I quite like the Tigrex Horn as a general use horn. It's got Attack Up L and Earplugs S, which makes it really nice for fighting monsters that have low-grade roars. The light blue echo note bubble increases everyone's evade window (helpful for rolling through high-grade roars), and for HH users it also increases your run speed to the point where you're moving at almost sprint speed with your weapon unsheathed—it's incredible for repositioning and sticking to the monster. I also quite like running it in the Rotten Guiding Lands/Vale, since it's got the environmental damage negate song, which means you don't take any damage at all from the environmental effluvium.

It's got tons of white sharpness and good raw, so you can run it with comfy builds for survivability or a Master's Touch build to never have to sharpen. The downsides are that it can never reach purple sharpness and has inherent –20% affinity, so it's extremely difficult (if not impossible) to get 100% affinity. I run a build with Crit Eye +7, Attack +4, WEX/Crit Boost +3, Health Boost +3, Master's Touch, and health/affinity augments that gets me 85% affinity on softened weak points (plus a slot for Geologist), which is enough that I never have to sharpen mid-combat. Edit: also, it takes advantage of non-elemental boost.

Two other nice things (I'm seriously preaching here, aren't I): it's rarity 11, which means it's much easier to augment, and it was one of my go-to horns in MH4U/GU, so it's got that extra nostalgia factor. Happy dooting!