Questions about the algorithm?

Ok, I stumbled across this group by accident, but it seems extremely
similar to stuff I've been trying myself (although I hadn't done any
research into this area before). I'm not familiar with any scientists'
names or theories, but I can sort of see what you are measuring, at
least for the simple two-part relationships (i.e. how well it can be
approximated to a simple integer ratio, with "s" being a measure of
how fussy you are about exact pitch).

However, I couldn't find a simple description of how the values are
actually calculated, because there were a lot of past posts to read
through, and most of them seemed to only make sense if you had some
kind of prior knowledge of the terminology. If somebody could give me
a simple description of the maths behind it, it would be greatly
appreciated (especially how it is expanded to deal with chords).

Also, does your method only return a single value for complexity (or
decency of approximation or whatever you call it)?
And are octaves treated specially or not?

--G

--- In harmonic_entropy@yahoogroups.com, "geraintluff"
<geraintluff@h...> wrote:
>
> Ok, I stumbled across this group by accident, but it seems extremely
> similar to stuff I've been trying myself (although I hadn't done any
> research into this area before). I'm not familiar with any
scientists'
> names or theories, but I can sort of see what you are measuring, at
> least for the simple two-part relationships (i.e. how well it can be
> approximated to a simple integer ratio, with "s" being a measure of
> how fussy you are about exact pitch).
>
> However, I couldn't find a simple description of how the values are
> actually calculated, because there were a lot of past posts to read
> through, and most of them seemed to only make sense if you had some
> kind of prior knowledge of the terminology. If somebody could give
me
> a simple description of the maths behind it, it would be greatly
> appreciated (especially how it is expanded to deal with chords).

See

/harmonic_entropy/topicId_347.html#350

Does that help? I'd be happy to fill in any holes you're unsure about.

For triads, you have to start with a 2D representation of triads,
such as

/harmonic_entropy/files/Erlich/fun.gif

Then use 2D instead of 1D bell curves.

I haven't actually completed any triadic (or bigger-chord) harmonic
entropy calculations yet . . .

> Also, does your method only return a single value for complexity (or
> decency of approximation or whatever you call it)?

It returns a single value for entropy for each interval, as you can
see on the graphs.

> And are octaves treated specially or not?

Normally they are not, but we have a version called octave-equivalent
harmonic entropy, where all octave-equivalents of the seed ratios are
included right off the bat. Examples of that include:

/harmonic_entropy/files/dyadic/secorent.j
pg

/harmonic_entropy/files/Erlich/alison.gif

Please bombard me with questions!