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#1125234 - 01/24/04 09:16 PM Logarithmic scale?
Dan M Offline
500 Post Club Member

Registered: 12/30/03
Posts: 770
Loc: California
I've been hearing about logarithmic scales with regards to piano design. What does this mean? Logarithmic with regards to tension? String length? Something else? Why would this be an advantage or not?

Just curious from a layman's perspective, but I'm also a physicist, so can handle the real explanation \:\)

Does anybody have any references (books or online) to basic piano design? Curious subject.

Dan
_________________________
The piano is my drug of choice.
Why are you reading this? Go play the piano! Why am I writing this? ARGGG!

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#1125235 - 01/24/04 11:34 PM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by Dan M:
I've been hearing about logarithmic scales with regards to piano design. What does this mean? Logarithmic with regards to tension? String length? Something else? Why would this be an advantage or not?

Just curious from a layman's perspective, but I'm also a physicist, so can handle the real explanation \:\)

Does anybody have any references (books or online) to basic piano design? Curious subject.

Dan [/b]
It simply means that the length of each string is longer or shorter than its neighbor by some fixed logarithmic multiplier. That same multiplier will be used throughout the scale. At least the tenor scale. This is a concept that has long been talked about but has seldom actually been practiced. Indeed, even when the rare pianomaker of today claims to have a log scale it is generally only partially true. Nearly all pianos on the market today have bass bridges that ďreverseĒ curved opposite to the direction they would curve if they sported log bass scales. The single exception among current production pianos is the Walter 190 grand.

Log scales are quite easy to develop using a simple spreadsheet. I canít speak for others but I start at C-88 and work down. I know itís backwards, but it works easier that way ó at least for me. Depending on the desired tonal characteristics of the piano in question Iíll usually start with a speaking length of something between 50 mm to 54 mm at C-88. Then, knowing how many unisons I will have on the tenor bridge and knowing what lengths I want to start with and end with it is a simple matter to plug in the numbers and come up with a printout of string lengths.

Using a log scale enables the designer to use an even progression of wire sizes starting, usually, with #13 (or 0.031Ē) at C-88 and getting progressively larger on down the scale. Depending on the log multiplier used this progression will typically be something like 6 unisons of #13 (0.031Ē) wire, 4 unisons of #13 Ĺ (0.032Ē) wire, 6 unisons of #14 (0.033Ē) wire, 4 unisons of #14 Ĺ (0.034Ē) wire, etc. This progression may vary some depending on the log sweep of the bridge.

The main advantage of adhering to a log sweep to the bridges is the uniformity of string characteristics and bridge loading it makes possible. It is very helpful in balancing the tone quality of a piano across the full compass of the scale. It is also makes it possible to achieve a relatively uniform string inharmonicity curve which helps the tuner in setting a uniform stretch to the tuning.

Of course, coming up with lengths for the speaking portion of the strings is the easy part. Laying them all out into a workable form, balancing them against an appropriate soundboard assembly and coming up with a good looking and beautifully performing piano in the end ó now thatís the tricky part. As the saying goes, the devilís in the details.

Del
_________________________
Delwin D Fandrich
Piano Research, Design & Manufacturing Consultant
ddfandrich@gmail.com
(To contact me privately please use this e-mail address.)

Stupidity is a rare condition, ignorance is a common choice. --Anon

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#1125236 - 01/25/04 05:50 AM Re: Logarithmic scale?
88Key_PianoPlayer Offline
1000 Post Club Member

Registered: 02/02/02
Posts: 1905
Loc: El Cajon, CA
 Quote:
Originally posted by Del:
 Quote:
Originally posted by Dan M:
I've been hearing about logarithmic scales with regards to piano design. What does this mean? Logarithmic with regards to tension? String length? Something else? Why would this be an advantage or not?

Just curious from a layman's perspective, but I'm also a physicist, so can handle the real explanation \:\)

Does anybody have any references (books or online) to basic piano design? Curious subject.

Dan [/b]
It simply means that the length of each string is longer or shorter than its neighbor by some fixed logarithmic multiplier. That same multiplier will be used throughout the scale. At least the tenor scale. This is a concept that has long been talked about but has seldom actually been practiced. Indeed, even when the rare pianomaker of today claims to have a log scale it is generally only partially true. Nearly all pianos on the market today have bass bridges that ďreverseĒ curved opposite to the direction they would curve if they sported log bass scales. The single exception among current production pianos is the Walter 190 grand.

Log scales are quite easy to develop using a simple spreadsheet. I canít speak for others but I start at C-88 and work down. I know itís backwards, but it works easier that way ó at least for me. Depending on the desired tonal characteristics of the piano in question Iíll usually start with a speaking length of something between 50 mm to 54 mm at C-88. Then, knowing how many unisons I will have on the tenor bridge and knowing what lengths I want to start with and end with it is a simple matter to plug in the numbers and come up with a printout of string lengths.

Using a log scale enables the designer to use an even progression of wire sizes starting, usually, with #13 (or 0.031Ē) at C-88 and getting progressively larger on down the scale. Depending on the log multiplier used this progression will typically be something like 6 unisons of #13 (0.031Ē) wire, 4 unisons of #13 Ĺ (0.032Ē) wire, 6 unisons of #14 (0.033Ē) wire, 4 unisons of #14 Ĺ (0.034Ē) wire, etc. This progression may vary some depending on the log sweep of the bridge.

The main advantage of adhering to a log sweep to the bridges is the uniformity of string characteristics and bridge loading it makes possible. It is very helpful in balancing the tone quality of a piano across the full compass of the scale. It is also makes it possible to achieve a relatively uniform string inharmonicity curve which helps the tuner in setting a uniform stretch to the tuning.

Of course, coming up with lengths for the speaking portion of the strings is the easy part. Laying them all out into a workable form, balancing them against an appropriate soundboard assembly and coming up with a good looking and beautifully performing piano in the end ó now thatís the tricky part. As the saying goes, the devilís in the details.

Del [/b]
I don't think I quite understand log scale / wire sizes / whatever the relationship is... it's not like you take the speaking length of C8 at, for example, 50mm, and multiply by 2 to the 1/12 power, do you, to get the next note (and multiply each result by 2^(1/12)?
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#1125237 - 01/25/04 07:00 AM Re: Logarithmic scale?
Calin Offline
Full Member

Registered: 09/11/03
Posts: 418
Loc: Bucharest
 Quote:
Originally posted by Del:
It simply means that the length of each string is longer or shorter than its neighbor by some fixed logarithmic multiplier. That same multiplier will be used throughout the scale.

[...]
Log scales are quite easy to develop using a simple spreadsheet. I canít speak for others but I start at C-88 and work down. I know itís backwards, but it works easier that way ó at least for me. Depending on the desired tonal characteristics of the piano in question Iíll usually start with a speaking length of something between 50 mm to 54 mm at C-88.
[...]
Del [/b]
Hello Del!

Does the Walter grand (I understood that it is your own design, right?) have a logarithmic string length progression even in the bass?

Could you please elaborate on the different tonal characteristics you can obtain by starting at C88 with a length between 50 & 54 mm?

What is the factor of multiplication used to achieve the logarithimic scale? And why?

Any thoughts on a scale that uses double lengths for each octave? I have heard about this used in old harpsichords, but not in pianos.

Regards,

Calin
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The Bechstein piano discussion group: http://launch.groups.yahoo.com/group/bechstein/
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#1125238 - 01/25/04 08:37 AM Re: Logarithmic scale?
Rich Galassini Offline
9000 Post Club Member

Registered: 05/28/01
Posts: 9172
Loc: Philadelphia/South Jersey
In my understanding of scale design the logarithmic scale is more of a starting point - a theoretical "ideal" that has rarely been put into practice.

Del, do you mean to say that the Walter is a log. scale?

Does anyone know of any pianos, built now or in the past, that use a fairly pure log. scale?
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#1125239 - 01/25/04 09:32 AM Re: Logarithmic scale?
Dan M Offline
500 Post Club Member

Registered: 12/30/03
Posts: 770
Loc: California
Thanks Del - great answer (of course I hoped you would reply). I can see how this would help the dreaded "fixing your fixes" problem. I work as an engineer, and I've noticed that if you start a design without a basically good solid framwork, you end up putting fixes in pretty quickly to patch up problems with the first draft.

Well, those fixes usually come with a cost, so then often you have to put in fixes, to smooth out those fixes. You can see that quickly you get to some kind patchwork of compromises, unless it gets so bad you have to start over.

I assume it's similiar to piano design, where starting out with some regularity in the scale design helps you from having to accept too many compromises in the end, or just happening to hit a design finally by accident.

Dan

 Quote:
Originally posted by Del:
 Quote:
Originally posted by Dan M:
I've been hearing about logarithmic scales with regards to piano design. What does this mean? Logarithmic with regards to tension? String length? Something else? Why would this be an advantage or not?

Just curious from a layman's perspective, but I'm also a physicist, so can handle the real explanation \:\)

Does anybody have any references (books or online) to basic piano design? Curious subject.

Dan [/b]
It simply means that the length of each string is longer or shorter than its neighbor by some fixed logarithmic multiplier. Del [/b]
_________________________
The piano is my drug of choice.
Why are you reading this? Go play the piano! Why am I writing this? ARGGG!

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#1125240 - 01/25/04 07:24 PM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by 88Key_PianoPlayer:
 Quote:
Originally posted by Del:
 Quote:
Originally posted by Dan M:
I've been hearing about logarithmic scales with regards to piano design. What does this mean? Logarithmic with regards to tension? String length? Something else? Why would this be an advantage or not?

Just curious from a layman's perspective, but I'm also a physicist, so can handle the real explanation \:\)

Does anybody have any references (books or online) to basic piano design? Curious subject.

Dan [/b]
It simply means that the length of each string is longer or shorter than its neighbor by some fixed logarithmic multiplier. That same multiplier will be used throughout the scale....

Del [/b]
I don't think I quite understand log scale / wire sizes / whatever the relationship is... it's not like you take the speaking length of C8 at, for example, 50mm, and multiply by 2 to the 1/12 power, do you, to get the next note (and multiply each result by 2^(1/12)? [/b]
Note that I said "some fixed logarithmic multiplier..." Not the 12th root of 2. But, yes, each succesive length is obtained by multiplying the previous length by the same number.

Del
_________________________
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Piano Research, Design & Manufacturing Consultant
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#1125241 - 01/25/04 07:55 PM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
_________________________
Delwin D Fandrich
Piano Research, Design & Manufacturing Consultant
ddfandrich@gmail.com
(To contact me privately please use this e-mail address.)

Stupidity is a rare condition, ignorance is a common choice. --Anon

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#1125242 - 01/25/04 08:10 PM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by Rich Galassini:
In my understanding of scale design the logarithmic scale is more of a starting point - a theoretical "ideal" that has rarely been put into practice.

Del, do you mean to say that the Walter is a log. scale?

Does anyone know of any pianos, built now or in the past, that use a fairly pure log. scale? [/b]
Well, yes, it is a theoretical ideal but itís much more than a ďstarting point.Ē Though you are correct in that it has rarely been put into practice. There are several reasons for this. Even back when Wolfenden wrote ďA Treatise on the Art of Pianoforte ConstructionĒ he was lamenting the fact that most manufacturers, when bringing out a ďnewĒ piano exercised the false economy of simply copying something already in production rather than mathematically working out a proper scale. This observation was echoed in the collection of minutes of the Piano Technicians meetings of roughly 1914 to 1919. Even though the principles of good (tenor) scaling were generally understood at least by a few designers they were rarely utilized.

Sadly, not much has changed over the years.

Yes, the Walter grand is a true log scale through both the tenor and the bass (though, for obvious reasons, the bass uses a different multiplier). As is now the tenor section of the Walter vertical.

Iíve not kept a record of them, but there are a few around. Sometimes in a surprising package. Several years ago I was asked to do some redesign work on a 4í 7Ē Howard grand (no, donít ask why) and in evaluating the stringing scale found it to be laid out to a nearly perfect log progression. As for current production, the new M&H AA almost certainly has a true log scale along its tenor bridge. As probably does the new Seiler grand.

Del
_________________________
Delwin D Fandrich
Piano Research, Design & Manufacturing Consultant
ddfandrich@gmail.com
(To contact me privately please use this e-mail address.)

Stupidity is a rare condition, ignorance is a common choice. --Anon

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#1125243 - 01/25/04 08:27 PM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by Dan M:
Thanks Del - great answer (of course I hoped you would reply). I can see how this would help the dreaded "fixing your fixes" problem. I work as an engineer, and I've noticed that if you start a design without a basically good solid framwork, you end up putting fixes in pretty quickly to patch up problems with the first draft.

Well, those fixes usually come with a cost, so then often you have to put in fixes, to smooth out those fixes. You can see that quickly you get to some kind patchwork of compromises, unless it gets so bad you have to start over.

I assume it's similiar to piano design, where starting out with some regularity in the scale design helps you from having to accept too many compromises in the end, or just happening to hit a design finally by accident.

Dan

[/b]
Yes, it is. Much of what now passes for piano design is really design patching. There are some fundamental design flaws built into the tradition design formula. A great deal of innovative tweaking goes into ameliorating the limitations imposed by these flaws. It is a credit to some of todayís piano builders that they do as well as they do. For example, the Shiguru concert grand. This instrument is relatively similar to the Steinway Dís fundamental design. Still, it is exceptionally smooth and dynamic. The bass/tenor break is barely, if at all, discernable. There is little, if any, drop-off in killer octave region. The limitations of the fundamental design have been masked over to a remarkable degree through a combination of design tweaks and superb workmanship.

Now, while I admire the effort made by the Shiguruís designers and builders, I would prefer to see the industry moving on to a cleaner design base as a starting point. I think the industry has at least one more evolutionary step left. Perhaps more, but that is the limit of my vision just now.

Del
_________________________
Delwin D Fandrich
Piano Research, Design & Manufacturing Consultant
ddfandrich@gmail.com
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#1125244 - 01/25/04 08:57 PM Re: Logarithmic scale?
Dan M Offline
500 Post Club Member

Registered: 12/30/03
Posts: 770
Loc: California
 Quote:
I.e., does the manufacturer want a bright, powerful sound of a more subdued, melodic and dynamic sound.
Hi Del,
Could you share what Charles Walter asked for on the CW190? I'm curious to see how it compares to my perception of the piano (which I really love).

Dan
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#1125245 - 01/25/04 11:30 PM Re: Logarithmic scale?
BDB Online   content
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21394
Loc: Oakland
The thing that I have notice since delving into some of these mysteries is that there are pianos with very good scale designs which don't necessarily have outstanding sound, and pianos with outstanding sound that don't have good scale designs. The latter group can often be improved with careful string selection. (There are some models I would like to get my mitts on, to see what the results would be.) It leads me to believe that not everything can be reduced to math calculations, though.

I find that some of the conclusions that Frank Hubbard came to in his book on harpsichord construction hold true for piano design as well, such as the fact that shorter scales seem to work better on lighter instruments, like Steinways, and longer scales work better on heavier instruments, like M & Hs. But I haven't done nearly as much research as Del.
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#1125246 - 01/26/04 02:01 AM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by Dan M:
 Quote:
I.e., does the manufacturer want a bright, powerful sound of a more subdued, melodic and dynamic sound.
Hi Del,
Could you share what Charles Walter asked for on the CW190? I'm curious to see how it compares to my perception of the piano (which I really love).

Dan [/b]
Remarkably little at first. In part because we share many of the concepts of piano performance. He wanted a very smooth inharmonicity curve and he wanted a smooth and balanced scale. Beyond that he specified the length of the piano and expressed his general desire for tone quality. Then he monitored the progress of the design all the way through and made me justify every design decision I made. In so doing he ended up with the piano design he wanted and left me happy with it as well.

Del
_________________________
Delwin D Fandrich
Piano Research, Design & Manufacturing Consultant
ddfandrich@gmail.com
(To contact me privately please use this e-mail address.)

Stupidity is a rare condition, ignorance is a common choice. --Anon

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#1125247 - 01/26/04 08:05 AM Re: Logarithmic scale?
Dan M Offline
500 Post Club Member

Registered: 12/30/03
Posts: 770
Loc: California
 Quote:
Originally posted by Del:
 Quote:
Originally posted by Dan M:
 Quote:
I.e., does the manufacturer want a bright, powerful sound of a more subdued, melodic and dynamic sound.
Hi Del,
Could you share what Charles Walter asked for on the CW190? I'm curious to see how it compares to my perception of the piano (which I really love).

Dan [/b]
Remarkably little at first. In part because we share many of the concepts of piano performance. He wanted a very smooth inharmonicity curve and he wanted a smooth and balanced scale. Beyond that he specified the length of the piano and expressed his general desire for tone quality. Then he monitored the progress of the design all the way through and made me justify every design decision I made. In so doing he ended up with the piano design he wanted and left me happy with it as well.

Del [/b]
Nice, sounds like you both got what you wanted, something that doesn't always happen when consulting.

I'll admit it, I really admire the CW thus far. I was trying to describe it's tone to my wife last night, but couldn't do it. It's too elusive, which I believe is a positive. Best I could do was say "Well, on a scale of Bosendorfer to M&H, I'd say it goes

Bosie - Steinway - CW - M&H

With the bosie being the most mellow and melodic (low harmonics), and the MH being the most individualistic with high harmonics."

I also have difficulty describing the tone of a Steinway. Other than it (and the CW) both have a powerful bass and singing treble.

Dan
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#1125248 - 01/26/04 09:28 AM Re: Logarithmic scale?
Calin Offline
Full Member

Registered: 09/11/03
Posts: 418
Loc: Bucharest
Hi Del and thanks for taking the time to answer!

Here are a few more questions:

What is the difference between a small and great sweep in the bass? Which one is preferable? I guess the greater sweep, as it should have a smaller increase in inharmonicity and would mean you get fundamental frequencies in the lowest bass closer to the correct pitch?

[2] Why do long scales induce backscale problems? Isn'y there a limit for backscale length beyond which there is no gain in flexibility?
What is the minimum feasible backscale for A0, that doesn't restrict the free movement of the bridge?

[4] I don't mean to have all the octaves doubling. Just for the plain wire. I made a small calculation that shows that, for instance, with a C88 of 50 mm, one could make a scale that doubles at each octave until let's say E20 which would be 2540mm - a length that would probably fit in a concert grand. The bass, of course, must be made with another multiplication factor. Would such a scale work? It should have much less inharmonicity than normal ones. But how would this influence other factors?

Another issue: when you want to design a grand of a specified length, how do you decide where the bass break should be?
Just see what the longest plain wire string is (from a logarithmic progression), that fits in the case?
That would of course mean that the smaller the piano, the more bass strings it should have, which doesn't always happen in practice.

Regards,

Calin
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The Bechstein piano discussion group: http://launch.groups.yahoo.com/group/bechstein/
The Schweighofer piano site: http://schweighofer.tripod.com

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#1125249 - 01/26/04 01:00 PM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by Calin:
Hi Del and thanks for taking the time to answer!

Here are a few more questions:

What is the difference between a small and great sweep in the bass? Which one is preferable? I guess the greater sweep, as it should have a smaller increase in inharmonicity and would mean you get fundamental frequencies in the lowest bass closer to the correct pitch?

[2] Why do long scales induce backscale problems? Isn'y there a limit for backscale length beyond which there is no gain in flexibility?
What is the minimum feasible backscale for A0, that doesn't restrict the free movement of the bridge?

[4] I don't mean to have all the octaves doubling. Just for the plain wire. I made a small calculation that shows that, for instance, with a C88 of 50 mm, one could make a scale that doubles at each octave until let's say E20 which would be 2540mm - a length that would probably fit in a concert grand. The bass, of course, must be made with another multiplication factor. Would such a scale work? It should have much less inharmonicity than normal ones. But how would this influence other factors?

Another issue: when you want to design a grand of a specified length, how do you decide where the bass break should be?
Just see what the longest plain wire string is (from a logarithmic progression), that fits in the case?
That would of course mean that the smaller the piano, the more bass strings it should have, which doesn't always happen in practice.

Regards,

Calin [/b]
Itís not so much that one sweep is more or less desirable in the bass, itís more a matter of which is possible within a given overall length. Things all have to fit within a given length and shape.

[2] Again, within a given piano length, everything has to fit. That means if the speaking length is made longer the backscale is going to be shorter unless the piano is made longer. Making the piano longer is usually not an option.

I donít know the limits. It usually doesnít become an issue because the range is usually restricted by other factors. I do know that 50 mm is so short as to essentially prevent any bridge motion in the 27.5 to 55 cycles per second range. Anything shorter than that (and there are some) begins also to restrict meaningful motion through the 2nd harmonic range as well. I donít know how long is too long.

[4] Iíve not done any work with strings this long. It would take building a monochord and measuring the tonal characteristics to get a general idea of what was there. But, in the long run, youíre going to have to build the piano.

F-21 is approximately 1830 mm to 1850 mm in the typical 275 cm concert grand. And it is already a difficult fit. Making any string on the tenor bridge another 600 or 700 mm longer would mean substantially lengthening the piano. Again, these decisions usually boil down to what is practical within a given piano length.

Yes, the decision of where the bass/tenor break should be is primarily based on what will physically fit. And, yes, in the smaller piano more wrapped strings should be used. I am aware that this doesnít always happen in practice, but it should.

Del
_________________________
Delwin D Fandrich
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ddfandrich@gmail.com
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#1125250 - 01/26/04 04:33 PM Re: Logarithmic scale?
pianoloverus Online   content
Yikes! 10000 Post Club Member

Registered: 05/29/01
Posts: 19263
Loc: New York City
Del:

I hope this hasn't already been covered in one of your other replies(which are beyond my understanding) already. I think you said in one of your first posts that in a logarithmic scale each string length is the same multiple of the string length adjacent to it. Being a math teacher, I first assumed that the multiplier had something to do with logaritms. Is that true or is the multiplier some number unrelated to logs(and if so, why the name *logarithmic* scale?)?

Thank you!

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#1125251 - 01/26/04 05:39 PM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by pianoloverus:
Del:

I hope this hasn't already been covered in one of your other replies(which are beyond my understanding) already. I think you said in one of your first posts that in a logarithmic scale each string length is the same multiple of the string length adjacent to it. Being a math teacher, I first assumed that the multiplier had something to do with logaritms. Is that true or is the multiplier some number unrelated to logs(and if so, why the name *logarithmic* scale?)?

Thank you! [/b]
Tradition. And when it's plotted on a log scale it makes a nice, straight line.

Del
_________________________
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#1125252 - 01/27/04 04:21 PM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by Del:
 Quote:
Originally posted by pianoloverus:
Del:

I hope this hasn't already been covered in one of your other replies(which are beyond my understanding) already. I think you said in one of your first posts that in a logarithmic scale each string length is the same multiple of the string length adjacent to it. Being a math teacher, I first assumed that the multiplier had something to do with logaritms. Is that true or is the multiplier some number unrelated to logs(and if so, why the name *logarithmic* scale?)?

Thank you! [/b]
Tradition. And when it's plotted on a log scale it makes a nice, straight line.

Del [/b]
That was a simplistic answer.

Basically, the process is this:

Let's assume you want to start with a C-88 having a 50 mm long string and you want to end up one octave lower (C-76) with a length of 93 mm.

93/50 = 1.86. This is the octave sweep.
So 50 mm * 1.86 = 93 mm.

There are 12 notes to the octave so, taking the 12th root of 1.86, or 1.0531 gives you the note to note multiplier. Multiplying 50 mm by 1.0531 = 52.7 mm, the speaking length of B-87.

Or, put another way, 50 mm * 1.0531^12 = 93 mm, (the speaking length of C-76), 50 mm * 1.0531^1 = 52.7 mm (the speaking length of B-87), and if you want to know the length of A-85 (3 notes down) you can multiply 50 mm * 1.0531^3 and come up with 58.4 mm. Etc.

There is a much cleaner way to write this with an equation editor, but you get the picture.

Del
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#1125253 - 01/27/04 05:02 PM Re: Logarithmic scale?
pianodevo Offline
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Hi Del,

Thanks so much for explaining in detail why the term "logarithmic scale" is used, per PianoLoverus's query.

One more question though ... It's not crystal clear to me why the octaves aren't in the ratio 2:1 (in your example the ratio is 93/50 or 1.86).

Going all the way back to Pythagoras and his school, I had learned that octaves were 2:1, and thus consecutive semitones would have the ratio of the 12th root of 2; apparently not, though, according to your figures.

Care to clarify?
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#1125254 - 01/27/04 05:32 PM Re: Logarithmic scale?
BDB Online   content
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Because if you start with the strings on note 88 about 2" long and doubled each octave, the piano would end up being over 20 feet long.

A logarithmic scale is a way of keeping a reasonable length while keeping the characteristics of the notes from varying too much.

Incidentally, if the strings are too long, it becomes very difficult to get them going.
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#1125255 - 01/27/04 06:05 PM Re: Logarithmic scale?
Del Offline
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 Quote:
Originally posted by pianodevo:
Hi Del,

Thanks so much for explaining in detail why the term "logarithmic scale" is used, per PianoLoverus's query.

One more question though ... It's not crystal clear to me why the octaves aren't in the ratio 2:1 (in your example the ratio is 93/50 or 1.86).

Going all the way back to Pythagoras and his school, I had learned that octaves were 2:1, and thus consecutive semitones would have the ratio of the 12th root of 2; apparently not, though, according to your figures.

Care to clarify? [/b]
My example of 1.86 might be typical of a rather short piano. A scale of a different length would have some other bridge sweep. No piano that I am aware of uses a bridge, or scale, sweep of 2.0. The piano would have to be quite long. See my earlier post on the subject.

Del
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#1125256 - 01/27/04 06:42 PM Re: Logarithmic scale?
88Key_PianoPlayer Offline
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 Quote:
Originally posted by Del:
 Quote:
Originally posted by pianodevo:
Hi Del,

Thanks so much for explaining in detail why the term "logarithmic scale" is used, per PianoLoverus's query.

One more question though ... It's not crystal clear to me why the octaves aren't in the ratio 2:1 (in your example the ratio is 93/50 or 1.86).

Going all the way back to Pythagoras and his school, I had learned that octaves were 2:1, and thus consecutive semitones would have the ratio of the 12th root of 2; apparently not, though, according to your figures.

Care to clarify? [/b]
My example of 1.86 might be typical of a rather short piano. A scale of a different length would have some other bridge sweep. No piano that I am aware of uses a bridge, or scale, sweep of 2.0. The piano would have to be quite long. See my earlier post on the subject.

Del [/b]
Assuming a 51mm (2") length for C1, the bass/tenor break on a 9-foot grand piano, using the sweep of 2.0, would have to be up around A2/A#2 or A#2/B2, right?
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#1125257 - 01/27/04 07:25 PM Re: Logarithmic scale?
Axtremus Offline
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 Quote:
Originally posted by BDB:
Incidentally, if the strings are too long, it becomes very difficult to get them going.
What is the limit of the lenght, then, for it to move in response to hammer strike without created too much delay as to make the piano un-playable? Is it just length or also mass since mass adds to inertia? (Fat Short strings versus Thin Long strings... this reminded me of Klavin's ultra-long wall-mount upright piano...)

Great thread! Learning lots of stuff hear. Thanks!
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#1125258 - 01/28/04 01:35 AM Re: Logarithmic scale?
Del Offline
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 Quote:
Originally posted by Axtremus:
 Quote:
Originally posted by BDB:
Incidentally, if the strings are too long, it becomes very difficult to get them going.
What is the limit of the lenght, then, for it to move in response to hammer strike without created too much delay as to make the piano un-playable? Is it just length or also mass since mass adds to inertia? (Fat Short strings versus Thin Long strings... this reminded me of Klavin's ultra-long wall-mount upright piano...)

Great thread! Learning lots of stuff hear. Thanks! [/b]
I don't know.

There seems to be little to be gained in going much beyond a sweep of approximately 1.9 or so. Plus or minus a bit this is the sweep commonly used in 275 cm grand pianos. (Note, pianos like the Steinway D do not use a consistent sweep across the length of the bridge. It varies both from section to section and within each section.)

There have only been a few instruments built that are larger than this and from all reports their performance has not been all that outstanding. At least not enough to keep pursuing length at all costs.

A point is reached at which the structural problems exceed any possible acoustical advantage gained by the longer strings.

Del
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#1125259 - 01/28/04 01:47 AM Re: Logarithmic scale?
Del Offline
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 Quote:
Originally posted by 88Key_PianoPlayer:
 Quote:
Originally posted by Del:
[QUOTE]Originally posted by pianodevo:
[qb]
Del [/b]
Assuming a 51mm (2") length for C1, the bass/tenor break on a 9-foot grand piano, using the sweep of 2.0, would have to be up around A2/A#2 or A#2/B2, right? [/b]
I don't know. The break is determined by a number of factors, both acoustical and physical. Without actually laying out the scale I can't answer this type of question.

Del
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#1125260 - 01/28/04 07:25 AM Re: Logarithmic scale?
Calin Offline
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 Quote:
Originally posted by Del:


There have only been a few instruments built that are larger than this and from all reports their performance has not been all that outstanding. At least not enough to keep pursuing length at all costs.


Del [/b]
Hi!

Del, what instruments are you talking about?

Actually, when I was referring to the scale with double lengths for each octave, I thought of it used in normal sized pianos. I guess that would mean a reloction of the bass break in a higher position though. They would need more wrapped strings than standard scales.

Calin
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#1125261 - 01/28/04 10:01 AM Re: Logarithmic scale?
Del Offline
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 Quote:
Originally posted by Calin:
 Quote:
Originally posted by Del:


There have only been a few instruments built that are larger than this and from all reports their performance has not been all that outstanding. At least not enough to keep pursuing length at all costs.


Del [/b]
Hi!

Del, what instruments are you talking about?

Actually, when I was referring to the scale with double lengths for each octave, I thought of it used in normal sized pianos. I guess that would mean a reloction of the bass break in a higher position though. They would need more wrapped strings than standard scales.

Calin [/b]
Well, there was the 11' 8" (356 cm) Challen, of which only one or two were ever built. And then there is the 308 cm (10' 1") Fazioli, which I have found to be rather unimpressive. But then I've only seen three or four of them.

It seems the point of diminishing returns kicks in somewhere around 300 cm.

Of course, one very real problem with investigations of this type is the high cost of such pianos. Developing a new piano of this size (at least as a commercial venture) is going to run upwards of several hundred thousand dollars. And for what? Even if the design is successful, the market is so limited as to make recovering that investment problematic. Who is willing to take the gamble? If some piano manufacturer wants a big new grand itís much easier to simply copy an existing design. Not much new is discovered this way, but itís a whole lot cheaper. And so what if the results are less than spectacular ó the company has proven it can build a concert grand. Well, at least its proven it can build a big piano even if no self-respecting pianist would ever use one on a concert stage.

Del
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#1125262 - 01/28/04 11:57 AM Re: Logarithmic scale?
mikewu99 Offline
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Del:

What about string diameter (gauge)?

I assume that it is desirable to keep the tension close to constant (is this true?). I also assume that frequency is directly proportional to the square root of tension and inversely proportional to both length and diameter. In this case, for a length sweep less that 2 there is a corrseponding diameter sweep greater than 1 such that

length sweep * diameter sweep = 2

To illustrate, using your example length sweep of 1.86 requires a diameter sweep of 1.0875; taking the twelfth root says that each string diameter should be multiplied by 1.007 as you go down the ovtave. Since strings gauges are discrete diameters, I guess you'd pick the closest standard diameter and make up the difference by accepting some variation is tension?

Of course if uniform tension is not a key goal this whole post is a waste of typing....

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#1125263 - 01/28/04 10:04 PM Re: Logarithmic scale?
Del Offline
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 Quote:
Originally posted by Calin:
 Quote:
Originally posted by Del:


There have only been a few instruments built that are larger than this and from all reports their performance has not been all that outstanding. At least not enough to keep pursuing length at all costs.


Del [/b]
Hi!

... Actually, when I was referring to the scale with double lengths for each octave, I thought of it used in normal sized pianos. I guess that would mean a reloction of the bass break in a higher position though. They would need more wrapped strings than standard scales.

Calin [/b]
Actually, Iím not at all sure why so many folks consider a sweep of 2.0 to be all that desirable. It really isnít. For example, starting with a length of 52 mm for C-88 this would make C-28 1664 mm (65.5Ē) long. C-16 would be 3328 mm (131.0Ē) long. OK so far. But, using a #13 wire (0.031Ē or 0.79 mm) at C-88, which is typical, will give a tension of 162 pounds (or 73.5 kgf.). OK so far. But you must then continue using the same wire size all the way down. I havenít actually built and tested a monochord of this length and diameter, but I suspect there will be a decided time lag between hammer impact and voice. I also suspect there will be a very real power problem. A wire of that diameter and tension is going to be whipping around quite a bit. And for what?

A lot is said about Pythagorasís theories, but Pythagoras never designed or built pianos.

Del
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#1125264 - 01/28/04 10:05 PM Re: Logarithmic scale?
Del Offline
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 Quote:
Originally posted by Del:
 Quote:
Originally posted by Calin:
 Quote:
Originally posted by Del:


There have only been a few instruments built that are larger than this and from all reports their performance has not been all that outstanding. At least not enough to keep pursuing length at all costs.


Del [/b]
Hi!

... Actually, when I was referring to the scale with double lengths for each octave, I thought of it used in normal sized pianos. I guess that would mean a reloction of the bass break in a higher position though. They would need more wrapped strings than standard scales.

Calin [/b]
Actually, Iím not at all sure why so many folks consider a sweep of 2.0 to be all that desirable. It really isnít. For example, starting with a length of 52 mm for C-88 this would make C-28 1664 mm (65.5Ē) long. C-16 would be 3328 mm (131.0Ē) long. OK so far. But, using a #13 wire (0.031Ē or 0.79 mm) at C-88, which is typical, will give a tension of 162 pounds (or 73.5 kgf.). OK so far. But you must then continue using the same wire size all the way down. I havenít actually built and tested a monochord of this length and diameter, but I suspect there will be a decided time lag between hammer impact and voice. I also suspect there will be a very real power problem. A wire of that diameter and tension is going to be whipping around quite a bit. And for what?

A lot is said about Pythagorasís theories, but Pythagoras never designed or built pianos.

Del [/b]
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#1125265 - 01/28/04 10:11 PM Re: Logarithmic scale?
Del Offline
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 Quote:
Originally posted by mikewu99:
Del:


Of course if uniform tension is not a key goal this whole post is a waste of typing.... [/b]
It is not. Tension at C-88 is limited by the tensile strength of the wire. From there down it becomes more a fuction of the type of sound desired.

Del
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#1125266 - 01/28/04 10:15 PM Re: Logarithmic scale?
Dan M Offline
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Registered: 12/30/03
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 Quote:
A lot is said about Pythagorasís theories, but Pythagoras never built pianos.
Love it! That's a quote to keep.

 Quote:
Originally posted by Del:
 Quote:
Originally posted by Calin:
 Quote:
Originally posted by Del:


There have only been a few instruments built that are larger than this and from all reports their performance has not been all that outstanding. At least not enough to keep pursuing length at all costs.


Del [/b]
Hi!

... Actually, when I was referring to the scale with double lengths for each octave, I thought of it used in normal sized pianos. I guess that would mean a reloction of the bass break in a higher position though. They would need more wrapped strings than standard scales.

Calin [/b]
Actually, Iím not at all sure why so many folks consider a sweep of 2.0 to be all that desirable. It really isnít. For example, starting with a length of 52 mm for C-88 this would make C-28 1664 mm (65.5Ē) long. C-16 would be 3328 mm (131.0Ē) long. OK so far. But, using a #13 wire (0.031Ē or 0.79 mm) at C-88, which is typical, will give a tension of 162 pounds (or 73.5 kgf.). OK so far. But you must then continue using the same wire size all the way down. I havenít actually built and tested a monochord of this length and diameter, but I suspect there will be a decided time lag between hammer impact and voice. I also suspect there will be a very real power problem. A wire of that diameter and tension is going to be whipping around quite a bit. And for what?

A lot is said about Pythagorasís theories, but Pythagoras never designed or built pianos.

Del [/b]
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#1125267 - 01/29/04 12:57 AM Re: Logarithmic scale?
88Key_PianoPlayer Offline
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What about one like this?
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#1125268 - 01/30/04 10:03 AM Re: Logarithmic scale?
Calin Offline
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Hi Del!

I thought about this Pythagorean scale because it would have much less inharmonicity. But indeed a problem migth be posed by the hammer/string contact time, which could be too long.

What do you mean by "real power problem"? Less power than a normal scale? If yes, why?

Calin
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#1125269 - 01/30/04 10:08 AM Re: Logarithmic scale?
Calin Offline
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 Quote:
Originally posted by 88Key_PianoPlayer:
What about one like this?
[/b]
Hi 88Key_PianoPlayer!

What piano is that?

Calin
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#1125270 - 01/30/04 10:33 AM Re: Logarithmic scale?
Axtremus Offline
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An 1883 Bluthner (for sale too: http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=3700908717&category=43376 ).

First time I see this big a plate and that funny configuration of the three bridges. Interesting stuff. Any tech/scale designer care to comment? ;\)
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#1125271 - 01/30/04 10:56 AM Re: Logarithmic scale?
ChickGrand Offline
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 Quote:
Originally posted by Axtremus:


First time I see this big a plate and that funny configuration of the three bridges. Interesting stuff. Any tech/scale designer care to comment? ;\) [/b]
I check "new today" every day. I saw that and thought that was a highly unusual arrangement on the tenor bridge myself.

P.S. what's that wierd little rod connecting the bass-most strut to the one next to it about a foot this side of the dampers?

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#1125272 - 01/30/04 11:55 AM Re: Logarithmic scale?
Del Offline
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 Quote:
Originally posted by chickgrand:
 Quote:
Originally posted by Axtremus:


First time I see this big a plate and that funny configuration of the three bridges. Interesting stuff. Any tech/scale designer care to comment? ;\) [/b]
I check "new today" every day. I saw that and thought that was a highly unusual arrangement on the tenor bridge myself.

P.S. what's that wierd little rod connecting the bass-most strut to the one next to it about a foot this side of the dampers? [/b]
Not me. I can't possibly imagine why anyone would consider this string layout to be advantageous.

The little rod you refer to is probably a coupler. I would guess those long plate struts developed some unwanted resonances and this was their way of damping them down. The only way to know for sure would be to take it out and see what happens. (Itís obviously non-structural.)

Del
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#1125273 - 01/30/04 12:19 PM Re: Logarithmic scale?
Del Offline
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 Quote:
Originally posted by Calin:
Hi Del!

I thought about this Pythagorean scale because it would have much less inharmonicity. But indeed a problem migth be posed by the hammer/string contact time, which could be too long.

What do you mean by "real power problem"? Less power than a normal scale? If yes, why?

Calin [/b]
Itís not just hammer/string contact time. As the string gets longer the length of the string itself becomes an increasing problem. Aside from the practical consideration of string spacing (room must be provided side-to-side for string whip), it takes time for the wave motion to reach the end of the string where the bridge is. And once it gets there it is going to have trouble driving the bridge/soundboard assembly.

Unless, of course, the wire diameters are made absurdly large in which case other problems ó like building a plate capable of withstanding the increasing mechanical stress ó would begin to raise their ugly heads. Another obvious problem is that of building a keyset with enough stiffness to the keys to avoid the early onset of action saturation (assuming, of course, that you want to maintain anything close to a 1:8 hammer strike point ratio).

But, it is your first comment I continue to wonder about. What is it about ďmuch less inharmonicityĒ that is regarded as being so desirable? (And you are certainly not alone in this belief!) It is almost impossible for the human ear to discern subtle levels of inharmonicity. None at all is readily obvious to us, but once just a bit of inharmonicity is dialed in we have trouble picking out levels.

Keeping a uniform inharmonicity curve is important from a tuning standpoint ó jumps in inharmonicity, or an inconsistent inharmonicity curve, can make life exceedingly difficult for the tuner ó but, beyond that, it is well down on my list of important string scale design considerations. We just donít hear it.

Del
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#1125274 - 01/30/04 12:42 PM Re: Logarithmic scale?
ChickGrand Offline
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 Quote:
Originally posted by Del:
I can't possibly imagine why anyone would consider this string layout to be advantageous.

The little rod you refer to is probably a coupler. I would guess those long plate struts developed some unwanted resonances and this was their way of damping them down. The only way to know for sure would be to take it out and see what happens. (Itís obviously non-structural.)

Del [/b]
Isn't any significant deviation from anything nearest a straight diagonal line (never actually done) a compromise to "fix" a scale design? When I saw that tenor bridge positioned perpendicular to the bass bridge, practically forming a tee, I wondered how they could possibly get so far afield from ideal.

Your explanation for the rod is just what I expected. Another clue to a bad job on that one overall?

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#1125275 - 01/30/04 04:14 PM Re: Logarithmic scale?
Del Offline
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 Quote:
Originally posted by chickgrand:
 Quote:
Originally posted by Del:
I can't possibly imagine why anyone would consider this string layout to be advantageous.

The little rod you refer to is probably a coupler. I would guess those long plate struts developed some unwanted resonances and this was their way of damping them down. The only way to know for sure would be to take it out and see what happens. (Itís obviously non-structural.)

Del [/b]
Isn't any significant deviation from anything nearest a straight diagonal line (never actually done) a compromise to "fix" a scale design? When I saw that tenor bridge positioned perpendicular to the bass bridge, practically forming a tee, I wondered how they could possibly get so far afield from ideal.

Your explanation for the rod is just what I expected. Another clue to a bad job on that one overall? [/b]
I'm not sure I would call this a "bad" job in the context of when this piano was built. In 1883 a lot of things were being tried out by most pianomakers, some of which worked and some of which didn't. Still, they were trying hard to make sense of it all and to make acoustical progress. Quite unlike the industry of today when most everybody seems frightened to death to do anything different. In part, I suppose, because when they do they so often reap critism from so many.

While I don't pretend to understand what the designer of this piano was up to -- well, other than trying out an idea about smoothing out the bass/tenor break -- I can't be any more critical of it than I can of the manual choke used in my first car (a 1950 Chevy fastback). It was state of the art back in 1883.

Del
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#1125276 - 01/30/04 06:35 PM Re: Logarithmic scale?
BDB Online   content
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I can imagine that the designer wanted to minimize the acoustic coupling between the tenor strings and the bass strings, so the cross-strung strings don't cross many of the tenor strings.

Note that there are three levels of strings at the cross-over, the tenor strings, the aliquot strings and the bass strings, both wound and unwound. I've actually seen a triple-cross-strung upright, with a set of tenor strings crossed over the rest, and then the bass strings crossed over both of them.

You can't see the grain of the soundboard, but one of the ideas behind cross-stringing was to move the bridges closer to the center of the soundboard, and to put them on the longest straight-grain lengths of it.

A while ago I mentioned that the Steinway model, with cross-stringing, cupola plates, continuous rim, Erard-Herz action, and sostenuto pedal has become pretty much the standard for modern grands. This piano is an example of trying to go beyond that model, I think, but it is also an example of a design that didn't become a model for others. (I bet it has a Bluthner action!) Although Bluthner still uses the aliquot strings, none of the innovations in this piano have been adopted by other manufacturers, and as such, really represents a dead end in piano design. That doesn't mean itis a bad piano.
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#1125277 - 01/30/04 06:39 PM Re: Logarithmic scale?
Calin Offline
Full Member

Registered: 09/11/03
Posts: 418
Loc: Bucharest
 Quote:
Originally posted by Del:
 Quote:
Originally posted by Calin:

Calin [/b]
It's not just hammer/string contact time. As the string gets longer the length of the string itself becomes an increasing problem. Aside from the practical consideration of string spacing (room must be provided side-to-side for string whip), it takes time for the wave motion to reach the end of the string where the bridge is. And once it gets there it is going to have trouble driving the bridge/soundboard assembly.

Unless, of course, the wire diameters are made absurdly large in which case other problems — like building a plate capable of withstanding the increasing mechanical stress — would begin to raise their ugly heads. Another obvious problem is that of building a keyset with enough stiffness to the keys to avoid the early onset of action saturation (assuming, of course, that you want to maintain anything close to a 1:8 hammer strike point ratio).

But, it is your first comment I continue to wonder about. What is it about “much less inharmonicity” that is regarded as being so desirable? (And you are certainly not alone in this belief!) It is almost impossible for the human ear to discern subtle levels of inharmonicity. None at all is readily obvious to us, but once just a bit of inharmonicity is dialed in we have trouble picking out levels.

Keeping a uniform inharmonicity curve is important from a tuning standpoint — jumps in inharmonicity, or an inconsistent inharmonicity curve, can make life exceedingly difficult for the tuner — but, beyond that, it is well down on my list of important string scale design considerations. We just don't hear it.

Del [/b]
Hi Del!

About inharmonicity: I thought it might be desirable to have less of it, since this would lead to less stretch in the tuning.
But I am not so sure if this is desirable after all. Some say (e.g. Klaus Fenner) that there should be a certain level of inharmonicity because of the particularities of the human ear, which percieves it as pleasant. I have no idea what the "correct" level might be. Do you know more abut this thing?

Anyway, my Pythagorean scaling idea was related to building a normal-sized piano, not some huge monster. So the strings won't get much longer overall than in the average grand - but they would, of course, be somewhat longer for each unison, meaning the bass break must be in a higher place and more bass strings must be used than in a comparably sized "normal" piano.
If the outcome would be worth the trouble, I don't know...

It's still not clear to me why a such a scale would have less power - I believe the smaller weight of the thinner strings could be compensated by their greater length - so the mass should be about the same, or...?

What are your most important considerations for scale design?

Calin
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Calin

The Bechstein piano discussion group: http://launch.groups.yahoo.com/group/bechstein/
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#1125278 - 01/30/04 11:51 PM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by Calin:
Hi Del!

[1] About inharmonicity: I thought it might be desirable to have less of it, since this would lead to less stretch in the tuning.
But I am not so sure if this is desirable after all....

[2] Anyway, my Pythagorean scaling idea was related to building a normal-sized piano, not some huge monster. So the strings won't get much longer overall than in the average grand - but they would, of course, be somewhat longer for each unison, meaning the bass break must be in a higher place and more bass strings must be used than in a comparably sized "normal" piano.
If the outcome would be worth the trouble, I don't know...

[3] It's still not clear to me why a such a scale would have less power - I believe the smaller weight of the thinner strings could be compensated by their greater length - so the mass should be about the same, or...?

[4] What are your most important considerations for scale design?

Calin [/QB]
[1] Some inharmonicity is inevitable whether we want it or not or whether we think it is desirable or not. It is a natural consequence of a taut string possessing stiffness and mass.

Yes, a scale with higher inharmonicity will require a slightly wider tuning spread. But so what? Unless the scaling is really bonkers the tuning spread difference between a piano of a given length with a practical long scale vs. a piano of the same length with a practical short scale is going to be so slight itís doubtful it will be noticeable by even the most discerning pianist. There would be differences in the tone quality that would mask anything happening with the tuning spread. (Of course, this also assumes the tuning is properly done.)

[2] Well, unless the piano is exceedingly long the transition to wrapped strings will have to take place rather far up the scale. Again, I still donít see the advantage of the so-called Pythagoras scaling notion. As I said, Pythagoras didnít design or build pianos. If he had he would have encountered a number of practical issues that take precedence over any arbitrary doubling of string length ever octave.

[3] What can I say. Try it and see. Beyond a certain point a long, thin string is no longer able to put enough energy into the bridge to efficiently drive it. The solution is to add mass to the string, but this drives the tension up rather quickly unless you shorten the speaking length. And now youíre back to conventional scaling.

Not that there isnít some flexibility in this mass/length relationship. I think in an earlier post I went into this some.

[4] The two most important criteria are the overall length of the piano in question and the tone quality desired by the client. Once these two issues are settled it becomes a question of choosing an appropriate length/tension relationship and then physically fitting it all into the size available in a suitable manner. Sadly, Pythagoras is of no help whatsoever in this endeavour.

Del
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#1125279 - 01/31/04 04:02 AM Re: Logarithmic scale?
Calin Offline
Full Member

Registered: 09/11/03
Posts: 418
Loc: Bucharest
 Quote:
Originally posted by Del:
 Quote:
Originally posted by Calin:
Calin [/b]
[1] Some inharmonicity is inevitable whether we want it or not or whether we think it is desirable or not. It is a natural consequence of a taut string possessing stiffness and mass.

Yes, a scale with higher inharmonicity will require a slightly wider tuning spread. But so what? Unless the scaling is really bonkers the tuning spread difference between a piano of a given length with a practical long scale vs. a piano of the same length with a practical short scale is going to be so slight itís doubtful it will be noticeable by even the most discerning pianist. There would be differences in the tone quality that would mask anything happening with the tuning spread. (Of course, this also assumes the tuning is properly done.)

[2] Well, unless the piano is exceedingly long the transition to wrapped strings will have to take place rather far up the scale. Again, I still donít see the advantage of the so-called Pythagoras scaling notion. As I said, Pythagoras didnít design or build pianos. If he had he would have encountered a number of practical issues that take precedence over any arbitrary doubling of string length ever octave.

[3] What can I say. Try it and see. Beyond a certain point a long, thin string is no longer able to put enough energy into the bridge to efficiently drive it. The solution is to add mass to the string, but this drives the tension up rather quickly unless you shorten the speaking length. And now youíre back to conventional scaling.

Not that there isnít some flexibility in this mass/length relationship. I think in an earlier post I went into this some.

[4] The two most important criteria are the overall length of the piano in question and the tone quality desired by the client. Once these two issues are settled it becomes a question of choosing an appropriate length/tension relationship and then physically fitting it all into the size available in a suitable manner. Sadly, Pythagoras is of no help whatsoever in this endeavour.

Del [/QB]
Hello Del!

Pythagoras has nothing to do with pianos and scaling. It's just a way I tried to describe a scale that doubles in length for each octave with less words :-)

Could you please tell us more about the relationship between tone quality and scaling / soundboard construction etc.?

Also about length and tension relationship?

Calin
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Calin

The Bechstein piano discussion group: http://launch.groups.yahoo.com/group/bechstein/
The Schweighofer piano site: http://schweighofer.tripod.com

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#1125280 - 01/31/04 09:35 AM Re: Logarithmic scale?
Toddler2 Offline
500 Post Club Member

Registered: 01/09/04
Posts: 760
Loc: Hillsborough, NC
How's that book coming along Del?? \:\)

Todd ;\)
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#1125281 - 01/31/04 11:49 AM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by Calin:
[/QB]
Hello Del!

Pythagoras has nothing to do with pianos and scaling. It's just a way I tried to describe a scale that doubles in length for each octave with less words :-)

Could you please tell us more about the relationship between tone quality and scaling / soundboard construction etc.?

Also about length and tension relationship?

Calin [/QB][/QUOTE]


Not in a few words. We're rapidly getting beyond anything I can afford the time to answer. I've already written about this a bit on this list and on pianotech. I've also written about it in the Piano Technicians Journal. It is also an integral part of most of my all-day seminars.

Basically, there are four extremes:
ó Long scales with high tension.
ó Long scales with low tension.
ó Short scales with high tension.
ó Short scales with low tension.

In broad terms, long scales with low tension will be richer in fundamental energy (warmer and more melodic) and short scales with high tension will be richer in upper harmonic energy (sharper and more linear). Remember, these are extremes and there are many, many mitigating elements that will alter the final outcome. The idea is pick that combination that will yield the desired results within the size instrument available.
_________________________
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Piano Research, Design & Manufacturing Consultant
ddfandrich@gmail.com
(To contact me privately please use this e-mail address.)

Stupidity is a rare condition, ignorance is a common choice. --Anon

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#1125282 - 01/31/04 11:51 AM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by Toddler2:
How's that book coming along Del?? \:\)

Todd ;\) [/b]
Well, as my wife has been pointing out, the more time I spend here the less time I have to work on it.

I've got to get back to work now.

Del
_________________________
Delwin D Fandrich
Piano Research, Design & Manufacturing Consultant
ddfandrich@gmail.com
(To contact me privately please use this e-mail address.)

Stupidity is a rare condition, ignorance is a common choice. --Anon

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#1125283 - 01/31/04 03:19 PM Re: Logarithmic scale?
Manitou Offline
1000 Post Club Member

Registered: 01/08/02
Posts: 1044
Loc: Colorado
Thought:

Is not the aim of scale desig also to create strings of equal length on each note, to keep inharmonicity levels equal in unisons ?

If you mathematically make each string (even within a single note) longer, then you cannot possibly achieve the desired identical levels of inharmonicity, in each unison ?

Manitou - Pianist - Technician
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Manitou - Pianist - Technician

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#1125284 - 01/31/04 03:36 PM Re: Logarithmic scale?
Toddler2 Offline
500 Post Club Member

Registered: 01/09/04
Posts: 760
Loc: Hillsborough, NC
I thought I read that inharmonicity is related to string gauge/stiffness too, so keeping the lenths the same wouldn't keep the level even.
No?
Todd
_________________________
M&H AA (2006)

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#1125285 - 02/02/04 12:10 PM Re: Logarithmic scale?
Del Offline
5000 Post Club Member

Registered: 09/04/03
Posts: 5226
Loc: Olympia, Washington
 Quote:
Originally posted by Manitou:
Thought:

Is not the aim of scale desig also to create strings of equal length on each note, to keep inharmonicity levels equal in unisons ?

If you mathematically make each string (even within a single note) longer, then you cannot possibly achieve the desired identical levels of inharmonicity, in each unison ?

Manitou - Pianist - Technician [/b]
Sorry, I think there is a misunderstanding here. The individual strings within the unison are of equal length. At least in most pianos they are. There are a few exceptions.

When a scale is laid out it is to either the center string of the unison or to the centerline of a bi-chord unison. The other strings are filled in later.

Del
_________________________
Delwin D Fandrich
Piano Research, Design & Manufacturing Consultant
ddfandrich@gmail.com
(To contact me privately please use this e-mail address.)

Stupidity is a rare condition, ignorance is a common choice. --Anon

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