harmonic

American Heritage® Dictionary of the English Language, Fourth Edition

1. adj. Of or relating to harmony.
2. adj. Pleasing to the ear: harmonic orchestral effects.
3. adj. Characterized by harmony: a harmonic liturgical chant.
4. adj. Of or relating to harmonics.
5. adj. Integrated in nature.
6. n. Any of a series of musical tones whose frequencies are integral multiples of the frequency of a fundamental tone.
7. n. A tone produced on a stringed instrument by lightly touching an open or stopped vibrating string at a given fraction of its length so that both segments vibrate. Also called overtone, partial, partial tone.
8. n. The theory or study of the physical properties and characteristics of musical sound.
9. n. Physics A wave whose frequency is a whole-number multiple of that of another.

Century Dictionary and Cyclopedia

1. Pertaining or relating to harmony of sounds; of or pertaining to music; in general, concordant; consonant; in music, specifically, pertaining to harmony, as distinguished from melody and rhythm.
2. In acoustics, noting the secondary tones which accompany the primary tone in a complex musical tone. See II., 1.
3. In mathematics, involving or of the nature of the harmonic mean; similar to or constructed upon the principle of the harmonic curve. The first application of the adjective harmonic (in Greek) to mathematics was in the phrase harmonic proportion, said to have been used by Archytas, a contemporary of Plato. Three numbers are said to be in harmonic proportion when the first divided by the third is equal to the quotient of the excess of the first over the second divided by the excess of the second over the third; or, otherwise stated, when the reciprocal of the second is the arithmetical mean of the reciprocals of the first and third, the second number is said to be the harmonic mean of the first and third. Pythagoras first discovered that a vibrating string stopped at half its length gave the octave of the original note, and stopped at two thirds of its length gave the fifth. Now, as 1, ⅔, and ½ are in harmonic proportion, and as this phrase arose among the Pythagoreans, the word harmonic has always been held to have reference here to this fact (although Nicomachus explains it otherwise, from the properties of the cube, as ἁρμονία, or norm). The harmonic proportion or ratio, as thus defined, plays a considerable part in modern geometry as an important case of the anharmonic ratio, and has given rise to the phrases harmonic axis, center, pencil, etc. (See below.) A harmonic curve is the figure of a vibrating string. It can assume many forms, but all may be regarded as derived, by summation of displacements, from simple harmonic curves, or curves of sines. The development of this idea has given rise to the theory of harmonics, which is one of the great engines of mathematical analysis. This gives the phrases harmonic analysis, function, motion, etc.
4. In anatomy, forming or formed by a harmonia: as, a harmonic articulation or suture.
5. Also harmonical.
6. In music, the analysis of the harmonic structure of a piece.
7. The amplification of a harmonic passage by the introduction of passing-notes, etc.
8. n. In acoustics: A secondary or collateral tone involved in a primary or fundamental tone, and produced by the partial vibration of the body of which the complete vibration gives the primary tone. Nearly every tone contains several distinct harmonics, which are always taken from a typical series of tones the vibration-numbers of which, beginning with that of the fundamental tone, are proportional to the series 1, 2, 3, 4, 5, 6, 7, etc. The interval from the fundamental tone to the first harmonic is, therefore, an octave; to the second, an octave and a fifth; to the third, two octaves; to the fourth, two octaves and a major third; to the fifth, two octaves and a fifth; to the Sixth, two octaves and somewhat less than a minor seventh; to the seventh, three octaves; etc. (See illustration.) Harmonics result from the elasticity of the tone-producing body, which leads it to vibrate, not only entire, but in its aliquot parts; thus, a violin-string tends to vibrate throughout its whole length, and also at the same time in each of its halves, thirds, quarters, etc. The vibration of the whole, being much the greater, gives the primary or fundamental tone; while the several partial vibrations, which diminish rapidly in force as they rise in pitch, give the harmonics. In a given tone the harmonics may usually be roughly detected by the unaided ear; but for precise and minute analysis specially constructed resonators are necessary. Tuning-forks and large stopped organ-pipes give only insignificant harmonics; certain reed-instruments, like the clarinet, give only selected sets of harmonics, as the second, fourth, sixth, etc.; while the human voice is capable of the greatest richness of harmonics. What is technically known as quality or timbre in a tone is due to the number and the relative strength of the harmonics contained in it. Different instruments and voices are thus distinguished from each other, and different uses of the same instrument or voice. In the voice, in particular, the essential difference between different vowel-sounds is a matter of harmonics. In any tone the lower harmonics are strictly consonant both with the primary tone and with each other: hence the use in the organ of mutation- and mixture-stops, whereby the consonant harmonics of a given tone are much emphasized. Many of the higher harmonics, on the other hand, are strongly dissonant both with the primary tone and with each other: hence the discordant quality of such instruments as cymbals, and the peculiar construction of the pianoforte, whereby dissonant harmonics are suppressed. In instruments of the viol and harp classes very beautiful effects are produced by suppressing the primary tone, leaving one set of its harmonics to sound alone. Such tones are called harmonic tones, or simply harmonics (though they are themselves compounded of a primary tone and its harmonics). In instruments of the trumpet class, like the horn, all the tones ordinarily used are really harmonics of the natural tone of the tube, and are produced by varying the pressure of the breath and the method of blowing. The same is true to a less degree of instruments of the wood-wind group. Harmonics are also called overtones. All the tones, primary and secondary, entering into the constitution of an actual tone are often called partial tones, or partials, the fundamental tone being the first partial, and the harmonics the upper partials.
9. n. A harmonic tone. In mathematics, a function expressing the Newtonian potential of a point in terms of its coördinates.
10. In function theory, two pairs of points, one pair the intersections of a circle about with a circle through the other pair.

Wiktionary

1. adj. pertaining to harmony
2. adj. pleasant to hear; harmonious; melodious
3. adj. mathematics attribute of many mathematical entities that only in few cases are obviously related
4. n. physics a component frequency of the signal of a wave that is an integer multiple of the fundamental frequency

GNU Webster's 1913

1. adj. Concordant; musical; consonant.
2. adj. (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. adj. (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.
4. 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.

WordNet 3.0

1. adj. relating to vibrations that occur as a result of vibrations in a nearby body
2. adj. of or relating to the branch of acoustics that studies the composition of musical sounds
3. adj. of or relating to harmony as distinct from melody and rhythm
4. n. a tone that is a component of a complex sound
5. n. any of a series of musical tones whose frequencies are integral multiples of the frequency of a fundamental
6. adj. of or relating to harmonics
7. adj. involving or characterized by harmony