The slide is
the graph.

Move one mechanism. Watch tube length, pitch, hand distance and waveform change as a single physical system.

A full-width brass trombone on a birch measurement bench with a rubber slide collar

start here · the guided path

Never held a trombone? Start at the beginning.

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.

Begin the path ▸

▶ Jam: play along to a tune →∑ The science of the horn →♪ The listening room: why this instrument →⊙ The F attachment, measured →✎ Teach it in a maths or science class →

the reference library

Eight practice rooms.

  1. I.

    The Instrument

    Physics and mechanics. How a lip buzz becomes a standing wave, and why the slide goes out to go lower.

    Enter →
  2. II.

    The Map

    Seven positions × the harmonic series — every note the horn can play, drawn as a grid you can fly through.

    Enter →
  3. III.

    Notes

    Bass clef from zero, sequenced by harmonic series rather than alphabet. The mic listens.

    Enter →
  4. IV.

    Intervals

    Any interval, up or down, from any note — and every connection from it: when the slide moves, when only the lips do.

    Enter →
  5. V.

    Scales

    Every key, ten scales, and the classic practice patterns — each drawn as a route along the slide, textbook or smart.

    Enter →
  6. VI.

    Chords & Degrees

    Arpeggios on a one-note-at-a-time instrument: any chord, every inversion, four shapes, and where each tone sits on the slide.

    Enter →
  7. VII.

    The F Attachment

    What the thumb trigger really does to the slide: every position measured in centimetres, side by side, and when to use it.

    Enter →
  8. VIII.

    In the Classroom

    Play the real horn in front of a class while the screen measures it. Ready-made demonstrations for maths and science, ages 11–18.

    Enter →

the method library

Built on the shoulders of the masters.

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.

  • 01Arban · Method for Trombone
  • 02Rochut / Bordogni · Melodious Etudes
  • 03Remington · Warm-Up Studies
  • 04Kopprasch · 60 Selected Studies
  • 05Schlossberg · Daily Drills
  • 06Concone · Lyrical Studies

the maths & physics of this instrument

The trombone is a number line you can hear.

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.

i

Pitch times length is a constant

Inverse proportion · the reciprocal graph

On one lip setting, 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. Change rung and you get a new constant, same curve.

You can slide along the graph with your arm, and hear the curve while you draw it.

open it →

ii

Equal steps need growing distances

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.

open it →

iii

Two numbers, and only two

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.

open it →

iv

One tube, a whole-number ladder

Multiples · the harmonic series

Without moving the slide, the same tube sounds 58.3 × 1, 2, 3, 4 … Hz — the pedal note and its multiples. The everyday B♭ is rung 2; your lips choose the rung.

The multiples aren't drawn on a diagram — you select them with your face.

open it →