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Fourier analysis. Related transforms. In mathematics, Fourier analysis(/ˈfʊrieɪ,-iər/)[1]is the study of the way general functionsmay be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as ...
The Railsback curve contrasts a theoretically correct equal-tempered piano tuning against one that compensates for a piano's inharmonicity. The Railsback curve, first measured by O.L. Railsback, expresses the difference between inharmonicity-aware stretched piano tuning, and theoretically correct equal-tempered tuning in which the frequencies of successive notes are related by a constant ratio ...
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 A 4), tuned to 440 Hz (referred to as A440). [ 1 ][ 2 ] Every octave is made of twelve steps called semitones.
The seven-string works well in a band setting, as its lowest note, B1 lines up well with the B0 commonly used for the lowest note of a 5+ string bass. Both the guitar and bass could drop tune as well using a lowest note of A1 and A0 respectively (with the bass this extends the range to the lowest note on a standard piano).
Harmonics of a string showing the periods of the pure-tone harmonics (period = 1/frequency) The 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 ...
New standard tuning (NST) is an alternative tuning for the guitar that approximates all-fifths tuning. The guitar's strings are assigned the notes C2-G2-D3-A3-E4-G4 (from lowest to highest); the five lowest open strings are each tuned to an interval of a perfect fifth { (C,G), (G,D), (D,A), (A,E)}; the two highest strings are a minor third ...
The red dots are the wave nodes. A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the note played.
A 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.
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