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increased pressure of breath and tension of lips, harmonics could be obtained.

10The successive terms of (21) are called the harmonics of the first term.

10increased pressure of breath and tension of lips, harmonics could be obtained.

10His last publication, which appeared in 1878, was on spherical harmonics (Beitreige zur Theorie der Kugelf unctionen) .

00For the subjects of this heading see the articles DIFFERENTIAL EQUATIONS; FOURIER'S SERIES; CONTINUED FRACTIONS; FUNCTION; FUNCTION OF REAL VARIABLES; FUNCTION COMPLEX; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; MAXIMA AND MINIMA; SERIES; SPHERICAL HARMONICS; TRIGONOMETRY; VARIATIONS, CALCULUS OF.

00Gauss in particular employed it in the calculation of the magnetic potential of the earth, and it received new light from Clerk Maxwell's interpretation of harmonics with reference to poles on the sphere.

00Some curious effects were observed in the formation of harmonics in the rear of the primary tone used.

00It may, however, be stated here that certain experiments of Helmholtz appear to show that the epoch of the harmonics has not much effect on the quality.

00Now we may resolve these trains by Fourier's theorem into harmonics of wave-lengths X, 2X, 3A, &c., where X=2AB and the conditions as to the values of y can be shown to require that the harmonics shall all have nodes, coinciding with the nodes of the fundamental curve.

00If then we resolve Ahbkc into harmonics by Fourier's theorem, we may follow the motion of the separate harmonics, and their superposition will give the form of the string at any instant.

00Further, the same harmonics with the same amplitude will always be present.

00But 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.

00The whole series forms the series of odd harmonics.

00The whole series of fundamental and overtones gives the complete set of harmonics of frequencies proportional to 1, 2, 3, 4, ..., and wave-lengths proportional to 1, 2, 3, 4 ..

00The complete series of harmonics FIG.

00Each 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.

00Since the quality of the note sounded depends on the mixture of harmonics, the quality therefore is to some extent dependent on the point of excitation.

00Thus, suppose a fundamental 256 has present with it overtone harmonics 512, 768, 1024, 1280, &c., and that we sound with it the major seventh with fundamental 480, and having harmonics 960, 1440, &c. The two sets may be arranged thus c 256 512 768 1024 1280 h 480 960 1440, and we see that the fundamental of the second will beat 32 times per second with the first overtone of the first, giving dissonance.

00See also Spherical Harmonics.) Geodesy.

00The third volume includes, however, some theological treatises, and the first part of it is occupied with editions of treatises on harmonics and other works of Greek geometers, some of them first editions from the MSS., and in general with Latin versions and notes (Ptolemy, Porphyrius, Briennius, Archimedes, Eutocius, Aristarchus and Pappus).

00The remarkable connexion between Bessel's functions and spherical harmonics was established in 1868 by F.

00For the mathematical investigation see Spherical Harmonics and for tables see Table, Mathematical.

00Aristotle also formed his Peripatetic school into a kind of college with common meals under a president (6tpxcov) changing every ten days; while the philosopher himself delivered lectures, in which his practice, as his pupil Aristoxenus tells us (Harmonics, ii.

00Aristoxenus, at the beginning of the second book of the Harmonics,, gives a graphic account of the astonishment caused by these lectures, of Plato, and of their effect on the lectures of Aristotle.

00It may be imagined further that, when he established himself at the Academy, his first care was to draw up a scheme of education, including arithmetic, geometry (plane and solid), astronomy, harmonics and dialectic, and that it was not until he had arranged for the carrying out of this programme that he devoted himself to the special functions of professor of philosophy.

00He showed, both by analysis and by synthesis, that quality depends on the order, number and intensity of the overtones or harmonics that may, and usually do, enter into the structure of a musical tone.

00The long vault has a certain keynote of its own, which, when firmly struck, excites harmonics, including tones of incredible depth and sweetness.

00To how many sad hearts did he come like an angel, with the rich tones of his voice waking harmonics of hope, where before there had been despair and silence?

00The harmonics of the string vibrations were supposed to correspond to the observed hadrons.

00Subjects with " absolute pitch " can resolve high-order harmonics.

00A non-linear amplifier will generate harmonics that are not present in the original signal.

00The leathered lips resulted in vaguely defined broad impulses being delivered to the air column in the pipe, such impulses containing fewer harmonics.

00harmonics produced at the same time as the fundamental.

00The current state of the art makes use of spherical harmonics.

00Envelope amplitude modulation occurs in cochlear filtered speech because of unresolved harmonics.

00Square Wave: A symmetrical rectangular waveform which contain a series of odd harmonics.

00The SAI pulses associated with the higher harmonics are relatively narrow with respect to the changes in period during the pitch glide.

00However they could vibrate at much lower harmonics, which could feasibly give rise to a low frequency hum.

00The ratio of odd to even harmonics (or half to full harmonics ).

00The album begins with a loop of guitar harmonics, into which a drum kicks in, then the vocal.

00This was at the fundamental frequency and/or low-order harmonics, not the high frequencies of noise.

00harmonics of the electron cyclotron frequency.

00matrixrotation matrices for the real harmonics are obtained from those of the complex ones.

00The last movement begins with overblown harmonics using piccolos and bass & contra bass flutes.

00rotation matrices for the real harmonics are obtained from those of the complex ones.

00spherical harmonics.

00A brief climax slowly brings the music to a calm, rapt end, with the solo violin musing in glistening harmonics.

00His last publication, which appeared in 1878, was on spherical harmonics (Beitreige zur Theorie der Kugelf unctionen) .

00Love has shown that the great features of the relief of the lithosphere may be expressed by spherical harmonics of the first, second and third degrees, and their formation related to gravitational action in a sphere of unequal density.'

00For the subjects of this heading see the articles DIFFERENTIAL EQUATIONS; FOURIER'S SERIES; CONTINUED FRACTIONS; FUNCTION; FUNCTION OF REAL VARIABLES; FUNCTION COMPLEX; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; MAXIMA AND MINIMA; SERIES; SPHERICAL HARMONICS; TRIGONOMETRY; VARIATIONS, CALCULUS OF.

00He further treated in a masterly manner of echoes and the mixture of sounds, and explained the phenomenon of grave harmonics as due to the occurrence of beats so rapid as to generate a musical note.

00The expressions designated by Dr Whewell, Laplace's coefficients (see Spherical Harmonics) were definitely introduced in the memoir of 1785 on attractions above referred to.

00Gauss in particular employed it in the calculation of the magnetic potential of the earth, and it received new light from Clerk Maxwell's interpretation of harmonics with reference to poles on the sphere.

00It is known (see Spherical Harmonics) that The maxima of C occur when d Ji(z) _Ji'(z) J1(z) =o; z) z z2 or by (17 when J2(z) =0.

00Some curious effects were observed in the formation of harmonics in the rear of the primary tone used.

00The successive terms of (21) are called the harmonics of the first term.

00It may, however, be stated here that certain experiments of Helmholtz appear to show that the epoch of the harmonics has not much effect on the quality.

00Now we may resolve these trains by Fourier's theorem into harmonics of wave-lengths X, 2X, 3A, &c., where X=2AB and the conditions as to the values of y can be shown to require that the harmonics shall all have nodes, coinciding with the nodes of the fundamental curve.

00If then we resolve Ahbkc into harmonics by Fourier's theorem, we may follow the motion of the separate harmonics, and their superposition will give the form of the string at any instant.

00Further, the same harmonics with the same amplitude will always be present.

00Using the term " note " for the sound produced by a periodic disturbance, there is no doubt that a well-trained ear can resolve a note into pure tones of frequencies equal to those of the fundamental and its harmonics.

00But 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.

00The whole series forms the series of odd harmonics.

00The whole series of fundamental and overtones gives the complete set of harmonics of frequencies proportional to 1, 2, 3, 4, ..., and wave-lengths proportional to 1, 2, 3, 4 ..

00The complete series of harmonics FIG.

00Each 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.

00Not only may the fundamental and its harmonics be obtained separately, but they are also to be heard simultaneously, particularly the earlier ones, which are usually more prominent than those higher in the series.

00Since the quality of the note sounded depends on the mixture of harmonics, the quality therefore is to some extent dependent on the point of excitation.

00Robert Smith (Harmonics, 2nd ed., 1 759, p. 95) states that Sauveur " inferred that octaves and other simple concords, whose vibrations coincide very often, are agreeable and pleasant because their beats are too quick to be distinguished, be the pitch of the sounds ever so low; and on the contrary, that the more complex consonances whose vibrations coincide seldom are disagreeable because we can distinguish their slow beats; which displease the ear, says he, by reason of the inequality of the sound.

00Thus, suppose a fundamental 256 has present with it overtone harmonics 512, 768, 1024, 1280, &c., and that we sound with it the major seventh with fundamental 480, and having harmonics 960, 1440, &c. The two sets may be arranged thus c 256 512 768 1024 1280 h 480 960 1440, and we see that the fundamental of the second will beat 32 times per second with the first overtone of the first, giving dissonance.

00See also Spherical Harmonics.) Geodesy.

00The third volume includes, however, some theological treatises, and the first part of it is occupied with editions of treatises on harmonics and other works of Greek geometers, some of them first editions from the MSS., and in general with Latin versions and notes (Ptolemy, Porphyrius, Briennius, Archimedes, Eutocius, Aristarchus and Pappus).

00The remarkable connexion between Bessel's functions and spherical harmonics was established in 1868 by F.

00For the mathematical investigation see Spherical Harmonics and for tables see Table, Mathematical.

00Aristotle also formed his Peripatetic school into a kind of college with common meals under a president (6tpxcov) changing every ten days; while the philosopher himself delivered lectures, in which his practice, as his pupil Aristoxenus tells us (Harmonics, ii.

00Aristoxenus, at the beginning of the second book of the Harmonics,, gives a graphic account of the astonishment caused by these lectures, of Plato, and of their effect on the lectures of Aristotle.

00v., on public buildings, has a preface on the theories of Pythagoras, &c. Its twelve chapters treat - (t) of fora and basilicae, with a description of his own basilica at Fanum; (2) of the adjuncts of a forum (aerarium, prison and curia); (3) of theatres, their site and construction; (4) of laws of harmonics; (5) of the arrangement of tuned bronze vases in theatres for acoustic purposes; (6) of Roman theatres; (7) of Greek theatres; (8) of the selection of sites of theatres according to acoustic principles; (9) of porticus and covered walks; (to) of baths, their floors, hypocausts, the construction and use of various parts; (ii) of palaestrae, xysti and other Greek buildings for the exercise of athletes; (12) of harbours and quays.

00It may be imagined further that, when he established himself at the Academy, his first care was to draw up a scheme of education, including arithmetic, geometry (plane and solid), astronomy, harmonics and dialectic, and that it was not until he had arranged for the carrying out of this programme that he devoted himself to the special functions of professor of philosophy.

00He showed, both by analysis and by synthesis, that quality depends on the order, number and intensity of the overtones or harmonics that may, and usually do, enter into the structure of a musical tone.

00The long vault has a certain keynote of its own, which, when firmly struck, excites harmonics, including tones of incredible depth and sweetness.

00To how many sad hearts did he come like an angel, with the rich tones of his voice waking harmonics of hope, where before there had been despair and silence?

00Harrison did not, for example, recast the Great mixture as a Harmonics, or revoice the great reeds as trombas.

00Analysis of nonlinearities of plasma harmonics and sideband noise which are uniquely related to dynamic complex impedance and chemistry.

00Be able to demonstrate the physical significance of closed shells by using plots of the spherical harmonics.

00A brief climax slowly brings the music to a calm, rapt end, with the solo violin musing in glistening harmonics.

00There are various abbreviated instructions for techniques such as harmonics, slides, etc. to aid the player in recreating the sound as authentically as possible.

00These slight variations apply to all kinds of picking techniques (pinch harmonics, pick slides, flat picking, etc.) so it's almost like playing an entirely new guitar when you first try a titanium guitar pick.

00Hedges would hammer-on bass lines with his left hand while inducing slap harmonics with the right hand, creating a beautiful, layered sound that defied labels.

00However, the video game guitar tabs notation can help with a few techniques to assist you with your music piece, like hammer ons and pull offs, slides, string bends, vibrato and harmonics.

00Not only may the fundamental and its harmonics be obtained separately, but they are also to be heard simultaneously, particularly the earlier ones, which are usually more prominent than those higher in the series.

01v., on public buildings, has a preface on the theories of Pythagoras, &c. Its twelve chapters treat - (t) of fora and basilicae, with a description of his own basilica at Fanum; (2) of the adjuncts of a forum (aerarium, prison and curia); (3) of theatres, their site and construction; (4) of laws of harmonics; (5) of the arrangement of tuned bronze vases in theatres for acoustic purposes; (6) of Roman theatres; (7) of Greek theatres; (8) of the selection of sites of theatres according to acoustic principles; (9) of porticus and covered walks; (to) of baths, their floors, hypocausts, the construction and use of various parts; (ii) of palaestrae, xysti and other Greek buildings for the exercise of athletes; (12) of harbours and quays.

01

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