Word Finder - harmonic

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A component frequency of the signal of a wave that is an integer multiple of the fundamental frequency.

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The place where, on a bowed string instrument, a note in the harmonic series of a particular string can be played without the fundamental present.

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One of a class of functions that enter into the development of the potential of a nearly spherical mass due to its attraction.

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One's child.

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Pertaining to harmony

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Pleasant to hear; harmonious; melodious

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Used to characterize various mathematical entities or relationships supposed to bear some resemblance to musical consonance

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The harmonic polar line of an inflection point of a cubic curve is the component of the polar conic other than the tangent line.

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Recurring periodically

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Exhibiting or applying constraints on what vowels (e.g. front/back vowels only) may be found near each other and sometimes in the entire word.

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Of or relating to a generation an even number of generations distant from a particular person.

In Wagner's harmonic style we encounter the entire problem of modern musical texture.

A similar method has frequently been applied to the study of variations of soil-temperatures by harmonic analysis of the annual waves.

We have seen (in the articles on Harmony and Music) how harmonic music originated in just this habit of regarding combinations of sound as mere sensations, and how for centuries the habit opposed itself to the intellectual principles of contrapuntal harmony.

The only illogical point in his system is that the beauty of his dreamlike chords depends not only on his artful choice of a timbre that minimizes their harshness, but also on the fact that they enter the ear with the meaning they have acquired through centuries of harmonic evolution on classical lines.

The brilliant success of Humperdinck's Hansel and Gretel, in which Wagnerian technique is applied to the diatonic style of nursery songs with a humorous accuracy undreamed of by Wagner's imitators, points a moral which would have charmed Wagner himself; but until the revival of some rudiments of musical common sense becomes widespread, there is little prospect of the influence of Wagner's harmonic style being productive of anything better than nonsense.

For the subjects of this general heading see the articles Mechanics; Dynamics, Analytical; Gyroscope; Harmonic Analysis; Wave; HYDROMechanics; Elasticity; Motion, Laws Of; Energy; Energetics; Astronomy (Celestial Mechanics); Tide.

The linear transformation replaces points on lines through the origin by corresponding points on projectively corresponding lines through the origin; it therefore replaces a pencil of lines by another pencil, which corresponds projectively, and harmonic and other properties of pencils which are unaltered by linear transformation we may expect to find indicated in the invariant system.

There is no linear covariant, since it is impossible to form a symbolic product which will contain x once and at the same time appertain to a quadratic. (v.) is the Jacobian; geometrically it denotes the bisectors of the angles between the lines ax, or, as we may say, the common harmonic conjugates of the lines and the lines x x .

The simplest form of wave, so far as our sensation goes - that is, the one giving rise to a pure tone - is, we have every reason to suppose, one in which the displacement is represented by a harmonic curve or a curve of sines, y=a sin m(x - e).

The chief experimental basis for supposing that a train of longitudinal waves with displacement curve of this kind arouses the sensation of a pure tone is that the more nearly a source is made to vibrate with a single simple harmonic motion, and therefore, presumably, the more nearly it sends out such a harmonic train, the more nearly does the note heard approximate to a single pure tone.

Now we can see that two notes of the same pitch, but of different quality, or different form of displacement curve, will, when thus analysed, break up into a series having the same harmonic wave-lengths; but they may differ as regards the members of the series present and their amplitudes and epochs.

We may regard quality, then, as determined by the members of the harmonic series present and their amplitudes and epochs.

For the superposition of these trains will give a stationary wave between A H A (16) Y which is an equation characteristic of simple harmonic motion.

But where it is appropriate, the disturbance sent out into the air contains the same harmonic series as the source.

But the harmonics are most readily heard if we fortify the ear by an air cavity with a natural period equal to that of the harmonic to be sought.

Now suppose that in addition to the internal force represented by, ux, an external harmonic force of period 27r/p is applied.

Each of the first few harmonics may be easily obtained by touching the string at the first node of the harmonic required, and bowing at the first loop, and the presence of the nodes and loops may be verified by putting light paper riders of shape A on the string at the nodes and loops.

When the harmonic is sounded the riders at the loops are thrown off, while those at the nodes remain seated.

The first overtone has frequency 6.25 that of the fundamental, and is not in the harmonic series.

If the wire is stretched across a room and stroked in the middle with a damp cloth the fundamental is easily obtained, and the first harmonic can be brought out by stroking it at a quarter the length from one end.

If it is clamped at one-quarter and threequarters of the length from the ends, and is stroked in the middle, the first harmonic sounds.

If we measure the time from an instant at which the two are in the same phase the resultant disturbance is y=a sin i t+a sin 27rn2t =2a cos ir(n i - n 2)t sin ir(nl-t-n2)t, which may be regarded as a harmonic disturbance of frequency (ni+n2)/2 but with amplitude 2a cos 7r(n i - n 2)t slowly varying with the time.

Take as a further example the fifth with harmonic overtones as under The fundamental and overtones of the second either coincide with or fall midway between overtones in the first, and there is no approach to a dissonant frequency of beats, and the concord is perfect.

Mehler, who proved that a simple relation existed between the function of zero order and the zonal harmonic of order n.

Also W = (V +IA)w i; or w1=W/(V+/A), w p =W/(V+plA), and wn =W/(Vd-nIA), or the densities of the several liquids vary inversely as the respective volumes of the instrument immersed in them; and, since the divisions of the scale correspond to equal increments of volume immersed, it follows that the densities of the several liquids in which the instrument sinks to the successive divisions form a harmonic series.

A spectroscope may be compared to a mechanical harmonic analyser which when fed with an irregular function of one variable represented by a curve supplies us with the sine curves into which the original function may be resolved.

In other spectra such " harmonic " ratios were also discovered, but their search was abandoned when it was found that their number did not exceed that calculated by the laws of probability on the supposition of a chance distribution.

The three commonest means are the arithmetical, geometrical, and harmonic; of less importance are the contraharmonical, arithmetico-geometrical, and quadratic.

The harmonic mean of n quantities is the arithmetical mean of their reciprocals.

Among the remaining buildings must be mentioned the town hall (17th century; restored 1823), the court-house, the concert-hall of the "Harmonic" club, the record office (1900), the leeskabuiet, or subscription library and reading-rooms, and the ten-storeyed Witte Huis (1897), which is used for offices and is one of the highest private buildings on the Continent.

The steam pressure in the heater may be periodically varied by the gauge in such a manner as to produce an approximately simple harmonic oscillation of temperature at the hot end, while the cool end is kept at a steady temperature.

This may be described as a simple harmonic oscillation whose amplitude diminishes asymptotically to zero according to the law ehlr.

In elliptic harmonic motion the velocity of P is parallel and proportional to the semi-diameter CD which is conjugate to the radius CP; the hodograph is therefore an ellipse similar to the actual orbit.

In the particular case where the motion is of the kind known as simple harmonic the disturbing force on the frame due to the reciprocation of the weight is equal to the component of the centrifugal force in the line of stroke due to a weight equal to the reciprocated weight supposed concentrated at the crank pin.

In balancing the mechanism of a steam engine it is often sufficiently accurate to consider the motion of the pistons as simple harmonic, and the effect on the framework of the acceleration of the connecting rod may be approximately allowed for by distributing the weight of the rod between the crank pin and the piston inversely as the centre of gravity of the rod divides the distance between the centre of the cross head pin and the centre of the crank pin.

The moving parts of the engine are then divided into two complete and independent systems, namely, one system of revolving weights consisting of crank pins, crank arms, &c., attached to and revolving with the crank shaft, and a second system of reciprocating weights consisting of the pistons, cross-heads, &c., supposed to be moving each in its line of stroke with simple harmonic motion.

The assumption that the pistons of an engine move with simple harmonic motion is increasingly erroneous as the ratio of the length of the crank r, to the length of the con oecting rod 1 increases.

In details of execution and harmonic combinations they illustrate the precision, logic, lucidity and cheerful spirit of the national genius.

This is a simple harmonic wave-line, whose mean distance from the axis is a, whose wave-length is lira, and whose amplitude is c. The internal pressure corresponding to this unduloid is as before p = T/a.

Whatever the deformation of the originally straight boundary of the axial section may be, it can be resolved by Fourier's theorem into deformations of the harmonic type.

Disturbances of the former kind lead to vibrations of harmonic type, whose amplitudes always remain small; but disturbances, whose wave-length exceeds the circumference, result in a greater and greater departure from the cylindrical figure.

The relative importance of two harmonic disturbances depends upon their initial magnitudes, and upon the rate at which they grow.

If, as before, the frequency be p7211, and a the radius of the sphere, we have p 2 =n(n-1)(n+2)P a3, (6) n denoting the order of the spherical harmonic by which the deviation from a spherical figure is expressed.

The cartesian equation, referred to the fixed diameter and the tangent at B as axes may be expressed in the forms x= a6, y=a(I -cos 0) and y-a=a sin (x/afir); the latter form shows that the locus is the harmonic curve.

Chandler afterwards made an important addition to the subject by showing that the motion was represented by the superposition of two harmonic terms, the first having a period of about 430 days, the other of one year.

Thomson's tide gauge, tidal harmonic analyser and tide predicter are famous, and among his work in the interest of navigation must be mentioned his tables for the simplification of Sumner's method for determining the position of a ship at sea.

A ray of light is reflected from this mirror and from another mirror which is rocked by a small motor driven off the same circuit, so that the ray has two vibratory motions imparted to it at right angles, one a simple harmonic motion and the other a motion imitating the variation of the current or electromotive force under test.

It has wit, economy and intellectual control, in a richly expressive harmonic idiom.

The polarized signal is recovered from the first harmonic at 40 kHz using lock-in amplifiers.

The Oxford Harmonic Society is a mixed voice choral society, based in Oxford, England with about 150 members.