Musical Acoustics Clive Greated (c.a.greated@ed.ac.uk)

In singing, air pressure from the lungs is used to set the vocal folds into periodic oscillation producing a pitched sound source at the base of the vocal tract. By changing the positions of the jaw, lips and tongue the resonances of the air in the vocal tract, called vocal formants, can be altered. We perceive the different tone qualities produced as the vowel sounds used in everyday communication. Vocal tract resonances can also be used to help explain how the trained singer can be heard over the sound of an entire orchestra.

Almost all brass instruments have air column resonances which are close to forming a harmonic series; this gives rise to the familiar pattern of “bugle call” natural notes. In the upper register the harmonics are close enough together to allow a diatonic scale to be played without modifying the tube length, although certain harmonics have to be modified in pitch by lipping or hand-stopping. The much larger pitch intervals between the lower harmonics can be filled in by changing the tube length: this can be done either by a slide as on the trombone, by a set of valves as on the trumpet, or by a set of finger holes as on the serpent.

The important acoustical characteristic common to members of the musical brass instrument family is not the material of construction, but the way in which the note is sounded by vibrating the lips against the rim of a mouthpiece. The lips act as a valve, open and closing periodically to modulate the flow of air into the instrument. The resulting pressure changes in the mouthpiece set up standing waves in the air column contained by the walls of the instrument. A small fraction of the sound energy stored in the standing waves is radiated at the bell of the instrument, and this is the sound heard by a listener. The frequency and pitch of the sound depend both on the resonant frequencies of the air column and on the natural resonant frequency of the lips, which can be controlled by the muscles of the player's mouth.

The original Hammond used rotating tone wheels to generate harmonics which were added using drawbars; not true harmonics though. The principle is known as additive synthesis. The organ is usually played through a Leslie speaker which utilizes the Doppler principle to produce chorale and tremolo effects. Modern digital synthesizers such as the Nord Electro simulate both the drawbars and the Leslie speaker. In subtractive synthesis, used for example on the Korg MS20, tones with complex spectra are generated and unwanted components filtered out. The most common transient generator is the ADSR where the letters stand for Attack, Decay, Sustain and Release. The Yamaha DX7 uses Frequency Modulation (FM). Sidebands are generated in the frequency spectrum spaced at multiples of the modulation frequency from the carrier. MIDI allows you to control the sounds of one instrument from the keyboard of another.

In concert halls it’s desirable that the time between the arrival of the direct sound and the first reflection is not greater that 20ms. Highly reflecting parallel walls may cause undesirable flutter echo. The distance from the source where the intensity levels of the direct and reverberant sound are the same is known as the Room Radius; a typical value for a large hall is 5m. Closer than the room radius you hear mostly direct sound and at greater distances mostly reverberant sound. Room modes are particularly important in small rectangular rooms such as recording studios. Tangential modes are combinations of two axial components and oblique modes are combinations of all three. The vineyard design of concert hall gives an even distribution of sound. Seats should be designed to minimize changes in reverberation between the hall being empty and full.

Sound rays obey Snell’s law of reflection. When they strike a surface the fraction of sound energy absorbed is known as the absorption coefficient, which varies with frequency. The time for the reverberant sound in a room to drop by 60dB is known as the reverberation time R. This can be calculated from the formula R = 0.16 V/A where V is the volume in cubic metres and a is the total absorption in metric Sabin i.e. the sum of the surface areas times their absorption coefficients. If R is large the sound in the room will lack clarity but the sound level will be large. If R is small the sound will be clear but the sound level will be low. Typically R will be 1s for a theatre and 1.5-2s for a concert hall.