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An eighth note or a quaver is a musical note played for one eighth the duration of a whole note (semibreve). Its length relative to other rhythmic values is as expected—e.g., half the duration of a quarter note (crotchet), one quarter the duration of a half note (minim), and twice the value of a sixteenth note.
A note played for one-eighth the duration of a whole note is called an eighth note, or quaver. [ 70 ] An octave , the interval between two musical notes with the same letter name (where one has double the frequency of the other), is so called because there are eight notes between the two on a standard major or minor diatonic scale , including ...
8 (six beats per bar, with each beat being an eighth note) and 12 8 (twelve beats per bar, with each beat being an eighth note; in practice, the eighth notes are typically put into four groups of three eighth notes. 12 8 is a compound time type of time signature). Many other time signatures exist, such as 2 2 or 3 8.
The lower note is a constant A (440 Hz in either scale), the upper note is a C ♯ in the equal-tempered scale for the first 1", and a C ♯ in the just intonation scale for the last 1". Phase differences make it easier to detect the transition than in the previous sample.
The figure-eight knot has played an important role historically (and continues to do so) in the theory of 3-manifolds.Sometime in the mid-to-late 1970s, William Thurston showed that the figure-eight was hyperbolic, by decomposing its complement into two ideal hyperbolic tetrahedra.
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein 's formula E = m c 2 {\displaystyle E=mc^{2}} is the quantitative representation in mathematical notation of mass–energy ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...