The length of the bar will, to some extent determine the number of vibrations it makes per second when it is struck, and this will equate to a certain frequency and therefore a certain pitch.  However, tuning bars is generally not as simple as just cutting the bars to length.  To bring them into tune, each marimba bar needs to have material cut away from the underside, altering the thickness about the middle so that the bar flexes more significantly.  This treatment will lower the frequency of vibrations the bar makes per second, and this in turn will lower the pitch of the note that the bar plays.

 

With most marimba keys the material removed is cut away in an arched pattern.  This can be achieved using a band saw and a sander.  However, band saws are a little harder to come by than routers, so I decided to use a router to cut away the material in a series of steps which I hoped would equate more of less to an arch.   With the help of a sanding block I then smoothed off the steps to make the undercut more arch-like.

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Since each bar will have material cut away from the underside to bring it into pitch, the length of the bar is not actually as critical as it might at first seem.  In general, the length of each bar need only be cut in proportion to its neighbours such that all the keys look aesthetically pleasing when set out on the rails that will ultimately support them.  However, the position of the nodes is critical and so once the length has been decided, the bar cut and the holes drilled then the destiny of the note in terms of which note it will become will have been sealed.

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My own rationale for cutting the bars was that I wanted to use the longest piece of wood I had (50cm) to make the lowest note I was targeting.  This was G2 on the baritone marimba.  Thereafter I needed to produce keys up to C6, two and a half octaves above this note.  Based on the fact I was going to produce a set of marimbas that could play in C and G (i.e they required both F and F# in each octave), that equates to a total of 27 notes.  Starting with a bar 50cm long, by cutting each subsequent note 1cm shorter I would end with a C6 that would be 13cm long.  This was fine as I had already estimated that a 12cm bar would the shortest key I could realistically produce.

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With the lengths of the bars being cut in regular intervals, the nodes follow the same pattern of proportionality.  This means that the nodes will lie happily over a straight set of rails that are spaced wider at one end than the other.  With each neighbouring note laid out on the rails with a centimetre between them, it is easy enough to work out the length that the rails have to be for the instrument in question.

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Finally, it is a good idea to make templates for the keys out of cardboard or some such material that you can write on.  I made mine from 5mm foam core and was able to cut this easily to length, mark on it the node positions and write down the name of the note, the dimensions, the fundamental frequency and the target harmonics that I was hoping to tune too.  These template proved to be extremely useful, saving me from having to write on the bars themselves, allowing me to identify notes that I had left lying about, and providing the critical information for notes which I needed to make again for the second instrument.

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If, therefore you find some hardwood that is suitable for making keys and comes in the right sorts of dimensions, but you don't know how long to cut it to make your keys, fear not.  You can just make a series of bars by cutting them 1cm longer each time, calculating the node positions based on the 22.5% rule and then drilling the holes.  Thereafter you try tuning the shortest bar you have to achieve a top C (C6) by taking away material from the underside.  It really is as simple as that.

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On a number of websites the dimensions the bars appear to be soaked in mystique.  But all this cloak and dagger stuff is all a bit unnecessary.  Yes, if the bars are wider for the lower notes they will be stronger even though they have had lots more material cut out from under them.  They will be louder too, and that's useful because the human ear doesn't hear the lower register notes as easily (apparently we are more in tune with the noise of a crying baby!), but other than that there is no musical reason why the lower notes need to be made wider.  They just need to be longer.  And the notes need to increase in length in such away that they look aesthetically pleasing and so their nodes lay over the rails.  These are the basic rules.  In theory you can make all the bars from wood of the same dimensions.  This is what I have done and I have managed to make two instruments that together cover a range of 27 different notes.  Okay, the lowest three notes are a little ropey, but nonetheless they do just about work.  Once I do find some larger bits of karagatch I will remove the three and make a baritone marimba instead.

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I hope this takes away some of the mystery. 

But just for completion, I will publish the dimensions that I have used here, so click the button to see them: