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(For example, 2 / 5 and 3 / 5 are both read as a number of fifths.) Exceptions include the denominator 2, which is always read half or halves, the denominator 4, which may be alternatively expressed as quarter/quarters or as fourth/fourths, and the denominator 100, which may be alternatively expressed as hundredth/hundredths or ...
For example, a just perfect fifth (for example C to G) is 3:2 (Play ⓘ), 1.5, and may be approximated by an equal tempered perfect fifth (Play ⓘ) which is 2 7/12 (about 1.498). If the A above middle C is 440 Hz , the perfect fifth above it would be E , at (440*1.5=) 660 Hz, while the equal tempered E5 is 659.255 Hz.
All-fifths tuning is based on the perfect fifth (the interval with seven semitones), and all-fourths tuning is based on the perfect fourth (five semitones). The perfect-fifth and perfect-fourth intervals are inversions of one another, and the chords of all-fourth and all-fifths are paired as inverted chords. Consequently, chord charts for all ...
The size of an interval between two notes may be measured by the ratio of their frequencies.When a musical instrument is tuned using a just intonation tuning system, the size of the main intervals can be expressed by small-integer ratios, such as 1:1 (), 2:1 (), 5:3 (major sixth), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third).
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Multiplication table from 1 to 10 drawn to scale with the upper-right half labeled with prime factorisations. In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.
The intervals of 5-limit just intonation (prime limit, not odd limit) are ratios involving only the powers of 2, 3, and 5. The fundamental intervals are the superparticular ratios 2/1 (the octave), 3/2 (the perfect fifth) and 5/4 (the major third). That is, the notes of the major triad are in the ratio 1:5/4:3/2 or 4:5:6.
The extremes of the meantone systems encountered in historical practice are the Pythagorean tuning, where the whole tone corresponds to 9:8, i.e. (3:2) 2 / 2 , the mean of the major third (3:2) 4 / 4 , and the fifth (3:2) is not tempered; and the 1 ⁄ 3-comma meantone, where the fifth is tempered to the extent that three ...