James McCartney wrote:
Somehow I am able to do just intonation just fine with 64 bit double
precision floating point.
Of course. And why bother to give instrumentalists a music sheet with
notes and staves? We could as well give them a listing of frequencies
expressed in Hz, durations in ms, and amplitudes in dB. Likewise, I
don't think you could have created SC, had you had to use only a bunch
of "0" and "1" to code it. My point is that data representation is as
important as data themselves. Speaking of the pythagorean mystics
would be off-topic here, suffice it to say that when you write 3/2,
you express a relation between 2 integers. This meaning, given by this
relation, is lost when you use the decimal form. That's why rational
numbers are so important in music, and more generally, in arts: they
express a relation.
I understand now that you had to give up a few things, like rational
numbers, for the sake of real time execution. This answer sounds
more...rational than saying that my request does not make sense. It
has been making sense for the last 25 centuries, and probably before.
Let us remind that a western aberration like 12-EQ has only been
raging for the last 2 centuries (may it die quickly). As for the
pertinence of taking into account rational expressions in the SC main
distribution, we could ask ourselves whether it would be less
pertinent than including the Pavaroh class.
Now, if it possible to have floats represented as rational numbers,
that is, if we can input arrays of ratios to functions which would
output arrays of ratios, this would solve the problem. Whether the
function uses floats or ratios to compute the ratios is irrelevant to
the user, as long as he can add, substract, divide, multiply and
generate single ratios and arrays of ratios. If this could be done by
simply appending .asRatio, as we do with .asFloat, this would be
ideal.
I could probably try to code my own hack for my own personal use. But
there is more to it. First, if this is done by a professional
programmer, it will be more efficient and elegant. And second, maybe
the more important, you understand that behind this matter of rational
numbers, lies another conception of music, and music scales. By
including in the main SC distribution a way of dealing with rational
numbers, you recognize this alternative conception of music. Likewise,
I guess that you included Pavaroh in the SC distribution as a way of
expressing your taste for ragas, didn't you?
Philippe.
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