[pianotech] Do fourths beat faster?

[Ed Sutton]

Thank you for your comments.
Please read Dan Levitan's articles. You will enjoy them, and they will 
provide the kind of authoritative and thorough answer you will need to be 
convinced that simple, idealized mathematics does not give a precise 
description of what pianos do in the real world. Read Ota's article in the 
Dec. 09 Journal. Find Al Sanderson's spread sheets of ideal and actual piano 
tunings. Read articles about scaling, and think about what happens when the 
relative inharmonicity between notes varies, as it does in real pianos.
Join PTG and get a big discount on CD ROMs of 20 years of the Journal.
Ed Sutton
----- Original Message ----- 
From: "Brian Wilson" <pianocare2 at bigpond.com>
To: <pianotech at ptg.org>
Sent: Friday, February 06, 2009 10:05 PM
Subject: Re: [pianotech] Do fourths beat faster?


> Sorry , but how can you have the "same rolling beat"? You think they all
> sound the same? 1 to 2 beats per second is a large difference, in fact 
> they
> are different speeds !
>
> Let's start at the beginning. A37 (let's say it's in tune") A fourth above
> is D42. The theory is that a fourth harmonics is 4:3. So the frequency of
> A37 (220 x 4 = 880) and the frequency of D42 (293.664776 x 3 = 880.994328)
> The difference is .994328 beats per second expanded... so we round that 
> off
> to 1 beat per second. If you are bothered to investigate further, you will
> find that the beat rates increase as you travel chromatically higher and
> decrease as you travel towards the bass.
>
> Now an example: F33 beats against A37 (major 3rd) approx 7 beats per 
> second.
> F33 beats against D42 approx 8 beats per second.(major 6th) A#38 beats
> against D42(major 3rd) approx 9.5 beats per second. Now do the math.... 
> does
> F33 and A#38 beat at 1 beat per second? NO it is slower... It works out to
> be .78917 beats per second. You work it out. Now try calculations in
> different octaves. Try remembering 1.0594631.
>
> The reason we say that fourths beat at 1 beat per second it so that it is 
> a
> guide, and to achieve equal temperament, we need to use 3rds and 6ths,
> otherwise you get something which is just near the ball park.
>
> Now before you start telling me about inharmonicity, when you are tuning
> octaves (towards treble) tune octave just above where you want it, check
> fifth (compressed) fourth beats slightly faster (expanded) Then listen to
> the 3rds, 6ths or 10ths to lock it in place.i.e  gradually increasing in
> speed. I then keep this process until I can use 2 octaves and 3rd, triple
> octaves etc. You compensate for inharmonicity in your stretch (better
> described as a temper) The fourths may "sound the same" because you should
> be using the same process from note to note.
>
> It is paramount that you understand the theory of the tuning process to
> apply that knowledge to achieve an equal tempered piano.
>
> Before any more posts on this subject, please work out the theory. It is a
> proven fact and not based on empirical or practical ideas. Look in a text
> book. I was examined on this several times.
> We don't need to discuss how many tunings we have all performed to justify
> our knowledge.
>
> Regards
> Brian
> -----Original Message----.
> From: pianotech-bounces at ptg.org [mailto:pianotech-bounces at ptg.org] On 
> Behalf
> Of Jeff Deutschle
> Sent: Saturday, 7 February 2009 11:36 AM
> To: pianotech at ptg.org
> Subject: Re: [pianotech] Do fourths beat faster?
>
> 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.
>
>
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