how would you change both the tension and the lenght and keep the pitch the same?

oh. i think this question is a bit too vague. what does the apparatus look like? otherwise it seems like you could do whatever you wanted to the string (e.g., attaching a weight to one end of the string as opposed to having it just suspended weakly by both ends).

To change both the tension and the length of a string while keeping the pitch the same, you would need to adjust both the tension and the length proportionally. Here's how you could accomplish that:

1. Increase Tension, Maintain Length: You can increase the tension in the string by using a different tuning peg or mechanism to tighten the string. This will stretch and tighten the string without changing its length.

2. Decrease Tension, Maintain Length: To reduce the tension in the string, you can use the tuning peg or mechanism to loosen the string. This will reduce the tension without changing its length.

3. Increase Length, Maintain Tension: If you want to increase the length of the string while maintaining the tension, you can effectively stretch the string by moving one or both of its endpoints farther apart. This can be done by adjusting the attachment points of the string on the instrument, such as moving the bridge or the nut.

4. Decrease Length, Maintain Tension: To decrease the length of the string while maintaining the tension, you can move one or both of its endpoints closer together. This can be done by adjusting the attachment points of the string on the instrument, similar to the previous step.

Remember, the key to maintaining the pitch is to ensure that both the tension and the length are adjusted proportionally. If the tension or length changes significantly without maintaining the correct balance, the pitch of the string may be affected.