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emainder update

🔗X. J. Scott <xjscott@...>

3/15/2002 7:21:31 PM

Marc et al,

Well I got the emainder working nicely -- it had the
result of encouraging me to take remainders of high
powers, which shook out some nice bugs to fix.

I just realized though that this whole very useful
tuning operation of finding remainders in logarithmic
space or whatever is actually a famous (notorious?)
operation of specific applicability and usefulness...
and futhermore that musical insights obtained have
usefulness in other fields, if you know what I mean!

Anyway, getting away from that, the result of the
operation is interesting -- historically it has been
called 'the comma'. In discussion with Jacky, I
discovered he calls it the "Interval of Completion",
which in all honesty, I find to be a much superior term
as 'comma' is rather archaic and non-self-explanatory.

The process of tempering is then the process of
reducing the size of the Interval of Completion.

Any other terms used out there for this idea?

I mysely find myself calling both the operation and the
result the 'emainder' (short obviously for exponential
remainder) and favor the symbol %%, which I now
consider to be the self-evident answer, though I
allowed the keyword 'emod' as an alias in the software.

- Jeff