Early in the 19th century when valves were just coming into use on brass instruments they probably were not quite as good as the ones we have today, and valve combinations did not work well on them. Early instrument makers probably figured that most notes would be played either open or with a single valve. Consequently, they made a semitone valve, a whole-step valve, and a minor third valve. Musicians soon found that they could get away with using the first and second valves for a minor third instead of using the third valve alone, and some experimented with making the third valve tubing longer. For example, Paul Bernard of the Paris Conservatory published fingering charts show the third valve used for a major third instead of a minor third, and this system was commonly used in Sweden until quite recently. Most trumpets and euphoniums as well as many British-style tubas have tuning slides on the third valve long enough to keep that option open, but it is rarely used today.

Although the original bass tuba patented by Wieprecht and Moritz in Prussia in 1835 had its valves arranged in a different order, the one corresponding to our modern fourth valve was tuned to a perfect fourth, just as it usually is today. The fifth valve on that instrument was a "long semitone" valve, similar to the one described in Example 1 in the section below about "adding a fifth valve". Such a valve reduces the need for slide-pulling when used instead of the second valve in combinations such as 123 or 24.

Four-valve tubas from the early 20th century were sometimes made with the fourth valve tuned to a major third (two whole-steps) like the "swedish" third valve described above. All of Fred Geib's tubas apparently were built that way. When Mr. Geib added a fifth valve it was natural to tune it to a perfect fourth, continuing the pattern, so that each interval down to the perfect fourth could be played with a single valve. It turns out that one can find valve combinations with this system that work pretty well for every note down to the pedal note and even beyond, but no one claims that those combinations are simple and easy to learn.

Tuning the fourth valve to a perfect fourth has been a more common practice, ever since the beginning. When a fifth valve was added to such an instrument it was tuned to two whole steps, like Geib's fourth valve. Perhaps because of Roger Bobo's influence this has been called the "Mirafone system" although it existed long before that brand name was in use. As with Geib's system, one can play chromatically down to the pedal note if one can remember the fingerings.

Around 1970 Chester Roberts began advocating a "long whole-step" fifth valve, which has become available on many brands of tuba and is in common use today. Instead of using 124 and lipping up to get a perfect fifth, one uses 45. It turns out that one can find reasonably good fingerings for all of the other notes with this system, too. For example, you can use 235 instead of 123 or 24. Some tubists find this set of fingerings a bit easier to understand and remember.

Ever since seeing a 5-valve tuba while in high school I wondered about its possibilities. Eventually I figured out a logical approach to the question and published an article about it in the T.U.B.A. Journal Vol. VII, No. 1, Summer, 1980. An expanded version is in this website.