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Originally Posted by Alex_
I earlier actiualy meant how to calculate the back scale of the treble section wich its not limited by space.

And I believe we have explained that that is not something that is calculated. It is a designer's choice what numbers to apply. There is no accepted formula.



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Thank you all for your wisdom.
I suppose that an ideal piano design would have an oveall back scale gradually increasing from trebble to bass as soundboard mobility increases from trebble to bass to match the strings frequencies. I cant figure why from high trebble to low tenor we see pianos with the same back scale distances all along the long bridge.

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Originally Posted by Alex_
Thank you all for your wisdom.
I suppose that an ideal piano design would have an oveall back scale gradually increasing from trebble to bass as soundboard mobility increases from trebble to bass to match the strings frequencies. I cant figure why from high trebble to low tenor we see pianos with the same back scale distances all along the long bridge.

First, there is no such thing as an “ideal” piano design. As well, most of your questions on the backscale seem to have already been answered, but I’ll make a few observations:

The “backscale”—I think introduced this word to our lexicon back in the 1970s, if anyone knows of an earlier reference please let me know.—refers to the length of the string segment between the trailing bridge pins and the back termination point of the strings. (This is not the number you need to supply to the string winder!) The back termination point could be a bearing bar (either cast as part of the stringframe or a separate bar (made of steel, iron, wood or, sometimes, hard felt) or it could be the hitchpin itself (as used in the Baldwin “Accu-Just” system).

The basic rule for backscale length is that it has to be long enough to allow the soundboard/bridge system to move adequately to produce the desired sounds yet not so long as to be susceptible to extraneous (unwanted) vibrations. I know, this is rather vague but this is a hard parameter to pin down with any exact rule.

In the treble the backscale length can be quite short. In some pianos it is as little as one-half the speaking length. That is, for a C-88 speaking length of 48 mm, the backscale length might be 24 mm. This is very short but the bridge/soundboard assembly doesn’t have to move much at these frequencies and they seem to get by with it. Kind of. In other pianos the backscale length may be equal to the speaking length. In the example given this means the backscale length would be 48 mm. Some manufactures attempt to “tune” this backscale length to some partial of the speaking length, i.e., the "aliquot" duplex scaling system. The advantages (if any) of this have long been debated. Personally, I see little value in the practice other than for marketing purposes.

In the bass, the rule—my rule, at least—is to make the backscale as long as is practical. That bridge needs to be able to move. In very short piano this may mean shortening the speaking length of the strings some. And it is in very short pianos that this really becomes an issue. It is not unusual, in shorter grands—say 150 – 185 cm in length—to find the backscale length at A-1 to be around 25 – 35 mm. I know, it may look longer than this but take another look, some of the string lies solidly on the felt covering the hitchpin riser and then there is the twisted tail that effectively acts as a rather thick steel rod. This acts like a very stiff spring resisting the motion of the bridge. Not exactly what we want in the bass of a piano. .

Backscale lengths this short effectively lock the bridge down and prevent any motion at low frequencies. Anyone who questions this is encouraged to build a string frame and try it out. The problem is that to produce any appreciable sound power at low frequencies we must move a lot of air. That means that the soundboard has to be free to move. But, with a very short backscale, there is no way it can move at lower frequencies. Certainly not enough to allow the soundboard to produce any meaningful sound energy below about the fourth to sixth partial. That is, even though the theoretical pitch of A-1 is 27.5 Hz, it is unlikely that there will be any significant sound energy produced at frequencies below 110 – 220 Hz. My own experiments on my string test frame have verified this at least to my satisfaction.

Several have mentioned the idea of moving the bass bridge forward (toward the agraffes) some. And I fully concur. I also believe in removing the ubiquitous bass bridge cantilever. This design atrocity should never have been developed in the first place and I will never willingly design a piano using one. Nor will I willingly leave one in a rebuilt instrument. (I’ve done it, but not willingly.) Yes, this necessitates shortening the speaking length by a small amount but this is more than compensated for by the increase in the mobility of the bridge/soundboard system.

Through the tenor section the backscale length does not seem to be critical. The early builders simple let the mechanical characteristics of the design dictate this. The (very) rough rule seems to have been to keep the back bearing point about the same distance from the bridge through the tenor section. As I say, it doesn’t seem to be all that critical. Again, it is a matter of soundboard mobility. But the frequencies are relatively high and the mobility needs of the soundboard assembly are not that great.

ddf


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Del
Thanks for the exhaustive datas. I have interests only in antique pianos or at least the ones with a good design, and I saw few erard grand pianos and concert pianos online and there is one in particular that got my attention, its an erard 2 meters 25 cm with a bichord tenor :

( http://hammerfluegel.info/coppermine15/displayimage.php?pid=2418&fullsize=1)
And
(http://hammerfluegel.info/coppermine15/displayimage.php?pid=2417&fullsize=1)

the bridge design seems to have a very nice and harmonious curve from trebble to bass but the back of the piano is too close to the bridges. If I could correct this I am not sure if I would;
1 extend the back of the piano (with all the complications arising)
2 float the back of the soundboard
3 shorten the tenor bridge and move the bass bridge further
What are your thoughts on that?
Again thanks to each one of you for the posts.
I hope the picture link works
Alex

Last edited by Alex_; 12/17/17 04:35 AM.
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It might help understanding the need for a long backscale in the bass to know that, for a given diaphragm area, and to produce given volume level, the diaphragm must move as the reciprocal of the square of the frequency ratio. For example, at a frequency of 30 Hz, the diaphragm must move 9 times the required movement at 90 Hz. A sobering truth...

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Originally Posted by Roy123
It might help understanding the need for a long backscale in the bass to know that, for a given diaphragm area, and to produce given volume level, the diaphragm must move as the reciprocal of the square of the frequency ratio. For example, at a frequency of 30 Hz, the diaphragm must move 9 times the required movement at 90 Hz. A sobering truth...



Roy,

For us math-challenged folks, could you possibly translate that into something a little more "concrete"?

Thanks,

Pwg


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Originally Posted by P W Grey
Originally Posted by Roy123
It might help understanding the need for a long backscale in the bass to know that, for a given diaphragm area, and to produce given volume level, the diaphragm must move as the reciprocal of the square of the frequency ratio. For example, at a frequency of 30 Hz, the diaphragm must move 9 times the required movement at 90 Hz. A sobering truth...



Roy,

For us math-challenged folks, could you possibly translate that into something a little more "concrete"?

Thanks,

Pwg


It simply means that, if a soundboard has to move 0.1 mm to produce a certain amount of volume at (to pick real world notes and pitches) F-21 (having a pitch of 87.3 Hz), it will have to move approximately 0.9 mm to produce the same volume of sound at A-1 (having a pitch of 27.5 Hz). This is not going to be possible even using every trick in the design book but there are some design "features" that are counter-productive. Short backscales are the biggest single restriction on the mobility of the bridge. Placing the bass bridge very close to the inner rim is a very close second. Cantilevered bass bridges act as high-pass filters that, while not actually restricting the motion of the bass bridge and soundboard, do absorb a lot of the low frequency energy that might otherwise be available to drive the motion of the soundboard.

This assumes the radiating area of the soundboard is the same in each case. Unfortunately, it is not. A-1 is usually the lowest note on the bass bridge and F-21 is often the lowest note on the tenor bridge. The effective radiating area around the bottom of the bass bridge is nearly always much less than that around the end of the tenor bridge.

The point being that we should be designing the bass sections for greater, not less, mobility.

ddf

Last edited by Del; 12/17/17 08:52 PM.

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(Perhaps I repost this in case was overlooked)
Thanks for the exhaustive datas. I have interests only in antique pianos with a good design, and I saw few erard grand pianos online and there is one in particular that got my attention, its an erard 2 meters 25 cm with a bichord tenor :

( http://hammerfluegel.info/coppermine15/displayimage.php?pid=2418&fullsize=1)
And a closeup
(http://hammerfluegel.info/coppermine15/displayimage.php?pid=2417&fullsize=1)

the bridge design seems to have a very nice and harmonious curve from trebble to bass but the back of the piano is too close to the bridges. If I could correct this I am not sure if I would;
1 extend the back of the piano (with all the complications arising)
2 float the back of the soundboard
3 shorten the tenor bridge and move the bass bridge further
What are your thoughts on that?
Again thanks to each one of you for the posts.
Alex

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Originally Posted by Del
Originally Posted by P W Grey
Originally Posted by Roy123
It might help understanding the need for a long backscale in the bass to know that, for a given diaphragm area, and to produce given volume level, the diaphragm must move as the reciprocal of the square of the frequency ratio. For example, at a frequency of 30 Hz, the diaphragm must move 9 times the required movement at 90 Hz. A sobering truth...



Roy,

For us math-challenged folks, could you possibly translate that into something a little more "concrete"?

Thanks,

Pwg


It simply means that, if a soundboard has to move 0.1 mm to produce a certain amount of volume at (to pick real world notes and pitches) F-21 (having a pitch of 87.3 Hz), it will have to move approximately 0.9 mm to produce the same volume of sound at A-1 (having a pitch of 27.5 Hz). This is not going to be possible even using every trick in the design book but there are some design "features" that are counter-productive. Short backscales are the biggest single restriction on the mobility of the bridge. Placing the bass bridge very close to the inner rim is a very close second. Cantilevered bass bridges act as high-pass filters that, while not actually restricting the motion of the bass bridge and soundboard, do absorb a lot of the low frequency energy that might otherwise be available to drive the motion of the soundboard.

This assumes the radiating area of the soundboard is the same in each case. Unfortunately, it is not. A-1 is usually the lowest note on the bass bridge and F-21 is often the lowest note on the tenor bridge. The effective radiating area around the bottom of the bass bridge is nearly always much less than that around the end of the tenor bridge.

The point being that we should be designing the bass sections for greater, not less, mobility.

ddf



Thanks Del,

I "sort of" get it now. But don't ask me to figure it out for any other notes!

Translation: It's REALLY hard to do with present construction techniques, but could be somewhat improved.

Pwg


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Originally Posted by P W Grey
Originally Posted by Del
Originally Posted by P W Grey
Originally Posted by Roy123
It might help understanding the need for a long backscale in the bass to know that, for a given diaphragm area, and to produce given volume level, the diaphragm must move as the reciprocal of the square of the frequency ratio. For example, at a frequency of 30 Hz, the diaphragm must move 9 times the required movement at 90 Hz. A sobering truth...



Roy,

For us math-challenged folks, could you possibly translate that into something a little more "concrete"?

Thanks,

Pwg


It simply means that, if a soundboard has to move 0.1 mm to produce a certain amount of volume at (to pick real world notes and pitches) F-21 (having a pitch of 87.3 Hz), it will have to move approximately 0.9 mm to produce the same volume of sound at A-1 (having a pitch of 27.5 Hz). This is not going to be possible even using every trick in the design book but there are some design "features" that are counter-productive. Short backscales are the biggest single restriction on the mobility of the bridge. Placing the bass bridge very close to the inner rim is a very close second. Cantilevered bass bridges act as high-pass filters that, while not actually restricting the motion of the bass bridge and soundboard, do absorb a lot of the low frequency energy that might otherwise be available to drive the motion of the soundboard.

This assumes the radiating area of the soundboard is the same in each case. Unfortunately, it is not. A-1 is usually the lowest note on the bass bridge and F-21 is often the lowest note on the tenor bridge. The effective radiating area around the bottom of the bass bridge is nearly always much less than that around the end of the tenor bridge.

The point being that we should be designing the bass sections for greater, not less, mobility.

ddf



Thanks Del,

I "sort of" get it now. But don't ask me to figure it out for any other notes!

Translation: It's REALLY hard to do with present construction techniques, but could be somewhat improved.

Pwg


Well, don't lose any sleep over it. It's not going to happen in any real-world piano. The best is the best we can do. That means (1) giving the low bass every advantage we can. (2) Move the bridge away from the inner rim as far as is practical. (3) Avoid the use of bridge cantilevers. Keep the backscale as long as is practical (goes along with #1). (4) Use vertical hitchpins for the wrapped strings. (5) Keep the soundboard relatively thin (or provide some method for "floating" the soundboard) around the end of the bass bridge. (6) Keep the string tensions as low as practical. (7) Use flexible core wires where practical.

I might be able to think of a few more but it's late....

ddf


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Flexible core wire???
Is this in relation to diameter or type of material???


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I would read that to mean both. A thinner core wire will be more flexible than a thicker one and, if one is hybrid scaling ala Paulello, you find that Type O is more flexible than modern wire and Type 1 more still. I would add that reducing the wrap size will further make the string more flexible.

Using the weaker wire types can also serva an important function in the monochords, in that good substitutions along with a smaller core will substantially raise the breaking percentage up into the realm of good tone. These sorts of combinations are what I believe Del is referring to when he says to keep the tensions as low as possible - reducing both cores and wraps certainly will lower the tensions.

Combine these elements skillfully and you will be surprised to find how much of an improvement you can make to the bass of smaller grands. These results cannot be achieved by other means.

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Thank you Will,
I typically use Tremaine Parsons' "P-Scale" to design the scale - bass included, and Ari Isaac builds my bass strings. He has his own technique for creating his idea of flexibility in the windings and he not always uses my core specs. However, they always sound superior, no complaints.
I have not tried Paulello yet.
Who builds your bass strings that will use the materials and sizes that you spec?
Also, back to the back scale - for every rebuild I do if allowed, I convert the standard hitch to vertical hitches as well as getting rid of the cantilever thing.
Im doing it to an old SS upright for the first time upright conversion.
I will likely hire Del to design his Z-Board for me as well on this one.

Last edited by Gene Nelson; 12/21/17 03:18 PM.

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Hi Gene:

I used to use P-Scale, but it has been about 5 years or so. Since I use Paulello wire exclusively, I have been using Arno Patin's Abacus Excel Spreadsheet to do my hybrid rescaling. JD Grandt in Canada makes almost all my bass strings, although I have ordered a set of Steinway O bass strings from Heller using Nickel plated cores with nickel plated soft iron wraps. (they are fabulous).
I have a list of all the wire types and sizes of Paulello wire that JD Grandt has, and his list for copper wraps as well. That way when I scale the bass, he can reproduce exactly what I want

I've done a couple of vertical hitch pin installs, its the real deal. I have a Steinway O in my shop and an I upright. Both of these will benefit from the vert hitch pins in the crowded monochords. I'm going to ask if I can dump the cantilever.

If you choose to start using Paulello wire and rescale, you will find that your horizons are much bigger for your choices. This can be true for the entire piano. You can have more than one choice of wire that will work. Each sounds different, so this allows you to voice the stringing in ways not possible before, allowing you to create differing tonal aesthetics.

Will


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Gene,

What model and year is your upright?

Pwg


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1913 SS-K52
Its an on going project destined to live in my living room when finished and got put on hold for health reasons.
About half way complete and just now digging it out for completion.

Last edited by Gene Nelson; 12/22/17 12:01 PM.

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The cantilever bridge that I would modify in the K-52 and any other piano is any found in the treble where the string paths are crossing the bridge at close to a right angle. These undercut treble bridges allow longitudinal energy to disrupt the transverse mode termination points. They allow the L and T modes to mix because the bridge can rock. This mode mixing is a cause of many false beats.


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I agree about the undercut bridge. Since this is my piano I am in the process of building a new bridge core that will eliminate that and It will allow me to re-scale it as well. The stock scaling around those two upper struts/breaks is horrible and can be corrected by a couple of minor dog legs in a new bridge.

It is getting a new board too, hope to enlist Del to design his Z-Bar for me.

. There is one thing I would like to correct and it is not possible on an upright that dont have agraffes and that is to be able to notch the bass bridge so that the upper and lower terminations create a situation where both strings of wound bi-chords can be exactly the same length. A problem with most uprights but it is relatively minor.

Last edited by Gene Nelson; 12/22/17 01:00 PM.

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I believe it can be done...just a little tricky. I have not done it.

Pwg


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Originally Posted by P W Grey
I believe it can be done...just a little tricky. I have not done it.

Pwg


Actually, it's quite easy and can be done by eyeball. I most recently did it on a M&H B but have also done it on a S&S M where the bridge was beveled instead of notched.
Just do it before taking your string pattern -- or however you order your bass strings.


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