The Collaborative International Dictionary of English v.0.48:

Variation \Va`ri*a"tion\, n. [OE. variatioun, F. variation, L.
   variatio. See Vary.]
   1. The act of varying; a partial change in the form,
      position, state, or qualities of a thing; modification;
      alteration; mutation; diversity; deviation; as, a
      variation of color in different lights; a variation in
      size; variation of language.
      [1913 Webster]

            The essences of things are conceived not capable of
            any such variation.                   --Locke.
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   2. Extent to which a thing varies; amount of departure from a
      position or state; amount or rate of change.
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   3. (Gram.) Change of termination of words, as in declension,
      conjugation, derivation, etc.
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   4. (Mus.) Repetition of a theme or melody with fanciful
      embellishments or modifications, in time, tune, or
      harmony, or sometimes change of key; the presentation of a
      musical thought in new and varied aspects, yet so that the
      essential features of the original shall still preserve
      their identity.
      [1913 Webster]

   5. (Alg.) One of the different arrangements which can be made
      of any number of quantities taking a certain number of
      them together.
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   Annual variation (Astron.), the yearly change in the right
      ascension or declination of a star, produced by the
      combined effects of the precession of the equinoxes and
      the proper motion of the star.

   Calculus of variations. See under Calculus.

   Variation compass. See under Compass.

   Variation of the moon (Astron.), an inequality of the
      moon's motion, depending on the angular distance of the
      moon from the sun. It is greater at the octants, and zero
      at the quadratures.

   Variation of the needle (Geog. & Naut.), the angle included
      between the true and magnetic meridians of a place; the
      deviation of the direction of a magnetic needle from the
      true north and south line; -- called also declination of
      the needle.
      [1913 Webster]

   Syn: Change; vicissitude; variety; deviation.
        [1913 Webster]

WordNet (r) 3.0 (2006):

variation
    n 1: an instance of change; the rate or magnitude of change
         [syn: variation, fluctuation]
    2: an activity that varies from a norm or standard; "any
       variation in his routine was immediately reported" [syn:
       variation, variance]
    3: a repetition of a musical theme in which it is modified or
       embellished
    4: something a little different from others of the same type;
       "an experimental version of the night fighter"; "a variant of
       the same word"; "an emery wheel is the modern variation of a
       grindstone"; "the boy is a younger edition of his father"
       [syn: version, variant, variation, edition]
    5: an artifact that deviates from a norm or standard; "he
       patented a variation on the sandal"
    6: the angle (at a particular location) between magnetic north
       and true north [syn: magnetic declination, magnetic
       variation, variation]
    7: the process of varying or being varied
    8: (astronomy) any perturbation of the mean motion or orbit of a
       planet or satellite (especially a perturbation of the earth's
       moon)
    9: (biology) an organism that has characteristics resulting from
       chromosomal alteration [syn: mutant, mutation,
       variation, sport]
    10: (ballet) a solo dance or dance figure [syn: pas seul,
        variation]
    11: the act of changing or altering something slightly but
        noticeably from the norm or standard; "who is responsible
        for these variations in taxation?"

Moby Thesaurus II by Grady Ward, 1.0:

321 Moby Thesaurus words for "variation":
   Nachtmusik, Proteus, aberrancy, aberration, about-face,
   absolute music, accommodation, adaptation, adjustment, air varie,
   aleatory, aleatory music, allotropism, allotropy, alteration,
   altering, alternation, amelioration, anacrusis, analysis,
   anatomization, apostasy, arrangement, atomization, bass passage,
   bend, betterment, bias, bourdon, branching off, break, bridge,
   burden, cadence, capriciousness, chamber music, chamber orchestra,
   change, change of heart, change of pace, changeability,
   changeableness, changing, choice, choppiness, chorus,
   circuitousness, coda, composition, constructive change, continuity,
   contrariety, contrast, conversion, corner, crook, curve,
   dappleness, declination, defection, deflection, degeneration,
   degenerative change, demarcation, departure, descant,
   desultoriness, desynonymization, deterioration, detour,
   development, deviability, deviance, deviancy, deviation,
   deviousness, difference, differencing, differentiation, differing,
   digression, disaccord, disaccordance, disagreement, disconformity,
   discongruity, discontinuity, discordance, discrepancy,
   discreteness, discrimination, discursion, disequalization,
   disjunction, disorder, disparity, dissent, dissimilarity,
   dissonance, distinction, distinctness, distinguishment, divagation,
   divarication, divergence, divergency, diversification, diversion,
   diversity, division, dogleg, double, drift, drifting, eccentricity,
   electronic music, errantry, erraticism, etude, excursion, excursus,
   exercise, exorbitation, exposition, far cry, fickleness, figure,
   fitting, flightiness, flip-flop, fluctuation, folderol,
   freakishness, gradual change, hairpin, harmonic close,
   harmonization, her infinite variety, heterogeneity, heteromorphism,
   improvement, impulsiveness, inaccordance, incidental music,
   incompatibility, incongruity, inconsistency, inconsonance,
   inconstancy, indirection, individualization, individuation,
   inequality, inharmoniousness, inharmony, instability,
   instrumental music, interlude, intermezzo, introductory phrase,
   invention, irreconcilability, irregularity, jerkiness,
   manifoldness, measure, melioration, mercuriality, mitigation,
   mixture, modification, modifying, modulation, moodiness,
   motleyness, movement, multifariousness, multiplicity,
   musical phrase, musical sentence, mutability, mutation, nocturne,
   nonconformism, nonconformity, nonstandardization, nonuniformity,
   novelty, obliquity, odds, omnifariousness, omniformity, opposition,
   opus, orchestration, ornament, oscillation, otherness, overthrow,
   part, particularization, passage, pendulation, pererration, period,
   permutation, personalization, phrase, piece, pluralism,
   polymorphism, production, program music, qualification,
   radical change, raggedness, rambling, re-creation, realignment,
   redesign, reform, reformation, refrain, remaking, renewal,
   reshaping, resolution, response, restlessness, restructuring,
   reversal, revival, revivification, revolution, ricercar,
   ritornello, score, section, seesawing, segregation, separateness,
   separation, severalization, severance, shapeshifter, sheer, shift,
   shiftiness, shifting, shifting course, shifting path, shuffling,
   skew, slant, sonata, sonatina, specialization, stanza, statement,
   strain, straying, string orchestra, string quartet, study,
   sudden change, sweep, swerve, swerving, swinging, switch, tack,
   tailpiece, teeter-tottering, teetering, theme and variations,
   total change, tottering, transition, trio, turn, turnabout,
   turning, tutti, tutti passage, twist, uncertainty, unconformism,
   unconformity, undependability, unfixedness, unlikeness,
   unorthodoxy, unpredictability, unreliability, unsettledness,
   unstableness, unsteadfastness, unsteadiness, upheaval, vacillation,
   variability, variance, variegation, variety, variousness, varying,
   veer, versatility, verse, vicissitude, violent change, wandering,
   wantonness, warp, wavering, waywardness, whimsicality, work,
   worsening, yaw, zigzag