Search results
Results from the WOW.Com Content Network
Definition and divergence. The harmonic series is the infinite series in which the terms are all of the positive unit fractions. It is a divergent series: as more terms of the series are included in partial sums of the series, the values of these partial sums grow arbitrarily large, beyond any finite limit.
The harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a fundamental frequency. Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously.
Harmonic series, partials 1–5 numbered. In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios (such as 3:2 or 4:3) of frequencies. An interval tuned in this way is said to be pure, and is called a just interval. Just intervals (and chords created by combining them) consist of tones from a ...
List of mathematical series. This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. is a Bernoulli polynomial. is an Euler number. is the Riemann zeta function. is the gamma function. is a polygamma function. is a polylogarithm.
Percussion bars, such as xylophone, are hung at ≈2/9 and ≈7/9 length, and struck at 1/2 length, to reduce inharmonicity. In music, inharmonicity is the degree to which the frequencies of overtones (also known as partials or partial tones) depart from whole multiples of the fundamental frequency (harmonic series).
In mathematics, the n -th harmonic number is the sum of the reciprocals of the first n natural numbers: [1] Starting from n = 1, the sequence of harmonic numbers begins: Harmonic numbers are related to the harmonic mean in that the n -th harmonic number is also n times the reciprocal of the harmonic mean of the first n positive integers.
In Western musical theory, a cadence (from Latin cadentia 'a falling') is the end of a phrase in which the melody or harmony creates a sense of full or partial resolution, especially in music of the 16th century onwards. [ 2 ] A harmonic cadence is a progression of two or more chords that concludes a phrase, section, or piece of music. [ 3 ]
In music theory, an interval is a difference in pitch between two sounds. [ 1 ] An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord. [ 2 ][ 3 ] In Western ...