Posted by Joe Baker on October 30, 2000 at 15:34:30:
In Reply to: A theoretical question posted by Mario on October 30, 2000 at 09:05:50:
From each note in the overtone series of the open instrument, you can descend by adding tubing. The distance you can descend is constant no matter how high you go, but the overtones (also called 'partials') get closer and closer together as you go higher. As such, there is overlap between a particular open overtone and the lowered higher overtones.
If that still doesn't make sense, imagine a building with 19 stories, and people on each of the first, seventh, twelfth, sixteenth, and nineteenth floors, each with a rope that will hang down six stories. Between them, they can reach any floor in the building, and many floors can be reached by a couple of them. For example, the seventh floor can be reached by the guy on the seventh (because he's there), and the guy on the twelfth floor (by lowering his rope five stories). Well, the first story is the low (not pedal) open note, say the BBb on a BBb tuba. Each story is up one half step, so the seventh story is the F below the staff, the twelfth is the Bb in the staff, the sixteenth is the D above that, and the 19th is the fourth line F -- the notes in the open overtone series. Their ropes are the distance they can descend by pressing valves (on a 3-valve horn -- more valves give more alternative fingerings!)
Hope that makes sense!