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). Every octave is made of twelve steps called semitones. A jump from the lowest semitone to the highest semitone in one octave doubles the frequency (for example, the fifth A is 440 Hz and the sixth A is 880 Hz). The frequency of a 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 Hz by the twelfth root of two. To go from A4 up two semitones (one whole tone) to B4, multiply 440 twice by the twelfth root of two (or once by the sixth root of two, approximately 1.122462). To go from A4 up three semitones to C5 (a minor third In music th ...
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Fundamental Frequencies
The fundamental frequency, often referred to simply as the ''fundamental'' (abbreviated as 0 or 1 ), 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.) According to Benward 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 positive value T for which the following is tru ...
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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). Every octave is made of twelve steps called semitones. A jump from the lowest semitone to the highest semitone in one octave doubles the frequency (for example, the fifth A is 440 Hz and the sixth A is 880 Hz). The frequency of a 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 Hz by the twelfth root of two. To go from A4 up two semitones (one whole tone) to B4, multiply 440 twice by the twelfth root of two (or once by the sixth root of two, approximately 1.122462). To go from A4 up three semitones to C5 (a minor third In music th ...
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Octave
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. 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'' (), ''8va bassa'' (, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing this mark above or below the staff. ...
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Ukulele
The ukulele ( ; ); also called a uke (informally), is a member of the lute (ancient guitar) family of instruments. The ukulele is of Portuguese origin and was popularized in Hawaii. The tone and volume of the instrument vary with size and construction. Ukuleles commonly come in four sizes: soprano, concert, tenor, and baritone. Ukuleles generally have four nylon strings tuned to GCEA. They have 16–22 frets depending on the size. History Developed in the 1880s, the ukulele is based on several small, guitar-like instruments of Portuguese origin, the , and , 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 arriv ...
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Guitar Tunings
Guitar tunings are the assignment of pitches to the open strings of guitars, including classical guitars, acoustic guitars, and electric 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 (82.41 Hz), A (110 Hz), D (146.83 Hz), G (196 Hz), B (246.94 Hz), and E (329.63 Hz), 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 memoris ...
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Double Bass
The double bass (), also known as the upright bass, the acoustic bass, the bull fiddle, or simply the bass, is the largest and lowest-pitched string instrument, chordophone in the modern orchestra, symphony orchestra (excluding rare additions such as the octobass). It has four or five strings, and its construction is in between that of the gamba and the violin family. The bass is a standard member of the orchestra's string section, along with violins, violas, and cellos,''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 violoncello ( , ), commonly abbreviated as cello ( ), is a middle pitched 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; the tenor clef and treble clef are 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 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. Figured bass music ...
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Viola
The viola ( , () ) is a string instrument of the violin family, and is usually bowed when played. Violas are slightly larger than violins, and have 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 higher) and the cello (which is tuned an octave lower). The strings from low to high are typically tuned to 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 heyday of five-part ...
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Violin
The violin, sometimes referred to as a fiddle, is a wooden chordophone, and is the smallest, and thus highest-pitched instrument (soprano) in regular use in the violin family. Smaller violin-type instruments exist, including the violino piccolo and the pochette (musical instrument), pochette, but these are virtually unused. Most violins have a hollow wooden body, and commonly have four strings (music), strings (sometimes five-string violin, five), usually tuned in perfect fifths with notes G3, D4, A4, E5, and are most commonly played by drawing a bow (music), bow across the strings. The violin 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 ...
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Vocal Range
Vocal range is the range of pitches that a human voice can phonate. A common application is within the context of singing, where it is used as a defining characteristic for classifying singing voices into voice types. It is also a topic of study within linguistics, phonetics, and speech-language pathology, particularly in relation to the study of tonal languages and certain types of vocal disorders, although it has little practical application in terms of speech. Singing and the definition of vocal range While the broadest definition of "vocal range" is simply the span from the lowest to the highest note a particular voice can produce, this broad definition is often not what is meant when "vocal range" is discussed in the context of singing. Vocal pedagogists tend to define the vocal range as the total span of "musically useful" pitches that a singer can produce. This is because some of the notes a voice can produce may not be considered usable by the singer within performan ...
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Michigan Tech University
Michigan Technological University (Michigan Tech, MTU, or simply Tech) is a public research university in Houghton, Michigan, United States. It was founded in 1885 as the Michigan Mining School, the first post-secondary institution in the Upper Peninsula of Michigan. The university comprises five colleges and schools: the College of Engineering, the College of Computing, the College of Sciences and Arts, the College of Business, and the College of Forest Resources and Environmental Science. They offer more than 140 degree programs to nearly 7,000 graduate and undergraduate students. Its main campus sits on on a bluff overlooking Portage Lake. The campus consists of 36 buildings, the first of which was built in 1908. Michigan Tech's athletic teams are nicknamed the Huskies and compete primarily in the NCAA Division II Great Lakes Intercollegiate Athletic Conference (GLIAC). The men's hockey team competes in Division I as a member of the Central Collegiate Hockey Association ( ...
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Hertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base units is 1/s or s−1, meaning that one hertz is one per second or the Inverse second, reciprocal of one second. It is used only in the case of periodic events. It is named after Heinrich Hertz, Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. For high frequencies, the unit is commonly expressed in metric prefix, 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. T ...
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