A spectroscope may be compared to a mechanical harmonic analyser which when fed with an irregular function of one variable represented by a curve supplies us with the sine curves into which the original function may be resolved.
In the particular case where the motion is of the kind known as simple harmonic the disturbing force on the frame due to the reciprocation of the weight is equal to the component of the centrifugal force in the line of stroke due to a weight equal to the reciprocated weight supposed concentrated at the crank pin.
Some sections of the latter, especially those on the connexion between music and architecture, the scale of harmonic proportions, and the Greek use of bronze vases to reverberate and strengthen the actors' voices in the theatre, are now almost wholly unintelligible.
The last two examples at the end of the article on Harmony show almost all that is new in Wagner's harmonic principles.
Moreover, the opening theme is formed of slow arpeggios; and the more modern harmonic elements, though technically chromatic, consist, from the modern point of view, rather in swift changes between nearly related keys than in chromatic blurring of the main key.
A similar method has frequently been applied to the study of variations of soil-temperatures by harmonic analysis of the annual waves.
When the harmonic is sounded the riders at the loops are thrown off, while those at the nodes remain seated.
This may be described as a simple harmonic oscillation whose amplitude diminishes asymptotically to zero according to the law ehlr.
Those instruments of which the tones and compass are most suitable for polyphonic melody are for the most part high in pitch; a circumstance which, in conjunction with the practice (initiated by the monodists and ratified by science and common sense) of reckoning chords upwards from the bass, leads to the conclusion that the instruments which hold the main threads in the design shall be supported where necessary by a simple harmonic filling-out on some keyed instrument capable of forming an unobtrusive background.
Discords must not be taken unprepared, because a singer can only find his note by a mental judgment, and in attacking a discord he has to find a note of which the harmonic meaning is at variance with that of other notes sung at the same time.