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#2259968 - 04/10/14 08:41 PM What causes 3 strings to be flat after tuning 3 on pitch?
Grandpianoman Offline
2000 Post Club Member

Registered: 03/12/05
Posts: 2244
Loc: Portland, Oregon
I have read something about this phenomenon somewhere in a post here, but can't find it.

I first tune the left string by the ETD, then the middle string to the left string by ear, and finally the right string to the other two strings. I get a clean unison and good sustain, however, when I play the 3 strings together, the ETD is reading flat, quite a bit flat in fact...sometimes almost a cent...this is happening on just about every tri-chord......how does one counteract that, if one can, or is it necessary for the ETD to show all 3 strings are pretty much on target? Thanks



Edited by Grandpianoman (04/10/14 09:06 PM)

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#2259974 - 04/10/14 09:05 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
accordeur Online   content
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Registered: 06/23/06
Posts: 1110
Loc: Québec, Canada
If your unison is within a cent and sounds good, I would not worry about it.

I use tunelab a lot. I find that when I set the first string dead on, then ignore the display for the two other strings, the result is always within a cent sharp or flat. It really changes in realtime, bridges, soundboard etc... The piano starts to go out of tune as you tune it. The trick is minimize the damage. Solid unisons are the foundation.

At that point honestly I don't care. The unison is dead on and any musician trying to figure out on which side of theoretical Et of WT or UT would not be concentrating on playing the music.
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#2259976 - 04/10/14 09:09 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: accordeur]
Grandpianoman Offline
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Registered: 03/12/05
Posts: 2244
Loc: Portland, Oregon
Interesting Jean....logically, if every tri-chord is somewhat flat, even though the unisons are clean, with good sustain, how does that translate into a good sounding overall tuning, or perhaps it does not matter, as you say.


Edited by Grandpianoman (04/10/14 09:10 PM)

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#2259982 - 04/10/14 09:34 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
beethoven986 Online   content
3000 Post Club Member

Registered: 01/20/09
Posts: 3295
In 1998, Virgil Smith wrote an article in the PTG Journal titled, "Coping with the Pitch Difference Between One String Alone & the Tuned Unison." According to the article, "...I became aware that in part of the temperament and above, one string of a three-string unison sounding alone gave off a higher pitch than the three strings sounding together." This occurs regardless of whether one tunes aurally or by ETD.

I wouldn't worry about it too much. For reference, the PTG exam has a two-cent tolerance starting at C5 (1 cent from C3-B4), three cents for the 6th octave, and six cents for the top octave. In the temperament section, an examinee is allowed 8 errors of 1-1.9 cents each, from the master tuning, to still pass the temperament section of the exam, nevermind the rest of the exam. Now, I'm not advocating for sloppy tuning, or saying that a skilled aural tuner would not notice, but that is what the PTG has determined is acceptable to be considered proficient... just trying to put it into perspective!
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#2259988 - 04/10/14 09:51 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
accordeur Online   content
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Registered: 06/23/06
Posts: 1110
Loc: Québec, Canada
Originally Posted By: Grandpianoman
Interesting Jean....logically, if every tri-chord is somewhat flat, even though the unisons are clean, with good sustain, how does that translate into a good sounding overall tuning, or perhaps it does not matter, as you say.


Somewhat flat OR sharp. It really changes all the time. Within one cent, you're all good.
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#2260007 - 04/10/14 10:17 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
jim ialeggio Offline
500 Post Club Member

Registered: 06/03/05
Posts: 529
Loc: shirley, MA
Hey there GP,

Using Stopper's program and my ear, always together, often, if I proceed as you describe, there will be a pitch difference as you describe. However, if I tune one string first as you do first, nailing the display, as I tune the 2nd string aurally to the 1st (middle first for me, 2 mutes), I find a whole aural continuum of possible placements for that 2nd string. Many placements in that continuum sound like a nice unison. Playing within that continuum of acceptable placements for the 2nd string, I can find a placement where the machine is not having to average the pitches (or whatever it does). I can find the place where the 2 string unison displays the correct target pitch with 2 strings sounding.

Same with the 3rd string. The placement of that 3rd string can sound real nice within a continuum of acceptability, aurally. But if the 1st and 2nd string were reading correct pitch when sounding together, and the 3rd pitch sounds good, but is a hair flat, the machine will average the pitch differential, and read flat.

Try tuning the 1st string, as you do. Then tune the 2nd string aurally to the 1st. Then mute the 1st string and see what pitch the ETD is calling that second string at the point in the aural unison continuum you placed it. If I see a pitch drop when tuning the 2nd string,and check the 2nd string all on its own, the 2nd string will indeed often be flat. I can nudge that 2nd string up just I tiny hair...couple 10ths of a cent, still have a nice unison and have the machine displaying target pitch.

Still playing with this and trying to find the point where it matters and where it doesn't matter.


Jim Ialeggio


Edited by jim ialeggio (04/10/14 10:20 PM)
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#2260008 - 04/10/14 10:20 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Bob Offline
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Registered: 06/01/01
Posts: 3789
It does make a difference in the tuning if you compensate by tuning the first string sharp. Virgil Smith taught me to do that 25 years ago. Aurally, I'll tune the first string sharp by a slow roll - not a beat -just a roll. Same on the ETD - tune it a bit sharp. That's if the piano is already at pitch. If not, you have to further allow for pulling the note up in pitch - any increase more than 4 cents requires compensation as you tune - or the octave will be narrow when all string are tuned. A good stretch makes the piano come alive.
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#2260036 - 04/10/14 11:22 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Mark Cerisano, RPT Offline
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Registered: 01/24/10
Posts: 783
Loc: Montreal, Quebec, Canada
The pitch variation due to the phenomenon Weinreich mentions, can be up or down. Tuning slightly sharp will anticipate bridge tilt/soundboard settling, etc, but not the Weinreich effect. Of course, there is no drop due to bridge/soundboard shifting on a pitch drop, it would rise.

Tuning a Double String Unison first, eliminates the effect, because it already has happened by the time you are ready to check the interval. Using P4 and P5 windows for the double and triple octaves and 12ths, which checks all octave notes as you go, and then correcting the ones that settle, takes care of bridge and soundboard settling for me.

When going for clean single/double/triple octaves and 12ths, this small shift (Weinreich Effect) can be noticeable.


Edited by Mark Cerisano, RPT (04/10/14 11:24 PM)
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#2260268 - 04/11/14 02:13 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Mark Cerisano, RPT]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6342
Loc: France
Originally Posted By: Mark Cerisano, RPT
Of course, there is no drop due to bridge/soundboard shifting on a pitch drop, it would rise.



Wado you say ??? I don't get that at all the pitch would rise with bridge settling ? I do not get you there.
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#2260282 - 04/11/14 02:54 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Jon Page Offline
Full Member

Registered: 03/13/09
Posts: 185
Loc: Harwich Port, Cape Cod, Massac...
It's a known phenomenon that the three coupled strings are slightly flatter than the individuals strings. Check the pianotech archives for 'string coupling'; Jim Coleman, Sr. has a good amount of input there.
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#2260298 - 04/11/14 03:22 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6342
Loc: France
Hi Jon (was it for me ?) that sound logical as the small portion of bridge between the strings is made alive and enter in the equation of mass.
Then as wrote Ed Foote different strings coupling may modify the 3 strings impedance one way or another, making the strings keeping energy more or less long and transferring energy more or less fast to the bridge. That is what G. Weinreigh stated as an hypothesis.
AN effect on pitch is not surprising then be it on partials distribution in time, some use more energy than others (lower partials need more usually)

But most tuners use strategies to keep the effect to be too annoying, while at the same time tuning "high" fight the lowering (not raising) due to bridge tilt and soundboard settling.

That may be the reason why the effect is not given as much attention in regard of pitch.

I probably use it for other means (shaping the decay)without thinking of the pitch effect.

also, when tuning after using a mute strip, I know no tuners that would tune the other strings low of the first, it does not sound natural to do so.

What I do not really get is why, while that is known from some time now, the tuners do not make the link between their current practice and those effects, not clearly, it is told now in tuner's schools but recently.

The level of control on the strings must be good enough, but we are helped by the tone quality. Then why tuning only for pitches and not to make a nice musical tone ("bloom" of course represents that)
So where do the "bloom" comes from. not an ETD, they can help you tobe near but cannot dealwith coupling, phase etc...
Only our listening and perceptions with the playing hand can tell us.



Best regards


Edited by Olek (04/12/14 06:24 AM)
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#2260550 - 04/12/14 02:30 AM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Toni Goldener Online   content
Full Member

Registered: 08/27/11
Posts: 87
Loc: Switzerland
In cases when tree strings together sound too flat, I tune the first to the verituner, the second to the first aurally ( there is already a tendency hearable) then the third to the rest, compare to the verituner again. The measured unison is e. g. 0.9 c flat I retune the whole unison starting with 1 c sharp. The next unisons I tune directly 1 c sharp, till this sounding effect is over, mostly somewhere in the last two octaves. That is why my verituner is not only an ETD, I call it my "third ear" wink


Edited by Toni Goldener (04/12/14 02:31 AM)
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#2260564 - 04/12/14 04:50 AM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6342
Loc: France
As you say, Tony the way it goes is perceived when tuning the second string yet.
A goo strong argument to tune the temperament with unison, which is difficult for beginners.

What I notice is a tendency to "straighten" the unison more when using an ETD as a control, the direct contact with the tone energy is somewhat lowered due to visualization.

I am not arguing for pitch fluctuations, but some exists with the phase plane orientation.

(
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#2260572 - 04/12/14 05:43 AM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6342
Loc: France
High treble (D#7) tuning.
comparaison 2 strings and 3 strings
Looking for tone projection and energy preservation.




sound file :
d#`7 tuning - time stretch /2
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#2260577 - 04/12/14 06:29 AM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Bob]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6342
Loc: France
Originally Posted By: Bob
It does make a difference in the tuning if you compensate by tuning the first string sharp. Virgil Smith taught me to do that 25 years ago. Aurally, I'll tune the first string sharp by a slow roll - not a beat -just a roll. Same on the ETD - tune it a bit sharp. That's if the piano is already at pitch. If not, you have to further allow for pulling the note up in pitch - any increase more than 4 cents requires compensation as you tune - or the octave will be narrow when all string are tuned. A good stretch makes the piano come alive.


When I was using an ETD I always tuned doublets to be sure, but in the end that turns to an habit of being always sharp of the display.
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#2260640 - 04/12/14 10:32 AM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Emmery Offline
2000 Post Club Member

Registered: 04/02/08
Posts: 2328
Loc: Niagara Region, On. Canada
If I encounter a piano that is flat and is getting trued up to A440, and, the shift is less than 10-15cents, I compensate by adjusting my ETD calibration 1 or 2 cents so that its actually targeting higher. With RCT, I actually just use a smart tune function with the compensation put in there. I find that the highest octave might actually end up gradually a little sharp in the end but I can live with that since it just adds an effect of brilliance to the sound in my opinion.

I don't bother trying to adjust a slow roll or any individual guessed compensation as I tune, the piano will respond fairly evenly on its shift flat as the unisons get pulled in. I might find a small area near the breaks which might needa bit of tidying up in the end but its less stressful to do it this way than trying to do it on the fly as I tune.
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#2260676 - 04/12/14 12:25 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
kpembrook Offline
1000 Post Club Member

Registered: 04/06/10
Posts: 1252
Loc: Michigan
Originally Posted By: Grandpianoman
I have read something about this phenomenon somewhere in a post here, but can't find it.

I first tune the left string by the ETD, then the middle string to the left string by ear, and finally the right string to the other two strings. I get a clean unison and good sustain, however, when I play the 3 strings together, the ETD is reading flat, quite a bit flat in fact...sometimes almost a cent...this is happening on just about every tri-chord......how does one counteract that, if one can, or is it necessary for the ETD to show all 3 strings are pretty much on target? Thanks



I may have mentioned it previously. I first learned of the phenomenon in an article that I think was published in Scientific American. However, I find it in my copy of "Five Lectures on the Acoustics of the Piano" published by Royal Swedish Academy of Music. The article by Gabriel Weinreich is titled "The coupled motion of piano strings".

What happens is a phenomenon that can happen with weights swinging on a wire or other kinds of mechanically linked pendulums. There is a tiny mechanical linkage happening through the bridge that "links" the strings together so that they affect each other. The typical result is for two strings vibrating together to be flat of either string alone (other damped and unable to vibrate).

Yes, Virgil Smith was one of the better-known exponents of dealing with this phenomenon. Those of us who have been exposed to his teachings (directly or indirectly through his book or videos) find that a "tighter" tuning can be achieved if this phenomenon is accounted for rather than just hoping that the discrepancy is so small nobody will notice.

It is indeed audible -- especially on larger pianos. Rather than using a pitch measuring device to verify the existence of the phenomenon, it is also possible to just tune an octave (say, A-37 from A-49). If you tune a perfect (however your ear defines that) octave with a single string of A-37 and then tune an additional string on the note 37 unison, the unison will be flat to the original perfectly tuned octave with A-49. You can repeat the phenomenon simply by changing the muting back and forth from one to two strings. There is normally no additional change perceivable by adding the third string

I was personally never really happy with my concert tunings until I started accounting for this phenomenon using Virgil's techniques. Now, I do it on most grands that are close to pitch.

I'm not sure how well this can be accounted for with an ETD since there is no algorithm that can account for it because it varies from one individual instrument to another in addition from one scale to another. I guess that you could note the pitch discrepancy and change it accordingly. You still aren't likely to get the "locked in" kind of tuning that is possible if you simply "crack the unison".
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#2260679 - 04/12/14 12:37 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Ed McMorrow, RPT Offline
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Registered: 12/09/12
Posts: 1459
Loc: Seattle, WA USA
I find the coupling effect strongest in the mid-section of strings. You can hear/feel the unison strings pull together very, very slightly. It certainly helps smooth out slow false beats.

I tried to explain about unison coupling to Virgil and he just gave me a blank stare. I don't think the physics interested him.
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#2260696 - 04/12/14 01:32 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Ed McMorrow, RPT]
kpembrook Offline
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Registered: 04/06/10
Posts: 1252
Loc: Michigan
Originally Posted By: Ed McMorrow, RPT
I find the coupling effect strongest in the mid-section of strings. You can hear/feel the unison strings pull together very, very slightly. It certainly helps smooth out slow false beats.

I tried to explain about unison coupling to Virgil and he just gave me a blank stare. I don't think the physics interested him.


Yes, the phenomenon is definitely below the threshold of perception by the time you get up out of the tenor section -- and maybe not even the top of that. Mid-range down into bass is where it matters.
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USA Distributor for Isaac Cadenza hammers and Profundo Bass Strings
Supporting Piano Owners D-I-Y piano tuning and repair

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#2260746 - 04/12/14 04:45 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Chris Leslie Offline
Full Member

Registered: 01/01/11
Posts: 452
Loc: Canberra, ACT, Australia
Let's not ignore Mark Cerisano's Double String Unison technique as a method that inherently accounts for the Weinreich effect. However, Grandpianoman is using an EDT and I am not sure how DSU can be adapted to EDT methods.
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#2260755 - 04/12/14 05:05 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Grandpianoman Offline
2000 Post Club Member

Registered: 03/12/05
Posts: 2244
Loc: Portland, Oregon
Thanks for all the replies...interesting subject.

Having tuned my smaller Grand about 2 months ago, tuning it now, I found it to be mostly sharp. It usually goes flat. Because of that normal flattening, I usually try to tune the first string with the ETD, the left one, slightly sharp, between 0.01 to 0.02 sharp, then tune the middle string by ear to the left one, then the right string to the the other 2, listening to all 3 together to get the optimal bloom, sustain and clarity.

Bob, is that close to what Virgil Smith was suggesting to you?

In the end, is there a consensus on what is he best way/technique to reduce this phenomenon, using an ETD?





Edited by Grandpianoman (04/12/14 05:16 PM)

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#2260789 - 04/12/14 06:23 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Olek Online   content
6000 Post Club Member

Registered: 03/14/08
Posts: 6342
Loc: France
Hello,

To me, ETD can be used for 2 strings as the envelope is stable enough.

I just noticed first couple tuned immediately, not what happens when using a strip mute or unison as you go, so the final unison is always the same type, while aural tuners have more liberty.

Also the very strong coupling obtained for a better reading on the ETD tend to straighten the tone, and the tuner have a tendency to keep the same feeling for the 3d string, producing then a somewhat hard tone (or straight tone)

I was never able to verify exactly the drift in the end (3strings) as the bridge tilt add to the lowering, often in a more noticeable way, (but less in mediums than around and after the treble plate .)

I imagine wannabee tuners reading the thread, or, more aware, beginners or students, that have yet a good appreciation of the difficulty. This may sound discouraging...
Hopefully it is not so bad, we have a sort of "grey zone" with beats speed, that are not really something regular in time and modulate slowly. The Weinreich effect may hide within that grey zone too.

We certainly cannot expect the wire to vibrate the same vertically, horizontally, longitudinally, in a long enough period of time.
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#2260795 - 04/12/14 06:40 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
ando Online   content
3000 Post Club Member

Registered: 11/23/10
Posts: 3329
Loc: Melbourne, Australia
So if this effect is, as some say, more pronounced in the middle range of the piano, why not just set the temperament using single strings via a temperament strip, then tune the unisons. Wouldn't they all tend to flatten together? Then bass bi-chords and high treble by ear using whatever stretch you like. Is there a need to be more precise than this? The whole piano might be a cent flat, but as long as it sounds in tune.

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#2260800 - 04/12/14 06:51 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: ando]
Mark Cerisano, RPT Offline
500 Post Club Member

Registered: 01/24/10
Posts: 783
Loc: Montreal, Quebec, Canada
Originally Posted By: ando
So if this effect is, as some say, more pronounced in the middle range of the piano, why not just set the temperament using single strings via a temperament strip, then tune the unisons. Wouldn't they all tend to flatten together?


No. Weinreich states, and I have confirmed, the final pitch will go up, or down, or stay the same. There's no way to tell.
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#2260802 - 04/12/14 06:54 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Olek]
Mark Cerisano, RPT Offline
500 Post Club Member

Registered: 01/24/10
Posts: 783
Loc: Montreal, Quebec, Canada
Originally Posted By: Olek
Originally Posted By: Mark Cerisano, RPT
Of course, there is no drop due to bridge/soundboard shifting on a pitch drop, it would rise.



Wado you say ??? I don't get that at all the pitch would rise with bridge settling ? I do not get you there.


Not settling. Soundboard rises in a pitch drop situation. This is not a pitch raise.

Also, the bridge will tilt backwards, increasing tension on surrounding strings.
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#2260804 - 04/12/14 06:57 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: kpembrook]
Mark Cerisano, RPT Offline
500 Post Club Member

Registered: 01/24/10
Posts: 783
Loc: Montreal, Quebec, Canada
Originally Posted By: kpembrook
Originally Posted By: Ed McMorrow, RPT
I find the coupling effect strongest in the mid-section of strings. You can hear/feel the unison strings pull together very, very slightly. It certainly helps smooth out slow false beats.

I tried to explain about unison coupling to Virgil and he just gave me a blank stare. I don't think the physics interested him.


Yes, the phenomenon is definitely below the threshold of perception by the time you get up out of the tenor section -- and maybe not even the top of that. Mid-range down into bass is where it matters.


I find tuning double and triple octaves in the 5th and 6th octave to be as beatless as possible, to be the place where I want the most precision. Small changes in cents mean huge changes in Hz, which mean beats.
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#2260806 - 04/12/14 07:01 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: kpembrook]
Mark Cerisano, RPT Offline
500 Post Club Member

Registered: 01/24/10
Posts: 783
Loc: Montreal, Quebec, Canada
Originally Posted By: kpembrook

What happens is a phenomenon that can happen with weights swinging on a wire or other kinds of mechanically linked pendulums. There is a tiny mechanical linkage happening through the bridge that "links" the strings together so that they affect each other. The typical result is for two strings vibrating together to be flat of either string alone (other damped and unable to vibrate).


I posted an excerpt from an email from Professor Weinreich to me, stating that the pitch can go up, or down, or not move at all, and he had no way to predict what it would be.

I will post it again if someone is interested.
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#2260814 - 04/12/14 07:10 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Mark Cerisano, RPT]
Chris Leslie Offline
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Registered: 01/01/11
Posts: 452
Loc: Canberra, ACT, Australia
Yes, but we tune aurally by changes in Hz, not cents, which in the 5th and 6th octave corresponds to small changes in cents.
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#2260816 - 04/12/14 07:10 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Mark Cerisano, RPT]
ando Online   content
3000 Post Club Member

Registered: 11/23/10
Posts: 3329
Loc: Melbourne, Australia
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: ando
So if this effect is, as some say, more pronounced in the middle range of the piano, why not just set the temperament using single strings via a temperament strip, then tune the unisons. Wouldn't they all tend to flatten together?


No. Weinreich states, and I have confirmed, the final pitch will go up, or down, or stay the same. There's no way to tell.


The pitch dropping seems fairly easy to understand, but I'm struggling to understand why the pitch would go up. And if the pitch stays the same, who's to say the effect is present at all?

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#2260848 - 04/12/14 09:43 PM Re: What causes 3 strings to be flat after tuning 3 on pitch? [Re: Grandpianoman]
Bob Offline
3000 Post Club Member

Registered: 06/01/01
Posts: 3789
Originally Posted By: Grandpianoman
Thanks for all the replies...interesting subject.

Having tuned my smaller Grand about 2 months ago, tuning it now, I found it to be mostly sharp. It usually goes flat. Because of that normal flattening, I usually try to tune the first string with the ETD, the left one, slightly sharp, between 0.01 to 0.02 sharp, then tune the middle string by ear to the left one, then the right string to the the other 2, listening to all 3 together to get the optimal bloom, sustain and clarity.

Bob, is that close to what Virgil Smith was suggesting to you?

In the end, is there a consensus on what is he best way/technique to reduce this phenomenon, using an ETD?




A piano tuned 2 months ago will likely be slightly sharp now that the weather is warming and the humidity is higher.

To answer your question, Yes, that is what Virgil suggested, only aurally, and he tuned all three strings, then checked the note didn't sound flat and adjusted if needed. To use an ETD, one approach would be to determine the amount of pitch deviation needed aurally, then adjust the ETD, but as said above, that will vary from piano to piano and within a piano. Accounting for this is more towards a higher level of tuning that one gains with experience. I usually tune 1/2 an octave, then do some quick checks to see how the stretch, beats, and chords are sounding. If I don't like something, I can easily modify things as I go.

When I get a good stretch, the piano comes alive with personality. It's only worth worrying about on a fine tuning. Pitch raises need not apply.
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