The 6061 is a beam tetrode and a special quality version of the commercial 6BW6.
The valve is described as an audio output beam tetrode, for single ended or push pull use. It was most common in radio transmitters for the audio power stages of the amplitude modulator. In the latter application, with 315 Volts on the anodes, a pair would produce 30 Watts in class AB1.
The 6061 can also generate RF power at a few tens of megahertz.
In the 1960s this valve was still current production for its manufacturers Brimar.
The T on the envelope stands for Trustworthy the Brimar description for its special quality products.
The thin glass tube envelope is 20 mm in diameter and excluding the B9A base pins, is 60 mm tall.
References: Datasheet & 1040. Type 6061 was first introduced in 1951.