The first type is just regular applause. The sort you hear at concerts and award ceremonies and the like. Applause is in a weird position for me because I realise it's necessity but I find it ugly. When you want to acknowledge appreciation for someone and you are also part of a crowd, applause is - admittedly - a good way to do that. Everyone does the same thing (though not precisely at the same time), so you avoid the confusion that would arise if, for example, everyone said something specific to communicate appreciation. And since it's an audible sign of recognition, it has a greater effect than if people just saluted or something.
But it's the not-at-the-same-time feature that annoys me. Because everyone claps at different rates and volumes, it just ends up being this cacophonous noise. I hate it when people clap at me because it's just such an ugly sound.
The second type of clapping is the audience participation type of clapping. At concerts during easily count-able songs (usually 4/4, I should think), audiences feel the need to clap at every fourth beat. It's one thing if a band asks the audience to do this, but it's eye-rollingly banal and annoying when the audience does it on its own. In my opinion, clapping to every fourth beat adds no-thing to the music. It's just noise. And I'm sure that bands don't have any problem with keeping up with the beat (if they did, there would not be people coming to their shows). The audience's acting as a giant, collective metronome is not effective.
I think an-other part of this that annoys me is that by starting the fourth-beat clapping, the audience asserts that it knows how the music should be accompanied. And as a musician, I feel that that should be the musicians' decision. So when a band asks the audience to do this, I'm not as annoyed because they're sanctioning the clapping, but I still think it's aurally ugly.
The third type of clapping is syncopated clapping, and it is the only type that I like. Unlike clapping to every fourth beat, syncopated clapping has some complexity. There's rhythm in it, and because of that, it doesn't getting monotonous like fourth-beat-clapping does. Sometimes, it can be one of the most exciting parts of a song.
So syncopated clapping is permissible and perhaps even encouraged; applause is decent until some other method of wide-spread recognition is developed; and fourth-beat-clapping is terrible.
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