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Those who have happened, like ourselves, to see the effect of passionate music and "deep-inwoven harmonics" upon the feeling of an idiot, we may conceive what we mean.
He draws an analogy from the production of music in which purely physical factors are concerned; the laws of harmonics account for all; but back of all is something that is not mechanical and chemical there is the mind of the composer, and the performers, and the auditors, and something that takes cognizance of the whole effect.
Just incidentally noticing the circumstance that the epoch we are describing witnessed the evolution of algebra, a comparatively abstract division of mathematics, by the union of its less abstract divisions, geometry and arithmetic a fact proved by the earliest extant samples of algebra, which are half algebraic, half geometric we go on to observe that during the era in which mathematics and astronomy were thus advancing, rational mechanics made its second step; and something was done towards giving a quantitative form to hydrostatics, optics, and harmonics.
The atoms and molecules in the wood and strings of the violin, as well as the sounds produced from them, are modes of motion or vibration. In order to bring forth musical and harmonious notes, the vibratory conditions of the physical elements of the violin must be in harmonious vibratory relationship with Nature's harmonics in the universe of sound.
We used to sit together on the wharfs down on the New York water-front, he with a bassoon and me with an oboe, and we'd blend minor keys in African harmonics a thousand years old until the rats would crawl up the posts and sit round groaning and squeaking like dogs will in front of a phonograph." Ardita roared. "How you can tell 'em!" Carlyle grinned. "I swear that's the gos "
After more than twenty-two centuries it still survives, a model of accuracy, perspicuity, and a standard of exact demonstration. This great geometer not only wrote on other mathematical topics, such as Conic Sections and Porisms, but there are imputed to him treatises on Harmonics and Optics, the latter subject being discussed on the hypothesis of rays issuing from the eye to the object.
The sweetness of tone, its melodiousness, its legatos, octaves, trills and harmonics all bear the mark of the individual who uses his strings like his vocal chords. When an artist is working over his harmonics, he must not be impatient and force purity, pitch, or the right intonation.
But God meant music; and we may, If we will keep our lives in tune, Hear the whole year sing roundelay, December answering June. God ever at his keyboard plays, Harmonics, right; and discords, wrong: "He that hath ears," and who obeys, May hear the mystic song.
Does any man in dying do more than, on a larger and more complete scale, what he has been doing on a small one, as the most essential factor of his life, from the day that he became "he" at all? When the note of life is struck the harmonics of death are sounded, and so, again, to strike death is to arouse the infinite harmonics of life that rise forthwith as incense curling upwards from a censer.
A slower theme follows in the tonic major; it is a jollificational air, dancing from the first violins with a bright use of harmonics. The first two themes return and end the picture. It adds to the usual instruments only the piccolo, the English horn, the tambourine, and triangle and cymbals. The slow introduction gives forth an original theme in the most approved and most fetching darky pattern.
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