I.
The Instrument
Physics and mechanics. How a lip buzz becomes a standing wave, and why the slide goes out to go lower.
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Never played before? Start with the big button — your first sound is about four minutes away.
Atlas · An Illustrated Method
A B♭ tenor instrument with an F-attachment. The bell flares forward; the hand slide draws through seven positions; pressing the thumb trigger turns the rotor, diverting the air through the wrapped F tubing for a lower fundamental.
start here · the guided path
A step-by-step course that teaches one idea at a time on the horn and puts it straight under your hands. From your first buzz to clean, connected playing — no quizzes, progress saved.
▶ Jam: play along to a tune →∑ The science of the horn →♪ The listening room: why this instrument →
the reference library
Already playing? Jump straight to any topic. The guided path above weaves these together into a route; here they’re open sandboxes to explore and drill freely.
Physics and mechanics. How a lip buzz becomes a standing wave, and why the slide goes out to go lower.
Seven positions × the harmonic series — every note the horn can play, drawn as a grid you can fly through.
Bass clef from zero, sequenced by harmonic series rather than alphabet. The mic listens.
Smart movement. When you change harmonic series, when you don’t, and the laziest slide between any two notes.
Bb major first — the horn’s home key. Each scale drawn as a path through the grid, with and without the F.
Arpeggios on a monophonic instrument. Outline any chord using only the positions you choose.
the method library
Every module is woven with the foundational literature of the trombone — Arban, Rochut and Bordogni, Remington, Kopprasch, Schlossberg. The original notation, untouched. The animated grid and the listening ear, added.
the maths & physics of this instrument
Every other instrument in the band is built out of steps — 88 fixed keys, frets, valves that bolt on fixed lengths of pipe. The trombone has none of it: a tube that slides smoothly through every length in between, so it plays every pitch in between too. It is the one instrument in the room that is a continuous interval rather than a set of dots, and almost everything below follows from that single fact.
Inverse proportion · the reciprocal graph
f × L = 319 Hz·m, so f = 319 ÷ L. First position holds 2.74 m and sounds 116.5 Hz; seventh holds 3.87 m and sounds 82.4 Hz.
You can slide along the graph with your arm, and hear the curve while you draw it.
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Geometric sequences vs arithmetic ones
Each position drops one semitone, but the gaps grow 8.1 → 8.6 → 9.1 → 9.7 → 10.3 → 10.9 cm — every one is the last × 2^(1/12) = 1.0595.
Equal musical steps are equal multiplications, not equal distances — which is why seventh position is a stretch.
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Coordinates · continuous versus whole-number axes
Any note = (slide position, harmonic partial). Across is continuous — position 3½ is a real place. Up is whole numbers only: there is no partial 3½.
One picture holding both kinds of number, on an instrument where you can play each axis separately.
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Multiples · the harmonic series
Without moving the slide, the same tube sounds 116.5 × 1, 2, 3, 4 … Your lips choose which rung.
The multiples aren't drawn on a diagram — you select them with your face.
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