One thing I’ve been thinking about lately is how we conceptualize where each note lies in the harmonic series, and how this knowledge can help us navigate the range of the horn more efficiently.  In trying out various instruments over the last several months, one characteristic I was very interested in was the shape of each “groove” or “notch” for a note, particularly in the high and mid-low range.  It was fascinating noticing which instruments tended to favor certain ranges, i.e. which range of notes tended to be more stable, versus which range tended to be more unstable.  Granted, much of what I experienced was probably due to the characteristics of my own playing, but I could definitely tell when these characteristics were magnified (both positively and negatively) on a given horn.  Though the concept can be a little bit difficult to describe, the easiest way for me to think of it is to imagine that every harmonic has a a certain generic shape, like this.

The large depression is the “notch” or “slot” for the note, with higher pitches to the right, and lower pitches to the left.  You can feel this shape for yourself by picking any note (preferably one in the middle range to start).  Experiment by bending the note up as far as you can without popping up to the next harmonic, then bending it down as far as possible without slipping down to the next harmonic.  Pay attention to the sound, and try to find where that note has maximum resonance. Chances are it won’t be at the lowest or highest point where you could bend it, but somewhere in the middle.  The generic drawing above could of course be altered to reflect the characteristics of a specific horn.  For instance, I have played some horns where the notes slot very well, but can’t be bent very far up or down without popping to the next harmonic.   In this case, our note visualization might look like this.

The benefit to having a horn with narrow notches is that it might not take as long (or as much work) to find where each note resonates the best.  However, in terms of intonation, the horn might limit just how far each note can be adjusted before the sound begins to deteriorate and the harmonic becomes unstable.  Going further, there are some horns where the notes tend to slot just a little on the high side, as in the following illustration.

I’ll go ahead and apologize for my meager illustrative abilities, but I hope that you can tell what I’m getting at with this image.  It’s almost like there is a groove within a groove for a particular note, with the note slotting best when you blow up on it.  I’ve noticed this with some Yamaha horns, particularly the 667 and 667v models. Does this mean that it’s ok to play sharp?  Absolutely not!  However, it does mean there is less flexibility to bend notes flatter, and the horn itself needs to be tuned a bit lower so that things are still in tune when you blow up on a note.   On the other hand, some horns have a groove within a groove on the bottom side of each note, like this.

In this case, the note will sound best when played a bit lower in the groove. I  like this characteristic because it demands that we play each note as relaxed as possible, which the horn rewards with a centered, resonant sound.  There are of course numerous other ways to think about the idiosyncrasies of various makes and models of horn, but the images above have been useful to me in both testing out instruments and finally adjusting to a new one.  There are several exercises out there designed specifically to help you find the best place for each note, although virtually any long tone exercise can be used.  One that I like using myself and with students is called “Shwarmaaaaaa!” found in The Brass Gym: A Comprehensive Daily Workout for Brass Players, by Sam Pilafian and Patrick Sheridan, edited for Horn by John Ericson (Focus on Music, 2007).  This exercise consists of a series of note-bending studies, and is great for working on both intonation and tone quality.