complexity measures, HE and hacked scale analysis

Subject: Re: complexity measures
> >
> > Robert Valentine wrote,
> >
> > >take output into excel and ooo and ahhh when sensible
> > > results appear (like 204c being the 'best' B for
> > > the Ionian, followed by 194c)
> >
> > Can I ask you where this is coming from? I always get
> > something like 194_ as best.
> >

I did some more investigation over the weekend.

The most successful experiment I did was to insert a
complexity cap. This has the effect of constraining
the precision of the 'ears' by making some of the more
remote consonances fall above the cap. What this does is
decrease the number of local minima in the complexity
graph. As I varied the cap, the 'best' scale moved from
204c to 194c.

Here is the RI interpretation of the Pythagorean major
with three different caps. In the first case, 194c, with
the same RI interpretation was the minimum. In the other
two cases, 194 was a local minimum, but 204c was the
minimum. 194 was also interpreted as 19/17 with the
higher caps.

cap RI comment
100 '1/1 '9/8 '5/4 '4/3 '3/2 '5/3 '15/8 not minimum
250 '1/1 '9/8 '14/11 '4/3 '3/2 '27/16 '19/10 minimum
500 '1/1 '9/8 '19/15 '4/3 '3/2 '27/16 '19/10 minimum

So, the program is behaving pretty much as intended. If
you assume that the 'ears' are sharp enough to find those
exotic thirds, then that plus all those 3/2's may well be
a best tuning.

Other experiments that didn't pan out.

Summing instead of taking minimum produced a big mess,
so I'm doing something wrong. Unless someone tells me
the formula for an HE point at a given value in cents,
or the algorithm that produces it, I'll be investigating
things using whatever method produces what I
think may be 'similar'.

Logs, prime factors, distance measures on the lattice
etc tended to produce mostly the same results or noisier
results (more rather than fewer local minima, with some
of them at very bizarre points).

>
> >Oh, an IMPORTANT point (probably THE most important) is the
> >data culling.
>
> Not really understanding but it all sounds overly complicated.
>
>

I'm just producing a list of perhaps a few hundred
scales and wish to sort them into "candidates to investigate" and
"candidates not to investigate at the current time". Those to
investigate should be local minima in a graph of 'B' vs
'complexity' or whatever measure is used.

With the 'really good ears', there are lots of local minima, whether
analyzed by intervallic complexity or some combination of
complexity and accuracy.

> >The point here is that harmonic entropy mixes complexity of
> >the intervals being heard and the accuracy that they are being
> >produced at. Until I feel that I am mixing them in a sensible
> >manner, I'll get more trustworthy results by seperating them.
>
> Oh, OK. I'm here to help you with the mixing. I don't think the
> two can be > separated, actually -- in harmonic entropy they're
> pretty much one and the same.
>
> You might want to look over the discussion of octave-equivalent
> harmonic entropy models and graphs.

Yeah, I should probably just go back to the archives. On the other
hand, I can blindly move forward and perhaps find something
interesting.

thanks,

bob