Acoustics & Music Theory
why it sounds like that
Concept

Spherical wave — where it appears

Sound spreading outward over a growing sphere, whose intensity therefore falls by six decibels for every doubling of distance. Indoors this holds only near the source, since past the critical distance the reverberant field does not fall at all.

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

What a 60 cm tube supports, by how its ends are closed. The first 6 modes of a stopped cylinder and a cone, all of the same acoustic length. A cone supports every whole multiple of the fundamental and reaches the second mode an octave up. A cylinder stopped at one end supports only the odd multiples and reaches its second mode 1902 cents up, which is a twelfth. Its fundamental is also an octave below the others, because it fits a quarter of a wavelength where they fit a half.

A cone is not a cylinder

A saxophone has a reed at a closed end, exactly as a clarinet does, and it overblows at the octave rather than the twelfth. If the previous essay's argument were about reeds that would refute it. It is about geometry, and a cone closed at its apex has the complete harmonic series for a reason that takes one line of algebra and is genuinely surprising.

instruments · Air column Direct and reverberant sound in a shoebox concert hall. The direct sound falls six decibels for every doubling of distance and the reverberant field does not fall at all, so they cross once — at 5.5 metres in a room of 18700 cubic metres with a 2-second decay. Both are drawn relative to their level at that crossing. Everything past the crossing is a seat at which the room is louder than the instrument.

How far away the room takes over

Direct sound falls six decibels every time the distance doubles and the reverberant field does not fall at all, so the two cross once. In a concert hall the crossing is at about five and a half metres, which is nearer than nearly every seat — so almost everybody in almost every hall is hearing the building more than the players, and the number that says so is built from two quantities already computed — a room's reverberation time and an instrument's directivity.

perception · Room acoustics

Named alongside it

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

AbsorptionBoreBoundary conditionDiffuse fieldHarmonic seriesLocalisationOverblowingPrecedence effectRegisterReverberationSabine equationTruncation

All concepts