A question about the TE/TOP-RMS best val

Hi all,

There's been some clashing on here about the best val vs the patent val. For
example, 23-equal is one of the cases where the "best" val is not set equal
to the patent val:

http://x31eq.com/cgi-bin/rt.cgi?ets=23&limit=7

If you pick the 23d val, and stretch the octave to the TOP-RMS value, you do
indeed end up with lower error than you do with the patent val. The same
applies for 17c vs 17. So my question is: if you don't stretch the octave,
and you prefer to work within the pure octave, how does this affect things?
Or would the patent val then be the winner?

-Mike

Mike Battaglia <battaglia01@...> wrote:

> If you pick the 23d val, and stretch the octave to the
> TOP-RMS value, you do indeed end up with lower error than
> you do with the patent val. The same applies for 17c vs
> 17. So my question is: if you don't stretch the octave,
> and you prefer to work within the pure octave, how does
> this affect things? Or would the patent val then be the
> winner?

If you don't stretch the octave, you probably want smaller
intervals to be more important than larger ones. One rule
is that about half of intervals within a Tenney limit are
smaller than an octave, and some are very large. For
example, in the 23-limit, 23:22 is 77 cents and clearly
audible (whether or not the 23-ness means anything) but
23*22=506:1 is almost 9 octaves and that's beyond some
people's hearing. Even where they are audible, intervals
much larger than an octave aren't that important musically.
They don't fuse, they don't have many clashing partials,
and you don't get many of them in chords.

When you start biasing the weighting towards small
intervals, the resulting badness is much the same as you
would have got by allowing the octave to be optimized. So
the easiest thing is to consider octaves on their merits.
You can unstretch the scale to get pure octaves for tuning
if that's what you want.

There are measures that work directly for pure octaves.
You have to PDF if you want to research them.

Graham