[PD] making scales from frequency values

[Matt Barber]

> It is a ratio problem I believe. The initial problem stems from trying to
> shoehorn the original ratios/partials from the analysis of my 5 chimes, into
> equal temperament.  There are a couple of reasons for this;  I've been
> playing around on the piano after assigning each partial to its nearest
> midi/equal temperament note, and was liking the results that ensued whilst
> listening to them on the piano. Obviously the tones generated on the piano
> are much richer than individual sines. The original wind chime has been sat
> over my desk for the last 18 months,  so I'm also very attuned to the
> original sounds. I would also like to have the various partials to be as
> modular as possible with the idea that I can 'mix'n'match' the various
> frequencies of the chimes to create new sonorities.
>
> When I listen to the results of using equal temperament within my patch my
> ears don't like the results in comparison to the original frequencies, which
> has led to the current predicament.


One other question for you that might be a bit unrelated:  are you
looking for an equal temperament for your chimes?  And if so, should
the modular interval necessarily be an octave?

For instance, a scale I have liked lately is 19-tones per
octave+fifth, which is very very close to 12-tones per octave, but you
can do some interesting additive synthesis to "stretch" the partials
so they match the equal temperament (that is, every partial number
that is a power of two is now an octave+fifth higher than the last,
rather than an octave in "normal" harmonic series... then all the
other partials are just fit in logarithmically).  Another is 11-tones
per perfect 5th, which corresponds quite a bit to 19-tones per octave.

Equal temperaments can give you a systematic way of handling pitch
that in my experience is a bit harder to navigate with just
intonation/unequal temperament; at least they take a little bit less
planning and experimentation.

It seems possible you could maybe reverse-engineer a "best-fit" equal
temperament for your chimes that would not just give you the selection
of the original partials, but a compositional space you could use with
some more expression, so that the chimes fit in "organically" if they
want to, but aren't the only thing going on.  I haven't looked hard at
your numbers though -- the more you have the harder it will be to find
a "best-fit."  Remember though, that a great deal of the expression in
traditional Western classical music comes from some of the partials
being out of tune with the underlying scale.


The "combine 5 partials, each chosen from one of the chimes" problem
is quite a bit easier to solve, but attack transients and decays for
each of partials, assuming you really will be using [osc~] will be
paramount: they are a lot of what makes your chimes sound the way they
do.

Sorry for the long wind,

Matt