The tuba and euphonium both use the same general set of fingering patterns, dictated through the work of several instrument manufacturers during the 19th century. In all tubas and euphoniums, the first three valves follow the exact same descending pattern (all intervals in equal temperament): first valve lowers a whole step, second valve lowers a half step, and third valve lowers one-and-a-half steps. After that, the tuning of the additional valves begins to diverge slightly depending on instrument type. In a compensating system (as seen in most modern euphoniums and some Eb and BBb tubas), the fourth valve lowers the instrument a perfect fourth, while also activating secondary tubing on valves one through three. In a non-compensating system, the fourth valve still lowers the instrument a perfect fourth. The fifth valve almost uniformly lowers the instrument a flatted whole step; this allows for the note a perfect fifth down from the open partial to be more in-tune, as well as many notes that are subsequently lower in the pedal range.[1] When present, the sixth valve commonly lowers the tuba by a flatted half-step, to further facilitate the proper tuning of the lower range of the instrument.
For an exhaustive look at the evolution of the early tuba’s fingering pattern system, and for a discussion of a new quarter-tonal system that revises the modern fingering patterns, the author highly recommends Robin Hayward’s writings on his microtonal tuba design.[2]

Fig. 5 – Euphonium (Compensating) Fingering Pattern Chart

Fig. 6 – Euphonium (Non-Compensating) Fingering Pattern Chart

Fig. 7 – F Tuba Fingering Pattern Chart

Fig. 8 – Eb Tuba (Non-Compensating) Fingering Pattern Chart

Fig. 9 – Eb Tuba (Compensating) Fingering Pattern Chart

Fig. 10 – CC Tuba Fingering Pattern Chart

Fig. 11 – BBb Tuba Fingering
Pattern Chart
[1] The instrument manufacturer Miraphone had a different system for the fifth valve through the middle part of the twentieth century, in which the fifth valve lowered the open partial by a tritone. Although useful, this tradition would eventually lose ground to the now-common fifth valve tuning of a flatted whole-step.
[2] Robin Hayward, “The Microtonal Tuba,” The Galpin Society Journal 64 (March 2011).