Unit 3: Acoustics of Musical Instruments

octave

doubling of frequency

whole tone

whole step; 2 half steps

semitone

half step

Just tuning

defining intervals based on simple ratios

• select a starting note

Problem with Just tuning

The frequency of some notes change based on the starting note

ex: D5 is not double the frequency of D4

Pythagorean tuning

always increase in 5th or decrease in 4th

Equal tempered tuning

the octave is divided into 12 equal intervals

Each semitone is 1.059463 times higher than the previous frequency

There is no dependence on the starting note

Cents

more precise measure of frequency differences

How many semitones and cents is an octave?

1200 cents

12 semitones

how many cents is one semitone?

100 cents

how many cents is one whole tone?

200 cents

Mechanical instruments

• woodwind

• brass

• strings

• percussion

Mechano-electric instruments

• electric guitar

• electric violin

• electric cello

• turntable

Electric instruments

• synth

• keyboard

• theremin

• electric organs

Source for mechanical instruments

• blowing

• bowing

• striking

• plucking

• rattling

Resonator for Mechanical instruments

• string

• air column (pipe)

• bar/membrane

• cavity

• body

Radiator for Mechanical instruments

• bell

• tonehole

• body

• bar/membrane

• sound board

Source

generates the acoustic energy and is responsible for setting the pitch

Resonator

filters the sound from the source and creates the tone color

Radiator

effects how the sound leaves the instrument (sometimes same as resonator)

Temporal Aspects

attack, sustain, decay

Attack time

time it takes for note to develop

• depends on note being played

• bowed string have longer attack time than woodwind/brass

Vibrato

intentional frequency modulation

• can result in different upper harmonics

Tremelo

intentional amplitude modulation

• can result in different upper harmonics

Choral Effect

when two or more instruments play together without perfect synchrony

Tone color

the spectral character of the sound (the partials)

• resonator defines what the partials are emphasized

How is pitch adjusted in singing?

it is adjusted by changing the tension of the vocal folds

Vocal Register

different configuration of the vocal folds

Pulse register (vocal fry)

vocal fold compact and loose to hear individual pulses

• low frequency, low tension

Chest register (modal)

vocal folds are short and thick so effective mass is large

• vibration amplitude large

• speech is in this register

Falsetto

vocal folds long and thin so the effective mass is small

• muscular tension high

• high frequency

Formant tuning

when the fundament is near or above the 1st formant frequency

• changing the vocal tract shape to shift formants in order to reinforce the fundamental or a harmonic

Example of Mechanical Reeds

saxophones, clarient, oboe, bassoon

Source of mechanical reeds

blowing air over a reed causes it to oscillate and pulsate the air flow

Resonator of mechanical reeds

air column within the instrument (bore)

Radiator of mechanical reeds

Primary: open toneholes

Secondary: the bell (important when all toneholes are closed)

How does a single reed work?

As air flows past the reed, a pressure is created which pushes the reed against the mouthpiece (Bernoulli’s principle)

The stiffness of the reed pushes the reed away from the mouthpiece.

What creates a pulsating flow of the reed?

The wave in the air column created by the oscillating reed reflects at the open end and travels back to the reed. It forces the reed away from the mouthpiece.

Cylindrical bore

ex: clarient

• odd harmonics

• register key = +12 intervals

Conical bore

ex: oboe, sax

• all harmonics

• register key = +8ve

Reed motion during loud dynamics

more abrupt

• more energy in higher harmonics

Example of Lip Reeds

brass- trumpet, tuba, trombone

Source of Lip Reeds

blowing through tightened lips against mouthpiece to create pulsating flow

Resonator of lip reeds

air column within instrument (mix of cylindrical and conical bore)

length is adjusted by valves/slides

Radiator of lip reeds

primary radiator is the bell

What type of airflow does buzzing make?

periodic airflow

What opens the lips in buzzing?

positive pressure from lungs

What closes the lips in buzzing?

negative pressure from airflow and lip tension will close lips

Purpose of mouthpiece

boost amplitude of higher harmonics

purpose of bore

determine fundamental frequency and modes

purpose of bell

generate acoustic radiation and shift harmonic frequencies

Effect of mute

disrupts sound radiation from bell

changes ratio of harmonics. to produce a different tone color

What does increases the air speed do on a lip reed?

lips begin oscillating at higher modes of the instrument and the perceived pitch increases

Example of air jets

flute, piccolo, recorder, organ pipe

Source of air jets

blowing over thin edge creates oscillating airflow

*related to velocity of air, not pressure

Resonator of air jets

air column within instrument (bore)

Radiator of air jets

any open hole (open end of pipe, honehole, blowhole)

What paritals does a flute produce?

all harmonic partials

End Correction

The pressure at the open end isn’t actually zero. It is a small distance past the open end

How to calculate end correction

ΔL= 0.6r

L* = L + ΔL1 + ΔL2

What adjustments are needed to play the upper register on the flute?

The lip position and the blowing pressure must be increased

types of pipes on pipe organ

flue pipe and reed pipes

characteristics of reed pipes

brighter sound (higher amplitude partials)

lower air speed

shorter attack time

Examples of bowed strings

violin, viola, cello, bass

Source of bowed strings

bowing over string; the bow periodically grabs and releases the string

Resonator of bowed string

the string is the main resonator

at low frequencies the body acts a secondary resonator

Radiator of bowed strings

Primary radiator is the body

Secondary radiator is the f-hole

How does bowing work?

frictional forces cause the bow to stick to the string

after the bow overcomes frictional forces, the string slips back to equilibrium position

What does the speed of the bow match?

equals the rate at which the wave travels on the string

Slipping time

time it takes the bend in the string to travel from the bow to the bridge and back

bow → bridge → bow

Sticking Time

time it takes the bend in the string to travel from the bow to the finger and back to the bow

bow → nut → bow

Period of oscillation of bowed strings

T = sticking time + slipping time

What paritals do bowed string produce?

harmonic partials due to bowing

How to play louder on bowed string?

increase bow speed and bow closer to the bridge

Example of pluck strings

guitar, harp, harpsichord

Source of plucked strings

string is displaced by finger/pick where it then moves into free decay

*not a constant flow of energy

Resonator of plucked strings

string determines fundamental f and partials

Radiator of plucked strings

Primary radiator is body or soundboard

Secondary is sound hole

What partials do plucked and struck strings produce?

slightly inharmonic partials

What happens at location of pluck?

amplitude at the point of plucked (the node) is forced to be non-zero → not all harmonic will be present

How does shape of plucked string influence it?

if volume increases, the air cavity resonance will decrease

Example of struck string

pianos

Source of struck string

string is struck by hammer or mallet which then puts it into free decay

• not a constant flow of energy

Resonator of struck string

string determines fundamental frequency and paritals

soundboard is secondary resonator

Radiator of struck string

Primary is soundboard/soundbox