Hi, Jeff---Here is what I know, based on empirical, practical evidence from thousands of tunings: in a highly idealized equal temperament, the fourths I can hear, usually from C1-F1 to around C6, are all expanded, and all beating the same slow rolling beat---between 1-2 bps. All the fifths are slightly compressed, with no discernible beat. I tune the ends of the piano with double and triple octaves---in the treble, the double octave is usually slightly stretched, with a barely discernible beat, and the triple octave is beatless. In the bass, both double and triple octaves "appear" or sound beatless. David Andersen On Feb 6, 2009, at 7:06 AM, Jeff Deutschle wrote: > Ed: > > I am confused. You say David is right "... The fourths and fifths stay > the same rate all the way up and down the scale ..." but you also say > "... fourths and fifths progress more slowly in the mid-range of the > piano. ..." Well, are you saying that they stay the same or are you > saying that they progress more slowly? > > Please don't think I am nit-picking your post. I have had this > discussion with others and there is a difference between intervals > beating the same and intervals appearing to beat the same. > > I do not get the Journal. There may be something that I don't > understand about this. Maybe someone can steer me right. I understand, > and can hear, how a certain octave stretch will keep the 5ths beating > at the same rate. I do not understand, and do not hear, how this also > can keep the 4ths beating at the same rate. Stretching octaves can > prevent the speeding up of narrow intervals such as 5ths. How can it > also prevent the speeding up of wide intervals, such as 4ths? When an > octave is stretched, wouldn't all the narrow intervals be made less > narrow and beat slower but all the wide intervals be made wider and > beat faster? > > On Fri, Feb 6, 2009 at 9:05 AM, Ed Sutton <ed440 at mindspring.com> > wrote: >> David's right. Because of inharmonicity and octave stretching, >> fourths and >> fifths progress more slowly in the mid-range of the piano. I >> suppose on >> organs they follow the octave/double rule. >> Read Dan Levitan's 2007-08 series to understand this. Plan on >> studying for 2 >> or 3 weeks and taking notes! >> Remember that on piano we are tuning "Imitation ET," which is not >> the same >> as theoretically perfect ET. >> >> Ed Sutton >> >> ps I apologize for the blank messages. If you have Windows Vista with >> erratic slowdowns, you know why. >> >> ----- Original Message ----- >> From: David Andersen >> To: pianotech at ptg.org >> Sent: Friday, February 06, 2009 1:01 AM >> Subject: Re: [pianotech] Do fourths beat faster? >> Brother, I beg to differ. The fourths and fifths stay the same rate >> all the >> way up and down the scale---at least in idealized equal >> temperament, which >> what what I use. >> David Andersen >> >> On Feb 5, 2009, at 9:43 PM, Scott Jackson wrote: >> >> Yep, every interval beats faster as you move up; by the time you >> reach an >> octave higher, twice as fast. >> >> Scott Jackson >> >> >> ----- Original Message ----- >> From: Byron >> To: pianotech at ptg.org >> Sent: Friday, February 06, 2009 1:08 PM >> Subject: [pianotech] Do fourths beat faster? >> Do fourths beat faster as they climb chromatically? How about fifths? >> >> Thanks >> > > > > -- > Regards, > Jeff Deutschle > > Please address replies to the List. Do not E-mail me privately. > Thank You. >
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