Trumpeting at Intervals

I'm having a problem with the trumpet. Something it does that is unlike any other instrument I play. And I think the only way to fix it is to move into sight-reading.

The problem is intervals.

A melody or motif isn't a fixed set of pitches, it is the relationships between those pitches. This distance between two pitches, this interval, can be so distinctive it will still be audible from the first "dit-dit-dit-dah" to the last cadence of Beethoven's Fifth. So distinctive you know from that first minor seventh that you are about to hear "Somewhere" from West Side Story.

The various intervals have emotional content, they fit into certain classical relationships, they relate in various ways to the scale; they are all distinct structural elements that can often be inferred from the rest of a tune. So it follows that intervals is how we usually remember, or reconstruct -- or for that matter construct -- a melody.

And, yeah. I'm mostly playing by ear and I'm finding my way on the fingerboard or tone holes by thinking about the intervals I'm trying to play.

The guitar is the most straight-forward.

Each fret is a half-step. So to get that perfect fourth that opens "Amazing Grace" or "Oh Tannenbaum" you count up five half-steps; five frets. And the really cool thing is, as long as you remember how many steps are between your strings, you can always map from whatever arbitrary fret and string you are at to at least one place that meets the necessary interval. For instance, if you started on the open B string on a guitar, the top E is already that perfect fourth.

In one way violin is easier; all the strings are the same fifth apart. However, the academy finger position is spaced over what would be seven frets on the guitar; so that the fourth finger in first position is at the same pitch as the next higher open string. This is achieved by the same distribution of half steps and whole steps as underlies the classical modes or scales (of which the major and minor scales are most common in Western music). Still by shifting to a "low finger" or "high finger" the entire chromatic range is achieved -- thus it amounts to the same thing in the end.

Keyboards and most wind instruments present the pitches in a similar linear fashion, particularly if you are staying within the root scale; for piano, that would be the white keys. The full chromatic range -- the tones that fall outside the scale -- are presented in that example as black keys. On a recorder, they show up as half-holed and cross-fingered notes...but now is not the time for a lecture on accidentals and why there are transposing instruments.

Point is, the brass -- in the case I'm talking about, the trumpet -- don't present this way.

On a recorder, there are as many finger holes as there are scale tones in a single octave. On a trumpet, you have three valves. They each switch in an extra bit of tubing, increasing the length of the trumpet; nominally, to lower the pitch by a whole step for the first valve, a half step for the second valve, and a step and a half for the third (that is, the same decrease in pitch achieved by holding down the first and second valves).

So how do you get the 2 + octave range? By overblowing. Sort of. As you change your embouchure, you cause the air column inside the trumpet to vibrate at different multiples of the fundamental (you can actually play the fundamental -- known in those circles as a pedal tone -- but it isn't considered part of the usual written range of the instrument). If you look at the chart below, you can see the distance from the 1st overtone to the 2nd overtone is a perfect fifth; just one half-step more than what you get if you depress all three valves together. Thus the entire chromatic range is available to the performer.

Thing is, the harmonic series is a converging series of smaller and smaller intervals. The relationship -- the interval -- between any two notes is, unlike every other example I've given, dependent on what those specific notes are. At one set of pitches a major third might require first and second valves held down together, in another just a single valve, in another no valves at all!

(And yes, that means there are alternate fingerings for the higher notes; something that is of use in several advanced performance techniques). If it was just fingers changing, that would be bad enough, but the "slots" (brass player speak for the different harmonics) are achieved with subtle shifts in the tension of various facial muscles; more felt than targeted.

And that's the problem I have. There's no clear physical relationship between any arbitrary pair of pitches. You can't count frets to chart a path from one to the other. Each trumpet pitch is a unique entity. (Yes, yes...you can usually go down from where you are, but going up is...confusing).

This is why I need to move to sheet music. I can't approach a melody with intervals. I need to go to exact pitches; I need to link the dot on the page (or the written pitch) to the neuromuscular memory for that pitch. I need to sight-read if I want to expand my trumpet repertoire.