A multiple of a fundamental frequency or pitch. For example, 120 Hz, 180 Hz, 240 Hz, 360 Hz, are all harmonics of 60 Hz. Sometimes called overtones. Most acoustic instruments have at least a few harmonics in their sound, and some are rich in harmonics.

Applying to some stringed instruments, one can utilize the vibrational properties of the string to create a purer harmonic tone (i.e. one with fewer overtones). On a guitar, for example, lightly place one finger on the string above the fifth fret and pluck the string sharply. The sound that emits is a harmonic frequency that is a multiple of the string's base frequency; in this case, a fractional multiple. This can be used to produce cool sounds, and also to tune the guitar or other stringed instrument more accurately.

Most instruments do not produce a pure sine wave when played, as a computer does. They produce a loud basic tone, along with other tones, indistinguishable to the human ear, forming a type of chord. These extra tones are called overtones or harmonics, and they are what make a clarinet sound different from a flute, an oboe, or a guitar. These harmonics are at integral multiples of the base tone. For example, the first harmonic of the A at 440 Hz will be at 880 Hz, the second at 1320 Hz, the third at 1760 Hz, etc.

Depending on which overtones are present and how loud they are, the sound of different instruments can vary greatly. For example, a flute's, overtones are very quiet, producing a very pure sound. This sound is the most like a sine wave out of any normal instrument sound.

The clarinet, however, only produces the odd harmonics, and their amplitudes are in inverse proportion to them. For example, it contains the first harmonic (the base tone), the third harmonic at a volume of one third of the base tone, the fifth harmonic at a volume of one fifth the base tone, and so on. The sum of these waves produces a square wave, rather than a sine wave.

The oboe produces both odd and even harmonics, but still in inverse proportion to their amplitudes. The result of this is a sawtooth wave, which is also the type of wave produced by most string instruments. This is why the oboe's sound is very similar to the sound of a violin.

The last major type of wave is the triangle wave, which consists of only odd harmonics, and amplitudes which are inversely proportional to the squares of the harmonics. It sounds similar to a sine wave, but slightly more metallic.

Sources:
  • http://www.teachnet.ie/amhiggins/squaresaw.html
  • http://www.csm.astate.edu/music.html
  • http://www.wikipedia.org/wiki/Triangle_wave
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Har*mon"ic (?), Har*mon"ic*al (), a. [L. harmonicus, Gr. ; 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, <-- reference to diagram of a circle with radius having point P on the circle, and a diameter with point A in the diameter. THe motion of point A, plotted over time, will describe a sine wave! -->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 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 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 harmonic, and harmony. -- Harmonic triad Mus., the chord of a note with its third and fifth; the common chord.

 

© Webster 1913.


Har*mon"ic (?), n. Mus.

A musical note produced by a number of vibrations which is a multiple of the number producing some other; an overtone. See Harmonics.

 

© Webster 1913.

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