Mirror Form of Multiplication
Herbert Eimert described what he called the "eight modes" of the twelve-tone series, all mirror forms of one another. The inverse is obtained through a horizontal mirror, the retrograde through a vertical mirror, the retrograde-inverse through both a horizontal and a vertical mirror, and the "cycle-of-fourths-transform" or Quartverwandlung and "cycle-of-fifths-transform" or Quintverwandlung obtained through a slanting mirror (Eimert 1950, 28–29). With the retrogrades of these transforms and the prime, there are eight permutations.
Furthermore, one can sort of move the mirror at an angle, that is the 'angle' of a fourth or fifth, so that the chromatic row is reflected in both cycles. . . . In this way, one obtains the cycle-of-fourths transform and the cycle-of-fifths transform of the row. (Eimert 1950, 29; trans. Schuijer 2008, 81)Read more about this topic: Multiplication (music)
Famous quotes containing the words mirror and/or form:
“The barriers of conventionality have been raised so high, and so strangely cemented by long existence, that the only hope of overthrowing them exists in the union of numbers linked together by common opinion and effort ... the united watchword of thousands would strike at the foundation of the false system and annihilate it.”
—Mme. Ellen Louise Demorest 1824–1898, U.S. women’s magazine editor and woman’s club movement pioneer. Demorest’s Illustrated Monthly and Mirror of Fashions, p. 203 (January 1870)
“It is absolutely impossible to transcend the laws of nature. What can change in historically different circumstances is only the form in which these laws expose themselves.”
—Karl Marx (1818–1883)