Harmonic series (music)A harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a fundamental frequency. Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously. At the frequencies of each vibrating mode, waves travel in both directions along the string or air column, reinforcing and canceling each other to form standing waves.
ResonatorA resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator can be either electromagnetic or mechanical (including acoustic). Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use acoustic resonators that produce sound waves of specific tones.
Delay differential equationIn mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state, i.e.
Sound board (music)A sound board, or soundboard, is the surface of a string instrument that the strings vibrate against, usually via some sort of bridge. Pianos, guitars, banjos, and many other stringed instruments incorporate soundboards. The resonant properties of the sound board and the interior of the instrument greatly increase the loudness of the vibrating strings. "The soundboard is probably the most important element of a guitar in terms of its influence on the quality of the instrument's tone .
String vibrationA vibration in a string is a wave. Resonance causes a vibrating string to produce a sound with constant frequency, i.e. constant pitch. If the length or tension of the string is correctly adjusted, the sound produced is a musical tone. Vibrating strings are the basis of string instruments such as guitars, cellos, and pianos. The velocity of propagation of a wave in a string () is proportional to the square root of the force of tension of the string () and inversely proportional to the square root of the linear density () of the string: This relationship was discovered by Vincenzo Galilei in the late 1500s.
Tuning forkA tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it against a surface or with an object, and emits a pure musical tone once the high overtones fade out. A tuning fork's pitch depends on the length and mass of the two prongs. They are traditional sources of standard pitch for tuning musical instruments.
Spherical harmonicsIn mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, each function defined on the surface of a sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular functions (sines and cosines) via Fourier series.
Renaissance musicRenaissance music is traditionally understood to cover European music of the 15th and 16th centuries, later than the Renaissance era as it is understood in other disciplines. Rather than starting from the early 14th-century ars nova, the Trecento music was treated by musicology as a coda to Medieval music and the new era dated from the rise of triadic harmony and the spread of the contenance angloise style from Britain to the Burgundian School. A convenient watershed for its end is the adoption of basso continuo at the beginning of the Baroque period.
ModulationIn electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a separate signal called the modulation signal that typically contains information to be transmitted. For example, the modulation signal might be an audio signal representing sound from a microphone, a video signal representing moving images from a video camera, or a digital signal representing a sequence of binary digits, a bitstream from a computer.
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
