Melody, which is a succession of single sounds, is the basis of harmony, although it is essentially distinct from it. Music to be performed by one voice or by an instrument which is capable of giving but one tone at a time is written as a melody. As the voice or any of these solo instruments, as they are called, are rarely heard alone, being generally accompanied by other instruments, the compositions in which they occur are usually written in harmony, that is two or more different musical sounds at different pitches are produced simultaneously, and melody pure and unaccompanied is little heard. In fact, the impression has grown that melody without harmony does not exist. Nevertheless melody was the only form of composition in existence for thousands of years and it still exists as the sole form known to many nations of the East. Their melodies are perhaps not tuneful to our ears, but according to the scales and to the aesthetic sense of the people to whom they belong the music fulfils all the requirements of the melody.
The Greeks are the most ancient people whom we know to have used a musical scale similar to the one which we use, and there are still in existence a few melodies belonging to them. The signs used to represent the tones are not easily interpreted, but notwithstanding the differences of opinion among researchers concerning some notes it is possible to give a fairly accurate reproduction of these ancient melodies. The signs indicating the tones were placed immediately above the syllables which they were to accompany and those who have translated the melodies into our notation have been guided as to the difference in the duration of the tones by the varying shapes and sizes of the Greek signs. The compositions appear crude and without musical purpose when heard by modern ears.
More modern and, according to our standard, less crude are the melodies used by the early Christian Church. There was in use at that time a more definite notation than in the Grecian days and as a consequence the melodies have been preserved in a more complete form. In nearly every Roman Catholic church the Gregorian music is now heard in accordance with the wishes expressed by Pope Pius X. in 1903. In spite of the renovations which church music has undergone at various periods, each time there has gradually grown into use music which entirely lacked the simple, purely religious qualities possessed by that which it is claimed was established by the early church fathers. Even the strictly Gregorian music had been completely changed in character by the addition of harmonies agreeing with more modern tonality to the original melodies which had been arranged according to the ancient church modes. Stripped of the modern changes to the best ability of the researchers and arranged in accordance, with the old church modes the music presents a totally different appearance, and is even deficient in metre. Neither is there evidence of systematic tonality, there being no scale in the modern sense of the word, although the intervals are less without reason than those in the music of the Greeks.
Here let us pause and attempt a realization of what the church has done for music. In the beginning there were a few fragments of pagan and Hebrew music which were remodeled and built upon little by little. Pope Gregory in the Sixth Century is said to have collected and systematized the hymns and chants which had resulted from these fragmentary beginnings and had them copied into a complete book called his antiphony which was fastened to the altar so as to be ever available for reference. This collection in turn is said to have formed a foundation for many marked improvements. The unchangeable law of life is progress which manifested itself in music as well as in all else and the greatest composers of all ages have left no more striking examples of their ability than in their masses, offertories and other sacred forms. It was in the monasteries that notation was developed. As the inmates labored day by day in copying their sacred music better methods suggested themselves and were employed.
We have learned how the Troubadours had rejected the more confining church modes and had made use of two modes that later became known as major and minor and are now employed. These modes afforded more variety for the musicians in their gay songs, which, as we have also learned, cast the composers and singers into sad repute among the churchmen. It is natural, that having used the same modes, the melodies of these worldly singers bear a strong resemblance to the melodies of today.
Each year brought to musicians a realization of the value which lay in a systematic tonality, a realization of the better results to be gained by having an accepted plan to follow in constructing their compositions. Metre was also growing into its position as an essential part of music until there appeared the three qualities which melody, in order that it may be true melody, must possess :
The tones which compose it must be selected from a properly authorized scale.
Throughout they must be subservient to a key-note, and fulfil the laws of tonality.
They must be so evidently metrical in their construction that quality shall be easily apparent to the hearer.
Beyond these three essentials there are no rules governing the quality of melody. What tones are to be used and how they are to be arranged lie entirely within the pleasure of the composer. Melody may be pleasing or distasteful without a reason. Again we have arrived at something which can only be explained by a reference to the aesthetic sense. The good qualities of a melody are determined variously by individual hearers, and any flights of imagination and fancy which the composer or performer may allow himself are likely to find favor with a few hearers at least.
Whereas melody is a succession of tones, harmony is the effect produced by two or more sounds heard simultaneously. Inherent in melody is the idea of motion, while in harmony is that of rest. A musical idea in melody can only be expressed by a moving succession of tones, while a group of tones, sounded simultaneously in what is called a chord, expresses a complete idea, even though it may stand still. Progressions or a series of chords having different pitches but related musically occur in harmony as do changes of pitch in melody, but a chord may express an idea so beautiful that singly it will be able to hold the attention of the hearer. The progressions of melody may be likened to the succession of words which make a sentence, while those of harmony more resemble the succession of sentences forming a story.
Not only is harmony artistically important, but the reasons why certain combinations are considered beautiful and others are considered discordant and the manner in which the rules which govern harmony have come into existence has ever appealed to scientists as possessing great interest and have been made the subject of innumerable treatises. It is in this theoretical fashion that we will consider harmony and its rules and not as the student who desires to write music. To him these rules are the grammar of music, but to us it is only the manner in which they came into existence that is of interest. They are in nearly every case artificial and their origin can be traced to none of the fundamental laws of nature.
There is a striking analogy between music and language. The poets refer to music as the language of the soul and say that through it alone can souls communicate. In fact music resembles language in its growth and in the manner in which it differs in its appreciation by nations and individuals. Both are governed by man-made laws which are equally without scientific explanation. Just as different nations have languages entire unintelligible to the people of other nations until an acquaintance has been formed, so there is in existence music which cannot be appreciated by any but the people to whom it belongs. The English without suitable training can neither understand the music nor the language of the Chinese. Language is constructed of words and music of notes. Words can be so joined together that wonderful tales can be told, but even more wonderful tales can be told by the combining of notes.
Man's aesthetic sense creates a perpetual desire for that which is beautiful for new beauties, and the first beauty that he perceived could be obtained from the unbounded mass of musical sounds which are possible, was in combining them to form a succession. Harmony, or the sounding of notes simultaneously, was a much later development.
We ever turn to the Greeks when seeking the beginning of our music, for to them we owe the foundation of our system. Of their knowledge and use of melody we have substantial evidence in a few hymns to the gods which have been preserved through the ages. It is positively proved that they understood the relations which are recognized in harmony. There are certain intervals which are referred to as consonances, and others which are termed dissonances. A consonance is the combination of sounds which when sounded together has an effect upon the hearer of. being complete in itself and not needing anything to follow as an ending. It is similar to that inflection of the voice which is only associated with the end of a statement. It alone gives us the impression of completion. On the other hand a dissonance is the combination of sounds which when occurring together produce an impression of incompleteness. It is felt that something more is needed, just as when a speaker is interrupted his voice is at a pitch which tells that more is to follow. The Greeks possessed a realization of the consonance of the intervals of an octave, a fifth and a fourth, and used an expression concerning them which means a mixing of two things so that they are blended and form a compound. This is the same way in which they are now considered. How-ever, there is no record of the practise of harmony by the Greeks. None of their writers have mentioned it and although there was in use a word, symphony, which carries in its etymology a reference to different tones sounded simultaneously, it more likely applied to the system of voices singing in unison, that is, giving the same tones, or of singing the distance of an octave apart. This primitive practise is by no means harmony in our sense of the word.
The first reference to anything resembling harmony that is worthy of serious consideration was made by a Roman writer named Colonius, living about the third century after Christ. He defined the intervals capable of producing symphony as the diatesseron, meaning fourth; diapente, meaning fifth ; and the diapason, containing the two other intervals and thus identical with our octave. The next important record of the use of harmonious intervals is in the church of the Middle Ages. Isidore, who was Bishop of Seville about the year 600, was rather an extensive writer on miscellaneous as well as ecclesiastical subjects. He was a friend of Pope Gregory and his writings were considered of much worth during the medieval period. He refers to the combinations of simultaneous sounds and speaks of the intervals of an octave, a fifth and a fourth, as consonant intervals which easily lent themselves to practise.
Hucbald, a Benedictine monk in Flanders about the Tenth Century, wrote extensively of things musical and with many details showed that melody could be accompanied in a number of ways which were termed Diaphony or organizing. According to this system the melody was accompanied by itself taking certain intervals above or below, the two simultaneous tones which were usually employed giving it the name of diaphony, although it was permissible to make use of three tones at times. In other words, the accompaniment was composed of the same sequence of tones as was the melody, each tone at a distance of the same interval from the corresponding one of the melody. The intervals which were considered proper were octaves above or below, fifths above, fourths above, fifths above or fourths below, or fourths above and fifths below. Formerly melody had only been accompanied in the octave and the acceptance of these new intervals for practical use afforded many new possibilities for variety. However, even this new system appears crude to modern ears familiar with more elaborate harmony, but it must be remembered that this was the first attempt at sounding tones simultaneously, and although these intervals fail to recommend themselves to the harmony of today, without doubt they sounded beautiful to medieval ears. If such had not been the case they would surely not have enjoyed such general use. The system of diaphony has been greatly criticized and has even been referred to as "brutal," but it is not well to lose sight of the fact that we have no way by which to judge it for the condition of affairs — a condition utterly without harmony in any sense — is beyond our comprehension after the many centuries of its use.
Hucbald, who did much to establish the system of diaphony, did much for the development of harmony by also being instrumental in establishing the use of the intervals of seconds and thirds. He likewise figured extensively in the development of counterpoint. Throughout the history of harmony it has been a very difficult matter to keep the two forms distinct, harmony being the outgrowth of counterpoint and having been subsidiary to it for many centuries, but counterpoint is much more intricate and is usually discussed after harmony in the study of musical forms. However, even with the utmost care it is impossible to obviate all reference to counterpoint in the discussion of harmony.
Adam de la Hale, who was born about 1240 in Arras, is a romantic character in history. He was for a time a monk, but forsook his vows and married. Later he forsook his family and left his home and after various travels reached Italy, where he died after a time. He was called the Hunch-back of Arras, although he seems to have been without deformity. His " Jeu de Robin et de Marion " may be considered as the first specimen of comic opera and was first performed at the court of Naples in 1285. He was prominent in the use of discant, the name given at a later period to the accompanying part which had been added to the melody. The system began to assume importance and at an early date in the Fourteenth Century it acquired rules all its own.
As musicians become more venturesome in discant counterpoint appeared. The Troubadours were largely instrumental in creating this new development. They rather enjoyed the disrepute in which they were held by the church-men, and in an effort to further irritate formed a custom of combining a hymn or chant with some merry song often sadly lacking in purity. The melodies of each, changed a trifle to fit them for their new use, were placed one above the other in a rude form of counterpoint, for this new musical form was nothing more than two independent melodies sounded together. It was, of course, necessary that they possess certain qualities in common so that they would not conflict in too great a sense, although without doubt they did not agree completely.
This marks the opening of a long era in music termed the polyphonic from the system of combining independent parts. Following the custom of combining two parts the next step was the combination of three parts. Compositions of this character appear in a crude and nebulous state early in the Twelfth Century, but had acquired a comparative perfection by the middle of the Thirteenth Century. Progress brought about the addition of new parts to be sounded together, and with each addition the increased multiplicity of sounds required more delicate handling and presented themselves more forcibly for attention regarding their harmonic relations, thus laying the foundation for independent harmony.
Harmony as we know it did not appear until the Sixteenth Century. Composers devoted their entire attention to the writing and arranging of independent parts. Each was a separate and distinct melody and all were fitted together in a manner that reminds us of a child fitting his blocks to form a design. Each melody was first carefully composed, and the most telling efforts were expended in producing individual perfection. When they had been combined they were very frequently happily related, but at many points there were sad dissonances. However, it soon became evident that these not only could be tolerated but by being subjected to certain conditions could be made to add beauty to the composition. This is one respect in which counterpoint and harmony are related, for it is on account of this extensive and necessary use of dissonant intervals by writers of counterpoint that they play such an important part in harmony.
Dissonances may in strictness be employed only when they are followed by the proper consonances so that their incompleteness is not evident. How to make them acceptable and beautiful to the ear occupied much of the attention of the contrapuntists, for, as we have seen, dissonances to them were a necessary evil. Ingenuity was afforded full play in arranging them properly, and, naturally, when counterpoint became superseded by harmony, this opportunity for ornamentation was not thrown aside; but the secret of many of the intricacies and beauties of harmony lies in the cunning manner in which these intervals are handled.
During the early half of the Sixteenth Century the chromatic scale appeared complete with twelve notes to an octave, and with the increased number of notes opened a possibility for more dissonances, and, as a consequence from arranging the dissonant chords, greater variety in composing. Music immediately acquired more life. Greater ingenuity came into play and even the music of the church lost its reserved dignity and the Gloria, the Kyrie, the Credo and the Agnus were sung to ballad and dance music far too frolicsome for propriety. Musicians lost sight of good taste entirely and allowed all other considerations to be subservient to the artistic combining of consonances and dissonances. The most absurd tunes were used in the masses and even lent their secular names to the sacred use, for instance ; the mass of " The Man in Armor " and the mass of " With Two Faces and More " were in existence. At last the music became so unfitted for the use to which it was put that it was impossible to allow the abuse to continue and a reformation along this as, well as many other lines was precipitated.
The foremost musician of the time was Palestrina (1524-1594) who was given his name from his birthplace, Palestrina, near Rome. Palestrina's musical ability gained recognition and between 1550 and 1555 Pope Julius III. appointed him as one of the twenty-four collegiate singers in the Pope's private chapel, although the act was greatly in violation of the rules governing this selection. Palestrina was trebly ineligible for he was a layman, was the father of a family, and had a particularly bad voice. The position was not permanent, for in about two years the Pope died and the succeeding Pope only lived twenty-three days, when Pope Paul IV. ascended to the Papal chair. Prompted by a desire to adhere to the rules of his office and influenced by the jealous clergy who were Palestrina's associates but who disliked him because of his superior musical qualities, the Pope displaced him from his position and Palestrina was left to face most severe poverty and hardship for a brief time. However, his greatest triumph was before him. The Council of Trent when considering the abuses so prevalent in the church music were at a loss to discover a remedy and even contemplated discarding music entirely from the service. Fearing this to be a too extreme measure they modified it by ordering Palestrina to compose three masses which should possess the qualities of truly religious music. In 1565 the masses were submitted to the Council and the first two were received with great joy, for they indeed seemed fitted for the use for which they were designed. The third possessed even more wonderful qualities and completely entranced the hearers. Pope Pius IV. declared that " of such a nature must have been the new song heard by John the apostle in the heavenly Jerusalem." It was dedicated to Pope Marcellus II. Palestrina had now established a standard for ecclesiastical music which is still followed, in which, however, the use of chromatic notes was strictly forbidden. Palestrina, upon whose tomb is the inscription " Prince of Music," left nearly one hundred masses and hymns, besides about sixty motets and other compositions. He is said to have been the first to combine the art with the science of music.
The example set by Palestrina which did away with chromatic notes was a drawback to the development of harmony, for in the church, the greatest branch of music, the means of affording variety was cut off. The secular branch of the art still held out possibilities and the all too brief use of the chromatic scale had shown composers what might be done.
This was an epoch-making period. A great desire to emulate the example of the Greeks, who were then considered to have had the most perfect music, led musicians to increase their little store of historical facts with many suppositions until they had little or no idea of what Grecian music might have been. They multiplied and intensified the dissonances, for in order to make them bearable composers had to resort to all manner of ingenious methods, and the more difficult the task the more like the ancient music they felt their new music to be. In striving to imitate they instead created what has since lived as the greatest of musical forms. Monteverde was a most audacious composer of the period and dared to use many unusual combinations of notes. He created readily, but failed to polish and the specimens of his compositions which remain are incorrectly written. However, he introduced chords and progressions without which music could never have attained the dramatic grandeur which is now possible. In 1600 he and a few associates produced what they hoped was an exact duplicate of the Grecian style, but which instead was the first opera ever written. Its name was " Orpheus and Eurydice."
A long period was occupied while harmony was becoming separated from counterpoint. As has been seen, counter-point consisted of several melodies founded simultaneously and consequently is made up of groups of notes sounded together, although these groups did not occupy the interest of composers as groups, but only in a dissected condition, each note being independent of the others of the group and only bearing .the proper relations of tonality to the other notes of its respective melody. By thus combining melodies the effect of harmony was gained.
Gradually the groups, or chords, as they are called, gained a foothold to the interest of musicians and there came into existence a realization of the beauties that could be gained by progressions of chords, although musicians were not conscious of the change that was occurring. Church music had been arranged as counterpoint, accompanied by the organ. The organ can sound many tones simultaneously and it was very easy in the absence of any of the voices to have the instrument fill in the vacancies to fulfil the contrapuntal effect. In order to enable the organist to do this the music was written with what is known as a figured bass. The bass alone was written out and the other notes of the chord were indicated by figures placed above the notes, representing the intervals, counting from the bass upwards, at which these notes should stand. This bass was called basso continuo (continuous bass).
It seems to have been first employed by Peri, Monteverde and others about 1600, in the accompaniments of their recitatives and songs. Its use survived for a long time, for, e. g., it is to be found in the scores of Bach and Handel, and even later. It is practically no longer employed in this way. Until this point it has been difficult to not encroach upon counterpoint when describing the rise of harmony, but now this difficulty is past and harmony begins to assume the importance it now holds. First it was an accidental effect produced by part-writing, later it insinuated its importance upon the attention of the writers of counterpoint, of which it remained a dependent part, until at last it attained its true importance and stood alone and independent in readiness to grow into its rightful position in the scheme of things musical.
The Frenchman, Jean Philippe Rameau, was the first well-known writer who treated independent harmony theoretically and attempted to explain the reasons for it and the rules governing it. Rameau was indeed a musical genius. His gifts early manifested themselves and as he was of a musical family his training was for their cultivation. He was exceedingly versatile and was excellent as composer, theorist, organ and clavichord virtuoso and teacher ; to him belongs the honor of having first observed and grasped the true philosophy of harmony.
The student who desires to write music makes a thorough study of the production of standard composers in an effort to learn what combinations of chords and what progressions of chords create good effects in much the same manner as the aspiring author studies the grammar of his language for correct forms and the classics of literature for proper and pleasing style.
Still more interesting to discover that which is best is the reason which creates good qualities. Music as an art differs from painting and sculpture in these reasons. In the last two genius merely copies beauties already in existence, and a reason for the beauty of the production of these arts lies not in the productions themselves but must be sought for beyond in that which has been copied. Music, on the other hand, possesses beauties newly created and in the art itself must be found the explanation.
These explanations have little basis on any natural laws, and theoretical writers have created hypotheses, many of them incorrect, until a study of the theories or systems of harmony tend to confuse, and many of them are without practical use to students. Such men as have proved themselves truly capable of handling this subject have shown how artificial are the foundations of the systems of harmony. They are artificial in the same degree as are the foundations of the rules governing grammar. Here again is a striking analogy between the two arts of literature and music. We who have been born to a use of the English language read Chaucer and unconsciously wonder at the unnatural and awkward phraseology. We consider how much more flowing and easy of comprehension is the language used in the Twentieth Century until our better judgment reminds us that it is entirely beyond our power to decide what is correct or beautiful in anything that is so absolutely governed by arbitrary laws. In the same manner the musical compositions of the Elizabethan period appear to us childish in simplicity and at times appalling in awkwardness. Even the simple melodies and harmonies that occupied the attention of amateurs during the first half of the Nineteenth Century are ridiculed by the more sophisticated amateurs of the present who have tasted of a knowledge of the classical composers. The past sixty years have witnessed an example of the complete change which the tastes of the public may undergo.
There are two senses which act in determining that which is beautiful in music : One is the physical sense of hearing which has in truth established certain fundamental and unchangeable rules, to be explained later. The other is the aesthetic sense which differs in individuals as to its dictates. Beyond the few laws laid down by the physical effect of certain tones, combinations and progressions, both senses are prone to change with education and environment and they establish a most artificial standard of right and wrong. Hence it must only be expected that this standard will change in the future as it has done in the past.
The rules that do exist fail to apply in all cases and, as in grammar and orthography, there are likely to be more exceptions to rules than there are rules themselves, thus tending to make the study of the philosophy of music complicated and confusing. As has been seen, harmony is the effect of two or more tones sounded together. These groups or chords may each carry a sense of completion as each word in a literary production may express an idea. However, the composer must not only aspire for beauty and perfection in chords but he must consider with equal care the progressions formed by combining chords, and both subjects are included in the study of harmony.
The most simple form by which the effect of harmony is produced is in two sounds taken together. These combinations possess a great importance, for in them are comprised the elementary germs of all harmony as the more complex combinations can be analyzed and found to rely upon these germs. Among these combinations are some which please the ear and others which are less agreeable. They are known as consonances and dissonances, respectively.
A scientific explanation of this phenomenon involves the explanation of the formation of single tones. All tones are compound affairs. They consist of a fundamental and a number of harmonies or partials. An absolutely pure tone is only found in theory, for it is only the fundamental or foundation of the tone that is regarded and which gives a name to the tone. It is the strongest part of the tone and the casual ear does not realize that what appears to be a pure, simple tone is a mass composed of the one strong fundamental and a group of weaker, less noticeable, harmonies. There is consequently no tone which fulfils the requirements of an ideal consonance, for some of the accompanying harmonies do not blend well with the fundamental. Those harmonies which are nearest to the fundamental blend best with it. There are always present some harmonies which bear a disagreeable relation to the fundamental, and it is when they are too much in evidence that we hear a tone which does not seem to be homogeneous whole but appears to be composed of an insufficient tone itself accompanied by weaker and even less complete tones, the entire group producing a disagreeable noise. Instrument makers employ their cunning in silencing the unpleasant harmonies and in making the fundamental sound as pure as possible, although some of the harmonies are retained as they add a charm to the tone.
Just as those harmonies situated nearest to the fundamental possess more consonance with it than do those farther away, the simultaneous combinations of octaves, fifths and fourths possess greater consonance, for these are the harmonies possessing the simplest ratios with the fundamental, as has been shown in the chapter on tonality. They are not the smallest intervals by any means but their consonance rests upon the simplicity of their ratios.
The ratio of the ideal consonant interval is as 1 is to 1 which, of course, is a unison and it is only logical that those tones bearing the next simplest relations would possess the next greatest consonance. Musicians have established arbitrary decisions as to the consonance and dissonance of certain intervals and in the discussion of harmony it is necessary to recognize the distinction thus determined upon. Those intervals whose ratios are expressed by any of the figures from one to six are consonances, all others except those that are merely a former interval doubled as 2:6, 1 :12, 4:8, 6 :12, etc., are dissonances. The tables of consonances and dissonances read thus:
CONSONANCES. Ratio
Octave 1:2
Fifth 2:3
Fourth 3:4
Major third 4:5
Minor third 5:6
Major sixth 3:5
Minor sixth 5:8
DISSONANCES.
Major second 8:9
Minor second 15:16
Major seventh 8:15
Minor seventh 9:16
Dissonant intervals produce the effect of being rough or harsh, a quality which is due to reinforcements of the intensity of the sound occurring at regular intervals. We have learned that difference of pitch in tones is due to difference in the number of vibrations per second which cause them.
A string which is made to vibrate transmits its motion to the air about it in the form of waves which travel just as water waves travel through the water. If a stone is thrown into a pool there will immediately appear upon the surface irregularities, the water seeming to rise and fall in waves. However, the motion in the water is not horizontal but is longitudinal. The entrance of the stone into the water compresses the adjoining atoms, the compression causing the surface of the water to rise, forming the crest of a wave. In turn the compression is transmitted to the next adjoining atoms causing what had been the crest of the wave to relax and to become a trough. The transmission of motion continues, the force of the contact growing less and less until all effect dies out and all disturbance disappears from the water. Just so, the vibrations of a string, a column of air, or any vibrating substances are transmitted to the air in the form of waves, which travel as do the water waves until the motion reaches the auditory nerve, and becomes sound.
Each vibration of a string produces a distinct wave in the air It is easily seen that if two tones, one caused by vibrations occurring at the rate of 256 per second and the other at the rate of 246 per second, are sounded together the one whose vibrations occur more rapidly must gain on the other to the amount of ten vibrations during a second. The waves will, in a sense, pass each other. In a similar manner allow two men to walk around a circle, one at the rate of fifty-six times an hour, and the other at the rate of forty-six times an hour. The man going at the more rapid rate of speed will pass the other ten times during the hour.
During the passage of the sound waves through the air there will be instants when what represents the crest of one wave is in a position analogous to the trough of the other wave, at which instant they would counteract each other and their power will be destroyed, producing instantaneous silence. Naturally these instants of silence which constitute what are called beats, will occur at regular intervals, breaking the continuous tones into pulsations and causing them to be recognized as dissonant. The number of beats per second will be equal to the difference in the vibration numbers of two tones. In a unison, the ideal of consonance, no beats occur, but as tones diverge in ratios the number of beats per second grows more rapid up to the point, so Helmholz affirms, where thirty-three occur, as when C and D flat are sounded together. Beyond this point the beats lose their intensity in inverse order as they gain in speed per second until their disagreeable effect passes away. In treble C and E in the second octave above middle C 128 beats occur, but there is no perceptible dissonance, as the beats are so short and have such meager intensity that there are no appreciable reinforcements of strength in the sound. The united tones appear continuous, there seeming to be an entire absence of the pulsations. The intensity of the beats increases in proportion to the loudness of the notes which cause them.
In the study of harmony it is necessary to understand the names by which the degrees of the scale are known to musicians. In tonality we have learned that all other degrees must bear a certain relation to the first, which has heretofore been spoken of as the key-note. Technically it is known as the Tonic, a name derived from an abbreviated form of the Latin word, Tonica, meaning tone and signifying that this is the chief tone of the scale.
The next most important degree is the fifth above the tonic and is called Dominant, because of the manner in which it appears to rule over the other degrees of the scale. Next in importance comes the Subdominant, or lower dominant, which is situated a fifth below the tonic. When inverted to preserve the upper succession of degrees it becomes the fourth above the tonic. The third degree is called the Mediant, because it is midway between the tonic and the dominant. The sixth degree is called the Submediant or lower mediant. It derives its name in a manner similar to that of the mediant, since it is situated half way between the tonic and subdominant. The second degree is called the Supertonic, as it is the one just above the tonic. The seventh degree receives the name Leading Tone from the tendency to rise or lead up to the tonic, which the ear demands that it possess. In their successive order the names of the degrees are Tonic, Supertonic, Mediant, Subdominant, Dominant, Submediant and Leading Tone.
Until this point we have dealt with combinations of two tones only. These, however, do not constitute harmony in the true acceptance of the term. In order to produce the effect of harmony it is necessary to combine three or more notes into what is called a Chord, a name derived from the French word, accord, meaning sounded together. The notes of a chord are placed one above the other with an interval of a third between. When the chord is composed of but three notes it is termed a triad. The lowest note is designated as the root of the chord and it is from this note that the other notes of the chord can be spelled or built up in thirds. The second member is at the interval of a third from the root and the third member at the interval of a fifth. Any tone bearing a relation to the root which fulfils these requirements is termed a chord tone. If the triad comprises a major third and a perfect fifth it is called a major triad, but if it comprises a minor third and a perfect fifth it receives the qualifying name of minor. If the third is a major one and the fifth augmented the triad is an augmented triad. If, on the other hand, the fifth is less than a perfect fifth the interval is a diminished fifth and the triad which contains it is a diminished triad, the third in it being a minor third.
When glancing over a page of music it is indeed hard to realize that all the chords are merely superposed thirds. Their changed appearance is due to the inversion of certain members of the chord. Each triad is subject to the first and second inversions. By the first inversion the second member of the triad takes a position as the lowest member of the chord, or in the words of musicians, is in the bass. The lowest tone of a chord is said to be in the bass, the next in the tenor, the third in the alto, and the fourth in the soprano. The first inversion is called the Chord of the Sixth, for the second member occurring as the bass of the chord is an interval of a sixth from the root. The second inversion of a triad occurs when its third member is in the bass and it is called the Chord of the Sixth and Fourth, for the third member forms the interval of a fourth with the root and an interval of a sixth with the second member. When seeking the root of a chord it is necessary to find that tone from which the others may be spelled up in thirds. Therefore, its most natural position, and, in practise, the most satisfactory, is at the bottom of the chord. This fact is recognized in the adoption of the custom that every piece of music shall close with a chord in which the root occupies this position.
It is worthy of note at this point that in harmony the interval of an octave does not find a place, but when any of the tones of a chord are doubled by the introduction of their octaves, the doubled tones are considered as one. The root is generally the best tone that can be doubled, although, when it is found necessary in order to bring about a progression that sounds well, one of the other tones may be doubled.
The intervals of the major diatonic scale are arranged thus : 1—2—3 4—5—6—7 8. The interval of a tone is designated by —; that of a semitone by.
It will be seen that if each one of the first seven degrees be taken as a root a triad may be formed, although not all of them will contain intervals of like magnitude. Beginning with the first degree as a root, the triad will contain the degrees 1, 3 and 5. The interval of a third between the root and the second member is a major third and the fifth between the root and the third member is a perfect fifth, the chord being called a major triad.
Using the second degree as a root the triad would contain the degrees 2, 4 and 6. The interval between the root and the second member is a minor third instead of a major third, but the interval between the root and the third member remains a perfect fifth. Hence, this chord is a minor triad.
Using the third degree as a root, a triad will contain the degrees 3, 5 and 7. The fact that the intervals of this triad are of the same magnitude as those of the preceding triad makes it self-evident that this also is a minor triad.
Using the fourth degree as the root, a triad will contain the degrees 4, 6 and 8. The intervals of this triad prove to be of the same magnitude as those of the triad on the first degree, and the chord is a major triad.
Using the fifth degree as the root, a triad will contain the degrees 5, 7 and 2, and the triad will be major.
Using the sixth degree as the root, a triad will contain the degrees 6, 8 and 3, and upon inspection the chord proves to be a minor triad.
Using the seventh degree as the root, a triad will contain the degrees 7, 2 and 4. This combination brings about a new chord. Hitherto the third had been the only interval to change, and the fifth has remained perfect. In the triad on the seventh degree, the third is minor and the fifth is diminished; hence, the chord is known as a diminished triad.
By this method we find that the triads formed on the first, fourth and fifth degrees are major, those formed on the second, third and sixth degrees are minor, and that formed on the seventh degree is diminished. In the key of C the tones comprising the triads would be named as follows :
First degree as root C E G
Second degree as root D F A
Third degree as root E G B
Fourth degree as root F A C
Fifth degree as root G B D
Sixth degree as root A C E
Seventh degree as root B D F
We learned in the preceding chapter that in order to preserve the sequence of intervals proper for the major mode the key of G requires the omission of F as it is found in the key of C, and the introduction of F sharp, the tone half way between F and G. Consequently in the key of G the tones forming the triads would be named in the following manner :
First degree as root G B D
Second degree as root A C E
Third degree as root B D F sharp
Fourth degree as root C E G
Fifth degree as root D F sharp A
Sixth degree as root E C B
Seventh degree as root F sharp A C
In the mere matter of names most of these triads bear a striking similarity to those found in the key of C. However, it will be seen that in the key of C, D occurs on the second degree and the triad formed with it as a root is a minor triad, while in the key of G it occurs on the fifth degree and by the introduction of F sharp the triad becomes major. In the key of C, F occurs on the fourth degree and the triad formed with it as a root is major, but in the key of G its substitute, F sharp, occurs on the seventh degree and the triad of which it is the root is diminished. In a similar manner there may be noticed other differences in the triads here named and there may also be noticed the numerous and even more pronounced differences brought about by using as tonics tones which necessitate the introduction of several chromatic tones in order to preserve the proper sequence of intervals. The great variety of combinations that may thus be brought about is also apparent.
A like number of triads may be formed on the degrees of the minor scale in the harmonic form of which the intervals occur in the following order : 1—2 3—4—5 6+7 8, the interval of a tone and a half being indicated by +.
Following the same method of procedure as in the case of the major mode it will be found that major triads can be built on the fifth and sixth degrees, minor triads on the first and fourth degrees, diminished triads on the second and seventh degrees, and because of the interval of a tone and a semitone between the sixth and seventh degrees an augmented triad is built on the third degree.
If the tonic in the minor mode is changed there will appear a similar number of differences in the triads as there did in the major scale. There are fourteen diatonic triads in each key in the minor and major modes combined, and since each triad is subject to two inversions there is a very large number of combinations which upon analyzation prove to belong to this class.
By placing another third on the top of a triad the chord of the seventh is formed. The new tone is the interval of a seventh from the root and consequently creates a dissonant effect in the chord. Although it is possible to build up a chord of the seventh on every degree of the scale, that one which has as a root the fifth degree or the dominant is the most important and is used most frequently. From its root it received its name of Dominant Seventh and is the same in both major and minor modes. In both modes the chord of the seventh on the supertonic is second in importance and the chord of the seventh on the leading tone is third. The one on the leading tone in the minor mode, however, is more important that that in the major. In the major mode it contains a minor seventh; but the diminished form of the chord is much used in the major, the proper or raising the root interval being secured by lowering the seventh of the chord a half-step by the same interval. The other chords of the seventh are less often used.
When or why chords of the seventh were invented can-not be stated. It is safe to suppose that because of their dissonant interval of a seventh they recommended them-selves to such composers as were seeking for means of obtaining variety. The chord was a dissonance requiring resolution, that is, a following consonance. In the early history of music it was considered imperative that, by way of preparation, the tones which created the dissonance, the seventh in the case of the chords of the seventh, should appear as a member of a chord immediately preceding the dissonance, but as early as the close of the Sixteenth Century Monteverde is found using the chords of the dominant, leading tone, and diminished sevenths without any attempt at preparation. This points to an early use of the chords, for after the introduction of the new dissonances enough time must have elapsed to allow it to become familiar to the ears of the world and a still longer time to allow composers to acquire enough assurance in its use to disregard the positive rule of preparation. The other chords of the seventh were not used in this manner until two centuries later, when Bach introduced the custom.
So far only diatonic chords have been discussed, in other words, only chords whose roots can be readily discovered and whose intervals conform to those of the diatonic scale in the major or minor mode. They have been built up systematic-ally and can stand the test of analysis, for it is possible after any inversion to discover the root, the third, and the fifth. There are, however, certain combinations in which the diatonic tones have been chromatically altered, which combinations have proved so effective and useful that they have acquired an individuality and are used as generally as are the diatonic chords.
This chromatic alteration of which we speak must not be confused with the chromatic tones that are necessitated by certain key-notes, such as F sharp in the key of G. There F sharp is as essential a part of the diatonic scale of G as is F natural of the diatonic scale of C. However, if in the key of G the triad D F sharp A were formed and F sharp were lowered to F, F would be chromatically altered and the new tone would be foreign to the key of G. In like manner if in the key of C the triad D F A were formed and F were raised to F sharp, F would be chromatically altered, the new tone being foreign to the key of C. When a chromatic chord has been used the tendency is to progress to a chord containing tones a semitone above or below those which have been altered, the progression continuing in the same voice. This, of course, presupposes that there was an interval of a tone between the chromatically altered tone (before its alteration), and the tone to which the progression is made. The established altered chords in some instances are difficult to classify when undergoing the process of analysis and the reasons which brought about their peculiar alterations at times puzzles the theorist. They are most used in the unaccented part of a measure, and are often preceded by the real tone of the chord, allowing the hearer to perceive in advance what the chord would be in its normal condition. Nevertheless, some very striking effects are produced by directly introducing a chord in its altered form. More than one tone of a chord may be altered the same way, and some may be raised and some lowered.
Harmony, which to the uninitiated has the appearance of being composed of notes built upon each other in any manner which may satisfy the caprice of the composer, consists, in fact, of a series of chords which have been built up according to an established system, a system based entirely upon arbitrary laws. These specified and systematically arranged integers are not permissible unless they can be intellectually verified. By analyzation it must be possible to show that the chords have been built up from a root in the approved manner, or they are debarred from being classified as proper harmony.
It will be seen that a composer is always supplied with material for his work. He is furnished with a prearranged assortment of chords which he may link together as he considers best, his observation of the work of others telling him what will be acceptable. He should understand the relations of one chord to another and the effects produced by certain successions and should think in chords instead of in words, recording his impressions by means of notes. To the well informed musician a chord is as intelligible as is a word to an ordinary reader and at a glance he can determine its root and formation.
First the system of building chords was established, then musicians by experiments found that certain chords were more effective when following certain others, and their discoveries began to take on the character of rules governing progressions from chord to chord, for very naturally those progressions which were considered most pleasing and satisfying were repeated until their use became established. Fundamentally progressions are based upon mutual relations existing between the chords, and, as a consequence, unity is preserved by grouping the chords according to keys.
By introducing a new simile the ever-ready supply of chords may be likened to the pigments which the artist has. upon his palette. Both artists and composers are limited by certain customs, but each must possess the faculty of under-standing how to combine his material so as to depict beauties which the artist sees and the composer mentally hears. It is upon this faculty that genius rests.
In all the arts a practical use is made of the fact that the appreciation of the beautiful is increased when it is brought into contact with that which is not beautiful. It is this phenomenon which insures the acceptance of dissonances in music. It is true that there are certain dissonances which are integral parts of the chords with which they appear, such as those in the chords of the seventh, and which are deemed essential to harmony, but there are still other dissonances wholly artificial and foreign to the harmony which are introduced for no other purpose than to create a feeling of the necessity of consonances, by that means making the latter even more pleasing when heard. This method of ornamentation adds grace and spirit to music which might otherwise be grave and monotonous.
If throughout a piece of music all the members of every chord progressed simultaneously to the following chord there would prevail a sameness of motion and a striking absence of expression in the musical sentences, the words of which are represented by the chords. A new interest is created by introducing an irregular method of binding together or connecting the chords. This irregular connection will naturally arise if all the members of a chord do not progress simultaneously, allowing one or more to linger in their places while the others become component parts of the next chord, the delayed members forming a link between the two chords. By this means a dissonance is created because parts of two chords are momentarily sounded together. This chaining together of harmonies is technically known as suspension.
The sounding of the tone to be suspended as a member of a chord is termed the preparation, the holding of that tone over the chord of which it forms no part is the suspension, and the progression of the delayed member to its proper position in the new chord is the resolution. Throughout the process the delayed tone or tones must occupy the same part. They either may be merely held over or tied until the new chord is sounded or they may be repeated with it. When tied the fact is signified by connecting the two notes with a curved line.
Suspensions usually occur on the accented beat of a measure. Their harshness is only limited by the composer's idea of what is permissible and by the possibilities of a proper and satisfactory resolution. The more intense the dissonance of the suspension, if there follow a thoroughly satisfactory resolution, the more agreeable is the effect. The suspension may resolve up or down and notes may be inserted between the suspension and the resolution.
Suspension was the first method discovered for introducing unessential dissonances. Formerly only those which are natural to the harmony had been accepted. Of course, the so-called essential discords, such as chords of the seventh, had been the outgrowth of man's ingenuity in the same degree as were suspensions, but all things through extensive use grow to be considered natural and lose their power to excite interest. Such was true of so called essential discords and something new and consequently unnatural was sought, the search leading to the introduction of suspension. Monteverde did much to develop this device. With his daring and ingenuity he used much harsher suspensions than his predecessors had deemed permissible. Their first steps in the departure had been faltering, and a realization of the pleasing effects to be obtained were only reached gradually.
We will now proceed to other varieties or ornamentation in which dissonances are employed. A passing tone is one that is foreign to the chord with which it sounds and must be approached and left by the interval of a tone or a semi-tone, the motion continuing in one direction. The number of passing tones which may occur is only limited by the distance between two harmony notes and may be one or more. They may be the consequence of melodic motion. The melody in this case may be of an elaborate character, but may be accompanied by an extremely simple harmony, the harmonic intervals of progression being much slower than those of the melody. For instance, the harmony may be written in whole notes and the melody in quarter or eighth notes. The necessary changes in pitch due to the more rapid progression of the melody bring into use tones which are dissonant with the harmony, but their dissonance is only momentary and is immediately remedied by a following consonance. The use of passing tones dates from the Sixteenth Century.
Similar to the passing tone is what is variously termed returning dissonance, auxiliary tone, and broderie. It differs from the passing tone in that the dissonance is not interpolated during the passage from one tone to another, but returns to the consonance from which it came. It may occupy a stronger or a weaker beat in the measure than does the harmony note to which it belongs and the distance between the two may be a tone or a semitone above or below.
An Appoggiatura, by some wrongly termed an unprepared suspension, is a dissonant tone entirely foreign to the chord with which it sounds, but which by resolution passes into the proper member of the chord whose place for the time it had usurped ; it differs from a suspension in that it is not prolonged from the preceding chord. It is usually on the accented beat of a measure. When an appoggiatura, instead of passing to its resolution, skips to an appoggiatura on the other side of a note of resolution it is a double appoggiatura. Appoggiaturas may be used in two or more parts simultaneously.
Anticipation (the opposite of suspension), is made by one or more unaccented tones, usually shorter in value than the following ones, which move to the appropriate tone or tones in the next chord in advance of the other voices.
Pedal tones are still another method of introducing artificial dissonances. They probably derived their name from the fact that such notes appear extensively in organ scores, and are played upon the pedals. The fact that they are also called organ points assists in this conclusion. Pedal tones are sustained by one or more voices through a succession of harmonies forming a consonant part of some of them but entirely foreign to the rest. It is generally found in the bass, although this need not always be the case. The pedal tone is usually the tonic or dominant, the latter being the more common and the tonic appearing more often near the end of a movement.
It is indeed striking to note how hedged in by rules are these oramental effects which themselves are but the out-growth of man's ingenuity at a comparatively recent date. They have served as a nucleus around which have gathered rules resulting entirely from what musicians have considered beautiful.
Not alone does harmony have to deal with the simultaneous sounding of tones in chord but the progressions from chord to chord are vitally important. No wrong will be committed if any chord of any key follow a chord entirely foreign to it. However, the composer is telling a story or describing an emotion and he must arrange the progressions in such an order that he may logically carry out his purpose. Hence, to produce valuable music, each new combination of tones must bear some relation to the combination which pre-cedes it. In this respect the rule is not akin to the multitude of purely arbitrary rules which govern music, but has a reason to uphold it. Nevertheless, the reason itself rests upon custom and upon man's idea of the beautiful, as shall be seen later.
In order to thoroughly appreciate and enjoy music the mind must act in the same manner as it does when listening to an oration or when reading a book. Unless a break occurs which is recognized as intentional and significant of a change of thought no abrupt transition is countenanced. There must be a continuance of ideas along a similar vein until a new subject is introduced, when another family of thoughts may be ushered in.
Students of harmony have gleaned through observation of music which has been accepted and is still deemed proper that certain relations have been found most satisfactory, and these relations have been repeated time and again until the rules governing them have grown into the rules governing harmony.
There are various ways in which chord relationships may exist. That which appears most simple and most obvious is that the chords should have the same tonality, that the tones which form them should belong to the same key of the same diatonic scale. Chords can be formed upon the various degrees of the scale, and if these, chords are not dissonant the passage from one group to another appeals to the ear as being entirely proper and to the mind as possessing a logical sequence. Another device by which the ear is made to realize a proper relation to exist between chords is by having one or more notes common to both chords.
There are also physical reasons which are allowed to figure in determining what are considered proper relations to exist between them. When discussing the fundamental and its natural harmonics it was learned that the octave as the first harmonic bears the simplest relation to the fundamental, but it has also been learned that the interval of an octave is not considered in harmony. The harmonic bearing the next simplest relation is that which is the interval of a fifth from the fundamental and the next simplest relation exists between the third harmonic and the fundamental which are separated by the interval of a fourth. The fifth assumes the place of dominant among the degrees of the scale and the fourth that of subdominant. As long as harmony has been in existence the chords on the dominant and subdominant have been recognized as bearing the closest relation to the chord on the tonic, but it was not until Rameau, in 1722, that the explanation of this custom involving the relation of harmonics to their fundamental was advanced. It is peculiar that these three chords contain between them every note of the scale. Throughout every composition they are used more frequently than any others and thus serve in preserving unity and in firmly impressing the key upon the mind of the hearer.
A cadence is the ending of a phrase in music and that found at the close of a composition is composed of the chord of the tonic, which is always at the end of a composition, ordinarily preceded by the chord on the dominant or that on the subdominant. That containing the chord on the dominant is termed the authentic cadence and is used much more frequently than that containing the chord on the subdominant called the plagal cadence.
The importance of the dominant and subdominant chords shows in what degree the laws of acoustics affect the progressions of chords although these progressions were recognized by musicians before the study of acoustics became a part of the study of music. Musicians instinctively demanded that the three chords under discussion should be available. In major scales they are all major triads, the second member of each forming with the root an interval of a major third and the third member an interval of a perfect fifth. In order to produce the desired effect the tones of the chords must bear these relations, and it was found that among all the authentic and plagal church modes or the ancient Greek modes as arranged by Glareanus and employed by secular musicians only one of the latter group, the Ionian, possessed intervals which allowed the degrees of the scale to be arranged in the proper manner. It was doubtless discovered when seeking a means of obtaining variety that in the AEolian mode these three important chords could be arranged with the intervals of a minor and a perfect fifth, thus forming the most striking contrast to those of the major scale, and still preserving a strong degree of similarity. The AEolian mode has descended as one of our modern minor scales.
These chords have been considered consonant and the relations which must exist between them are in a way very fundamental, the complications of harmony appearing with the introduction of dissonant intervals. The old rule that all dissonances must be prepared and resolved grew out of a custom brought into existence by the feeling that a consonance must follow a dissonance. This is perfectly logical, for a word cannot be inserted in a sentence where it has no meaning without robbing the sentence of all logical value; thus a dissonant chord is generally preceded by something very specially related to it and is always followed by some-thing else bearing a close relationship. Students of harmony learn this as one of the rules to be observed in writing music, but modern composers have assumed a broader and broader interpretation of the rule until they overlook it in so far as the preparation is concerned and precipitate a discord upon the ear of the hearer without having established any previous natural relation, also often disregarding the old custom of following dissonances by consonances.
Even an untrained ear can observe the incomplete effect of a dissonant chord, and unconsciously expects the following consonance, but it is seldom that the reason why the resolution of a dissonance has become customary is investigated. Immediately the answer comes that the reason is purely aesthetical, as are nearly all the reasons for the phenomena of music. The physical reason why certain combinations of two tones are consonant and others are dissonant in no sense constitutes a reason for the progression of chords containing these intervals. The mind derives real pleasure only from dwelling upon agreeable impressions, although it temporarily tolerates those which are disagreeable because it is the latter which produce excitement and tend to accentuate the agree-able impressions. We speak of a novel or a drama as interesting when it embodies more or less exciting situations, involving anxiety and distress, but how prone we are to disparage one which does not carry these situations to a happy or more settled close, in other words, to a proper resolution. Our aesthetic sense in nearly all cases requires an agreeable sequence of events. In like manner the mind agrees to dwell momentarily upon dissonant intervals, but the unsettled condition which thus arises must not last but must give place to the more soothing consonance. Dissonances are introduced for the same reasons as are the tense situations of the story or of the drama, that is, to satisfy the unconscious demand for excitement or change which is ever present.
The writer of music must not only realize that dissonance must be followed by consonance but he must understand the particular manner in which the progression takes place. Counterpoint was the birthplace of dissonances. Strictly this branch of the art deals with voice, and it was necessary that the passage from the discord to the concord should be made in the easiest way possible, which was by means of single diatonic steps. It was considered that an especial effort was required for a voice to properly pass to a tone forming a discord with another voice and the custom of preparation now appeared, for it was far easier to retain a tone from a preceding concord than to attack an entirely new one, creating a discord, so the voice which was to intro-duce the discordant tone was allowed to have it in the pre-ceding chord. It was likewise considered especially laborious for the voice to leave the discord, and the single step at once recommended itself as the most simple method. The fact that resolution is more generally affected by discant than by ascent is explained by the impression of increased effort given by heightened pitch. It requires an exertion to reach higher tones, which is not the case in descending to lower ones. In the latter case the voice may be allowed to relax somewhat.
Beyond the two general principles that a chord should possess an easily recognizable relationship with the one pre-ceding it, and that dissonant notes should pass to their proper places in the next chord by the easiest method possible, philosophy cannot assist in determining the progression of chords, but the resolution of dissonances- must be accomplished by applying the most expedient means. There are various rules that may be applied in all cases, and it is the composer's right to select that one best fitted to his purpose. There was a time in the history of harmony when only one resolution was considered proper for each discord, but now the composer may allow his own fancy to dictate the method he will employ and the world is being trained to accept the most unusual resolutions as satisfactory.
Modulation, the passing from one key to another, is one of the most important departments of music and to be handled well requires thorough musical education on the part of the composer. If a musical composition were written in but one key there would result a monotonous effect, for the material at the disposal of the composer would be too limited to afford a refreshing variety. Therefore, more than one key is used in compositions having a length of more than a few measures and the methods of passing from key to key and eventually returning to the first key in order that the music may end with the original tonic, comprises much that is intricate and much that requires both art and technique.
Certain keys are more closely related than are others. Hence, it is most natural to pass from one key to a nearly related one. Related major keys are those whose tonics are consonant ; the more perfect the consonance the closer the relationship. Any major key is most closely related to its dominant and subdominant and to the relative minors of these three keys. Any minor key is most closely related to its dominant and subdominant and the relative majors of these three keys.
There are three methods of modulation in common use : the diatonic, the chromatic and the enharmonic. In diatonic modulation only chords which are entirely diatonic in the keys concerned are employed. It has been noticed that certain chords may occur in two keys although they will be situated on different degrees of the scale. Such chords are called common chords and are employed in diatonic modulation. If the key of C has been in use and the triad on the dominant, G B D, is employed, it will be seen at once that this same chord occurs on the tonic of the key of C, hence, although only chords in the key of C have been used previous to this chord, after its introduction chords of either the key of C or the key of G may follow, and in the case chords in the key of G are used modulation has taken place. It is only necessary to establish the new key, which is done by observing its tonality through a progression of several chords. Passage to remote as well as to related keys may be made by common chords, although the process is less simple. It is done by means of transition or intermediate modulations. The new key must be reached by passing through other keys which are more closely related to each other. The keys through which transition is made do not need to be strongly marked, for they are of no importance except as a means of reaching the new key.
Chromatic modulation does not require common chords as does diatonic, but by again referring to the key of C it will be perceived that the triads D F A occur on the super-tonic and by studying the triads of the key of G it will be found that the combination most similar is D F sharp A on the dominant of the new key. Were it desired to modulate from C to G the chord of D F A could be used and by sharping F the chord of the new key would appear. In case it were desirable to pass to a key employing more sharps or several flats, more than one member of the triad might be changed. In fact, the alteration of triads may be made in any manner. It is evident that owing to the use of the tempered scale a key in which certain degrees are sharps may be the equivalent of a key in which certain other degrees are flats, because the same chromatic tones must be used in both cases. For instance, the keys of C sharp and D flat are enharmonic equivalents and if it should be desirable to modulate from one to the other the only change necessary would be to change the original flats or sharps as the case may be to their enharmonic equivalents, sharps if they be flats or flats if they be sharps. A chord which is very serviceable in modulation is the dominant seventh, which is capable of irregular resolution. Consequently it may serve as a medium through which passage may be made from any key to any other key.
Pivot notes also afford ease in modulation. In diatonic modulation it is necessary that the original key and the new key have a common chord. However, in case the chord of the original key and the chord of the new key possess but one note common to each, and termed a pivot not., a smooth modulation may be effected.
Modulation, well developed, enchances the charm of a piece of music without limit. By its means all the beauties of every key are at the disposal of a composer, while if restricted to one key throughout a piece he would have access to but one-thirtieth of them. A composer should not change from key to key without any reason, but as in all other departments of music he must be governed by as clear logic as though he were writing a treatise. Modulation into related keys is expressive of candid and simple feelings, but when the passage is to remote keys the effect is slightly abrupt and surprising, and should occur only when this effect is desired.
At times a composer wishes to remain in one key for an unusually long period, but fearing to create an unpleasant monotony he occupies the mind with a modulation to some distinct key thus refreshing it with an entire change of thought before resuming the first key. Or he may desire to draw a strong contrast between two keys which he will alternately employ for long periods. Ordinarily modulation occurs at frequent intervals during any piece of music.
Its use is the outgrowth of development extending through many centuries. Only the church modes were used until the Sixteenth Century when Glareanus introduced his conceptions of the Greek modes, without which harmony would have been impossible. First modes, or the systematic successions of intervals between the tones of the scale, were recognized. Then the importance of the method of the distribution of notes which we call key began to be realized. However, not until the Seventeenth Century did musicians to any great extent grasp the possibilities such a method presented. Without a comprehension of single keys there could of course be no modulation, but it became very essential to understand the artistic use of accidentals in chords, which is in fact chromatic modulation. Nevertheless, there was no attempt to establish a key after it had been introduced by an accidental and the composer was very likely to decide to use another accidental in the next measure and by so doing introduce another key. He was handling the notes merely as to their individual worth to him and no heed was paid to their relations to a common tonic.
To ears trained to the perception of keys and modulation, the older composers appear to have wandered aimlessly from one closely related key to another. Nevertheless, this use of accidentals was the foundation of modulation. The acute musical sense of the composers led them to search for closely related chords until at last there appeared groups of chords which corresponds to the present day tonality. By the use of accidentals very fine effects were produced, but there remains an impression of irregularity when judged by moderns.
In the early part of the Eighteenth Century composers came into a thorough realization of what pure tonality consisted, and for some time remained content to continue in one key for long spaces using modulation sparingly. This was the period when modulation was least in evidence. It was the turning point from its unsystematic to its systematic use. When it was employed passage was made only to the most closely related keys, such as to the dominant. No design seemed to underly the use of keys, but the composers wavered back and forth, fearing to go too far from the original key. This method is very evident when compared with the bold manner in which modern composers strike out and pass from one key to another without regard to their degree of relationship if the passage may be made smoothly and gracefully. They are upheld by a perfect confidence in their ability to go where they will and to return in safety.
To say that all the composers of the Eighteenth Century were faltering in their employment of modulation is too comprehensive, for there was one who was far in advance of his time, so far that his contemporaries could not comprehend the wonderful devices which he introduced. The methods of Johann Sebastian Bach were so beyond the comprehension of the period that other musicians failed to grasp the suggestions he extended them, but continued in their puerile fashion, allowing it to remain for the composers of a hundred years later to learn from him. After Bach came others who little by little advanced to the height which he had attained and at last a definite and clear system of key distribution was worked out.
Haydn and Mozart employed simple successions of keys. They distinctly established each key which played an important part in a composition and left no doubt whatever as to their intention, following out a logical order of changes.
Modulation may be considered as the opening of a comprehensive key system of which the key systems resting upon single tonics are integral parts. When harmony was first introduced there began an irregular succession of discoveries as to chords which effectively followed one another. The variety was limited to the scope of one key, but by modulation keys may be made to follow each other in a similar manner as did chords. This is a branch of the art which every day is being developed and which promises to be even more fruitful in the future than in the past in delightful effects.
