I should probably have asked this question before, but what is a piano's scale? (Not a musical scale and not how big a piano is, I'm willing to bet). I see it referred to a lot but I've not found an explanation of it. Thanks.

The scale usually refers to wire sizes - length, diameter and friquency.
In the design process they would start with note C-88 at lets say 53mm long and wire size 12.5 or .03 inch. The tension for this note could be around 170 lbs.
C - an octave below you think would be double the length at 106mm because it is half the frequency - but it is not. If this were practiced then C-1 at the bottom of the piano would be 6784mm in length. This problem is dealth with by increasing the wire diameter while increasing the octave wire length something less than double. In the bass the copper winding is added as the wire length does not get much longer than the lowest tenor note.
The size of the piano greatly influences this design.

Well. actually you could double the length an octave or more below C-88, and people have. You just start shortening the scale later. However, scale designers have done exactly that, but changed the wire gauge anyway.

Which just goes to show that scale design has evolved. At one point, it just was fitting the strings into the instrument. Then strike point became a factor, and then tensions and other physical properties. But at its heart, the scale of the piano is the way that the strings fit in it.

It also includes the number of trichords, bichords, and monochords, and also which ones are wound (there are wound trichords in some scales).

Some of the problems to manage are to keep the tension in a reasonable percent of the wire's breaking strength (usually around 2/3), to keep inharmonicity reasonable, and also to have all those variables change smoothly throughout the compass (range) of the piano. Here are some sample scales:
http://www.goptools.com/gallery.htm

It's common these days to "rescale" a piano when restringing it, because software is now available to do a better job of managing these variables. Rescaling can be done either with or without changing the length of the strings.

--Cy--

aha, thanks. That explains it!

interesting CY...thanks

something else to study