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Harmonics
A harmonic is a wave with a frequency that is a positive integer multiple of the '' fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the other harmonics are known as ''higher harmonics''. As all harmonics are periodic at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a '' harmonic series''. The term is employed in various disciplines, including music, physics, acoustics, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50  Hz, a common AC power supply frequency, the frequencies of the first three higher harmonics are 100 Hz (2nd harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50 Hz. In music, harmonics are used on string instruments and wind in ...
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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. Interaction with the surrounding air causes audible sound waves, which travel away from the instrument. Because of the typical spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency, and such multiples form the harmonic series. The musical pitch of a note is usually perceived as the lowest partial present (the fundamental frequency), which may be the one created by vibration over the full length of the string or ai ...
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Violin
The violin, sometimes known as a ''fiddle'', is a wooden chordophone (string instrument) in the violin family. Most violins have a hollow wooden body. It is the smallest and thus highest-pitched instrument (soprano) in the family in regular use. The violin typically has four strings (music), strings (some can have five-string violin, five), usually tuned in perfect fifths with notes G3, D4, A4, E5, and is most commonly played by drawing a bow (music), bow across its strings. It can also be played by plucking the strings with the fingers (pizzicato) and, in specialized cases, by striking the strings with the wooden side of the bow (col legno). Violins are important instruments in a wide variety of musical genres. They are most prominent in the Western classical music, Western classical tradition, both in ensembles (from chamber music to orchestras) and as solo instruments. Violins are also important in many varieties of folk music, including country music, bluegrass music, and ...
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Consonance
In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as German composer and music theorist Paul Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term ''sonance'' has been proposed to encompass or refer indistinctly to the terms ''consonance'' and ''dissonance''. De ...
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Cello Natural Harmonics
The cello ( ; plural ''celli'' or ''cellos'') or violoncello ( ; ) is a Bow (music), bowed (sometimes pizzicato, plucked and occasionally col legno, hit) string instrument of the violin family. Its four strings are usually intonation (music), tuned in perfect fifths: from low to high, scientific pitch notation, C2, G2, D3 and A3. The viola's four strings are each an octave higher. Music for the cello is generally written in the bass clef, with tenor clef, and treble clef used for higher-range passages. Played by a ''List of cellists, cellist'' or ''violoncellist'', it enjoys a large solo repertoire Cello sonata, with and List of solo cello pieces, without accompaniment, as well as numerous cello concerto, concerti. As a solo instrument, the cello uses its whole range, from bassline, bass to soprano, and in chamber music such as string quartets and the orchestra's string section, it often plays the bass part, where it may be reinforced an octave lower by the double basses. Figure ...
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Fundamental Frequency
The fundamental frequency, often referred to simply as the ''fundamental'', is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between adjacent frequencies. In some contexts, the fundamental is usually abbreviated as 0, indicating the lowest frequency counting from zero. In other contexts, it is more common to abbreviate it as 1, the first harmonic. (The second harmonic is then 2 = 2⋅1, etc. In this context, the zeroth harmonic would be 0  Hz.) According to Benward's and Saker's ''Music: In Theory and Practice'': Explanation All sinusoidal and many non-sinusoidal waveforms repeat exactly over time – they are periodic. The period of a waveform is the smallest value of ...
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Clarinet
The clarinet is a musical instrument in the woodwind family. The instrument has a nearly cylindrical bore and a flared bell, and uses a single reed to produce sound. Clarinets comprise a family of instruments of differing sizes and pitches. The clarinet family is the largest such woodwind family, with more than a dozen types, ranging from the BB♭ contrabass to the E♭ soprano. The most common clarinet is the B soprano clarinet. German instrument maker Johann Christoph Denner is generally credited with inventing the clarinet sometime after 1698 by adding a register key to the chalumeau, an earlier single-reed instrument. Over time, additional keywork and the development of airtight pads were added to improve the tone and playability. Today the clarinet is used in classical music, military bands, klezmer, jazz, and other styles. It is a standard fixture of the orchestra and concert band. Etymology The word ''clarinet'' may have entered the English language via the ...
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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 musical keyboard, 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 ...
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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 nu ...
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Timbre
In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musical instruments. It also enables listeners to distinguish different instruments in the same category (e.g., an oboe and a clarinet, both woodwind instruments). In simple terms, timbre is what makes a particular musical instrument or human voice have a different sound from another, even when they play or sing the same note. For instance, it is the difference in sound between a guitar and a piano playing the same note at the same volume. Both instruments can sound equally tuned in relation to each other as they play the same note, and while playing at the same amplitude level each instrument will still sound distinctively with its own unique tone color. Experienced musicians are able to distinguish between different instruments of the same ...
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Dynamic Tonality
Dynamic tonality is a paradigm for tuning and timbre which generalizes the special relationship between just intonation and the harmonic series to apply to a wider set of pseudo-just tunings and related pseudo-harmonic timbres.Duffin, R.W., 2006''How Equal Temperament Ruined Harmony (and Why You Should Care)''/ref> This misalignment, in any tuning that is not fully Just (and hence infinitely complex), is the defining characteristic of the Static Timbre Paradigm. Instruments Many of the pseudo-just temperaments proposed during this "temperament battle" were rank-2 (two-dimensional)—such as quarter-comma meantone—that provided more than 12 notes per octave. However, the standard piano-like keyboard is only rank-1 (one-dimensional), affording at most 12 notes per octave. Piano-like keyboards affording more than 12 notes per octave were developed by Vicentino, Colonna, Mersenne, Huygens, and Newton, but were deemed cumbersome and difficult to learn. The dynamic tonality para ...
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Sinusoidal Wave
A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in mathematics, as well as in physics, engineering, signal processing and many other fields. Formulation Its most basic form as a function of time (''t'') is: y(t) = A\sin(2 \pi f t + \varphi) = A\sin(\omega t + \varphi) where: * ''A'', ''amplitude'', the peak deviation of the function from zero. * ''f'', ''ordinary frequency'', the ''number'' of oscillations (cycles) that occur each second of time. * ''ω'' = 2''f'', ''angular frequency'', the rate of change of the function argument in units of radians per second. * \varphi, '' phase'', specifies (in radians) where in its cycle the oscillation is at ''t'' = 0. When \varphi is non-zero, the entire waveform appears to be shifted in time by the amount ''φ''/''ω'' seconds. A negative value r ...
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Resonator
A 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. Another example is quartz crystals used in electronic devices such as radio transmitters and quartz watches to produce oscillations of very precise frequency. A cavity resonator is one in which waves exist in a hollow space inside the device. In electronics and radio, microwave cavities consisting of hollow metal boxes are used in microwave transmitters, receivers and test equipment to control frequency, in place of the tuned circuits which are used at lowe ...
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