Re: Wire Size Calculation: Treble Strings
By Craig Brougher
Why everybody was thinking bass strings, I don't know. Guess it was because they are the ones more difficult to figure. I have a book that you can also buy, called Piano Rebuilder's Manual of Treble String Tensions, by Donelson. It has been a very valuable tool to me as the years went by, because now I don't have to mess with calculating it. But you still have a problem knowing what the design tension is, and how it increases toward the bass. (No such thing as equal temperament). So I have a rule of thumb to help me out. All treble strings can begin with a #13, frankly. And the breaks tell you a lot because you count notes in each section, multiply by three and divide by two, and whatever is odd becomes a tied hitch at the bass end of each section in American pianos.
The last tenor string size should be looked up according to the book, but you know it is going to range around #19. The important thing is the rate of change of string sizes from there. The more deeply angled the bridges are, ie. paralleled with the bass side of the piano-- then the faster the strings get long as you go down the scale. That is a characteristic of a high tensioned piano.
Let's take an example: C#53, 14 " long. #14 ga-- at 151 lbs. #15--170 lbs. #15.5--179.8 lbs. #16--190 lbs. #16.5--200.313 lbs. #17--211 lbs. (I hope I copied these right). These are the ranges of tension for that given wire to produce the desired note. Lets check the tensile strength of each: #14-- about 53%. #15--53%, #15.5--54%, #16--53%, etc. So we aren't going to break the wire. You have to exceed the modulus before it's going to break, and 70% of the elastic limit is about where you have to stop.
The question now is, what to do? Do we put 14 ga wire on that bugger, or do we use 17? Well, one formula computes the inharmonicity of the second partial (first overtone) in cents. So we could "idealize the scale," knowing this, and shoot for low inharmonicity, within our boundaries. So that's what we'll try. We will look at maybe a half dozen strings between our end notes, and just see if they all tend to have, at the tension chosen, a relatively low inharmonicity content. Our #14 = 1.96 C. Not bad. #14.5=2.08C, #15=2.20C, #15.5=2.33C, 16=2.46C, #16.5=2.59C, #17=2.73C. Hmmm. Whatdayaknowabout that? It gets worse as diameter increases(?)
Well then, I guess you could say something is wrong with the premise of looking strictly for cents inharmonicity, couldn't you? Because if that is the case, why not string your piano with guitar wire? The worse it could sound like is a bent Fender.
This is why I say that you must observe the bridges to see whether or not they are deeply angled. Little blunt baby grands are low tensioned, so you know to use tensions in the 150-160 lb range. Purity of tone and perfect partials may be just what tuners will like, but those pianos lack power and range of coloration. So just forget the purity of the partials and by elimination, decide about what kind of tension you need in the tenor section. Work your way up. Then if you end up landing on a #11 or 12 gauge in the treble, start compromising the progression until you get a #13. That is one way.
If you were to measure the percentage of the change that each octave makes in length as it goes up scale, calculating an ideal string gauge for each one, then observing the ideal tension of the lowest string in the treble section, scale everything around that tension (+ or - 10lbs, you would probably come out pretty close to ideal. I think that the lowest note in the treble section is close to the intended tension. But by looking up the octaves of, say C# or whatever else suits you, and noting their progression, you will develop the rest of the scale, using the information on the plate: How many notes in each section, how many tied hitches, the angle of the bridges, and even the degree of undercut in a section under a bridge. Let me explain that, too.
The maker undercuts a bridge when that section of his scale is too loud, basically. He always evens it out, but he never gets it perfect, that way. So when you see an extreme chiseled bridge contact at the soundboard, that is a correction for an otherwise "great" piano scale (ahem). Usually caused by strings that are a little too heavy at that point, but must be used to even the temperament. You can select a gauge smaller if you wish, or you can slow the progression of the string gauges as they descend, in that section, decreasing the progression of the tension in that section. There is a lot of "art" in this science, and much that cannot be said in a note like this. But you get the idea. Right? You do, don't you? Huh?
(Message sent Thu 25 Apr 1996, 14:46:50 GMT, from time zone GMT.)