--- In harmonic_entropy@y..., "gdsecor" <gdsecor@y...> wrote:

> > > 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.

actually, it doesn't work that way in the harmonic entropy model.
firstly, hearing harmonics is not even an issue, rather it's
*recognizing* notes *as* harmonics of an implied fundamental.
secondly, once you've reached a certain, fairly low point in the
harmonic series, ascribing equal importance to higher and higher
harmonics does *not* translate to seeing more bumps for more complex
ratios. rather, it remains the (relatively) simple ratios which
correspond to the visible bumps, because (and only because) these are
the regions in which the concentration of ratios (in whatever,
usually ridiculously high, limit is assumed) is lower; near the
simplest ratios one finds the *lowest* concentration of ratios (in
whatever limit).

harmonic entropy measures how crowded the ratios are.

> 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?

sure, but could it be that these are merely such tiny bumps in the
road that your tires just plow over them as if they weren't even
there?

>
> > 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.

as i mentioned, not taking the exponential, but looking at the actual
entropy itself, remedies this to some extent. here is the resulting
graph:

http://groups.yahoo.com/group/harmonic_entropy/files/dyadic/secorts2.g
if

please be as picky as you like -- there are still a lot of things one
can tweak.