This is actually not a very good estimate. It has many inaccuracies, and those inaccuracies are harder to nail down than the original problem, so you made it harder on yourself.

Some questions about your result: How many piano tuners work at any of those piano tuner companies? How many piano tuner companies are not on yelp? How many piano tuners are employees of instrument stores instead of working freelance/for a tuner company?

Those are all harder to answer without industry information than the simple deductions the handout makes from common sense/knowledge.

I have the feeling it is important that people understand the limits of technology. Even though we like to say something doesn't exist if it isn't on Google, things very often do irregardless.

Sweet! My guess was 6. I proceeded by estimating the number of pianos per person (my guess was 7000 in NYC), then by estimating the frequency of tuning. I came up with ~20 pianos/day needing tuning and guessing the average tuner could handle 3 pianos / day (when I was a kid I recall the tuner taking a couple of hours.) some edge cases like Carnegie Hall (where the piano is probably tuned quite frequently) probably skew the numbers somewhat. Also, I would guess that a city with mostly single family homes, say, Houston, has more pianos/capita than NY or Chicago, based on the pain in the assedness of moving a piano into an apartment, though that may be offset by the number of music schools and cultural institutions.

If this was Reddit this would pretty much be /thread, however I propose the following question:

While this may be a good estimate, what about businesses not on Yelp?

"Professional Piano tuner" doesn't seem the most technologically advanced profession, so I think it's safe to assume that there are several, if not dozens more in existence in the NY area.