Posted by Jay Bertolet on June 23, 1999 at 17:05:34:
In Reply to: Partials ? posted by Paul H on June 23, 1999 at 15:07:13:
Way to go Bob! That is a great explanation of the acoustical basics of the partial system. The only thing I would add may make the explanation a little less technical in nature and maybe easier to imagine and conceptualize:
Think of all the notes you can play with any single valve combination as a unit. This unit is called the Harmonic Series or Harmonic Sequence. Like Bob said, the notes that comprise the Harmonic Sequence are determined by their mathematical relationships. On a BBb tuba, pedal BBb would be the lowest note in the Harmonic Sequence produced by the valve combination of "open". Pedal BBb would be called the "first partial". Low BBb, just below the bass clef staff, would be the "second partial" and so on. The various different Harmonic Sequences always comprise the same numbers of notes and maintain the same interval pattern between notes but they start on different notes based on whatever valve combination they use.
In my mind, I think of the Harmonic Sequence as a ladder where the lower rungs are very far apart but that the rungs get closer together as you go higher up the ladder. And the reason that we have valves is that each separate valve combination has different rungs and at different places though some of the ladders intersect higher up. By combining ladders, we can have steps at even intervals all the way up to the top with no breaks. We can even select a specific ladder from a group of ladders with the same step to choose the one that helps keep the steps as uniform as possible (intonation).
If you take the time to understand the underlying concepts of the Harmonic Sequence, you will unlock the secrets of all brass instruments. I always try to explain this setup to my students (with varying degrees of success) because I feel that working with the system requires more of an understanding of it than simply knowing which fingering goes with each note. Good luck!