Huh?? was RE: pRCT got ears again...

[Mark Schecter]

Hi, Kent.

Thanks for taking the time to spell this out. You were thinking more 
globally, while I was thinking more locally. You and John are both 
correct in the sense in which you were thinking. Point acknowledged.

-Mark Schecter

Kent Swafford wrote:
> 
> On May 4, 2006, at 12:09 AM, Mark Schecter wrote:
> 
>> Hi, John.
>>
>> Sorry, but that's not correct.
> 
> No, John was correct. If you assume that equal temperament is being 
> tuned, then there is indeed an inverse relationship between the beat 
> rates of the fourths and fifths. That is, if you widen the octave within 
> which equal temperament is tuned, then all the fifths get wider (slower 
> beat rate) and all the fourths get wider (faster beat rate).
> 
>> If the fifth above the bottom note of a 4:2 octave is made less 
>> contracted, approaching just, the fourth below the top note will also 
>> get slower, as it contracts from its expanded state toward just.
> 
> The beat rate relationship that you cite is correct, but you describe 
> raising the C4 within an F3-F4 octave, which you cannot do and still 
> maintain equal temperament. If the F3-F4 octave is properly tuned, then 
> one could tune the C4 so that both the F3-C4 fifth and the C4-F4 4th are 
> just, but that is irrelevant to equal temperament.
> 
> The more useful note to look at might be A#3. In checking the 4:2 F3-F4 
> octave, the difference in beat rate between the F3-A#3 4th and the 
> A#3-F4 5th _is_ the beat rate of the 4:2 octave. Any change in the 
> tuning of A#3 will move the beat rates of the 4th and 5th in opposite 
> directions.
> 
> Assume an accurately tuned temperament octave; if you raise the F4 and 
> widen the F3-F4 octave, then you would also have to raise _both_ the A#3 
> and the C4, widening _all_ of the intervals within the octave. Widening 
> all the intervals would speed up the 4ths but slow down the 5ths.
> 
> You can't slow down both the 4ths _and_ 5ths and still maintain equal 
> temperament.
> 
> HTH.    8^)
> 
> 
> Kent
> 
> 
> 
> 
>> For example, if the octave is F3-F4, and the fifth above F3 is C4, the 
>> act of lowering C4 to contract the fifth, expands the fourth C4-F4. 
>> Contrariwise, if you then raise C4 to slow the fifth F3-C4, so doing 
>> also contracts the expanded fourth C4-F4 toward just, or beatless. 
>> It's easier to picture than to say. HTH.
>>
>> -Mark
>>
>> John M. Formsma wrote:
>>> How do you get 4ths and 5ths to both be slower? In equal temperament, a
>>> slower 5th means a faster 4th.
> 
>