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  2. Piano tuning - Wikipedia

    en.wikipedia.org/wiki/Piano_tuning

    A man tuning an upright piano. Piano tuning is the process of adjusting the tension of the strings of an acoustic piano so that the musical intervals between strings are in tune. The meaning of the term 'in tune', in the context of piano tuning, is not simply a particular fixed set of pitches. Fine piano tuning requires an assessment of the ...

  3. Stretched tuning - Wikipedia

    en.wikipedia.org/wiki/Stretched_tuning

    In stretched tuning, two notes an octave apart, whose fundamental frequencies theoretically have an exact 2:1 ratio, are tuned slightly farther apart (a stretched octave). If the frequency ratios of octaves are greater than a factor of 2, the tuning is stretched; if smaller than a factor of 2, it is compressed." [3]

  4. Pythagorean interval - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_interval

    In musical tuning theory, a Pythagorean interval is a musical interval with a frequency ratio equal to a power of two divided by a power of three, or vice versa. [1] For instance, the perfect fifth with ratio 3/2 (equivalent to 3 1 / 2 1) and the perfect fourth with ratio 4/3 (equivalent to 2 2 / 3 1) are Pythagorean intervals.

  5. Pythagorean tuning - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_tuning

    Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths [2] which are "pure" or perfect, with ratio :. This is chosen because it is the next harmonic of a vibrating string, after the octave (which is the ratio 2 : 1 {\displaystyle 2:1} ), and hence is the ...

  6. Piano acoustics - Wikipedia

    en.wikipedia.org/wiki/Piano_acoustics

    The Railsback curve shows how a piano tuned to compensate for inharmonicity deviates from theoretically correct equal-tempered tuning. The Railsback curve, first measured in the 1930s by O.L. Railsback, a US college physics teacher, expresses the difference between inharmonicity-aware stretched piano tuning, and theoretically correct equal-tempered tuning in which the frequencies of successive ...

  7. Equal temperament - Wikipedia

    en.wikipedia.org/wiki/Equal_temperament

    12 tone equal temperament chromatic scale on C, one full octave ascending, notated only with sharps. Play ascending and descending ⓘ. An equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequencies of any adjacent pair of notes is the same.

  8. Chromatic scale - Wikipedia

    en.wikipedia.org/wiki/Chromatic_scale

    As a result, in 12-tone equal temperament (the most common tuning in Western music), the chromatic scale covers all 12 of the available pitches. Thus, there is only one chromatic scale. [a] The ratio of the frequency of one note in the scale to that of the preceding note is given by . [1]

  9. Wolf interval - Wikipedia

    en.wikipedia.org/wiki/Wolf_interval

    with this set of chosen notes in bold face, and some of the omitted notes shown in grey. [e]This limitation on the set meantone notes and their sharps and flats that can be tuned on a keyboard at any one time, was the main reason that Baroque period keyboard and orchestral harp performers were obliged to retune their instruments in mid-performance breaks, in order to make available all the ...

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