Acoustics & Music Theory
why it sounds like that
Concept

Negative resistance — where it appears

A response in which the flow falls as the pressure driving it rises, which is the wrong sign for a resistance. It is the one thing in a wind instrument capable of turning a steady breath into an oscillation, and every self-sustaining instrument has some version of it.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

A reed that shuts at 5000 pascals, and the air it lets through. Volume flow through the reed channel against the pressure across it, in the quasi-static model: Bernoulli flow through an opening that closes linearly with pressure. The flow peaks at 1667 pascals — exactly a third of the closing pressure, for any reed, because that is where the two effects balance — and it is 0.18 litres a second there. Everything to the right of that peak is the argument: the flow falls as the player blows harder, from 0.18 to 0.05 litres a second by 4500 pascals, and a resistance that behaves that way supplies energy instead of taking it. There is no reed inertia in this model, so it cannot squeak.

The reed is a valve, not a vibrator

Three essays here have said that a clarinet's reed does not choose the note, and none of them said what it does instead. It chops a steady stream of air, and past a third of the pressure that closes it the flow falls as the player blows harder — a resistance with the wrong sign, which is the only thing in the instrument capable of putting energy into an oscillation that is otherwise losing it.

instruments · Air column Blowing harder is playing sharper. How far the played note is pulled from the bore's own resonance, against blowing pressure, for an air jet crossing a 4 mm embouchure. The jet's preferred frequency goes as the square root of the pressure, so it rises by a factor of 3.16 across the tenfold pressure range drawn, and the bore holds it to 272 cents of that — from -174 at the quietest to +98 at the loudest, about the player's own nominal. The rows below give the same pull for a drive one semitone sharp of the bore, for four valves: a clarinet reed is damped by the lip and pulls 4.9 cents, brass lips are not and pull 23.6.

Blowing harder is playing sharper

Every frequency computed so far for an air column is a resonance of the tube, and no wind instrument plays at its bore's resonance. It plays between the bore and whatever is driving it, weighted by how sharply each is tuned — and a flute's driver is an air jet whose own preferred frequency goes as the square root of the blowing pressure. Across a tenfold pressure range the jet's preference rises by a factor of 3.16 and the bore holds it to 112 cents of that. A wind player's dynamics and their intonation are one control, and the size of the coupling between them is the valve's Q.

tuning · Air column

Named alongside it

The objects these essays reach for when they reach for this one.

BoreOverblowingReedStanding waveThreshold pressureEnvelopeIntonationNonlinearityResonance

All concepts