consistency

On Thu, 19 Sep 1996, John Chalmers wrote:
> Re Consistency: I may have missed part of this discussion, but I don't
> quite grasph how fractional consistency can be defined on a closed,
> cyclic, and equally-tempered tuning system. Or am I just humor-impaired
> this AM (in general, perhaps, as I'm sweltering in the Texas heat and
> humidity preparing to become homeless if and when my house sale
> closes next week).

Well, here's the algorithm for calculating consistency level (perhaps I
should say _an_ algorithm):

consistency_level(ET_number, limit):
max <- 0
min <- 0
FOR loop <- 3 TO limit BY 2
exact_steps <- ET_number * log2(loop)
error <- exact_steps - round(exact_steps)
IF error > max THEN
max <- err
ELSEIF error < min THEN
min <- err
ENDIF
ENDFOR
RETURN integer_part(0.5 / (max - min))

Roughly speaking, find the interval within the limit which has the
greatest error, divide that error into half the stepsize, and truncate
to get consistency level. If you simply leave off that last step of
truncation, you get what might be considered a fractional consistency
level.

--pH (manynote@library.wustl.edu or http://library.wustl.edu/~manynote)
O
/\ "Foul? What the hell for?"
-\-\-- o "Because you are chalking your cue with the 3-ball."

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