Laser Measurement

As I understand the links you sent (great by the way), not many will have a different pitch when the beam is cut at a different position.

This should be the most involved part electronically for such a project if you use time of flight as a measurement method. Some time ago I was involved in time domain multiplexing for fiber optic sensors and found a time correlator chip that maybe fun to try. I could not find the reference yet.

Maybe you can use a camera like this musical table. The Reactable is an Open project... Some videos are available on Youtube.

I thought Jean Michelle Jarre did one some time ago altough his did not pick up the different tones by measuring the hand position, he just broke the beam. Even though there is this difference, you could try to find out by searching for his stuff on the net and find out about his version. Maybe it gives you some ideas about yours.

Sorry cannot be of more help, trying to learn a normal guitar is hard enough for me

This reminds me of the man next door who cut his lawns using nail scissors.
I assume this is intended to be a non-contact control method for a musical instrument. Practical laser harps do not measure distance, but sense position - that your hand is cutting a vertical beam. You can even use the duration of the cut (speed of hand through the beam) to control the loudness. The power can be quite low if you use modulated semiconductor lasers and filtered detectors, even if you want to play your harp under normal light levels.

If you wish to do control the harp by measuring distance as you imply, the photographic industry has developed quite cost-effective rangefinders, which could be adapted to cover this sort of range with reasonable resolution. But these don't use lasers. Measuring distance using light, on the other hand, requires one of the following:
that you track and sense a focus (practical, but specialised), or
that you use the target (hand?) as part of an interferometer (more difficult), or
that you pulse the laser and measure time of flight (quite specialised, seeing as the required resolution of 2.5" or less corresponds to 40-ps time resolution)

If you can be more precise about what you are really trying to do, someone here might be of more help

PS If you don't need to see the beams, modulated LEDs would do the job - they are much cheaper, and don't have the same safety issues.