Wiki has pretty good pages for some of the songs showing the correlation between skill (combined skill) and caps.
Example: for Valor Minuet IV (from:
http://wiki.ffxiclopedia.org/wiki/Valor_Minuet_IV )
* +54 Attack at 450 combined skill (natural skill cap for BRD75)
* +54 Attack at 454 combined skill
* +55 Attack at 457
* +55 Attack at 461
* +56 Attack at 462 (+12 skill)
* +56 Attack at 488
* +56 Attack at 529 (+79 skill)— so it seems that +56 is the cap.
* Cornette +1 adds +5 Attack.
* Each Merit upgrade of Minuet effect adds +1 Attack.
* +66 Attack, is the hard cap.
However one of the most important songs is Victory March and Kirschy has spent a lot of time and effort into analyzing haste in FFXI and determined that it does not have a hard cap in the same way as Minuet does. For some reason the link to the post with the chart showing the march tiers in it in it isn't working right now but here's a link to one that came before that (I think)
http://bluegartr.com/forum/showthread.php?t=52417 . There's more out there on haste, you just need to dig around for it. The important point to remember is that it's the combined skill (i.e. singing + wind) that will determine cap and there are tiers to it but there has not been a hard cap found because at that point we reach a cap in possible gear. It's not going to be a huge game-breaking difference because the end result is adding a few more swings in a melee party but for those of us who choose to play to the maximum potential it matters.
P.S. I didn't notice any change in my performance when changing from Jester's +1 to Astute. If it's true that 2CHR = 1 skill, they should in theory be equal but once again that requires testing to prove that.