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A unit fraction is a common fraction with a numerator of 1 (e.g., 1 / 7 ). Unit fractions can also be expressed using negative exponents, as in 2 −1, which represents 1/2, and 2 −2, which represents 1/(2 2) or 1/4. A dyadic fraction is a common fraction in which the denominator is a power of two, e.g. 1 / 8 = 1 / 2 3 .
7/8 may refer to: July 8 (month-day date notation) 7 August (day-month date notation) the Fraction seven eighths or 0.875 in decimal; the 7 8 time signature; ...
In the theory and practice of music, a fifth interval is an ordered pair of notes that are separated by an interval of 6–8 semitones. There are three types of fifth intervals, namely perfect fifths (7 semitones), diminished fifth (6 semitones), and; augmented fifth (8 semitones).
However, if the fraction 1/1 is replaced by the fraction 2/2, which is an equivalent fraction denoting the same rational number 1, the mediant of the fractions 2/2 and 1/2 is 3/4. For a stronger connection to rational numbers the fractions may be required to be reduced to lowest terms, thereby selecting unique representatives from the ...
The just perfect fifth can be heard when a violin is tuned: if adjacent strings are adjusted to the exact ratio of 3:2, the result is a smooth and consonant sound, and the violin sounds in tune. Keyboard instruments such as the piano normally use an equal-tempered version of the perfect fifth, enabling the instrument to play in all keys.
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By applying the fundamental recurrence formulas we may easily compute the successive convergents of this continued fraction to be 1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, ..., where each successive convergent is formed by taking the numerator plus the denominator of the preceding term as the denominator in the next term, then adding in the ...
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