This is one of those posts where analog meets digital. I’ve played trumpet since 4th grade. It’s an interesting bit of plumbing applied to your face. In essence, it’s 7 bugles welded together with a not-quite-binary switching system. In a trumpet, there are typically (but not always) 3 valves which are set up to drop the pitch being played by the following table:
|Valve setting||Drop in Pitch in semitones|
Now, this is not quite true binary. It’s a little unusual because there is one combination that isn’t in there: 001. 001 is equivalent to 110. Equivalent is a funny word for this though because it’s not. 001 is close to 110, but different. 001 is slightly out of tune and it gets used really only for pieces where you have to quickly switch between some other valve combination and 110 and them something else and it’s quicker to switch to 001 and something else. For example, if you have to trill between a concert F and a concert G, your choice is to quickly switch between 000 and 110 or 000 and 001.
So let’s talk about Gray Code. Gray Code is a way to encode binary digits such that only one bit changes between successive values. This is useful, for example, when you need to have a counter that fires relays and you need to minimize the number of relay changes to minimize mechanical wear.
This morning I was wondering about the relative differences in the difficlutie sof playing in different keys on the trumpet and if the valve layout was optimized to be as close to Gray Code transitions as possible.
Then I thought that really, what you want is to build a database of musical trigrams and maybe quadgrams in typical trumpet music and to compare the difference in valve changes from standard to non-standard layouts and see which is more optimal across most keys.
Part of the impetus is that there are certain keys on trumpet that are considered ‘hard’: Db, Cb, F#, B (and the corresponding parallel minor keys) and are they really hard or is it a mental block? There are some fingering exercises that are brutal in those keys (especially Clarke’s Second Study), but I remember my teacher being able to rip through the ‘hard’ keys as easily as the ‘easy’ keys.
I know how to do this analysis. Do I have time? Oh, god no.