Bardic music is one of my favorite abilities, but the rules on what is and isn't bardic music and what stacks versus what doesn't can be frustratingly vague. Did you know that it's not actually specified that you can't play/sing/chant multiple bardic musics at once? The Combined Song ability of War Chanters does imply this limitation, though this ability could be interpreted as simply improving the action economy of playing multiple songs. At least in this case it's pretty widely accepted (and relatively intuitive) that the Rules as Intended are you can only do one song at once without an ability that says otherwise (barring possible exceptions caused by vague wording, like Haunting Melody)
But there's a similar problem with the prestige class Dragonsong Lyrist. The ability this class revolves around is Greater Dragonsong:
Greater Dragonsong (Su): Once per day per class level, a dragonsong lyrist can use song or poetics to invoke the power of dragonsong. Invoking dragonsong requires a standard action. In the case of effects that require a saving throw, the DC is equal to 10 + lyrist' class level + lyrist's Cha modifier. The bonus from the Dragonsong feat also applies to this save DC. In cases where the character continues a greater dragonsong effect over the course of multiple rounds (such as song of strength), the dragonsong lyrist can fight while using greater dragonsong but cannot cast spells, activate magic items by spell completion (such as scrolls), or activate magic items by command word (such as wands). Maintaining a greater dragonsong effect does not require concentration. A deaf dragonsong lyrist has a 20% chance to fail when using greater dragonsong. If she fails, the attempt still counts against her daily limit.
It's clearly not bardic music, and no rules are given regarding overlap... so does that mean you can sing multiple greater dragonsongs at once? How about overlapping with regular bardic music? Does the RAI precedent of bardic music apply here?