Monday, August 29, 2016

Tone Wood The Nyquist stability criterion

The Nyquist stability criterion

If you want a long sustain you should have very little coupling from the string to the sound box. We can achieve that by making the breakover angle from your string over your bridge almost flat. Almost no force component will drive the top this way. If the string doesn’t have to deliver labor it will oscillate longer. Another method is using a very heavy bridge which causes all the string energy to reflect back from the bridge instead of driving the top plate. 


With these techniques you will get more sustain but it will cost you acoustic power (your guitar will not be acoustic loud). Carlos Santana has both, endless powerful sustain. He uses his Mesa Boogie amplifier to feedback acoustic energy into the string. Harry Nyquist came up with the stability criterion in 1932 which is used in control theory and predict if a system is stable. Without Harry it would be impossible that we ever could put our feet on the moon. The criterion is simple: the string energy is converted by a pickup into an electric signal, the electric signal is amplified and converted by the speaker into an acoustic audio signal. Only a small part of that acoustic audio signal will get the guitar in motion and causes the string to vibrate again which in turn is getting converted to an electrical signal by the pickup. 

The criterion says that:
When all the attenuation (conversion from string motion in electric signal, conversion from electric signal to speaker cone movement, the losses of the sound field from your amplifier to the location of your guitar) equals the amplification of your Mesa Boogie amplifier. The system is on the edge of stability.


If the attenuation is stronger the system is stable (the sustained tone fades away). If the amplification is stronger than the attenuation the system is instable and the system “explodes” (the sustain tone gets louder and louder).

Every note Carlos hits with endless sustain was exactly on the edge of instability. How did Carlos managed to do that for almost every note while he probably never had heard of Nyquist? Certainly don’t try to do this with a hollow body super 400. The brass plate under the bridge of his Yamaha 2000 guitar will also contribute. Every pronounced resonance, whatever it is the wooden body of your guitar (making it form a lot of layers different wood will help to cut pronounced resonances), pickup or the speaker of your amplifier, is not good for producing an even Santana sustaining guitar.