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Piano Acoustics
Piano acoustics is the set of physical properties of the piano that affect its sound. It is an area of study within musical acoustics. String length, mass and tension The strings of a piano vary in thickness, and therefore in mass per length, with bass strings thicker than treble. A typical range is from 1/30 inch (0.85 mm, string size 13) for the highest treble strings to 1/3 inch (8.5 mm) for the lowest bass. These differences in string thickness follow from well-understood acoustic properties of strings. Given two strings, equally taut and heavy, one twice as long as the other, the longer will vibrate with a pitch one octave lower than the shorter. However, if one were to use this principle to design a piano, i.e. if one began with the highest notes and then doubled the length of the strings again and again for each lower octave, it would be impossible to fit the bass strings onto a frame of any reasonable size. Furthermore, when strings vibrate, the width of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inharmonicity
In music, inharmonicity is the degree to which the frequencies of overtones (also known as partials or partial tones) depart from whole multiples of the fundamental frequency ( harmonic series). Acoustically, a note perceived to have a single distinct pitch in fact contains a variety of additional overtones. Many percussion instruments, such as cymbals, tam-tams, and chimes, create complex and inharmonic sounds. Music harmony and intonation depends strongly on the harmonicity of tones. An ideal, homogeneous, infinitesimally thin or infinitely flexible string or column of air has exactly harmonic modes of vibration. In any real musical instrument, the resonant body that produces the music tone—typically a string, wire, or column of air—deviates from this ideal and has some small or large amount of inharmonicity. For instance, a very thick string behaves less as an ideal string and more like a cylinder (a tube of mass), which has natural resonances that are not whole num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inharmonicity
In music, inharmonicity is the degree to which the frequencies of overtones (also known as partials or partial tones) depart from whole multiples of the fundamental frequency ( harmonic series). Acoustically, a note perceived to have a single distinct pitch in fact contains a variety of additional overtones. Many percussion instruments, such as cymbals, tam-tams, and chimes, create complex and inharmonic sounds. Music harmony and intonation depends strongly on the harmonicity of tones. An ideal, homogeneous, infinitesimally thin or infinitely flexible string or column of air has exactly harmonic modes of vibration. In any real musical instrument, the resonant body that produces the music tone—typically a string, wire, or column of air—deviates from this ideal and has some small or large amount of inharmonicity. For instance, a very thick string behaves less as an ideal string and more like a cylinder (a tube of mass), which has natural resonances that are not whole num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piano
The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboard, which is a row of keys (small levers) that the performer presses down or strikes with the fingers and thumbs of both hands to cause the hammers to strike the strings. It was invented in Italy by Bartolomeo Cristofori around the year 1700. Description The word "piano" is a shortened form of ''pianoforte'', the Italian term for the early 1700s versions of the instrument, which in turn derives from ''clavicembalo col piano e forte'' (key cimbalom with quiet and loud)Pollens (1995, 238) and ''fortepiano''. The Italian musical terms ''piano'' and ''forte'' indicate "soft" and "loud" respectively, in this context referring to the variations in volume (i.e., loudness) produced in response to a pianist's touch or pressure on the keys: the gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twelfth Root Of Two
The twelfth root of two or \sqrt 2/math> (or equivalently 2^) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory, where it represents the frequency ratio ( musical interval) of a semitone () in twelve-tone equal temperament. This number was proposed for the first time in relationship to musical tuning in the sixteenth and seventeenth centuries. It allows measurement and comparison of different intervals (frequency ratios) as consisting of different numbers of a single interval, the equal tempered semitone (for example, a minor third is 3 semitones, a major third is 4 semitones, and perfect fifth is 7 semitones). A semitone itself is divided into 100 cents (1 cent = \sqrt 2002^). Numerical value The twelfth root of two to 20 significant figures is . Fraction approximations in increasing order of accuracy are , , and . , its numerical value has been computed to at least twenty billion decimal digits. The equal-temp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Attack-decay-sustain-release
In sound and music, an envelope describes how a sound changes over time. It may relate to elements such as amplitude (volume), frequencies (with the use of filters) or pitch. For example, a piano key, when struck and held, creates a near-immediate initial sound which gradually decreases in volume to zero. Envelope generators, which allow users to control the different stages of a sound, are common features of synthesizers, samplers, and other electronic musical instruments. The most common form of envelope generator is controlled with four parameters: attack, decay, sustain and release (ADSR). Development The Hammond Novachord in 1938 used an early implementation of an ADSR envelope. A seven-position rotary knob selects preset ADS parameter for all 72 notes; a pedal controls the release. The envelope generator was created by the American engineer Robert Moog in the 1960s. While experimenting with the first Moog synthesizers, composer Herbert Deutsch suggested Moog find a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sustain
In sound and music, an envelope describes how a sound changes over time. It may relate to elements such as amplitude (volume), frequencies (with the use of filters) or pitch. For example, a piano key, when struck and held, creates a near-immediate initial sound which gradually decreases in volume to zero. Envelope generators, which allow users to control the different stages of a sound, are common features of synthesizers, samplers, and other electronic musical instruments. The most common form of envelope generator is controlled with four parameters: attack, decay, sustain and release (ADSR). Development The Hammond Novachord in 1938 used an early implementation of an ADSR envelope. A seven-position rotary knob selects preset ADS parameter for all 72 notes; a pedal controls the release. The envelope generator was created by the American engineer Robert Moog in the 1960s. While experimenting with the first Moog synthesizers, composer Herbert Deutsch suggested Moog find a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ."Sloane, Irving (1989). ''Classic Guitar Construction'', p.20. Bold Strummer. . "The sound board is the most important element in the guitar." The sound board operates by the principle of forced vibration. The string gently vibrates the board, and despite their differences in size and composition, makes the board vibrate at exactly the same frequency. This produces the same sound as the string alone, differing only in timbre. The string would produce the same amount of energy without the board p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acoustic Impedance
Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The SI unit of acoustic impedance is the pascal-second per cubic metre (), or in the MKS system the rayl per square metre (), while that of specific acoustic impedance is the pascal-second per metre (), or in the MKS system the rayl. There is a close analogy with electrical impedance, which measures the opposition that a system presents to the electric current resulting from a voltage applied to the system. Mathematical definitions Acoustic impedance For a linear time-invariant system, the relationship between the acoustic pressure applied to the system and the resulting acoustic volume flow rate through a surface perpendicular to the direction of that pressure at its point of application is given by: : p(t) = * Qt), or equivalently by : Q(t) = * pt), where * ''p'' is the acoustic pressure; * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies. Frequencies at which the response amplitude is a relative maximum are also known as resonant frequencies or resonance frequencies of the system. Small periodic forces that are near a resonant frequency of the system have the ability to produce large amplitude oscillations in the system due to the storage of vibrational energy. Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, orbital resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beat (acoustics)
In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, ''perceived'' as a periodic variation in volume whose rate is the difference of the two frequencies. With tuning instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a unison will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a tremolo as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception, the beating starts to sound like a note, and a combination tone is produced. This combination tone can also be referred to as a missing fundamental, as the beat frequency of any two tones is equiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
