I have used five types of barrel tuners.
1. Hoehn muzzle tuner- a heavy cylindrical device on the muzzle which can be screwed fore and aft in tiny increments. You can see the groups tighten up as you get it dialled in. Adjustments are repeatable and it is easy to take notes because there are hundreds of numbered settings.
2. Ruger 10/22 forend tuner. This works very well with a floated 10/22 barrel. It is basically just a screw mechanism in the foreend that puts adjustable pressure upwards on the barrel. It tunes the whole barreled action, not just the barrel. Makes a big difference on a properly bedded 10/22 because the barrel/receiver junction on a 10/22 is weak and fully floated barrels do not work well.
3. BRNO #3 forend tuner. Similar to the 10/22 tuner but factory installed and spring loaded. Puts spring pressure upwards on the barrel to damp vibrations.
My #3 shot better free floated.
4. Dual forend tuners. Two forend tuners at 45 degrees to each other, adjust upwards and inwards on the barrel. These were sometimes found on 1950s match rifles like Winchester 52's and Remington 40x's. The idea was to keep the barrel from moving around on top on the tuning screw and throwing off POI. Didn't work for me, I preferred bedding and floating. Has potential to work well on a 10/22.
5. Takedown screw tuning. Many rifles have a screw right into the barrel to hold the barreled action into the stock. Although not intended for tuning, I find using a micro torque wrench to adjust these screws can have a dramatic effect on accuracy.
Tuning barrel harmonics works. Forend tuners work on some rifles. Muzzle tuners work on all rifles. Basically a barrel vibrates like a plucked string when fired. The ends of a string are fixed, one end of a barrel is not. The muzzle is actually pointing in slightly different directions at different points in the cycle. A harmonic occurs when you introduce an additional node, or non moving point, into the vibration. This can reduce the amount the muzzle whips around. More nodes, smaller amplitude of vibration. Tuning the harmonics can move the nodes to different points on the barrel to further reduce muzzle whip. Tuning also aims to make barrel vibration more consistent from shot to shot ensure the barrel is pointing in the same direction each time a bullet exits the muzzle.
Tuning is most popular with rimfire benchrest shooters. Most shooters do not bother with harmonic tuning as it involves lengthy and tedious set up periods every time you change lots of ammo, and the process must be repeated as temperature changes. Detailed notes are required.