Simply put, when the tension is increased (by changing the wire size) the inharmonicity increases. This can be proven using the formulas posted earlier. Inharmonicity (inh) is caused by the stiffness of the wire from it's tension, it diameter and the fact that the wire is not hinged at the terminal points. Indeed, if the terminals were hinged there would be almost no inharmonicity. All stringed instruments have inh, albeit very low in some, and no matter what the string is made of. Some instruments like zithers or autoharps have inh so low it it hard to measure but it is there. The only way to uncouple inh and tension is to change the speaking length or to wrap the string with copper, iron or aluminum. Newton
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