But the long answer is: It will stay out of tune for a given definition of "in tune", because there is no perfect string.
A perfect string has a diameter of zero.
> The math of harmonics is really simple
If a string only had harmonics on it, the oscilation would form a stationary wave that never leaves the string and resonates between bridge and head.
It is the non-harmonics that create the sound.
A sound is made of a base frequency and overtones.
Overtones are never perfect multiples of the base frequency, because they are influenced by
(1) string length
(2) material bending stiffness
Because of bending stiffness, overtones have a lower frequency than their theoretical haromnics.
> The second harmonic is the one you get from the string vibrating in halves.
True in theory, false in practice due to bending stiffness.
> Guitars can’t be perfectly in tune
I don't see why. Overtone series are impossible to solve, but base frequencies can be tuned to your liking.
You can.
(1) Movable frets https://www.youtube.com/watch?v=EZC69A8TsJ8
(2) No frets https://www.youtube.com/watch?v=92TxCGBNEVg
(3) force the string sideways to a higher pitch https://www.youtube.com/watch?v=kbALdNDhKYE&list=RDkbALdNDhK...
But the long answer is: It will stay out of tune for a given definition of "in tune", because there is no perfect string. A perfect string has a diameter of zero.
> The math of harmonics is really simple
If a string only had harmonics on it, the oscilation would form a stationary wave that never leaves the string and resonates between bridge and head. It is the non-harmonics that create the sound.
A sound is made of a base frequency and overtones. Overtones are never perfect multiples of the base frequency, because they are influenced by
(1) string length
(2) material bending stiffness
Because of bending stiffness, overtones have a lower frequency than their theoretical haromnics.
> The second harmonic is the one you get from the string vibrating in halves.
True in theory, false in practice due to bending stiffness.
> Guitars can’t be perfectly in tune
I don't see why. Overtone series are impossible to solve, but base frequencies can be tuned to your liking.