"I've read an experienced builder can tell by the feel. I've also read that some builders tweak the spokes and listen to the tone. If it's too high or too low they can tell and make the adjustment.

That is a myth on both counts. An experienced builder is going to be able to get close just by being organized and doing everything in a logical pattern. The wheel isn't going to be crazy out of true like a disorganized amateur. But apparently even really expert builder goof tension without using a tensionmeter. One really good builder said he would get different levels on different days. The good builders don't have to check every spoke, but apparently they still benefit from using tensionmeters.

The musical pitch thing is supposed to be unreliable also. I did want to attach my Intelituner to the wheel and read the numbers, but for our kind of wheels the cross pattern dulls it out and makes for different pitches. And then there is the front and rear with dish on possibly both of them. Sounds more plausible for radial spokes. I read something by one of the experts as to why it plain doesn't work, but I don't remember those details... My feeling is that at the moment in time that a person feels the need to use pitch they are a candidate for a tensionmeter. However if one both owns a tensionmeter and is musical, then one could prove the point either way to oneself.

On a spoke replacement getting close is probably close enough. Keep in mind the info about tensionmeters and pros, they aren't hitting everything perfect. If you are only down one spoke, bet it near the ball park, and it is perfectly true, should be good enough. Amateurs are the guys fitting to get tension for every spoke perfect, and all the alignment factors. We rock.