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I have an upright Baldwin 88-key piano ("Style No. 2056A") that was made in 1991.

How can I determine the diameter of the tuning pins (so I can use the corresponding tuning tip)?

I took photos of the tuning pins for reference.

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You probably don't need to. I note from your photos that your piano has enough clearance between the bottom of the coil wound around the tuning pin and the plate/bushing that you could probably get a digital caliper in there and measure the diameter directly, if you wanted that value.

However, that measurement has little to do with the choice of a tip for your tuning lever. The most common sizes of tips are denoted #1, #2, and #3 and have no correlation to the diameter of tuning pins. They are chosen more for the type of fit a piano tuner prefers. This personal choice is generally developed over time by the tuner, along with their physical technique for turning the pins. Some of the factors in this choice are the style of tuning they use such as "smooth pull" vs. "impact," whether they prefer a snug fit or more play, how much swapping of tips they're willing to do to get the fit they like, etc.

Even if there was a correlation, the size of the star opening of the tip and the rate of taper varies between makers, even for the same size designation.

Caveat: I am aware there are some piano tuners who take a snug fitting tip very seriously, to the point where they try multiple tips on every piano they tune. One of these is a respected teacher at the PTG conventions, which I know because I was in his class when he described his technique :-) But again, it is a personal choice.

I wouldn't worry about it too much. Take Tim's advice and get a lever with a #2 tip, which is the default for many makes and models. This size is a good balance between snug fitting and being large enough to fit many piano's pins (including yours, which appears to have a relatively large tapered section.) Make sure the tip is removable so you have options if you decide later to try different sizes. That is how I started and the vast majority of pianos I tune are with the #2, occasionally swapping down to a #1 depending on circumstances.

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Nearly all modern piano pins are 'square tapered', and will use a No. 2 hammer These can be a square female, or more often an 8 sided star shape, to get a good angle on the pin. It wouldn't be a bad move to own all four tips, though, as sometimes pins may not be exactly the same, or have been damaged previously, and you may find that a different number tip may fit some pins more snugly.

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a 6,5MM DIAMETER tuning pin is the most common. NB this is the diameter of the pin in the wood (wrest plank) and where the string coils. Now this pin has been forged to a square taper for the tuning wrench to hold, this means that one should use the Number ONE tip so as to have a firm grip when rotating the pin !

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