��mitted to the force of the wind, and in conse- quence we hear lower or higher notes in com- binations of concord or dissonance, as the strings vibrate in longer or shorter sections due to the less or greater power of the wind, and its point of impact on the string. 1 The pulsations known as Beats, which may be heard by touching and holding down almost any key of a pianoforte not recently tuned, affect the ear by their fre- quency. If unapparent or nearly so, Helmholtz characterises the sound as 'continuous,' if per- ceptibly apparent as 'discontinuous,' and while continuity is harmonious and gratifies the ear, discontinuity is discordant and more or less pains the ear according to the frequency of the disconnection. Now the prime and upper partials which in strings, narrow tubes, reeds and the human voice form a musical note, proceed in a regular succession, the Arithmetical Progression of i, 2, 3, 4, 5, 6, etc. This succession may also be expressed in ratios which show by fractions the vibrating divisions of the string. We express the same succession by Unison, Octave, Twelfth, Double Octave, etc. Up to 8, which is the Third Octave from the Prime or Fundamental, the successive combination of these increasing divisions of the string (or of the air column) is sufficiently continuous or free from prominent beats to satisfy the ear as harmonious, but that point passed, the greater frequency of beats caused by the increasing nearness of the suc- cessive partials causes a disagreeable sensation which is extreme when a string vibrating in 1 2 sections and another vibrating in 13, are sound- ing together. The reader must take for granted that for simple tones the particles vibrate like the bob of a pendulum. For compound tones the form of the vibration is very different. The particular form in any case depends upon the number and intensity of the partials or simple tones of which it is compounded, and produces the effect called quality of tone. There is another circumstance called 'phase,' depending upon the points of their vibrations in which two partials coincide, when compounded ; this alters the form of vibration in the compound tone, but has no perceptible effect on its quality.
We have so far touched upon the voice, and those instruments of strings, reeds, and narrow pipes which may have a regular series of harmonic proper tones ; there are however irregular causes of musical or partially musical sound with inhar- monic proper tones, not following an arithmetical order of succession : among these are wide pipes, stretched membranes (as drums), plates (as gongs), elastic rods (as tuning-forks), and the various metal and wooden harmonicas. The use of nearly all these varieties is in consequence much restricted in our modern European music. As to Resonance, any elastic body fastened so as to be permitted to vibrate will have its own proper tones, and will respond sympathetically to
i The peculiar, touching, character of the jEolian harp harmony is determined by the frequent presence of the Harmonic Seventh, an interval rejected la our music and replaced by sharper dissonant sevenths oi on entirely different tone character.
the influence of other periodic vibrations, as may be commonly observed with violins, pianofortes, harps, and other stringed instruments, where the comparatively faint sound of the strings is materially reinforced by the responsive sound- board.
In many wind instruments the phenomena of Harmonics become of the first importance. In these they are caused by increase of pressure or force of blowing; and, in point of fact, as each higher note is gained by the rejection of a lower factor of sound, the quality of each note changes and gains in brilliancy as it ascends in pitch. In stringed instruments it is sufficient to touch the vibrating string gently with the finger, to damp all those simple vibrations which have segmental curves or loops at the point touched ; while at the apparent resting-places from vibration which are called nodes, the simple vibrations meeting there continue to sound with undiminished loud- ness. The quality is changed from the full sound- ing note ; the vibrating complex being simpler, sounds sweeter and purer, until in the very highest harmonics the difference to the ear be- tween string and wind seems almost lost. The greater consistency of metal assists the mainten- ance of a state of vibrating motion once assumed, and from this what we characterise as metallic tone is the comparatively steady lasting of the high upper partial tones, but with the possible fault of becoming tinkling. In the less elastio mass of wood, the upper partials rapidly die away. Unless this decrease be too rapid the ear delights in the greater prominence gained for the prime and its nearer upper partials. If too rapid we characterise the tone as woody.
In the Pianoforte we meet with the readiest application of the terms 'metallic ' and ' woody.' Modern pianos, where the framing which holds the strings and bears their draught is of iron, frequently have a ' metallic ' tone from the higher elasticity of the framing, which being metal does not allow the high upper partials of the string to die away so eoon as they did in the older pianos of iron and wood or of wood alone, the inferior elasticity of which permitted them to become extinct sooner and the string to pass more quickly into longer segments of vibration. The extreme influence of metal may be to main- tain a ' ringing ' or even a ' tinkling ' tone ; from the wood we get a 'dull' or 'woody' quality. There are however other conditions to be pre- sently referred to. To show the strength of the octave harmonic in a good pianoforte you will rarely find the tuner adjust the pitch note C (a) to its corresponding tuning-fork. He prefers the middle C (5) an octave lower, because its first upper partial (c) beats, for a certain space of tune, more
(a) (6) (c)
��I distinctly with the fork than the fundamental with
- which it is in unison. The scheme of strengthening
the octave harmonic by an additional octave string
is certainly a work of supererogation 1 But one