'Harmonic progression' definitions:

Definition of 'harmonic progression'

From: WordNet
noun
(mathematics) a progression of terms whose reciprocals form an arithmetic progression

Definition of 'Harmonic progression'

From: GCIDE
  • Progression \Pro*gres"sion\, n. [L. progressio: cf. F. progression.] [1913 Webster]
  • 1. The act of moving forward; a proceeding in a course; motion onward. [1913 Webster]
  • 2. Course; passage; lapse or process of time. [1913 Webster]
  • I hope, in a short progression, you will be wholly immerged in the delices and joys of religion. --Evelyn. [1913 Webster]
  • 3. (Math.) Regular or proportional advance in increase or decrease of numbers; continued proportion, arithmetical, geometrical, or harmonic. [1913 Webster]
  • 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. [1913 Webster]
  • 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. [1913 Webster]
  • 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. [1913 Webster]
  • 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. [1913 Webster]

Definition of 'Harmonic progression'

From: 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. [1913 Webster]
  • Harmonic twang! of leather, horn, and brass. --Pope. [1913 Webster]
  • 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. [1913 Webster]
  • 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. [1913 Webster]
  • 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. [1913 Webster]