Piano Key Frequencies
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Piano Key Frequencies
This is a list of the fundamental frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 108-key extended piano in twelve-tone equal temperament, with the 49th key, the fifth A (called A4), tuned to 440 Hz (referred to as A440). Since every octave is made of twelve steps and since a jump of one octave doubles the frequency (for example, the fifth A is 440 Hz and the sixth A is 880 Hz), each successive pitch is derived by multiplying (ascending) or dividing (descending) the frequency of the previous pitch by the twelfth root of two (approximately 1.059463). For example, to get the frequency one semitone up from A4 (A4), multiply 440 by the twelfth root of two. To go from A4 to B4 (up one whole tone, or two semitones), multiply 440 twice by the twelfth root of two (or once by the sixth root of two, approximately 1.122462). To go from A4 to C5 (which is a minor third), multiply 440 three times by the twelfth root of two (or once by the fourth root of ...
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Fundamental Frequencies
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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Piano Key Frequencies
This is a list of the fundamental frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 108-key extended piano in twelve-tone equal temperament, with the 49th key, the fifth A (called A4), tuned to 440 Hz (referred to as A440). Since every octave is made of twelve steps and since a jump of one octave doubles the frequency (for example, the fifth A is 440 Hz and the sixth A is 880 Hz), each successive pitch is derived by multiplying (ascending) or dividing (descending) the frequency of the previous pitch by the twelfth root of two (approximately 1.059463). For example, to get the frequency one semitone up from A4 (A4), multiply 440 by the twelfth root of two. To go from A4 to B4 (up one whole tone, or two semitones), multiply 440 twice by the twelfth root of two (or once by the sixth root of two, approximately 1.122462). To go from A4 to C5 (which is a minor third), multiply 440 three times by the twelfth root of two (or once by the fourth root of ...
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Eighth Octave C
C or Do is the first note and semitone of the C major scale, the third note of the A minor scale (the relative minor of C major), and the fourth note (G, A, B, C) of the Guidonian hand, commonly pitched around 261.63  Hz. The actual frequency has depended on historical pitch standards, and for transposing instruments a distinction is made between written and sounding or concert pitch. It has enharmonic equivalents of B and D. In English the term ''Do'' is used interchangeably with C only by adherents of fixed Do solfège; in the movable Do system Do refers to the tonic of the prevailing key. Frequency Historically, concert pitch has varied. For an instrument in equal temperament tuned to the A440 pitch standard widely adopted in 1939, middle C has a frequency around 261.63 Hz (for other notes see piano key frequencies). Scientific pitch was originally proposed in 1713 by French physicist Joseph Sauveur and based on the numerically convenient frequency of 256& ...
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Octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music," the use of which is "common in most musical systems." The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class. To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated ''8a'' or ''8va'' ( it, all'ottava), ''8va bassa'' ( it, all'ottava bassa, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing ...
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Ukulele
The ukulele ( ; from haw, ukulele , approximately ), also called Uke, is a member of the lute family of instruments of Portuguese origin and popularized in Hawaii. It generally employs four nylon strings. The tone and volume of the instrument vary with size and construction. Ukuleles commonly come in four sizes: soprano, concert, tenor, and baritone. History Developed in the 1880s, the ukulele is based on several small, guitar-like instruments of Portuguese origin, the ''machete'', '' cavaquinho'', ''timple'', and ''rajão'', introduced to the Hawaiian Islands by Portuguese immigrants from Madeira, the Azores and Cape Verde. Three immigrants in particular, Madeiran cabinet makers Manuel Nunes, José do Espírito Santo, and Augusto Dias, are generally credited as the first ukulele makers. Two weeks after they disembarked from the SS ''Ravenscrag'' in late August 1879, the ''Hawaiian Gazette'' reported that "Madeira Islanders recently arrived here, have been delighting the ...
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Guitar Tunings
Guitar tunings are the assignment of pitches to the open strings of guitars, including acoustic guitars, electric guitars, and classical guitars. Tunings are described by the particular pitches that are made by notes in Western music. By convention, the notes are ordered and arranged from the lowest-pitched string (i.e., the deepest bass-sounding note) to the highest-pitched string (i.e., the highest sounding note), or the thickest string to thinnest, or the lowest frequency to the highest. This sometimes confuses beginner guitarists, since the highest-pitched string is referred to as the 1st string, and the lowest-pitched is the 6th string. Standard tuning defines the string pitches as E, A, D, G, B, and E, from the lowest pitch (low E2) to the highest pitch (high E4). Standard tuning is used by most guitarists, and frequently used tunings can be understood as variations on standard tuning. To aid in memorising these notes, mnemonics are used, for example, Elephants And D ...
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Double Bass
The double bass (), also known simply as the bass () (or #Terminology, by other names), is the largest and lowest-pitched Bow (music), bowed (or plucked) string instrument in the modern orchestra, symphony orchestra (excluding unorthodox additions such as the octobass). Similar in structure to the cello, it has four, although occasionally five, strings. The bass is a standard member of the orchestra's string section, along with violins, viola, and cello, ''The Orchestra: A User's Manual''
, Andrew Hugill with the Philharmonia Orchestra
as well as the concert band, and is featured in Double bass concerto, concertos, solo, and chamber music in European classical music, Western classical music.Alfred Planyavsky

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Cello
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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Viola
The viola ( , also , ) is a string instrument that is bow (music), bowed, plucked, or played with varying techniques. Slightly larger than a violin, it has a lower and deeper sound. Since the 18th century, it has been the middle or alto voice of the violin family, between the violin (which is tuned a perfect fifth above) and the cello (which is tuned an octave below). The strings from low to high are typically tuned to scientific pitch notation, C3, G3, D4, and A4. In the past, the viola varied in size and style, as did its names. The word viola originates from the Italian language. The Italians often used the term viola da braccio meaning literally: 'of the arm'. "Brazzo" was another Italian word for the viola, which the Germans adopted as ''Bratsche''. The French had their own names: ''cinquiesme'' was a small viola, ''haute contre'' was a large viola, and ''taile'' was a tenor. Today, the French use the term ''alto'', a reference to its range. The viola was popular in the heyd ...
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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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Michigan Tech University
Michigan Technological University (Michigan Tech, MTU, or simply Tech) is a public university, public research university in Houghton, Michigan, founded in 1885 as the Michigan Mining School, the first post-secondary institution in the Upper Peninsula of Michigan. Michigan Tech is one of the eight research universities in the State of Michigan and is Carnegie Classification of Institutions of Higher Education, classified among "R2: Doctoral Universities – High research activity". There are 12 research areas including Space Sciences, Electronics, Ecosystems, Energy, Health, Ocean Sciences, and Robotics. There are 18 research centers on and off campus including the Michigan Tech Research Institute. The university is governed by an eight-member board of trustees whose members are appointed by the governor of Michigan and confirmed by the Michigan Senate. The university comprises five colleges and schools: the College of Engineering, the College of Computing, the College of Scienc ...
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Hertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one hertz is the reciprocal of one second. It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in multiples: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz). Some of the unit's most common uses are in the description of periodic waveforms and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. The units are sometimes also used as a representation of the energy of a photon, via the Planck relation ''E'' = ''hν'', where ''E'' is the photon's energy, ''ν'' is its freq ...
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