[pianotech] Do fourths beat faster?

[David Andersen]

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.
>