“I am a slow walker, but I never walk back.”

Indeed, Mr. Lincoln.

Better to be sure-footed and slow than fast and prone to mishap! Though sometimes I’ve been known to take it too far, that is one of my core philosophies for making instruments. For life, in fact. I like to smell the flowers.

Picking up where we left off – the keys are now cut to exact dimensions. Next comes a steady stream of shaping and sanding…

As if by magic, it seems every time I reach this point in a project (where lots of fine dust is being produced) the switch fails on my harbor freight dust collector. This time, instead of cleaning/repairing the crappy switch, I made a new one.

Next is rough tuning. I often tune across 3 or 4 phases, mostly depending on the weather. I didn’t get many pictures this time, so I’ll use some older photos to illustrate.

Each key is shaped on the bottom to bring the pitches down to target (called an “undercut”; see picture below).

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Tuning of the fundamental (primary pitch) and successive harmonics is accomplished in this way. For this initial tune, using a bandsaw and a drum or belt sander, I bring everything to within a quarter tone of the target pitch. This is done so that the key will only need a small amount of material removed to bring it to final pitch. Less heat will be generated sanding in the next phase; good as a heated key is more flexible and gives a falsely low pitch. That factor as well as temperature/humidity conditioning are why I tune in gradual steps.

Once the keys are near their target pitches, the nodes (points of least vibration for a given mode – we’re concerned with the fundamental) of each key can be found.  As with most things in the world, there is more than one way to tackle the nodal predicament. This is how I approach it these days.

 

 

When generating a node line (a perfectly straight line along which the frame rail will run), the idea is of course to get the line as close as possible to the actual nodes.

I find each key’s nodes and record the number, measuring from each end of the key, at the center of the width, averaging the end figures; they typically shouldn’t be skewed by much. I convert those nodal measurements to reference the centers of each key. (key_length/2 – node_from_end).

I like to look at the numbers and decide on the low/high key measurements for the candidate node line (these should be quite close to the ‘raw’ data for the corresponding keys). (nodel and nodeh below)

Keeping in mind spacer widths and any graduation in key widths, determine the slope ratio and angle of each rail (on many marimbas I build the rails are symmetrical/will have the same angle, but this is not the case for chromatic instruments).

CodeCogsEqn

CodeCogsEqn (5)

 

-Using that ratio, calculate the node line “intersection” at each key’s center (of width). This would look like:

CodeCogsEqn (4)

 

 

CodeCogsEqn (3)

 

This approach avoids cumulative error and works for graduated and non-graduated key widths. Keep in mind it is only measuring the line at one point per key, the center of each key’s width.

So, now we have a perfectly straight line that should intersect pretty well with the raw nodal data. If it doesn’t, adjust appropriately and generate another set of numbers. (I wrote an algorithm that does this, finding the best line based on total absolute value of the discrepancy between generated line and raw node/key data)

Once I am satisfied that the line and nodes match, it’s time to drill the line through the keys using angle from above.

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My jig setup references the ends of the keys, so I convert my generated measurements from center reference to end reference, to match. I set it up and adjust with each cut so the center of the hole passes through the intersection of key width/2 and the calculated distance from the key end.

The nodal holes are drilled from both sides, then countersunk. I sand the keys to 220 and bring them indoors to acclimate while I work on the frames. Moisture content and temperature can affect pitch substantially.

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Of course, you could always lay it out physically and circumvent the mathematics, but I find the calculations fun and much more accurate! 🙂

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That’s all for now. Off to the workshop!

P.S. – In case you’re curious, here is the output of my script  made in Python to cover the described tasks:

Baritone 1 – units: cm

Checked to a precision of: 0.02
Raw node data (from center):
[21.1, 20.346, 19.457, 18.683, 17.924, 17.178, 16.748, 15.932, 15.251, 14.695, 14.048, 13.366, 12.633, 12.0]
Best generated line:
[20.92, 20.188, 19.463, 18.747, 18.037, 17.336, 16.642, 15.956, 15.278, 14.607, 13.944, 13.288, 12.640, 12.0]
Absolute value difference between best list and raw data: 1.113
Best angle: 3.167231237775345

Dist between centers (of width) of outer keys with spacers: 161.2

spacer: 1.3
Best list was found on try # 1795
Sum of all key widths: 155.4 Sum of all widths plus spacers: 172.3
Best line from ends of keys:
[15.33, 14.809, 14.294, 13.787, 13.286, 12.792, 12.306, 11.826, 11.354, 10.888, 10.429, 9.978, 9.533, 9.095]

 

Icicle hands

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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:

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Adjustable straight-edge jig

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:

simple_key_interval

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:

Screenshot from 2016-01-08 19:07:37

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.)

 

 

Screenshot from 2016-01-08 19:26:16

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:

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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.

Ahoy, there.

It’s about time I set up a place where I can document my projects in semi-real time. Whether I’m building an instrument for you, you’re my mother, or you’re just curious about what’s going on, perhaps this blog will be of some interest.

To kick off, I recently returned from a musical mini-tour of OH and IL with Thomas Mapfumo and the Blacks Unlimited.

 

 

A new recording is also in the works, following the release of our album Danger Zone earlier this year.

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On the marimba front, 6 new instruments are about to find their way to a new home…

In the future I intend to document the building process in considerable depth, but for now just a few photos.