The tuba evolution is still actively progressing in many ways including technique and, of course, part of that amazingly expanding technique is the extension of the high register. I can point out with great clarity that what was considered high register 25 years ago has changed today. Further, the same situation exists between 25 and 50 (in my case 60) years ago. When we view the great tubists of today it is not unusual to see players successfully performing up to and beyond the C an octave higher than middle C on the piano.
In the process of developing a usable and functional high register our criteria, our success is best evaluated not only just by just getting the note but also by getting the note with clarity and good intonation. Part of that development is discovering the best fingering for that clarity and intonation, in fact, it can prove to be strategic.
For example, (all examples are calculate for an instrument in C, but, of course, it should be calculated for instruments in F, Eb, C or Bb.) Most of us have learned that playing a high D or Db usually sounds better if we play the 9th harmonic rather that the 10th harmonic, which has the same flatness tendency as octave lower 5th harmonic, that would mean the high Db with the 2nd valve, and the high D open.
Here is a small list of 15th harmonic fingerings all calculated for C tuba.
There is another advantage to these fingerings; there is a bigger margin of safety using the 9th harmonic in place of the 10th or the 15th in place of the 16th. Quite simply, that slightly larger margin between the harmonics above and below can create greater security as well as greater clarity and better intonation.
When I was a young man and just starting my career a wonderful piece by composer William Kraft called ENCOUNTERS #2 was written for me. It was said I was the only person who could play it; that lasted a very short time. Today that piece, while still difficult, is played frequently on college and university recitals and I have seen it occasionally performed by younger, high school age players. (Please read September 2009 [written in 2004] blog Roger Bannister and the Four Minute Mile).
The tuba is still experiencing an active evolution, which is unique in music history, never before has an instrument emerged and grown in status so rapidly. Viewing that rapid growth retrospectively lets us to more easily predict the changes that may come. The need for our expanding high register has already arrived; the 15th harmonic may prove useful.
July 18, 2014, Carlsbad, California