[pianotech] Do fourths beat faster?

[Jeff Deutschle]

Ed & Dave:

Thanks for trying to explain it. Maybe someday I will be exposed to the theory.

On Fri, Feb 6, 2009 at 6:41 PM, David Andersen
<david at davidandersenpianos.com> wrote:
> 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.
>>
>
>
>



-- 
Regards,
Jeff Deutschle

Please address replies to the List. Do not E-mail me privately. Thank You.