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Permutation vs Variation - What's the difference?

permutation | variation | Related terms |

In lang=en terms the difference between permutation and variation

is that permutation is a transformation of a set's prime form, by applying one or more of certain operations, specifically, transposition, inversion, and retrograde while variation is a technique where material is repeated with alterations to the melody, harmony, rhythm, timbre, texture, counterpoint or orchestration; but with some invariant characteristic, e.g. a ground bass.

As nouns the difference between permutation and variation

is that permutation is a one-to-one mapping from a finite set to itself while variation is the act of varying; a partial change in the form, position, state, or qualities of a thing.

permutation

English

Noun

(wikipedia permutation) (en noun)
  • (mathematics) A one-to-one mapping from a finite set to itself.
    • This permutation takes each element to the one following it, with the last mapped back to the first.
  • (mathematics, combinatorics) An ordering of a finite set of distinct elements.
    • There are six permutations of three elements, e.g. {abc, acb, bac, bca, cab, cba}.
  • (music) A transformation of a set's prime form, by applying one or more of certain operations, specifically, transposition, inversion, and retrograde.

    • Anagrams

    * importunate

    See also

    * (combinatorics) combination ----

    variation

    English

    (wikipedia variation)

    Noun

    (en-noun)
  • The act of varying; a partial change in the form, position, state, or qualities of a thing
  • * {{quote-magazine, year=2013, month=May-June, author= David Van Tassel], [http://www.americanscientist.org/authors/detail/lee-dehaan Lee DeHaan
    • , title= Wild Plants to the Rescue , volume=101, issue=3, magazine=(American Scientist) , passage=Plant breeding is always a numbers game.
  • A related but distinct thing.
  • (nautical) The angular difference at the vessel between the direction of true north and magnetic north. Also called magnetic declination.
  • (board games) A line of play that differs from the original.
  • (music) A technique where material is repeated with alterations to the melody, harmony, rhythm, timbre, texture, counterpoint or orchestration; but with some invariant characteristic, e.g. a ground bass.

    • Derived terms

    * magnetic variation * theme and variations

    Related terms

    * vary * variant

    References

    * US FM 55-501 MARINE CREWMAN’S HANDBOOK; 1 December 1999 * * ----