On tuning overtones in marimba bars - (Discussions with Pierre MARZIN)

-----Original Message-----
From: "Pierre MARZIN "
To: mailto:jim@percussionclinic.com
Sent: Friday, 4 July 2003 8:41 PM
Subject: Partials tuning

Hi,

I'm in the process of building (trying to) a classic chromatic marimba and face some difficulties about the tuning of the 2nd (4:1) and third (10:1) partials. On some bars, I can't manage to get the 3d partial high enough. On others, I have difficulties lowering the second one to 4 times the fundamental's frequency. On some others, I can't get rid of an unwanted partial (3:1) ! I'm an amateur acoustic guitar luthier but with no experience about percussion instruments. I've been reading every article I could on the web, without finding many serious practical information. I know this kind of tuning is an art that requires a lot of experience. I just want to learn enough to build a playable practice instrument (nice sounding if I can), and understand what I do.

If you could share just a little bit of your fine-tuning experience, it would help me a lot. I'd have tens of questions, but the main ones are:

• How can I locate the 3d partial (10:1) node and how can I tune it? What if it's too low?
• When should I stop lowering the fundamental (digging the center part) and start thinking about partials?
• What should be the amplitude ratios between the fundamental and the different partials?
• How should I modify the arch's shape from high to low bars?
• Do I have to "tune" the transverse vibrations?
• What should be avoided?
• etc.

I guess your time is rare and you're not going to answer all these. Anyway, any piece of your master's advice will be warmly welcome!

Thanks for answering and sorry for my "frog's english"!
Pierre MARZIN

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I'm not sure from the 1st part of your email if you have the right idea about what frequency the upper partials should be placed at, or not. On most percussion keyboards the bars are tuned so:

Fundamental = fundamental - antinode in the middle of the bar and nodes about 2/9 from each end.

2nd vibrational mode. (in a vibrating string this would be 1 octave above the fundamental and have a node in the middle as well as at either end.) On a bar, this should be tuned 2 octaves above the fundamental. It also has a node in the middle of the bar as well as 2/9 from each end. (all partials have nodes here, as this is where the bar is clamped by the strings.) The antinodes are halfway between the nodes.

3rd vibrational mode. = tuned 3 octaves + major 3rd above the fundamental. Nodes are at 1/3rd and 2/3rds between the nodes at the strings - antinodes 1/2way between.'

You cannot do anything about the relative amplitudes of the partials, so they will be what they will be. All but the fundamental are not amplified by the resonator, so it is mainly that which matters.

To tune any partial, hold the bar or clamp it on one of the nodes (not the string ones except for the fundamental), and strike the bar around one of the antinodes. To lower the pitch of that partial, remove material from the antinode area. Just be aware that the antinode area for the 2nd and 3rd partials are also going to lower the pitch of the fundamental. The idea is to try to get the partials at the correct ratios as early as possible, then keep them correct whilst getting them all down to pitch together. If the upper partials are too low, you can take timber more from the very middle of the bar to get it down faster - if its too low before you start - then your bar is probably too long or too thin overall.

As the bars get lower, they will of course get longer, but not in proportion, otherwise you would end up with bars really long and not practical. For this reason, the bars are more carved and thinner in the middle as they get lower. About a fifth above middle C, the bar shape may have to be a little different, and this is because of what you are calling the transverse mode. Actually, the transverse modes are the ones going along the bar that we have just been talking about. What YOU are calling the transverse mode is correctly called a lateral mode, or often simply called a cross mode. Usually the lateral mode is not loud enough to be a problem by itself, but around that pitch, it is often very close in frequency to the 3rd partial, causing a noticeable secondary tone. It doesn't matter what you change this transverse mode to, as you can't really hear it anyway, as long as you get it away from the 3rd partial. The lateral mode is turned through a process called wedging. There is a little picture of this on the website in one of my articles.

Sorry this has taken a while to get back to you - but I hope it has been helpful.

Jim McCarthy.

For more help on marimba building you can email Jim.

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