Everyone knows that certain notes on the trumpet are problematic; it is a consequence of the physics of trumpet design. Much has been written on the topic, but I only recently found a good description of the actual mathematics behind the phenomenon, written in 2003 by Joseph Monzo. I encourage you to read it. It is a generalized model, but it should apply in varying degrees to all Bb trumpets.
One weakness of the otherwise awesome write-up is that the data is never really rendered in a way that is easily digestible for a trumpet player. The following table is my attempt to distill his information into a simplified format. The left-hand column starts with the trumpet-player's "C" above the staff and descends chromatically down to the lowest non-pedal note, "F#". All fingerings for each note are placed in the table relative to the sharpness/flatness for that pitch (slightly sharp/flat, sharp/flat, very sharp/flat) .
Interestingly, based on this information, the most out-of-tune note in the most commonly used range of the trumpet is the "Db/C#" on the staff. If played 1+2+3, the note is very sharp but can be somewhat compensated for with the third and/or first slide. If played 1+2, you start closer to the correct pitch, but the note is flat and has to be lipped up. Either way, it requires listening.
Below the staff, the "Db/C#" and the "Gb/F#" have the same issue to a similar degree and there is no alternative to the overly sharp 1+2+3 fingering. Again, adjustment can be made by ear while throwing the third and/or first slide.
One other curiosity which I've never heard before: the most in-tune way to play the "B" on the staff is theoretically 4th overtone, 1+3 valve combination instead of 3rd overtone, 2nd valve (which is slightly flat).
Enjoy, and let me know if you find this interesting.
One weakness of the otherwise awesome write-up is that the data is never really rendered in a way that is easily digestible for a trumpet player. The following table is my attempt to distill his information into a simplified format. The left-hand column starts with the trumpet-player's "C" above the staff and descends chromatically down to the lowest non-pedal note, "F#". All fingerings for each note are placed in the table relative to the sharpness/flatness for that pitch (slightly sharp/flat, sharp/flat, very sharp/flat) .
Interestingly, based on this information, the most out-of-tune note in the most commonly used range of the trumpet is the "Db/C#" on the staff. If played 1+2+3, the note is very sharp but can be somewhat compensated for with the third and/or first slide. If played 1+2, you start closer to the correct pitch, but the note is flat and has to be lipped up. Either way, it requires listening.
Below the staff, the "Db/C#" and the "Gb/F#" have the same issue to a similar degree and there is no alternative to the overly sharp 1+2+3 fingering. Again, adjustment can be made by ear while throwing the third and/or first slide.
One other curiosity which I've never heard before: the most in-tune way to play the "B" on the staff is theoretically 4th overtone, 1+3 valve combination instead of 3rd overtone, 2nd valve (which is slightly flat).
Enjoy, and let me know if you find this interesting.
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