Amplifier: A device that attempts to increases the volume of a sound evenly. If the amplification is beyond the limits of the device clipping can occur.
Amplitude: The maximum height of a wave crest or depth of a trough. The amplitude corresponds to the loudness of the sound.
Anechoic chamber: a recording chamber that is specially designed to have no reverb or echo. When a sound is recorded in an anechoic chamber the reverb can be added electronically to make the sound more natural sounding.
Anharmonic: Not exhibiting evenly spaced resonant frequencies. For example, a round drum head has modes with frequencies f, 1.59*f, 2.14*f, 2.30*f, etc. where f is the fundamental (i.e. lowest) frequency. Compare with "Harmonic".
Anharmonic instrument: An instrument, such as a drum or bell, that generates a frequency spectrum that anharmonic, i.e. does not generate only frequencies that are integer multiples of the fundamental. See "Anharmonic".
Basilar membrane: A membrane located in the inner ear that is responsible for separating the different frequency components of a sound and sending the information to the brain. The membrane has different resonant frequencies along its length, so the different amplitudes of each frequency component present in a sound are detected as the sound passes over the membrane. Because of the similarity between this and the early attempts at doing Fourier transforms with sets of resonators, we say that the basilar membrane performs a "poor-man's Fourier transform".
Beat: The basic rhythmic unit in a piece of music. Also: the modulation heard when two tones are close together.
Blind analysis: A technique used by scientists to make sure that any preconceived notions that they have for what the answer of an experiment "should be" do not affect the actual results.
Brown noise: Background noise can be classified into different types by analyzing its spectrum content, that is taking the Fourier transform. Brown noise gets its name from Brownian motion, the motion that an object makes when doing a random walk. What this means is that if you made a plot of the path a particle makes when in random motion and took the Fourier transform of this signal you would see a spectrum characteristic of Brown noise. It turns out that this spectrum has lots of low frequency components and fewer high frequeny components. The exact amount of each frequency component goes roughly as 1/(frequency squared).
Cochlear Implant: Prosthetic for hearing that must be surgically implanted.
Consonance: The quality that we ascribe to two sounds that sound "nice" when played together. The opposite of dissonance. Occurs when the Fourier components of the sounds are far apart from one another or have perfect overlap.
Decibel: a measure of the amplitude of a sound. Because the decibel is on a logarithmic scale small increases in decibels correspond to huge increases in volume.
Density: a measure of the number of something per unit volume. Higher density air as more air particles in a given volme then lower density air.
Dissonance: The quality that we ascribe to two sounds that sound "harsh" when played together. The opposite of consonance. Occurs when the Fourier components of the sounds overlap partly on the basilar membrane.
Ethnomusicology: The study of the music of other cultures.
Formant: The pair of frequency peeks that characterize the different vowel sounds in our speech.
Fourier component: A Fourier component refers to the amount of a particular frequency present in a sound. In the Fourier domain (where frequency is the x-axis), we represent a single Fourier component by a line over the frequency that it corresponds to. The length of the line tells us "how much" of that frequency is present in the sound. In the time domain a Fourier component looks like a sine-wave that oscillates at the component's frequency.
Fourier spectrum: A plot of magnitude versus frequency showing all the different Fourier components present in a signal.
Fourier transform: It is a magical (actually mathematical) fact that any signal, no matter how complicated, can be made just by adding up a large (potentially infinite) number of sine waves of different frequencies and magnitudes. The Fourier transform refers to the mathematical method that we use to determine what sine waves actually make up a given signal. These sine waves are called Fourier components and we plot them on a graph called the Fourier spectrum of a sound. All sounds have a unique Fourier spectrum and vice-versa so the Fourier spectrum of a sound (what we call the frequency domain) is just as good as a representation as the time domain waveform.
Frequency: The number of times per second that a wave oscillates. The unit of frequency is the Hz (hertz) which is one cycle (oscillation) per second. Our ears perceive the frequency of a sound as the pitch. Our ears can detect sound frequencies of a few tens of Hz to around 20000 Hz.
Frequency spectrum A plot of the amplitude (amount) of each frequency that makes up a sound. A harmonic instrument, such as a whistle or violin, will have a frequency spectrum with evenly spaced peaks at the harmonics. An anharmonic instrument, such as a drum, will have unevely spaced peaks.
Fundamental: The lowest frequency component of a musical note. The fundamental sets the pitch of the note. The fundamental is also called the 1st harmonic.
Harmonic A frequency that is an integer (i.e. 1, 2, 3...) multiple of the fundamental frequency, i.e. 1*f is the 1st harmonic, 2*f is the second harmonic, etc. The 1st harmonic is also called the fundamental.
Harmonics All the harmonics of a given fundamental frequency. See "Harmonic".
Harmonic frequency See "Harmonic".
Impedance matching: When a signal moves from one medium to another the properties of each medium will determin how much of the signal will be transmitted through (the rest of the signal bounces off and is reflected backwards). When almost the entire signal is transmitted through with little degradation we say that the "impedances" of the materials are matched.
Logrithmic graph: Logarithms allow us to plot really small values on the same graph as really large values. We use logarithmic graphs in this class to plot frequencies because our ears have such a large range (20 Hz to 20,000 Hz)
Longitudinal wave: A wave in which the disturbance to the medium moves in the same direction as the propagation of the wave. Sound waves are longitudinal waves. Contrast with transverse wave
Masking: The presence of low notes can overpower high notes.
Mode: A standing wave in a string, air column, or 2-dimensional plate that has a characteristic frequency. The modes of a string or air column vibrate at the fundamental frequency and harmonics, i.e frequency = f, 2*f, 3*f .... The modes of a two dimensional plates, such as a drum heads, do not exibit the nice harmonic structure (see "Anharmonic instruments").
Node: The point on a standing wave where no disturbances occur.
Octave: An interval that represents a 2-1 ratio in frequencies. For example, a tone at 880Hz is one octave higher than a tone at 440Hz
Ossicles: Are made up a several small bones located between the inner and outer ear that serve to transmit as much of the sound as possible into the fluid-filled cochlea. This is an examples of impedance matching.
Overtones: The frequencies that an instrument produces in addition to the fundamental (the fundamental is not counted as an overtone). For a string or open ended air column, the 1st overtone is the 2nd harmonic, 2nd overtone is the 3rd harmonic, etc. For a cylindrical air column with one closed end (generating only odd harmonics), the 1st overtone is the 3rd harmonic, the 2nd overtone is the 5th harmonic, etc. For an anharmonic instrument (such as a bell or drum), the overtones are not harmonic. The 1st overtone is the mode that has a frequency closest to the fundamental. The next closest is the 2nd overtone, etc.
Pink noise: Background noise can be classified into different types by analyzing its spectrum content, that is taking the Fourier transform. Pink noise is often called "1 over F noise" because the amount of spectral content at a given frequency gets lower the higher the frequency. More precisely it falls off at 1/frequency. Pink noise thus has a Fourier spectrum that falls off slower than brown noise (which falls off at 1/(frequecy squared) )
Pitch: The quality of a note or sound that represents the how high or low the note is. The pitch is measured in terms of the frequency of the note's fundamental. See "Timbre".
Pressure: defined as the amount of force on a surface per unit area. Since higher density air corresponds to higher pressure we can figure out the time domain waveform of a sound simply by measuring the pressure on a membrane as a function of time.
Pure tone: A sound or note with a single frequency. Such a note lacks timbre. The frequency spectrum of a pure tone is a single peak at the tone's frequency.
Resonance: See "Resonant frequency".
Resonant frequency: A frequency at which a vibrating object, such as a string, naturally likes to oscillate. An object will have many different resonances corresponding to the particular modes that it supports. The lowest frequency is called the fundamental. If you try to force the object to vibrate at a frequency that is not one of its resonant frequencies, the object oscillations will damp quickly.
Reverberation: the echoes resulting from reflections off of the walls in a room that we hear when a sound is played. When the echoes follow the original sound quickly enough, we may hear a single richer sound. Since the amount of reverb that we hear is a property of the room that a sound is played in, it is important that are is taken in the design since too much reverb can ruin a performance.
Sampling: To store sounds on a computer it is necessary to sample the sound many times per second. Each sample point of the sound tells us the magnitude of the time domain waveform at the time the sample was taken. When we sample a sound, we are effectively throwing out all information that we know about the sound between two samples. The more frequently we sample a sound the more faithfully we can recreate a sound. Information theory tells us that if we sample above the "Nyquist Frequency", perfect reconstruction of a sound is possible.
Sawtooth wave: A waveform with following characteristic amplitude pattern. Sawtooth waves have a large number of high harmonics since they contain sharp corners.
Sonogram: A way of displaying the frequency spectrum of a sound over time. The verticle axis represents frequency and the horizontal represents time. The display sweeps across the time axis, drawing the current frequency spectrum as variations in colors or brightness along the vertical.
Sound body: The usually hollow body of a stringed instrument that takes the vibrations from the string and transfers them to the air. See "Transfer function".
Square wave: A waveform with following characteristic amplitude pattern. Square waves have a large number of high harmonics since they contain sharp corners.
Standing wave: The type of wave that appears on a string or in an air column when oscillating at a single frequency. A standing wave oscillates but doesn't move left or right. When we draw a standing wave, we draw it as a function of position along the string. Compare this with "traveling wave".
Superposition: When two sounds are played simultaneously, the resulting time domain waveform that we hear is just the sum of each sound. Because of this property, complex sounds can be analyzed as sums of simple sounds. For instance, we use Fourier transforms to decompose a sound into a sum of many very simple sounds (pure tones or Fourier components). If principal of superposition didn't hold this technique wouldn't be possible.
Tempered scale: The 12 tone Western scale can be built up by stacking perfect fifths (3/2 ratio) on top of each other. When this is done, after the twelfth note you find that you have wrapped completely around to the note that you started with (albeit several octaves higher). This would work out great except that this it not what happens. Mathematically the note you return to isn't "exactly" the note that you started at, a fact that has caused many musical problems. The solution to this dillema has been to "cheat" a little bit on the frequency value of each note of the scale to make this error go away. Scales that do this are called tempered (as opposed to "just" scales that do not do this).
Timbre: The quality of a note from an instrument that distinguishes it from a pure tone. The frequency spectrum of a note (for harmonic instruments) shows a number of frequency peaks: the fundamental and its harmonics.
Transfer function: A characteristic quantity of a sound body that describes the transfer of the standing waves in a string to the traveling waves in the air. The transfer function describes how well each frequency from the string gets transfered to the air. The transfer function does not change the frequencies themselves, just the fraction (or amount) of that frequency that reaches the air.
Transients: the frequecies heard only during the initial of a note. Musicians often refer this to "the attack". These extra frequencies die away quickly and are not present once the note has been sustained for a short time.
Transverse wave: A wave in which the disturbance to the medium moves in a direction that is perpendicular to the propagation of the wave. Examples are a football wave (the wave moves around the stadium, but the disturbance moves up and down), light waves, and water waves.
Travelling wave A travelling wave is the type of wave that moves, e.g. an ocean wave. A travelling wave starts at its source (such as an instrument) and propogates away from the source, usually spreading out and becoming weaker the further it is from the source. When we plot a travelling wave, we chose some point away from the source and draw the changes in the air pressure over time. Compare with "Standing wave".
Tritone: A very dissonant interval lying between a perfect 4th and a perfect 5th.
Tritone paradox: An auditory illusion involving two notes with a complex timbre. Depending on the listener, one can hear the interval as either an ascending tritone or descending tritone. Studies have shown that the likelihood that a person will the tones hear one way or the other is correlated with geographic and cultural factors.
White noise: A sound typically characterized by random fluctuations in air pressure, whose spectrum tends to span all frequencies. Examples of white noise are TV or radio static, applause, background conversation at a cafe, or the sound of rain.
Zeroth order approximation: The term that scientists use to describe their first best guess with all other complicating factors thrown out. As these other details are included in their analysis (often called higher order approximations) the approximation becomes closer and closer to reality. The more details that are included in an analysis the more complicated it becomes. Knowing what to leave out and what to include is an important skill to have as a scientist.