The behavior of single piano strings struck in their normal positions was investigated through measurement of the frequencies of the partials and their amplitudes as functions of time after striking. Three-dimensional figures showing partial amplitudes versus time are presented. The frequencies of the partials of the tone were found to be those of the normal modes of vibration and are therefore referred to as the modal frequencies of the string. The higher modal frequencies are progressively sharp with respect to true harmonics of the fundamental; the sharpening follows approximately a square law with respect to mode number, to the extent that in one case the 15th partial had just about the frequency of a 16th harmonic. The resulting inharmonicity in piano strings is least in the two octaves below middle C; it rises sharply at the high end and more or less sharply at the low end, depending upon the type of piano. A correlation between inharmonicity and subjective tone quality rating is suggested. It is shown that the commonly observed “stretched” tuning (sharpening of the treble, flattening the bass) is a natural consequence of the inharmonicity.
The behavior of single struck strings in their normal positions was investigated through measurement of the frequencies and amplitudes of their partials as functions of time after striking. Three-dimensional figures showing partial amplitudes versus time are presented. The frequencies of the partials of the tone were found to be essentially independent of striking force and time after striking, and directly identifiable with the modal frequencies of the string. The higher modal frequencies are progressively sharp with respect to true harmonics of the fundamental; for a particular string the sharpening follows approximately a square law with respect to modal number. The resulting inharmonicity in the tone is least in the two octaves below middle C, rises sharply at the high end and more or less sharply at the low end, depending upon the type of piano. A correlation between inharmonicity and subjective tone quality rating is suggested, and the effect of inharmonicity upon piano tuning is discussed.
Using the method of in vivo magnetic resonance spectroscopy we examined 17 patients with moderately advanced chronic renal insufficiency, 21 patients with chronic renal failure treated by haemodialysis, and 15 dialyzed patients with symptomatic renal osteopathy. The ratios of intracellular phosphocreatine and inorganic phosphate concentrations of these subjects measured at rest were compared with those found in healthy controls. While we noted significantly lower (p < 0.01) ratio values in all patients, subjects with osteopathy showed a lower value than dialyzed patients free of bone disease. Haemodialysis improved the result of examination in 7 patients. The results can be summarized as follows: (1) patients with altered renal function have significantly impaired energy metabolism of skeletal muscle, and (2) the disorder is more severe in patients with renal osteopathy than in those free of it.
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