Top resonance T(1,1)2 vs String tension and\or action

[johnparchem]

I went back to a few classical guitars and took new spectrum plots and noticed they all had top resonances 2-4 Hz higher than my initial plots. At first I thought it was related to the instruments breakin. This weekend as part of final setup on a classical guitar I lowered the action by 1 mm (two at the saddle). The spectrum plot showed a 3 Hz rise in the top resonance. I suspect it has to do with the tension on the top, in this case caused by lower torque.

Almost always with a new guitar I check the spectrum after I first string up the instrument with a fairly rough setup. I now suspect that the difference in the resonance I have been seeing initially vs the plots I have just taken is that a final setup occurred between the two measurements. In all cases I take the instrument from a high action (generally 4.5-5 mm to 3.5 mm.)

For me, with my limited data this is just a working hypothesis. Also worth checking in the future is the effect of on the top resonance changing the string tension. As anyone else seen this effect?

[Trevor Gore]

If you take 2mm off the saddle you'll lose a fair amount of mass, likely sufficient to raise the the T(1,1)2 by a couple of Hz.

On the whole, I've not found much difference in resonant frequencies between under tension and no tension, but others have told me they have, but other things might be going on, like the saddle not now adding to the mass of the top.

Having said that, I've generally found resonances to rise after slightly as the guitar ages over the first 3 months or so without making any changes to the instrument. I've put this down to finishes hardening up and inside wood surfaces oxidising (or whatever they do) and hardening. This surface hardening effect is apparent when planing an old surface vs. a new surface, though I don't know what the mechanism is.

[johnparchem]

Yes, the change in mass makes more sense given the the resonance frequency is proportional to the square root of the ratio of the stiffness to mass. There is nothing like missing a first order effect. I suppose I could blame my sudden insight on jet lag having just returned from Europe.