recorded a live performance. Sounds great on headphones, but high notes sound flat on laptop speakers. why?

The built-in speakers on a laptop? Laptops are meant to be small, and so the speakers are small. Small speakers sound crappy. Nothing will change that. Nothing to fix it, except buy larger speakers to plug into the audio output connector.

Although your headphones may be small, too, they go directly to your ears. They don't have to carry across open air space, and they use speaker technology to take advantage of that fact, which does not work for the open speakers on your laptop.

Smaller speakers, such as headphones, can output higher sounds than smaller speakers, such as he ones on your laptop. If whatever you're using to listen to/watch the recording, has a "treble reducer" setting for the audio, use that. It should help in your situation.