Towards Pure(er) 5ths in ET

Tom Cole tcole@cruzio.com
Tue, 10 Apr 2001 07:43:37 -0700


"Kevin E. Ramsey" wrote:
> 
>     Richard, with all due respect, I think you're wrong on this one. Fifth's
> are normally narrow, and fourths are expanded; therefore, if your fourths
> are beating too much, your fifths are too wide.

Kevin, I think that Ric and Jim had it right. With a given octave
stretch, the fifth will be tempered narrow (e.g., C4 - G4) and the
complementary fourth (G4 - C5) will therefore be expanded. If G4 is
tuned so that the G4/C5 fourth is beating too fast, then the C4/G4 fifth
will be too narrow. Tuning aurally, expanding the fourths does not cause
the other intervals to expand as well. 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


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