...and then, there were 4!

With the basic tuning process made relatively easy and predictable, I felt that yet more could be done. And so I remembered that Heather L Hill measured the bars of a Yamaha Marimba in her 2013 Bachelor Thesis Acoustics of Marimba Bars, and found a well tuned 4th partial. Although in Bork's paper (see previous post), the tuning process is only discussed for 3 partials, the diagrams very well show the necessary information for the 4th partial.

So another experimental spruce D-bar was made. In the course of making the bar, the benefits of using a router clearly showed: Taking the measurements of the previous D-bar, I could triple tune the bar in less than an hour, including the time to bevel the edges and sand the bar a bit. The search for the 4th partial, however, took a bit longer, but with satisfying results.

The D has a fundamental target frequency of f0=147Hz, and the second to fourth partial should be at f4=591Hz, f10=1448Hz and f20=2897Hz

Here is the bar in a state close to final.

A smaller router drill was used this time. The grooves for the f20 are the ones closest to the middle groove.

 In this state, the spectrum already looks very well (green line, red line is uniform bar). There's a nice D fundamental...

 ...and an acceptable f4...

 ...and a f10 that is too low; this was due to cutting the outer f10 grooves too early too deep again; ...A N D, here it is, number...

FOUR. A fourth partial at 2999Hz, which is a ratio of 29.5, is produced by the grooves left and right of the centre groove. It is a bit too high, but there's still wood left to remove!

 As a next step, the material between the groove of f4 and the centre was removed. This lead to the f20 raising up again to ~3500Hz, so this time it DID matter to remove the material. But, since a groove makes a spike in the spectrum ;), f20 was recovered again by adding a small groove in the new plain.
This is the final stage of this D bar (orange line). F0 a bit low...

 ...f4 a perfect D octave...

 ...f10 almost spot on!...

and a f20 almost spot on as well. The actual ratio is 20.9.

Was it worth the effort? Yes! The bar, even in spruce, now has that typical mellow, almost chiming marimba sound on the attack of the mallet (at least to my ears), which the other spruce bar has not. The difference is very noticeable, since it changes the sound at the attack, which is the predominant way our ears distinguish instruments. So yes, it now really sounds marimb-ish ;).

What follows from all this? Well, I will 

• quadruple tune bars C3 (131Hz) to G#3 (209Hz)
• triple tune bars A3(221Hz) to G#4(418)
• double tune bars A4(443Hz) to C6 (994Hz) (if at all possible)

With this, the harmonics of all pairs of bars should fit together, which is one of the main reasons for tuning the higher partials. Oh yes, and my reference A4=443Hz.

Next, plain wood work is on schedule: Bevel the upper edges of the bars, sand them and apply the first coat of glaze.

Stay quadruple tuned ;).