Which is the program in charge of reproducing the music when I watch a Youtube video?
 

Hi: say for example I'm listening to Tchaikowsky's 4th symphony via Youtube, with desktop environment = Xfce 4.10, web browser = Seamonkey 2.12.1. There must be some program acting as a player. Is it some of the programs lying in my hard disk? Is it a program sent to the computer memory by Youtube? I would like to know.

That depends -- if it's a "normal" YouTube video then it's Adobe Flash (or, more rarely I suppose Gnash) playing it. If it's an HTML8 video then the web browser is playing it.

Unbelievable! The web browser itself plays it (HTML8)! I had quite forgotten about flashplayer. I remember each time I installed a new Slackware version, I had to download and install the Adobe flashplayer too, and it had to be the right version. Now it comes within Slackware if I remember well. I haven't been able to find information about HTML 8.

Sorry, meant HTML5, mistyped:
https://en.wikipedia.org/wiki/Html5
If you open a video in YouTube in Firefox and run top you should see "plugin-containe" taking up stupid amounts of processor time and memory -- that's the wrapper around Flash.
I've not looked whether you see any libraries or anything being called when you play HTML5 ones.

Oh, I have also seen that plugin-containe in the output of 'ps -e'! While playing a video in Youtube with Xfce 4 and the Seamonkey web browser.

Well, that's what it is -- Seamonkey will be using the Flash plugin also.