← Trombone Positions Calculator
Many notes on a trombone can be played in more than one slide position: a pitch comes from the slide length and which harmonic (partial) of that length's overtone series you buzz, so different combinations often land on the same note. A trombonist picks one every time, and the choice matters -- it changes how far the slide travels, how often it changes direction, and how close to the bell it sits.
Position 1's fundamental is the horn's pedal B♭; each position down lowers that fundamental by a semitone, and each fundamental carries its own harmonic series (see The Harmonic Series for how that series itself comes from the tube's own physics). Build the table to see every combination:
Position 1 has no 7th partial: the slide is already all the way in, so there's no room to sharpen it back in tune.
Some notes appear more than once once the table is filled out -- C4 (middle C), for example, is the 5th partial in 3rd position and also the 6th partial in 6th position, so it can be played either way.
Inverting this table gives us, for every note, the list of positions that can play it -- one row per note, ordered from the highest pitch down, with a thumbnail showing where each one sits on the staff:
| Note | Positions |
|---|
Given a note with several playable positions, which one is "best" depends on what you're optimizing for. This widget scores every candidate on four things:
| Weight | What it means | How it's calculated |
|---|---|---|
| Position | Prefer a low position number ("closer to the bell"). | position ^ exponent × weight |
| Position exponent | Makes 5th-7th position disproportionately costlier than 1st-4th, rather than everything scaling together. | |
| Position change | Prefer less total slide travel between notes. | |position − previous position| × weight |
| Direction change | Prefer fewer reversals of slide direction. A clean reversal (the slide was moving one way, now moves the other) costs a full point; a turn via a note where the slide briefly stops costs only a quarter, since stopping on the way up or down isn't really the same problem as doubling straight back. | 1 × weight (clean reversal), 0.25 × weight
(via a stationary note), 0 otherwise |
The total cost of a position sequence is these four costs added up across every note: each note's own position cost, plus the position-change and direction-change cost between it and the note before it. A locally cheapest choice for one note can force an expensive one at the next, so the solver weighs the whole passage together as a dynamic program: moving through it one note at a time, it keeps track of the cheapest running total for every (position, incoming-direction) combination reachable so far, carrying forward whichever paths could still turn out cheapest overall, and only reads off the actual position sequence once it reaches the last note and knows which running total won.
The three fixed panels on the calculator page are this same solver, just weighted differently -- there's no single "correct" position policy, only different ways to choose what to optimize for. "Set Your Own Policy" lets you weight those same four things yourself and see what comes out.