This is Jim Coleman responding since my name was used. See answer at bottom of this message. Date: Tue, 10 Apr 2001 07:43:37 -0700 From: Tom Cole <tcole@cruzio.com> Subject: Re: Towards Pure(er) 5ths in ET "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 The confusion arises because some fail to understand that a pure 5ths temperament requires a larger stretching of the octave. When one does this, the 5ths do indeed become pure and as a consequence the 4ths get wider. If one tuned a pure 5th down from A4 to D4 and then a pure 5th down from D4 to G3, the G3 would be almost 4 cents flatter than it would have been if TEMPERED 5ths were tuned. since G3 is very close to the note A3, the A3-A4 octave is also stretched about 3 cents in a pure 5ths tuning. In this kind of tuning all the intervals progress in beat rate evenly just as in regular ET except the wide intervals are a tiny bit faster and the narrow intervals are a tiny bit slower. To say it another way, in the Pure 5ths type of tuning which I wrote about 3 years ago, all intervals are equally widened including the octave. Jim Coleman, Sr.
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