## Harmonic Sentence Examples

- Are the amplitudes of the component
**harmonic**waves of periods 24, 12, 8 and 6 hours; al, a2, a 3, a 4, are the corresponding phase angles. - There is some reason to hope that the day of these misconceptions is passed; although there is also some reason to fear that on other grounds the present era may be known to posterity as an era of instrumentation comparable, in its gorgeous chaos of experiment and its lack of consistent ideas of harmony and form, only to the monodic period at the beginning of the 17th century, in which no one had ears for anything but experiments in
**harmonic**colour. - Discords must not be taken unprepared, because a singer can only find his note by a mental judgment, and in attacking a discord he has to find a note of which the
**harmonic**meaning is at variance with that of other notes sung at the same time. - Moreover, the opening theme is formed of slow arpeggios; and the more modern
**harmonic**elements, though technically chromatic, consist, from the modern point of view, rather in swift changes between nearly related keys than in chromatic blurring of the main key. - Those instruments of which the tones and compass are most suitable for polyphonic melody are for the most part high in pitch; a circumstance which, in conjunction with the practice (initiated by the monodists and ratified by science and common sense) of reckoning chords upwards from the bass, leads to the conclusion that the instruments which hold the main threads in the design shall be supported where necessary by a simple
**harmonic**filling-out on some keyed instrument capable of forming an unobtrusive background. - But, when we look at the many passages in which the violas double the basses, we shall do well to consider whether there is room in the
**harmonic**scheme for the violas to do anything else, and whether the effect would not be thin without them. - A subject so vast and so incapable of classification cannot be discussed here, but its aesthetic principles may be illustrated by the extreme case of the trumpets and horns, which in classical times had no scale except that of the natural
**harmonic**series. - In another party line system a
**harmonic**principle is employed: the ringing machines deliver alternating currents of four frequencies, while each bell is constructed to operate at a particular frequency only. - In mathematics, he was the first to draw up a methodical treatment of mechanics with the aid of geometry; he first distinguished
**harmonic**progression from arithmetical and geometrical progressions. - Apart from the gain in tragic force resulting from Wagner's masterly development of the character of Brangaene, the raw material of the story was already suggestive of that astounding combination of the contrasted themes of love and death, the musical execution of which involves a
**harmonic**range almost as far beyond that of its own day as the ordinary**harmonic**range of the 19th century is beyond that of the 16th. - Its
**harmonic**style is, except in the Grail music, even more abstruse than in Tristan; and the intense quiet of the action is far removed from the forces which in that tumultuous tragedy carry the listener through every difficulty. - But elsewhere there are few passages in which the extremely recondite
**harmonic**style can be with certainty traced to anything but habit. - In Wagner's
**harmonic**style we encounter the entire problem of modern musical texture. - The last two examples at the end of the article on Harmony show almost all that is new in Wagner's
**harmonic**principles. - 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. - Haydn uses a true Straussian discord in The Seasons, in order to imitate the chirping of a cricket; but the harshest realism in Gatterdammerung (the discord produced by the horns of Hagen and his churls in the mustering-scene in the second act) has a
**harmonic**logic which would have convinced Corelli. - 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. - Under the general heading "Analysis" occur the subheadings "Foundations of Analysis," with the topics theory of functions of real variables, series and other infinite processes, principles and elements of the differential and of the integral calculus, definite integrals, and calculus of variations; "Theory of Functions of Complex Variables," with the topics functions of one variable and of several variables; "Algebraic Functions and their Integrals," with the topics algebraic functions of one and of several variables, elliptic functions and single theta functions, Abelian integrals; "Other Special Functions," with the topics Euler's, Legendre's, Bessel's and automorphic functions; "Differential Equations," with the topics existence theorems, methods of solution, general theory; "Differential Forms and Differential Invariants," with the topics differential forms, including Pfaffians, transformation of differential forms, including tangential (or contact) transformations, differential invariants; "Analytical Methods connected with Physical Subjects," with the topics
**harmonic**analysis, Fourier's series, the differential equations of applied mathematics, Dirichlet's problem; "Difference Equations and Functional Equations," with the topics recurring series, solution of equations of finite differences and functional equations. - 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 . - 0= {(n +I)Ar" - where P. denotes the zonal
**harmonic**of the nth order; also, in the exceptional case of =Ao cos 0, 4) = Ao/r; 4'= Bor, 49 = - Bo log tan 2B sh - lx/y. - This work included the "Logometria," the trigonometrical theorem known as "Cotes' Theorem on the Circle" (see TRIGONOMETRY), his theorem on
**harmonic**means, subsequently developed by Colin Maclaurin, and a discussion of the curves known as "Cotes' Spirals," which occur as the path of a particle described under the influence of a central force varying inversely as the cube of the distance. - 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. - Any periodic curve may be resolved into sine or
**harmonic**curves by Fourier's theorem. - It follows from this that any periodic disturbance in air can be resolved into a definite series of simple
**harmonic**disturbances of wave-lengths equal to the original wave-length and its successive submultiples, and each of these would separately give the sensation of a 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
are most readily heard if we fortify the ear by an air cavity with a natural period equal to that of the**harmonics****harmonic**to be sought. - If the
**harmonic**corresponding to the resonator is present its tone swells out loudly. - 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
may be easily obtained by touching the string at the first node of the**harmonics****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. - 36, for the fundamental and the first
**harmonic**. When a string is struck or bowed at a point, any**harmonic**with a node at that point is absent. - 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. - (2) On the arithmetic, geometric and
**harmonic**means between two straight lines, and the problem of representing all three in one and the same geometrical figure. - The three commonest means are the arithmetical, geometrical, and
**harmonic**; of less importance are the contraharmonical, arithmetico-geometrical, and quadratic. - A similar method has frequently been applied to the study of variations of soil-temperatures by
**harmonic**analysis of the annual waves.