The tenor horn usually sits in the middle of a brass band, this is because it's literally the middle pitched brass instrument.
Interesting tenor horn facts
The tenor horn's conical bore and deep mouthpiece produce a mellow, rounded tone which is often used as a middle voice, supporting the melodies of the trumpets, cornets or flugelhorns, and filling the gap above the lower tenor and bass instruments
In Europe they have been manufacturing tenor horns since 1852.
Within a British brass band, the tenor horn section usually plays a unique part in the middle of the band, with the Solo Horn having frequent solo passages.
The instrument known today as the tenor or alto horn was developed in the 1840s by the Belgian instrument maker Adolphe Sax and is part of his Saxhorn family of instruments.