Hertz and Cents

[Richard Moody]

>. That's the beauty of using logs, because it allows you to use
> numbers like 1 or 5 semitones to express ratios between factors,
> instead of nasty numbers like 2^(5/12). Semitones are intuitively
> graspable and "calculations" can be done with monochords without
> resorting to any numbers at all. It also better expresses the way the
> acoustics are perceived.

>Stephen

Ah, but there is beauty in "nasty numbers" to me at least.  Looking at
2^(5/12) I see an interval of 5   1/12th semitones  And how can it be nasty
if logs are beautiful?  The decimal equilivant of 5/12 is actually a log,
.41667 (of the 2).
Multiply that by 1200 and you get 500 cents or an ET Fourth.  Or 2^.41667 is
1.3348 or the division of the monochord (or fretboard) to give a Fourth (the
interval) of an octave equally divided into twelve parts. The"natural"
Fourth would be 4/3 or 1.33333.
    You said calculations could be done with monochrods without resorting to
any  numbers at all.  How is this done?    ---ric