Harmonica

“ A in alto; and see what a leap he will make to find it on the first string, and what a horrible screech he will bring out after all, when he might produce the note in the most perfect tune and tone by only touching the second open string that he is on already, harmonically at a fourth of the way from the head to the bridge, or at the same place that he would stop D on the second string.’
[Pg 145]
MELODY AND HARMONY [64] . THE object and end of all music is the expression and excitement of passion, of which its notes are the signs. ”

“ The Method herein proposed and followed, is to accompany the voice of the student, whether he be singing the diatonic or chromatic scales, the different intervals, or melodies of any kind, with a full harmony, in which as many ‘varied modulations are introduced as possible, in order to familiarize his ear with every harmonical combination, so that no transition, however abrupt, may take him by surprise.’— (Preface.)
There is no novelty in all this, we can assure the author; every good master has pursued the same plan. We grant that the number of such masters is not very great ”

“ To flat a flatted degree, use a double flat. Fig. 22.
6. To flat a sharped degree, use a natural. Fig. 23.
[Listen]
27. When two different notations represent the same pitch, the word enharmonic is applied. Thus we may say that F sharp and G flat (on keyboard instruments at least) are enharmonically the same.
This word enharmonic is used in such expressions as enharmonic change, enharmonic keys, enharmonic interval, enharmonic modulation, enharmonic relation, etc., and in all such combinations it has the same meaning, viz.—a change in notation but no change in the pitch represented. ”

“ HARMONICS, tones of higher pitch which accompany every perfect musical sound in a regular series. As they ascend they diminish in intensity, and approximate in pitch. If the piano be opened and a note—say D in the bass—be struck smartly and kept down, on listening attentively a succession of faint sounds will be heard, apparently rising out of the principal sound and floating round it. These are the harmonics. They are really constituents of the main musical tone, and are produced by the concurrent vibration of the aliquot parts of the string. ”

“ The theory of harmonies in optics is the same as in acoustics, the same as in everything—it is based on simplicity. Those colors, like those notes, the number of whose vibrations or waves in the same time bear some simple ratio to each other, are harmonious; an absolute equality produces unison; and a group of harmonies is melody both in music and in color. At this point we cannot but hint at the analogy already discovered between the elements of music and the elements of form. ”

“ Colored stuffs will sing in lights of different colors, but refuse to sing in others. The polarization of light being now accomplished, light and sound are known to be alike. Flames have a modulated voice and can be made to sing a definite melody. Wood, stone, metal, skins, fibers, membranes, every rapidly vibrating substance, all have in them the potentialities of musical sound.
"Radium receives its energy from, and responds to, radiations which traverse all space—as piano strings respond to sounds in unison with their notes. Space is all a-quiver with waves of radiant energy. ”

“ But since the seventeenth century our conception of music has gradually, from melodic, become harmonic; we hear vertically as well as horizontally; we hear the beauty of all chords as sounded together, and, unconsciously, we fill in the harmonies to every melody we hear. It would have been natural if the keyed instruments had adapted themselves to this altered musical conception, and had resigned the original conception of the scale to make way for harmonic conveniences. ”

“ They sound ethereal and flute-like. There are two kinds of harmonics: natural harmonics and artificial harmonics. The natural harmonics are found on the open strings at certain definite places. There are five of these on each string. The artificial harmonics are produced by stopping the string with one finger and touching it lightly with another. These harmonics are harder to master; and they are a great worry to a violinist, because if his violin gets out of tune (drops a little from the heat of a concert hall, perhaps) the proper harmonics cannot be played. ”

“ I shrugged. "It might be distracting."
"Captain, take my word for it," argued Farley. "Constant sonic feedback inside a spacesuit will set you rocking against the grain."
"Devise some regular system of interruptions," I suggested.
"Then the pattern will drive you crazy. Maybe in a few months, with luck, I could plan some harmonic scale you could tolerate—"
"We don't have a few months," I said. "How about music? There's a harmonic scale for you, and we can endure it, some of it. ”

“ Surely, it would be wiser to limit ourselves in our accompaniments to those harmonies which are as independent of “period” as the tunes themselves, for example, those of the diatonic genus, which have formed the basis and been the mainstay of harmonic music throughout its history, and upon which musicians of every age and of every school have, in greater or less degree, depended; and further, seeing that the genuine folk-air never modulates, never wavers from its allegiance to one fixed tonal centre, to avoid modulation, or use it very sparingly. ”

“ Again, the diatonic major scale is regarded by many musicians as the natural order of intervals on which the [Pg 231] compositions must be founded whenever the art of music has attained to a high degree of development, and which will therefore be universally adopted in the course of time. They form this opinion especially from the laws of Acoustics, since the intervals constituting the diatonic major scale are those which as harmonics stand in the most simple relation to the fundamental tone produced by a vibrating body. ”

“ The harmonic structure requires to be clearly ascertainable in works of art which are felt to be masterpieces of form, and to be perfectly understood and felt by those who attempt to follow such models: hence, in discussing the structure of works of this kind, the frequent use of such terms as Tonic, or Dominant or Subdominant harmony, which is only a short way of describing harmony of which these respective notes are the roots.
The simplest and most stable of complete combinations in music are the chords consisting of a bass note with its third and perfect fifth ”

“ More daringly, because the lower the pitch of a dissonant tone, the greater the number of its audible harmonics, and hence the greater the degree of its obscuration of the harmony. Even a consonance, such as the major third, sounds "muddy" when placed in the lower register. Readers interested in this matter should consult some convenient handbook of acoustics, such as Broadhouse's "The Student's Helmholtz," on the subjects of harmonics or partial tones, sympathetic vibration, etc., and Mr. Arthur Whiting's "Pedal Studies," for a highly suggestive discussion of color in piano music. ”

“ A succession of tones without harmonic regulation is not a perfect element in music; neither is a succession of tones which have harmonic regulation but are void of rhythm. The beauty and expressiveness, especially the emotionality, of a musical composition depend upon the harmonies which either accompany the melody in the form of chords (a group of melodic intervals sounded simultaneously) , or are latent in the melody itself (harmonic intervals sounded successively) . Melody is Harmony analyzed; Harmony is Melody synthetized. ”

“ That the Tone of a Violin is to be brought out, by laying on like a Blacksmith. Before we can convince such of our Readers as have no Knowledge in that Part of Pneumatics which is called Harmonics, of this Mistake, it will be necessary just to give a short Account of the Cause of Sound in stringed Instruments.
In the first Place, all Sound proceeds from Undulations in the Air, which is an elastic Fluid; and with regard to these Undulations, is much of the same Nature as Water, which is another Fluid, but differs from Air in many Respects. ”

“ Since all sound is caused by vibration, acoustics may be defined as the science which treats of the phenomena of sound-producing vibration.
2. All sound (as stated above) is produced by vibration of some sort: strike a tuning-fork against the top of a table and see the vibrations which cause the tone, or, if the fork is a small one and the vibrations cannot be seen, hold it against the edge of a sheet of paper and hear the blows it strikes; or, watch one of the lowest strings of the piano after striking the key a sharp blow ”

“ The third octave of the compass is obtained by the production of the higher harmonics (Fr. sons harmoniques; Ger. Flageolettöne) , of the fundamental scale, facilitated by the opening of certain of the finger-holes as “vent holes.” The quality of tone depends somewhat on the material of which the flute is made; silver and gold produce a liquid tone of exquisite delicacy suitable for solo music, cocus-wood and ebonite a rich mellow tone of considerable power suitable for orchestral music. ”

“ It is biblically asserted and scientifically demonstrable that space is full of causes of sound. To anyone capable of turning these causes to effects this sound is not dull and monotonous, but richly varied into songful music. Light makes its impression of color by its different number of vibrations. So music sounds its keys. We know the number of vibrations necessary for the note C of the soprano scale, and the number that runs the pitch up to inaudibility. We know the number of vibrations of light necessary to give us a sensation of red or violet. ”

“ I have found out that by uttering the true inner name of anything I can set in motion harmonics--harmonics, note well, half the wave length and twice the frequency!--that are delicate and swift enough to insert themselves between the whirling molecules of any reasonable object--any object, I mean, not too closely or coherently packed. By then swelling or lowering my voice I can alter the scale, size or shape of that object almost indefinitely, its parts nevertheless retaining their normal relative proportions. ”

“ Only by passing on and on, from chord to chord in ever-changing forms, from sweetest consonance to most brilliant dissonance, from exciting successions and combinations to calming ones, is harmonic texture provided for musical compositions. Sometimes, also, the melody remains unchanged when the harmonies are greatly altered, so that its expression may be varied, as the features of the same countenance may express varied emotions, and yet be always recognized. ”

“ To enter on the consideration of harmonics of fractional, irrational, or impossible degrees is beyond my purpose, which is to give as clear an idea as I can of what these harmonics are. I have done so by referring the harmonic, not to a system of polar coordinates of latitude and longitude, or to Cartesian coordinates, but to a number of points on the sphere, which I have called the Poles of the harmonic. Whatever be the type of a harmonic of the degree , it is always mathematically possible to find points on the sphere which are its poles. ”

“ Of the many possible modes only two are used in our present system of music, the major and the minor. There is only one form of the major mode, and it is the one most people recall when they think of the scale. There are three forms of the minor mode, but of these the harmonic is the most frequently used. ”

“ The solid and highly-compound tones of the organ, sustained with equal energy, caused the imperfections of the concords to be markedly apparent. They could not be ignored, as when occurring with the evanescent tone of a piano-forte. The super-harmonics, or summation-tones, disagreeing with each other, developed, in common with difference-tones, a mass of attendant dissonances, which even the employment of a double foundation (sixteen-feet manual stops) and powerful pedal-organ, etc., could barely hide. ”

“ No one can ponder upon the above-mentioned harmonic foundation of the musical scale without conceiving a new idea of the beauty and significance of that glorious art and science which may be proved to be based upon laws decreed by the Almighty himself. The one consideration that, in all probability, no single musical sound comes to us alone, but each one is accompanied by its choir of ascending harmonic sequences, is sufficient to afford matter for many a wholesome and delightful meditation. ”

“ The more simple is the relation the greater is the harmony. For example, if we take the first note, termed the fundamental note, of what is called the scale in music, it harmonizes better with the octave than with any other of the eight notes, because for every vibration in it there are just two in the octave. ”

“ In other words, no part of the energy depends on the product of the amplitudes of two different harmonics. When two modes of motion of the same system are conjugate to each other, the existence of one of them does not affect the other.
The simplest case of harmonic analysis, that of which the treatment of the vibrating string is an example, is completely investigated in what is known as Fourier’s theorem. ”

“ Looked at in the light of modern knowledge, however, we see in the drone an unconscious groping after the truth of the Harmonic Scale, on which all modern harmony rests. We now perceive that either the Tonic or Dominant, or even both together, may with perfect propriety be sounded through any Tonic, Dominant, or Supertonic harmonies, since these must always consist of harmonics generated by the Tonic or its harmonics, and the generator is therefore always a true bass. ”

“ Harmonic design, on the other hand—the setting of one key or series of keys against another—is often only dimly recognized, if at all, although it is of the greatest importance in all modern music. In sonata-form the harmonic plan (described above by the terms Duality, Plurality and Unity) adds an important element since it unifies the last section by stating both first and second theme in the same key. And in the middle, or development section, the freedom of harmonic progression—the multitude of keys—gives great variety and enables the composer freely to indulge his fancy. ”