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i was wondering that since the 5th and 6th rotors are on the fourth valve slide, does that mean that the only way you can use them is if the fourth valve is pushed down, and would this be the definition on a dependent system?

Yes, that's right, because the fifth and sixth valve are dependent on the use of the fourth valve to work. Hence, dependent system. Some, typically older, bass trombones have a dependent valve as well.

arpthark wrote:Some, typically older, bass trombones have a dependent valve as well.

Actually, quite a few companies still make dependant valves for bass trombone. (Yamaha, Bach, Getzen, Kanstul, Shires....) Quite a few people still use dependant valves....

A dependent valve is more like a selling point than anything on a trombone. The objective of the design is a smooth bore, the valves are less smooth.