[计] 调和级数

[经] 调和级数

[ noun ]
(mathematics) a progression of terms whose reciprocals form an arithmetic progression
<noun.group>

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.

Harmonic twang! of leather, horn, and brass. --Pope.

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.

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.

{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.


Progression \Pro*gres"sion\, n. [L. progressio: cf. F.
progression.]
1. The act of moving forward; a proceeding in a course;
motion onward.

2. Course; passage; lapse or process of time.

I hope, in a short progression, you will be wholly
immerged in the delices and joys of religion.
--Evelyn.

3. (Math.) Regular or proportional advance in increase or
decrease of numbers; continued proportion, arithmetical,
geometrical, or harmonic.

4. (Mus.) A regular succession of tones or chords; the
movement of the parts in harmony; the order of the
modulations in a piece from key to key.

{Arithmetical progression}, a progression in which the terms
increase or decrease by equal differences, as the numbers
[lbrace2]2, 4, 6, 8, 1010, 8, 6, 4, 2[rbrace2] by the
difference 2.

{Geometrical progression}, a progression in which the terms
increase or decrease by equal ratios, as the numbers
[lbrace2]2, 4, 8, 16, 32, 6464, 32, 16, 8, 4, 2[rbrace2]
by a continual multiplication or division by 2.

{Harmonic progression}, a progression in which the terms are
the reciprocals of quantities in arithmetical progression,
as 1/2, 1/4, 1/6, 1/8, 1/10.