Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum FAQ - Tuner-Technicians Forum Logarithmic scale?

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.

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

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?

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!

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

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

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

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 it’s much easier to simply copy an existing design. Not much new is discovered this way, but it’s a whole lot cheaper. And so what if the results are less than spectacular — 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

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....

Actually, I’m not at all sure why so many folks consider a sweep of 2.0 to be all that desirable. It really isn’t. For example, starting with a length of 52 mm for C-88 this would make C-28 1664 mm (65.5”) long. C-16 would be 3328 mm (131.0”) long. OK so far. But, using a #13 wire (0.031” 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 haven’t 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 Pythagoras’s theories, but Pythagoras never designed or built pianos.

Del

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

Love it! That's a quote to keep.

What about one like this?

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

Hi 88Key_PianoPlayer!

What piano is that?

Calin

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?

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?

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. (It’s obviously non-structural.)

Del

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