- published: 06 May 2016
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The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to measure extremely small finite intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is much too small to be heard between successive notes.
Alexander J. Ellis based the measure on the acoustic logarithms decimal semitone system developed by Gaspard de Prony in the 1830s, at Robert Holford Macdowell Bosanquet's suggestion. Ellis made extensive measurements of musical instruments from around the world, using cents extensively to report and compare the scales employed, and further described and employed the system in his edition of Hermann von Helmholtz's On the Sensations of Tone. It has become the standard method of representing and comparing musical pitches and intervals with relative accuracy.
Like a decibel's relation to intensity, a cent is a ratio between two close frequencies. For the ratio to remain constant over the frequency spectrum, the frequency range encompassed by a cent must be proportional to the two frequencies. An equally tempered semitone (the interval between two adjacent piano keys) decidedly spans 100 cents. An octave -- two notes that have a frequency ratio of 2:1 -- spans twelve semitones and therefore 1200 cents. Since a frequency raised by one cent is simply multiplied by this constant cent value, and 1200 cents doubles a frequency, the ratio of frequencies one cent apart is precisely equal to 21/1200, the 1200th root of 2, which is approximately 1.0005777895.
Cent may refer to:
Music is an art form whose medium is sound and silence. Its common elements are pitch (which governs melody and harmony), rhythm (and its associated concepts tempo, meter, and articulation), dynamics, and the sonic qualities of timbre and texture. The word derives from Greek μουσική (mousike; "art of the Muses").
The creation, performance, significance, and even the definition of music vary according to culture and social context. Music ranges from strictly organized compositions (and their recreation in performance), through improvisational music to aleatoric forms. Music can be divided into genres and subgenres, although the dividing lines and relationships between music genres are often subtle, sometimes open to individual interpretation, and occasionally controversial. Within "the arts", music may be classified as a performing art, a fine art, and auditory art. There is also a strong connection between music and mathematics.
To many people in many cultures, music is an important part of their way of life. Ancient Greek and Indian philosophers defined music as tones ordered horizontally as melodies and vertically as harmonies. Common sayings such as "the harmony of the spheres" and "it is music to my ears" point to the notion that music is often ordered and pleasant to listen to. However, 20th-century composer John Cage thought that any sound can be music, saying, for example, "There is no noise, only sound." Musicologist Jean-Jacques Nattiez summarizes the relativist, post-modern viewpoint: "The border between music and noise is always culturally defined—which implies that, even within a single society, this border does not always pass through the same place; in short, there is rarely a consensus ... By all accounts there is no single and intercultural universal concept defining what music might be."