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It is fairly easy - although it requires a bit of strength - to bend notes downwards on a trumpet. For example playing a F#, a F, or even lower notes with all valves open.

It does not sound nice, but it is possible.

It is however very hard to do the same upwards. Why is that?

I can nearly take a major third downwards from the middle G, but barely a quarter tone upwards.

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Bending notes on a brass instrument without the aid of valves is done by changing the tension, and therefore buzz frequency, of the lips. Quite simply, it's easier to bend notes downward because it's easier to release tension than to create it.

Also, as you go up in the harmonic series, the partials get closer together, so on any given note you'll be able to bend farther down than you can up before you end up jumping to a different partial.

The techniques you mention are not common. I could imagine a downward bend like the one you mention in some contemporary extended-technique music, but most brass "bends" that occur in jazz music (in either direction) are executed with half-valve techniques, like doits, falls, and drops.

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    @awe You should ask that as a separate question! – delete me May 12 '11 at 13:46
  • Makes sense. About the partials getting closer as you go up I see your point, but a major third down from G, and not a quarter tone up from the same G (between low C and middle C)... The difference is too big, I don't think this is what makes it difficult to bend up. The technique is not common indeed, I use it as practice and got curious. I didn't know of the word "doit", thanks! I do use half-valve in performance. – Gauthier May 13 '11 at 7:47
  • I have a related question: What are good techniques to bend notes on brass instruments – awe May 13 '11 at 12:17
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    I reflected a bit more about that, now I'm a bit skeptical to releasing tension. For the first half tone downwards, releasing tension works. Then for going further down I need on the contrary to have a lot of tension, to force my lip buzzing through the horn. That is actually a strength exercise. – Gauthier May 15 '11 at 15:23
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    @Gauthier That's mostly a conceptual explanation for why it's harder to bend upwards. You're absolutely right, it's huge for control of the embouchure since the tone likes to "slot" into the harmonic series of the instrument, but I still consider it to take more tension to bend upwards. There may be a better physics-based answer for this, but I guess we don't have too many acousticians on the site yet... – NReilingh May 15 '11 at 17:16
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I have developed a possible answer since I asked the question. The lip vibration is created by first pushing air through the lips (opening), then part of the pressure wave is reflected at the bell (change of impedance) and goes back to the lips, closing them. Then it starts again.

With that in mind, you can stiffen your lips, slowing down the vibration by delaying the openings and closings. On the other hand, nothing can make these closings happen earlier than when the pressure wave comes back to the mouthpiece, so it's hard to make the frequency go up.

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