--- In harmonic_entropy@y..., "emotionaljourney22" <paul@s...> wrote
[#603]:
> --- In harmonic_entropy@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > [pe:]
> > > there's also the s (resolution)
> > > parameter which can always be tweaked to give more or less
importance
> > > to more complex ratios (the better your hearing resolution, the
more
> > > easily you can identify the complex ratios "as such", because
the
> > > complex ratios are in more "crowded" areas amongst all the
ratios).
> >
> > For that we can refer to my graph:
> >
> > http://groups.yahoo.com/group/tuning-math/files/secor/consonce.gif
> >
> > It appears that the point at which I no longer heard n:d as a
local
> > consonance is when n*d reached a value around 150 (with 16:9 and
> > 17:10). So margo2.gif would have a little more sensitivity than
what
> > I observed.
>
> i think you're misunderstanding how s works here in the vos-based
> curve. also, my question above would seem to be relevant again --
> could it be that you're simply not noticing tinier and tinier bumps
> in the road, corresponding to more and more complex ratios?

I think we're talking about the same thing, but I just didn't say it
the right way. By sensitivity, I didn't mean y-axis resolution, but
rather sensitivity to hearing higher harmonics, which would translate
to seeing bumps for more complex ratios. I think that the bumps
should disappear when n*d gets up to around 150, which would not make
16:9 and 17:10 appear as local maximum points of consonance. So I
didn't want to see as many bumps as in margo2.gif. Is that making
any sense?

> now, notice that in margo2.gif, the most discordant interval not
near
> 80 cents is between 1100 and 1200 cents, and the most discordant
> interval not near either of these is between 700 and 800 cents.
this
> seems very promising for being able to attain the specifications
you
> requested. however, please note that "near" in this context doesn't
> mean quite what it meant in the original, "rounder" harmonic
entropy
> formulation -- even very near to the extreme peaks of discordance,
> there can be significant interruptions in the "plateau", 14:9 being
a
> perfect example for margo2.gif.

I have no problem with the larger one at 14:9. The dips at 17:11 and
19:12 are the ones that I would want to minimize.

> anyway, i'm now computing a version of margo2.gif where an s of 1%
> will be assumed -- should be hot off the grill within the hour . . .

And here it is:

--- In harmonic_entropy@y..., "emotionaljourney22" <paul@s...> wrote
[#605]:
> hey george, take a look at this curve:
>
>
http://groups.yahoo.com/group/harmonic_entropy/files/dyadic/secortst.g
if
>
> i left it unlabeled for your fun and amusement . . .
>
> (if you don't like seeing all those tiny local minima, not taking
the
> exponential should help . . . let me know).
>
> anyhow, the global maximum here is at 67 cents.

I imported the file into Paint and saved it as a bitmap so I could
read the x-coordinate for each point in the graph, which I can
convert to and from cents using a spreadsheet. The maximum in the
graph looks like a flat line ranging from 61 to 75 cents, so this
looks pretty good.

> the next most discordant intervals are kind of in that vicinity,
but
> don't form a contiguous region the way they did with the original,
> smooth harmonic entropy formulation.
>
> then, the next most discordant interval (within the octave) is at
> 1139 cents.

This is another flat line from 1133 to 1142 cents. This is also
pretty close to what I had, which was 1145.

> then more in the vicinities of 67 and 1139, with the caveat above.
>
> then, 758, followed by 757, followed by *750* . . .

I had 740 as a local maximum dissonance in this region, which was
somewhat different. That was the result of only a single experiment
in a single register, however. I need to do more testing on that, as
well as with a flattened fifth.

> let me know if these values are ok for you . . . if not, there's
> plenty more that can be tried on tomorrow's menu . . .

So smoothing out the curve a little (via the s resolution) so that
16:9, 17:10, and more complex ratios no longer appear as local
maximum points of consonance (or only as tiny dips) would be the only
change I would recommend at this point.

--George