Never played before? Start with the big button — your first sound is about four minutes away.
three valves · seven paths · B♭ or C
Each valve combination unlocks its own harmonic series — the trombone's seven slide positions, reborn under three fingers. This console is live: push the pistons and hear where they land, on a B♭ or a C horn.
open · partial 4 · sounds B♭ on your B♭ horn
plate i · the B♭ trumpet — press a valve above and watch the piston go down
start here · the guided path
A step-by-step course: the open bugle series, the three valves, your first fingerings, then a tune. Each lesson teaches one idea and puts it straight under your fingers — no quizzes, progress saved.
▶ Jam: play along to a tune →∑ The science of the horn →♪ The listening room: why this instrument →⋯ Alternate fingerings & slides →✎ Teach it in a maths or science class →
Eight modules. Read top to bottom, or jump to what your lip needs today.
the method library
Woven with the trumpet's foundational literature — the original studies, with the animated valves and the listening ear added.
the maths & physics of this instrument
A trumpet has three valves, each either down or up. That is three bits, and eight combinations — and the whole instrument is a machine for showing what happens when you try to do multiplication by adding. The error is not a manufacturing fault. It is in the mathematics, it is audible, and every player corrects it by hand for their entire life.
Binary · powers of two · subset sums
2³ = 8 fingerings from three valves. Each adds a fixed loop: valve 2 a semitone, valve 1 a whole tone, valve 3 a tone and a half.
Place value stops being an exercise when each bit is a piece of pipe you can press.
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Indices & powers · why 2^a + 2^b ≠ 2^(a+b)
Valves 1 + 3 give a tube of ×1.31167. A true five-semitone drop needs ×2^(5/12) = ×1.33484. The note lands 30.3 cents sharp.
Lengths add; pitches multiply. On this instrument the difference between those two operations is something you can hear.
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Measurement · solving for a shortfall
(1.33484 − 1.31167) × 1.48 m = 3.43 cm of missing pipe — a 1.71 cm pull, because the slide is a U and adds twice what you move.
The player's left hand solves an equation, several times a minute, forever.
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Length · addition · estimation
Open, the air travels 1.48 m. All three valves down, 2.03 m. Each loop is 1.48 × (2^(n/12) − 1): 8.8, 18.1 and 28.0 cm.
The note is decided by a distance, and the distance is visibly bolted to the instrument.
open it →