It can be a challenge mustering up the courage to venture from a warm, comfy chair into a frozen workshop. Such trying evocations of self-discipline are at the heart of being self employed. Some days are easier than others in that regard. Today I’m working on a new batch of instruments – a couple interesting baritones of cherry, and a tenor of padauk.
Among the tasks trailing the generation of a set of measurements is finding where, within a board, each key should lay. There are many things to consider in this process – lumber dimensions, wood quality and appearance, grain direction in all 3 dimensions, frequency and size of each note, efficient use of material, and any tonal goals you may have for the keyboard as a whole, or sections thereof.
Much of the lumber I find is neither straight-edged nor flat, and can require quite some work to bring it into the realm of use. There are many ways to “straighten” a board, but as most of my woodworking takes place in a single car garage, space is in short supply. A hand plane used to be my go-to method for truing up a curved side. Certainly there is no space for a large jointer. Recently I built this jig for the table saw; essentially a piece of plywood with an aluminum rail screwed onto it, which sits on top of the stock:
The adjustable (by way of screw) rail slides along the saw fence and provides a straight reference for the cut at the left side. The jig has a “foot” which grabs the trailing end of the board and pulls it along as you feed it through. If a board has a general bow, the concave edge should sit against the jig for stability. A featherboard complements this operation nicely.
With the rough stock straightened, the board can be further processed. Sometimes it makes sense to rip the boards to width first, but in this case, with graduated key widths, I cut each key length out and rip to final width afterwards.
When doing graduated key widths, it is important to remember that the slope created by the lengths of the keys (viewed from above, with keys facing upwards) should be linear and not curved. This means finding measurements is slightly more tricky.
Generally I like to approach the problem of key measurements by establishing (ideally) the lowest and highest keys’ dimensions/pitches and using those numbers to determine the rest.
A simple, non-graduated width keyboard’s length generation equation would look like this:
Where i is the interval between key lengths, L is Length, l stands for “low” and h “high”. K = number of keys in the keyboard.
My approach for graduated widths is something like this:
X is the ratio of difference in length of the highest and lowest keys divided by keyboard width (omitting the lowest key’s width (index 1)). “Wn” here should be thought of as Wh.
(EDIT: I neglected to account for spacers in this and the below equation. The difference is very small in practice (and only usefully-applicable to graduated keyset formulas), but indeed real. However, I’m not so keen on going back and re-doing these images. Basically, assuming you have squarish-ended keys, you want to add a spacer*(n-1) to the summation. If you had round ends, you’d shift the reference points to the centers of the key/s, so when viewed along their ends, the outermost point on each key will create the visual line. I hope this makes sense.)
And here, to get Ln, subtract from L1 (lowest key’s length) the product of x by the sum of widths up to n. This approach avoids cumulative error.
It’s fun trying to notate this stuff as I usually don’t.
I try not to get carried away with mathematics in making instruments. It certainly has its place, but I find it can get in the way of your senses if you let it. I never trust numbers alone to get me through a project… there are some things that are best determined by your eyes, ears and hands! I enjoy thinking about problems in different ways, and the mathematical approach is just one of many.
Anyway, here is the result of the above – 3 sets of keys:
A couple of side projects since last entry:
The first is a frame for a cabinet (lots of bridle joints!); the second a “steampunk” inspired lamp. The coolest aspect of the lamp (in my opinion) is the switch; I managed to integrate it into the valve. Check here for a clip of the action.