Towards Pure(er) 5ths in ET

[Tom Cole]

I've always thought that the fourth beating faster than the fifth was
indicative of an octave stretched beyond pure, that, as Jim just said
about his pure fifths temperament, you are expanding not only the octave
but all the intervals within. Thus the (narrowed) fifths slow down and
the (expanded) fourths speed up.

Another point that might explain the fourth being faster is that the
coincident partials of G4 - C5 are an octave higher than C4 - G4.

But as you say, it is a lofty subject.

Tom Cole

Richard Moody wrote:
> 
> |On the contrary, if you tune an
> | octave, then expand the fourth within that octave, you will
> | automatically contract the fifth.
> |
> | Does this cloudify the subject?
> |
> | Tom Cole
> 
> Well it is a lofty subject esp when you wonder why the G4--C5 fourth
> will beat twice as fast as the C4--G4 fifth.  And this is not the same
> thing as saying the 4th on top is twice as sharp as the 5th on the
> bottom.  ---ric