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The woman who talked of the sentimentalist's 'fiddling harmonics, herself stressed the material chords, in her attempt to escape out of herself and away from her pursuer. Meanwhile she was as little conscious of what she was doing as of how she appeared. Arthur went about with the moony air of surcharged sweetness, and a speculation on it, alternately tiptoe and prostrate.
"I have found out that by uttering the true inner name of anything I can set in motion harmonics harmonics, note well, half the wave length and twice the frequency! that are delicate and swift enough to insert themselves between the whirling molecules of any reasonable object any object, I mean, not too closely or coherently packed.
'I know thee by name, said Jehovah to the great Hebrew magician, 'and thou art mine. By certain rhythms and vibratory modulations of the voice it is possible to produce harmonics of sound which awaken the inner name into life and then to spell it out.
With octaves and tenths I have never had any trouble: I have a broad hand and a wide stretch, which accounts for it, I suppose. "Then there are harmonics, flageolets I, have never been able to understand why they should be considered so difficult! I never think of harmonics as 'harmonics, but try to give them just as much expressive quality as the notes of any other register.
Natural harmonics may be formed on the major triad of each open string, using the open string as the tonic. Where does the harmonic sound in each case? Two octaves and a third higher ; two octaves higher ; one octave and a fifth higher respectively, than the pressed-down note. If the harmonic on the octave were played, it would sound just an octave higher than the pressed-down note.
It is a very beautiful embellishment, and one much used; one finds it in Beethoven, Mendelssohn, Brahms, etc. "Double notes never seemed hard to me, but harmonics are not as easily acquired as some of the other violin effects. I advise pressing down the first finger on the strings inordinately, especially in the higher positions, when playing artificial harmonics.
There are three ways of taking the C before mentioned as an artificial harmonic. Now we have to combine the C and E as well as we are able. Rejecting the following combinations as impossible any violinist will see why "With regard to the actual execution of these harmonics, I advise all students to try and play them with every bit as much expressive feeling as ordinary notes.
Kepler was evidently transported with delight and wrote, "What I prophesied two and twenty years ago, as soon as I discovered the five solids among the heavenly orbits, what I firmly believed long before I had seen Ptolemy's 'Harmonics' what I had promised my friends in the title of this book, which I named before I was sure of my discovery, what sixteen years ago I urged as a thing to be sought, that for which I joined Tycho Brahe, for which I settled in Prague, for which I have devoted the best part of my life to astronomical computations, at length I have brought to light, and have recognised its truth beyond my most sanguine expectations.
The discovery of the third law was not effected until, several years afterwards, Kepler announced it to the world in his treatise on Harmonics . The passage quoted below is extracted from that work. Translator.
On the contrary, his passion for learning seemed to increase with the diminution of the time available for its gratification. He studied Italian, Greek, mathematics; Maclaurin's Fluxions served to "unbend his mind"; Smith's Harmonics and Optics and Ferguson's Astronomy were the nightly companions of his pillow. What he read stimulated without satisfying his intellect.
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