was
optimal
> > with respect to, and to then apply this same error function to
> > optimize temperaments with more than one comma. The posts asking
> > about this can be found in the archives here.
>
> Was it? Oh. Well, I found this thread:
>
> /tuning-math/message/2857
>
> The new thing is the concept of weighted minimax.
>
>
> Graham

Right, because I didn't know that weighted minimax is exactly what
results from 'applying' the octave-specific 'heuristic' (meaning
tempering such that it's exactly correct) until I actually thought
about it. Being sick (though mentally impaired by fever) and away
from the list for a while seemed to help revive independent thought.