Optimizing Marimba Tuning for Temperature Variations: A Scientific Approach

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Marimba Australia
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I make marimbas, and I have invented a few variations (www.marimbaaustralia.com)

I am interested in how sound moves through the wooden bars - in particular the effect that temperature has and how to compensate during tuning on different temperature days.

I have almost no algebraic knowledge though - sorry.

I have a thermometer set up with a scale along the degrees - with a 3 cent + or - for each degree Celsius, yet I don’t thing I have it right.

I would love to be able to tune bars flat or sharp in any temperature and have them exactly at A=440hz at 21 degrees Celsius.
Any help is appreciated.
 
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Thanks, I have done that now.