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5-limit Tonnetz. Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note (the base note) by products of integer powers of 2, 3, or 5 (prime numbers limited to 5 or lower), such as 2 −3 ·3 1 ·5 1 = 15/8.
In quarter-comma meantone, the frequency ratio for the fifth is 4 √ 5 , which is about 3.42157 cents flatter than an equal tempered 700 cents, (or exactly one twelfth of a diesis) and so the wolf is about 737.637 cents, or 35.682 cents sharper than a perfect fifth of ratio exactly 3:2, and this is the original "howling" wolf fifth.
A scale with five notes per octave is called a pentatonic scale. [32] A perfect fifth is the most consonant harmony, and is the basis for most western tuning systems. [33] In harmonics, the fifth partial (or 4th overtone) of a fundamental has a frequency ratio of 5:1 to the frequency of that fundamental. This ratio corresponds to the interval ...
The standard tempered fifth has a frequency ratio of 2 7/12:1 (or about 1.498307077:1), approximately two cents narrower than a justly tuned fifth. Ascending by twelve justly tuned fifths fails to close the circle by an excess of approximately 23.46 cents, roughly a quarter of a semitone, an interval known as the Pythagorean comma.
In arithmetic and algebra, the fifth power or sursolid [1] of a number n is the result of multiplying five instances of n together: n 5 = n × n × n × n × n. Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube. The sequence of fifth powers of integers is:
Metric modulation: 2 half notes = 3 half notes or Play with eighth note subdivision for tempo/metre comparison. Thus if the two half notes in 4 4 time at a tempo of quarter note = 84 are made equivalent with three half notes at a new tempo, that tempo will be:
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