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Spherical harmonic analysis
(gcide) | Harmonic \Har*mon"ic\ (h[aum]r*m[o^]n"[i^]k), Harmonical
\Har*mon"ic*al\ (-[i^]*kal), a. [L. harmonicus, Gr. "armoniko`s;
cf. F. harmonique. See Harmony.]
1. Concordant; musical; consonant; as, harmonic sounds.
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Harmonic twang! of leather, horn, and brass. --Pope.
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2. (Mus.) Relating to harmony, -- as melodic relates to
melody; harmonious; esp., relating to the accessory sounds
or overtones which accompany the predominant and apparent
single tone of any string or sonorous body.
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3. (Math.) Having relations or properties bearing some
resemblance to those of musical consonances; -- said of
certain numbers, ratios, proportions, points, lines,
motions, and the like.
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Harmonic interval (Mus.), the distance between two notes of
a chord, or two consonant notes.
Harmonical mean (Arith. & Alg.), certain relations of
numbers and quantities, which bear an analogy to musical
consonances.
Harmonic motion, the motion of the point A, of the foot of
the perpendicular PA, when P moves uniformly in the
circumference of a circle, and PA is drawn perpendicularly
upon a fixed diameter of the circle. This is simple
harmonic motion. The combinations, in any way, of two or
more simple harmonic motions, make other kinds of harmonic
motion. The motion of the pendulum bob of a clock is
approximately simple harmonic motion.
Harmonic proportion. See under Proportion.
Harmonic series or Harmonic progression. See under
Progression.
Spherical harmonic analysis, a mathematical method,
sometimes referred to as that of Laplace's Coefficients,
which has for its object the expression of an arbitrary,
periodic function of two independent variables, in the
proper form for a large class of physical problems,
involving arbitrary data, over a spherical surface, and
the deduction of solutions for every point of space. The
functions employed in this method are called spherical
harmonic functions. --Thomson & Tait.
Harmonic suture (Anat.), an articulation by simple
apposition of comparatively smooth surfaces or edges, as
between the two superior maxillary bones in man; -- called
also harmonia, and harmony.
Harmonic triad (Mus.), the chord of a note with its third
and fifth; the common chord.
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Spherical harmonic analysis
(gcide) | Spherical \Spher"ic*al\, Spheric \Spher"ic\, a. [L. sphaericus,
Gr. ???: cf. F. sph['e]rique.]
1. Having the form of a sphere; like a sphere; globular;
orbicular; as, a spherical body.
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2. Of or pertaining to a sphere.
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3. Of or pertaining to the heavenly orbs, or to the sphere or
spheres in which, according to ancient astronomy and
astrology, they were set.
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Knaves, thieves, and treachers by spherical
predominance. --Shak.
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Though the stars were suns, and overburned
Their spheric limitations. --Mrs.
Browning.
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Spherical angle, Spherical coordinate, {Spherical
excess}, etc. See under Angle, Coordinate, etc.
Spherical geometry, that branch of geometry which treats of
spherical magnitudes; the doctrine of the sphere,
especially of the circles described on its surface.
Spherical harmonic analysis. See under Harmonic, a.
Spherical lune,portion of the surface of a sphere included
between two great semicircles having a common diameter.
Spherical opening, the magnitude of a solid angle. It is
measured by the portion within the solid angle of the
surface of any sphere whose center is the angular point.
Spherical polygon,portion of the surface of a sphere
bounded by the arcs of three or more great circles.
Spherical projection, the projection of the circles of the
sphere upon a plane. See Projection.
Spherical sector. See under Sector.
Spherical segment, the segment of a sphere. See under
Segment.
Spherical triangle,re on the surface of a sphere, bounded
by the arcs of three great circles which intersect each
other.
Spherical trigonometry. See Trigonometry.
[1913 Webster] -- Spher"ic*al*ly, adv. --
Spher"ic*al*ness, n.
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