What is "harmonic motion"

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.

Motion \Mo"tion\, n. [F., fr. L. motio, fr. movere, motum, to move. See Move.]

1. The act, process, or state of changing place or position; movement; the passing of a body from one place or position to another, whether voluntary or involuntary; -- opposed to rest.

   Speaking or mute, all comeliness and grace attends thee, and each word, each motion, forms.
   --Milton.

2. Power of, or capacity for, motion.

   Devoid of sense and motion.
   --Milton.

3. Direction of movement; course; tendency; as, the motion of the planets is from west to east.

   In our proper motion we ascend.
   --Milton.

4. Change in the relative position of the parts of anything; action of a machine with respect to the relative movement of its parts.

   This is the great wheel to which the clock owes its motion.
   --Dr. H. More.

5. Movement of the mind, desires, or passions; mental act, or impulse to any action; internal activity.

   Let a good man obey every good motion rising in his heart, knowing that every such motion proceeds from God.
   --South.

6. A proposal or suggestion looking to action or progress; esp., a formal proposal made in a deliberative assembly; as, a motion to adjourn.

   Yes, I agree, and thank you for your motion.
   --Shak.

7. (Law) An application made to a court or judge orally in open court. Its object is to obtain an order or rule directing some act to be done in favor of the applicant.
   --Mozley & W.

8. (Mus.) Change of pitch in successive sounds, whether in the same part or in groups of parts.

   The independent motions of different parts sounding together constitute counterpoint.
   --Grove.

   Note: Conjunct motion is that by single degrees of the scale. Contrary motion is that when parts move in opposite directions. Disjunct motion is motion by skips. Oblique motion is that when one part is stationary while another moves. Similar or direct motion is that when parts move in the same direction.

9. A puppet show or puppet. [Obs.] What motion's this? the model of Nineveh? --Beau. & Fl. Note: Motion, in mechanics, may be simple or compound. Simple motions are:

   1. straight translation, which, if of indefinite duration, must be reciprocating.

   2. Simple rotation, which may be either continuous or reciprocating, and when reciprocating is called oscillating.

   3. Helical, which, if of indefinite duration, must be reciprocating.

      Compound motion consists of combinations of any of the simple motions.

      Center of motion, Harmonic motion, etc. See under Center, Harmonic, etc.

      Motion block (Steam Engine), a crosshead.

      Perpetual motion (Mech.), an incessant motion conceived to be attainable by a machine supplying its own motive forces independently of any action from without. According to the law of conservation of energy, such perpetual motion is impossible, and no device has yet been built that is capable of perpetual motion.

      Syn: See Movement.

n. a periodic motion in which the displacement is either symmetrical about a point or is the sum of such motions

Harmonic motion can mean:

• The motion of a Harmonic oscillator (in physics), which can be:
  • Simple harmonic motion
  • Complex harmonic motion
• Keplers laws of planetary motion (in physics, known as the harmonic law)
• Quasi-harmonic motion: Unit hyperbola#Parametrization
• Musica universalis (in medieval astronomy, the music of the spheres)
• Chord progression (in music, harmonic progression)