[pianotech] Do fourths beat faster?

[Ed Sutton]

David-

I wish I hadn't gotten into this!

 >> 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.

There is a logical inconsistency in my statement, but practically speaking, 
it's quite practical. Practically speaking, I have also said the upper of 
two contiguous fourths should sound "the same and not slower." For some 
people, this kind of thinking works. Other people are driven crazy by it.

If you want a perfect, logical parsing out of the situation, read Dan's 
articles of 1994 and 2007-08, about 60 pages total, and I will not try to 
summarize them.

On pianos we tune "Imitation Equal Temperaments." They are compromises, and 
more than one good compromise is possible. As I understand it, there's no 
one and only final and perfect answer, good for all pianos and all places.

Best regards,
Ed Sutton
----- Original Message ----- 
From: "Jeff Deutschle" <oaronshoulder at gmail.com>
To: "Ed Sutton" <ed440 at mindspring.com>; <pianotech at ptg.org>
Sent: Friday, February 06, 2009 10:06 AM
Subject: Re: [pianotech] Do fourths beat faster?


> 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.