the things of the senses, will rejoice to find, at every step of the way in which music handles numbers, expressions of deep mysteries which are not discerned but by the spiritual sight.
Since Felix Savart and Chladni and Helmholtz and Tyndal, and others, have studied the notes of our diatonic scale by the aid of such instruments as mechanical art has put into the hands of science in these last days, we have come to have a much more perfect understanding of music in its acoustical domain, and have been given to behold the beautiful mathematical measurements which Nature has applied in the marshalling of this host of the lower heavens; and which may suggest similar, though grander, and probably more complicated rhythms and harmonies in the astral heavens far off.
Different writers have put forth different views of what constitute a musical vibration, but their various views do not make any difference in the ratios which the notes of this sound-host bear to each other. Whether the vibrations be counted as single or double vibrations, the ratios of their relative motions are the same. Nevertheless, a musical vibration is an interesting thing in itself, and ought to be correctly defined.
A string when vibrating musically is passing and re-passing the central line of its rest or equilibrium with a certain range of excursion. Some writers have defined a vibration to be the passage of the string from one extreme of its excursion to the other, while some have preferred to define it as the passage of the string from the one extreme of its excursion to the other and back again. D. C. Ramsay has been led in his researches to define a vibration as the movement of the string from its central line of rest to the extreme of its excursion on one side, and back to the central line of rest; and from the central line of rest to the extreme of its excursion on the other side, and back again to the "right line," as he calls it, as a second vibration. His reasoning on this will be seen in what follows.1
1 See illustration, Fig. 3, Plate IV.
See Also
8.20 - Law of Sympathetic Oscillation
Center of Oscillation
co-oscillation
co-vibration
Differential Oscillation
double vibration
Figure 8.11 - Four Fundamental Phases of a Wave
Figure 8.9 - Four Fundamental Motions of a Pendulum
Law of Oscillating Atomic Substances
Law of Variation of Atomic Oscillation by Sono-thermism
Law of Variation of Pitch of Atomic Oscillation by Pressure
laws of oscillatory and vibratory motions
MOLECULAR OSCILLATING FREQUENCY
molecular oscillation
oscillate
oscillating proximately
oscillating range of motion
Oscillation
oscillatory motion
Pendulum Oscillation
Proximate Oscillation
Ramsay - PLATE IV - Oscillation and Vibration
Ramsay - PLATE V - Proximate and Differential Oscillations
Ramsay - The Marshalling of the Host of the Lower Heavens21
Ramsay - The New Way of Reckoning a Pendulum Oscillation
Ramsay - The New Way of Reckoning a Vibration
single vibration
Sympathetic Oscillation
Table 13.02 - Vibratory and Oscillatory Triple Force Functions
TREXNONAR MEASUREMENT OF MOLECULAR OSCILLATING FREQUENCIES
vibration