I had already increased my MaxClients setting to 120 a few weeks previously when I got about the same number through to "Your templating engine sucks and everything you've ever written is spaghetti code" post but I forgot that with people downloading those mp3 files, the connections would get held open for much longer so I had to put MaxClients up again to 220 and restart apache at one point (which I'm sure kicked a bunch of people off, some of whom would have abandoned trying to load the site at that point).
With MaxClients set at 220 the site was able to serve pages quickly and reliably the rest of the day as well as allowing roughly 5500 people to download my Dad's music files.
I'm running the site on Apache 2.x on a CentOS VM with php 5.2.x. We don't serve static assets with nginx so it's all coming out of the same apache instance so I have 2GB of RAM on that VM (yes I know I really need to get around to sorting that out).
We have a crappy cache in Decal CMS (which we make and which runs all our sites) right now which still serves pages from PHP but does so from cached content.
At some point we're going to move to using Varnish in front of nginx for static assets so that the only requests that get through to apache are to generate the pages after a site publish and requests where a cookie is present (ie. when someone is actually editing their site) but for now we're able to manage with just the shitty hack we've got in place to served cached documents.