Rough Tuning Begins

Hey guys!  Welcome to a long overdue entry about tuning the bars!  As you may know, I have now successfully cut ALL 61 BARS into their their rough, rectangular shapes!  HOORAYYYYY!!!

The keyboard arrangement, with the proper spacing between the bars (not shown here), is somewhere in the ballpark of nine feet long from side to side.  This is going to be a big instrument...  :D

Now I have come to the most difficult and daunting part of this project...the rough tuning process.  I'm not going to go into a lot of the physics behind tuning the bars, because I'd probably be sitting here typing for a few days and you guys wouldn't get to read much about how the actual progress of the build if I did, but I will discuss a few fundamentals that I have had to understand about crafting the bars into the proper shape to produce proper tones.

Each bar, when struck, produces not just one tone, but several at once.  While one note is most apparent (called the fundamental, or the first harmonic), there are many overtones that are produced as well, and they all contribute to the overall sound and quality of sound of each bar.  When tuning the bars, it is important to know not only what to tune the fundamental to, but some of the overtones as well.  (some overtones are nearly imperceivable and not necessary to tune).  While some very high end, commercial marimbas out there tune several modes of vibration on each bar, controlling many different overtones, I plan to only tune the fundamental, the first overtone, and the second overtone of each bar.

Sound waves traveling through the bar, produced by the energy transferred into the wood from the strike of a mallet, travel in several different directions across the bar, and they all contribute to one, rounded out vibration pattern that produced sound.  While some of the minor ones travel in transverse, horizontal or even diagonal patterns through the bar, the modes of vibration I will be concerned about are the first, second and third transverse modes, which produce, respectively, the fundamental, first and second overtones.  Below is a diagram of each wave's pattern as it travels through the bar:

My doodling may look a bit SKETCHY. (get it???!!!)  These drawings represent bars viewed from the side and the wave patterns that travel through them.

The first wave is the first transverse mode, and it produces the fundamental, which is the most prominent tone that can be heard from the bar.

The second wave is the second transverse mode, and it produces the first overtone, which usually is tuned to be two octaves above the fundamental, so it matches its pitch.

The third wave is the third transverse mode, and it produces the second overtone, which is really only perceivable in the mid to low range of the instrument.  It will be tuned to a different note from the other two, usually an octave plus a major third interval above the first harmonic.

Given those pitch differences, an example of a properly tuned middle C bar (called C4) will have a fundamental of C4, a first overtone of C6, and a second overtone of E7.

A marimba bar, when properly tuned, has an arch shape cut into the bottom.  This shape allows for the bar to vibrate more freely in the middle, and produce clearer, longer sustained tones.  Here is a diagram of a tuned bar:

(just ignore the letters for a second...I kinda borrowed this image.)

Cutting this arch shape is difficult, and at first I had a lot of trouble figuring out which tool was the best for the job.  One does not want to simply cut AN arch for the sake of the shapeliness, but the arch has a purpose: removal of wood from the bottom of the bar to form the arch LOWERS the pitch of the bar.  A flat, rectangular plank of wood with no cut produces a tone that is fairly high, so cutting this arch is how we tune the bars!  If one wants to lower the fundamental, you must remove wood from the very center (about where that letter B is).  To lower the first overtone, one must remove wood from just beside that center (between A and B).  To lower the second overtone, one must remove wood from even further away (about where the A is and a little further out).  Why does this work in this way?

If you look at the wave diagrams above, observe where each peak and trough of the respective wave patterns are.  For example, since the fundamental vibrates the most at the very center of the bar, removing wood from the center of the plank would most alter the fundamental.  The first overtone peaks just outside the center, and the second overtone peaks at the center and approximately at the quarters of the length of the bar.  Seeing the pattern?  To tune each of these three modes of vibration we must strategically shave off wood in locations where each respective wave would peak!

Soooo...this task was a bit daunting.  If I were to lower the pitch too far by cutting too deep of an arch, its is very difficult to bring back up, and attempting to raise it again would require some unsightly alterations to the edges of the bar, so I don't want to go too low!

Ultimately, The tools I decided to use were a router and a drum sander.  The router, especially for the bigger bars, is handy for removing a lot of the wood from the middle of a bar that I know for certain would not be necessary.  So the router really is a time saver.  The drum sander, which is really a drill press with a drum sanding attachment on it, is what I'll use to whittle away at the bar to form that pretty arch shape and tune the note properly.

Disclaimer: the diagrams are not really drawn to scale...I just doodled again.  :)  I plan to put up photographs of this process in the future.

The very first bar I tuned was A2.  This is a fairly large bar, and it is on the lower register of the instrument.  The rough plank was about 13/16ths of an inch thick.  I used the router to trim out about 1/4 of an inch thickness out of the middle of the bar:

Then I took an initial reading of what notes each of the three modes of vibration were registering.  I don't remember exactly what each pitch was, but I remember they were all way too high, which was to be expected.  It was time for the drum sander to do its work in lowering those pitches!

I used the drum sander to first form the curve of the arch on either end of the bar.  This allowed me to progress with the tuning with at least the proper, arcing shape in place.

At first I sanded mostly in the middle of the bar to lower the fundamental, which was SUPER high compared to where I needed it to be (I think it was at an F4...?)  I basically wanted to make the intervals between the modes correct as early as possible, so I could sand more evenly as I progressed.

So I sanded away in the middle and the just barely to the left and the right of the middle to lower the fundamental and the first overtone.  The second overtone needed only a little bit of lowering, so I didn't take much out of the ends near the arcing part.

Notice how thin the middle is!  Marimba bars are very thin in the middle, so they vibrate strongly, yet are still surprisingly sturdy.  The middle and around the middle was mostly flat for such a low register bar, and the arc was still very prominent.

When it was finally completed, I had a nice arch cut in the bar, and all of the intervals between the notes were just right!  One thing to note, though:  this process is merely ROUGH tuning.  When I say I finished ROUGH tuning this bar, I actually tuned the bar about a semitone above what the final pitch it will be.  The reason for this is that before I'm done with these bars, I'll need to drill holes in them in order to run the cord that suspends them on the frame.  Removing more wood in this way will lower the pitch further!  Not by much, but still an amount that makes me want to tune the note sharp.  At the end of the rough tuning of my A2 bar, the fundamental was A#2, the first overtone was A#4, and the second overtone was D6.  After drilling the holes and fine tuning this bar, the modes will be at A2, A4, and C#5, respectively.

Here it be:

So far, I have managed to complete the rough tuning of 12 of the 61 bars!  They all look and sound amazing....

One of the bars is missing for this photo, but nonetheless...12 are done!!!

Future updates are likely to be slow in coming, as I am now back in school and am very busy during the week.  On weekends, I will continue working on this amazing project, and I will most certainly keep posting my thoughts and methodologies as I go along.  I hope you'll continue to read along!  :D