Musical Acoustics

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...

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...

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...

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...

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...

In Pythagorean tuning the 5ths are true i.e. in the frequency ratio 3/2. In 1/4 Comma Mean Tone the major 3rds are true i.e. in the frequency ratio 5/4. Both tunings give rise to the wolf which restricts the number of playable keys to 6 major and 3 minor. In Equal Temperament all keys are playable but neither the 3rds or 5ths are true. In circular temperaments the total reduction in all 5ths round the circle is one comma; all keys are playable but some usually sound better in tune than...

The Boehm flute has a cylindrical body and a tapered headjoint, which is required to compensate for the flattening effect of increased lip cover over the embouchure hole in the upper register. Like the saxophone, the clarinet has a mouthpiece and a single reed. It has distinctive tone qualities in the low (Chalumeau) register and higher (clarinet) register. The tone quality of the oboe and bassoon, which both have double reeds, is characterized by distinctive formants.

In a woodwind the sound is generated by the resonating air column within the instrument, the material of construction being of secondary importance. To a first approximation the flute can be considered as a cylindrical tube open at both ends, the clarinet as a cylindrical tube closed at one end and the saxophone, oboe and bassoon as conical tubes closed at one end. All these instruments generate a complete harmonic series and overblow the octave, except for the clarinet which generates...

Rudiments There are twelve semitones to a complete octave, two semitones making a tone. The major diatonic scale has seven notes separated by the intervals of a tone (T) and semitone (S) in the sequence TTSTTTS. Each note has a separate letter name. In the scale of C major the most important intervals are C-E (major third), C-Eb (minor third), C-F (perfect fourth), C-G (perfect fifth); the triad CEG is referred to as chord I, chord DFA as chord II etc. In the diatonic major scale there are...