On Sound and Atmospheric Vibrations, with the Mathematical Elements of Music: Designed for the Use of Students of the University |
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Page xv
... the compass of an Octave • 101. On the necessity for Temperament , in reference to long series of harmonics , and to the combination of different instruments . 242 247 253 SECTION X .. . ART . ON THE HUMAN ORGANS CONTENTS .: XV.
... the compass of an Octave • 101. On the necessity for Temperament , in reference to long series of harmonics , and to the combination of different instruments . 242 247 253 SECTION X .. . ART . ON THE HUMAN ORGANS CONTENTS .: XV.
Page 171
... , where 2C I = 7 , every trigonometrical term = + 1 . Thus we have an incidental proof of the theorem , 1 = 8 I I +++ + 2/3 + 80 } ) . 9 25 mental note . There are none of the even harmonics MUSICAL STRING STRUCK AT ITS CENTER . 171 83 83.
... , where 2C I = 7 , every trigonometrical term = + 1 . Thus we have an incidental proof of the theorem , 1 = 8 I I +++ + 2/3 + 80 } ) . 9 25 mental note . There are none of the even harmonics MUSICAL STRING STRUCK AT ITS CENTER . 171 83 83.
Page 172
... harmonics , depending on cos 2παι เ COS Amat , & c . , but there are all the odd harmonics . 76. Vibration of a string which has been pulled aside at an excentric point . Suppose , as an instance , the string to be plucked 31 4 aside at ...
... harmonics , depending on cos 2παι เ COS Amat , & c . , but there are all the odd harmonics . 76. Vibration of a string which has been pulled aside at an excentric point . Suppose , as an instance , the string to be plucked 31 4 aside at ...
Page 177
... harmonics ; and the series of sounds which reach the ear may not possess the character of N harmonics . The pleasurable character of the complex sound will MUSICAL STRINGS UPON A SOUNDING BOARD . 177.
... harmonics ; and the series of sounds which reach the ear may not possess the character of N harmonics . The pleasurable character of the complex sound will MUSICAL STRINGS UPON A SOUNDING BOARD . 177.
Page 183
... harmonic is sounded , there will be nodes at the distances and 31 4 4 ; when the second harmonic is sounded , there will be nodes at the distances 7 37 57 6 ' 6 6 ; and so on . 80. Theory for a pipe closed at one end and open at the ...
... harmonic is sounded , there will be nodes at the distances and 31 4 4 ; when the second harmonic is sounded , there will be nodes at the distances 7 37 57 6 ' 6 6 ; and so on . 80. Theory for a pipe closed at one end and open at the ...
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Algebra applied at-x bell Cambridge changes cloth coefficient College concord Crown 8vo density depending diatonic scale direction distance disturbance divergent wave dR dr dr² dx dx dx dy dz Edition elastic force elastic pressure experiments expression factor fcap function fundamental note give gravity harmonics Hence increased integral interval investigation key-note law of sines length Mathematical mètres motion musical note number of vibrations Octave ordinate organ-pipe original oscillating Partial Differential Equations pendulum pendulum-bob perfect Fifths periodical function pipe plane wave produced prong proportion quantity radius reed reed-tongue remarked represented scale shews similar sin ct solution specific gravity sphere string student Suppose surface theory tion tone tube tuning-fork velocity of sound vibrations of air vocal ligaments vowel-sound wave of air weight wire
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