All sound is the result of vibrations in the air occasioned by the vibrations of some substance as the vocal cords, strings of instruments, columns of air, membranes, or sonorous bodies. The normal ear can perceive clearly sound vibrations occurring at a rate of from 16 to 36,500 per second. No possible statement can be made of the number of sounds produced between these two extremes. The more educated and trained the ear the more capable it will be of distinguishing differences in pitch. As a result this ability varies greatly in individuals just as some have by inheritance, environment and education a very finely developed sense of taste or smell.
Sounds are contained in all noises of nature, such as the wind blowing through the trees or in the roaring of the waterfall or of waves, but although the sound rises and falls in pitch, it is not music, for each tone has no definite pitch, neither does it bear a previously determined relation to the tones preceding or succeeding it. The tones which are gathered together to constitute any musical form are selected from a definite series whose individual tones progress in pitch by well defined degrees. This series is called a scale. The name is derived from the Latin word scala, a staircase, in recognition of the analogy existing between the progressing series of tones and the ascending steps of stairs. The Germans further express the comparison by using the name Tonleiter, a ladder of musical sounds, and the French employ the one word, ιchelle, to designate both scale and ladder.
This arranging of musical tones into a definite series has always been done by all races possessing music. Helmholz attributes it to a psychological reason similar to the natural feeling which has led to the rhythmical division in poetry. In other words, it is due to that inherent quality of rhythm whose reason lies beyond man's explanation but which is present in everything. It is within the realm of aesthetics. A constant factor in the problem of this science of the beautiful is to discover what it is in things that makes them beautiful or ugly, sublime or ludicrous. The explanation is ever receding and incomplete, universal laws of aesthetics cannot be established, for beyond a certain point training loses its power and each man becomes an authority unto himself, individuals having vastly different tastes.
The degrees of progression in the scale are not the same among the various races, but have differed with the epoch, the civilization, the tastes and the natural surroundings of the people. There are now in existence scales so different from our own that much training and familiarity are necessary before the beauties of their intervals can be appreciated by an alien ear.
Music in embryo is the sustained sound of a voice at different pitches. This constitutes the music of savage races whose scales may be limited but who delight in repeating a few tones, thus producing a species of chant. The true qualities of a primitive chant can only be appreciated when heard as the savage produced it, for when translated into the tones which constitute our scale it necessarily is changed owing to the difference in the number and magnitude of the intervals.
There are three points in which all scales agree. They each contain the octave, the fourth and the fifth. Scales of different civilizations and localities may contain any number of intermediate tones, but all agree in having established the natural relationship between the tones which are separated by the interval to which we refer as an octave, a name derived from the Latin word octo, meaning eight and used in this connection because the interval has been divided by eight tones, termed the degrees of the scale. The intervals between the other intermediate steps may be of various magnitudes, but the octave, fourth and fifth are always recognized. The reason for this is founded on the most simple laws of acoustics.
When a string vibrates in its entire length it produces the lowest tone of which it is capable, called its fundamental tone. If the string be lightly touched, or in technical language, stopped, in the middle of its length and caused to vibrate, it will do so in two equal lengths and, as these are each half of the entire length of the string, the vibrations will occur twice as fast, producing a tone an octave above the first. For instance, if a string in its entire length vibrated 128 times per second, the same string in two lengths would vibrate 256 times, just twice 128. If the string be stopped at a point one-third of its length, the smaller portion of it will produce a tone with 384 vibrations. Again, by stopping the string at a point one-fourth from the end, the smaller portion will produce 512 vibrations. The tone resulting from the 128 vibrations has been designated as C in the bass clef (to be explained later), and that containing 256 as middle C, the eighth tone above the first. The tone containing 384 vibrations is G occupying the fifth position above middle C, and that resulting from 512 vibrations is C occupying a fourth degree above G and two octaves above the lowest tone produced by the string.
This series of partial tones, as they are called, can be carried on infinitely, for, in theory, a string can be divided without end. Taking the partial tones in their numerical order, which corresponds to the vibrating sections of the strings, the intervals between decrease, for the ascending partials become nearer and nearer together. The ratio of the vibrations of sounds having the relations of an octave is as 1 : 2, for borrowing from the above example, as 128 is one-half of 256 the ratio of the two sounds would be as 1 is to 2, the ratio representing sounds in the relation of fifths is as 2: 3 for 256 is twice 128 and 384 is three times 128, hence, they and the sounds they produce bear the same relation to each other as 2 does to 3, and in a similar manner the ratio representing the relationship of fourths is as 3: 4.
The magnitude of an interval existing between two tones is determined by counting the intervening tones and including both the lower and the higher tones. Note several instances : The interval between any two tones having the relation of a third, in other words between two tones of which the higher is the third above the lower, such as the first and third, the second and fourth, the third and fifth, etc., is a third. The interval between any two tones having the relation of a fourth, such as the first and fourth, the second and fifth, the third and sixth, etc., is a fourth. The interval between any two tones having the relation of a fifth, such as the first and fifth, the second and sixth, the third and seventh, is a fifth. The interval between any two tones having the relation of a sixth, such as the first and sixth, the second and seventh, the third and eighth, etc., is a sixth. The interval between any two tones having the relation of a seventh, such as the first and seventh, the second and eighth, etc., is a seventh. The upper extremes of the intervals may be removed one or more octaves away but the magnitude and the name of the interval remains the same. The smallest interval is a second, for there can be no interval between a first and the duplicate of itself, but if two like tones are sounded it is termed a unison.
Music in its most primitive form probably arose from the very natural tendency to sustain the voice on one tone in shouting or chanting. This is monotonous and the easiest way of obtaining variety was by changing the pitch of the sustained tone. It is not natural that one individual should continue this form of music. A man's voice singing a certain tone can be imitated by another man's voice giving the same tone; but if a woman endeavors to imitate the sound she will find the pitch too low and will produce that tone nearest like it that her vocal organs allow, which will be an octave higher than that produced by the man. The two tones have a ratio of 1: 2, which is the most simple ratio possible.
Thus it is seen that the most simple laws in mathematics establish the octave, fifth and fourth, which have always appeared in the scales of all nations, and have served as guides in the formation of the rest of the scale, although the other intervals have been established at the will of man and owe their present character to the instinct for the beautiful as possessed by musicians.
It has already been mentioned that the scales of all nations agree in having established the intervals of an octave, a fourth and a fifth, but beyond these points of resemblance there are great differences in the intervals which divide the octave. We feel that our present musical system is the most perfect and it certainly has been subject to the most improving influences. There are, however, nations whose scales contain much smaller intervals than are found in ours, this fact indicating a more acute sense of hearing, for we are unable to appreciate the slight differences between some of the tones.
China, however, employs fewer tones than we do. Their system dates from nearly 3000 years before Christ and recognizes the octave, which they theoretically divide into twelve equal parts. This scale of thirteen tones bears a striking resemblance to our scale, as it is divided into semi-tones. There are in use only five tones which correspond to those represented by the black keys of the piano.
The Arabs have a complicated scale. In fact, their system possesses a great interest because of its extraordinary peculiarities. It agrees with ours in the two most important intervals, the octave and the fifth, but the resemblance ends with the introduction of the smaller intervals, of which there are sixteen or seventeen, according to different authorities.
The musical system of the Persians holds an unusual interest for us because in it we can faintly discern an ancestor of our own system. They have divided the octave into twenty-four intervals, each one being equal to half of one of our semitones. This resemblance suggests that our system may be derived from that of the Persians, and the suggestion is further substantiated by the fact that history tells us that the Persians, at a very early day, migrated to Greece, where they settled and in time received new names.
The scale which we use began its final development in the hands of the Greeks, the history of whose music is greatly obscured until about the Sixth Century before Christ, although in the meager records concerning a musician and poet named Olympus living about 1400 B.C., there is evidence of a regular system. The chief elements of the Greek scale had been reduced to four tones, which are sounded upon the four strings of the lyre known as the tetrachord. Without doubt, the interval between the two extreme strings was a fourth, which remained the chief element through all the subsequent changes of the Greek scale. The tuning of the intermediate strings is very uncertain and doubtless several methods were in use.
Terpander, who lived about 670 B.C., has received the name of Father of Greek Music because of the improvement which he wrought in the tetrachord by adding three strings, tuning the seven so that they formed a double tetrachord with one common tone at the junction. The common tone was the most important of the seven and was called Mese from its position in the middle.
The entire system was crystallized by Pythagoras, the Greek philosopher and mathematician, who lived about 600 B.C. Among other things he instituted a society at Crotona, whose precepts are most interesting although many of their beliefs and practises are shrouded in the secrecy with which the members invested themselves. They believed that the world subsisted by the rhythmical order of its elements. The distances existing between the heavenly bodies and the earth were considered to have been determined according to the laws and relations of musical harmony and each body in its motion was supposed to create a certain tone whose character depended upon the distance and the velocity of the body. The tones produced by the various bodies taken together formed a musical scale and the harmonious music produced was either unheard by the inhabitants of earth owing to the great distance of the heavenly bodies, or always having been accustomed to hearing it they did not perceive it, never having been able to compare the sound with stillness. Another possibility was that the sound was too great for their capacity of hearing. Herein is the theory of the Music of the Spheres which has ever since figured in literature and song.
Pythagoreans attached considerable importance to music and gymnastics in their daily life, each member of the society being compelled to possess a knowledge of the lyre, and none was allowed to retire at night without indulging in some form of music. It was used greatly as a means for exciting and appeasing the emotions. Pythagoras had a predilection for mathematical study and this led him to trace all things to number. He placed a numerical value, such as two or three, upon all the elements of nature and man, even associating this idea with music, which led to his numerical treatment of intervals. His great fondness for the art of music assisted him in his study of its science.
Pythagoras is well called the Father of Musical Science. He perceived natural laws and established acoustical facts which have stood the test of the many succeeding centuries. It has been impossible to discover a flaw in his reasoning and the only changes that have occurred have been added to the great foundation built by him. Previously, all intervals had been created according to the dictates of instinct, and Pythagoras fully realized the uncertainty of this guide. Therefore, he scientifically established the intervals and expressed the tones, marking them. by means of numbers corresponding with the number of vibrations which produced the tones. He studied the phenomena of sound vibrations by means of the monochord, an instrument whose body was a long, narrow, wooden box upon which was stretched a single string. Movable bridges were used by means of which the portion of the string to be vibrated could be limited at will. A similar instrument is still employed in studying sound vibrations.
He perceived that by dividing the string into shorter lengths, tones of higher pitch were produced. The most simple division was into two equal parts, giving a tone an octave above that produced by the vibrations of the entire string. The next simplest division of the string was into thirds, producing a tone which marks an interval called the fifth and conveniently dividing the octave. By dividing the string into four equal parts, a tone situated at an interval of a fourth from the last tone was produced. There is a remarkable symmetry in the fourth and the fifth, which at once presented itself to Pythagoras. After the fourth and fifth had been established they presented a means by which a much smaller interval could be determined by computing the difference between them, which was called a tone. By the use of the tones as a unit of division it was possible to complete the subdivision of the octave. Pythagoras in doing this turned his attention to the tetrachord.
Terpander had changed the four stringed lyre into one having seven strings by combining two lyres and giving them a common string. Pythagoras added still another string, in fact, combining two tetrachords with an interval of a tone between them, thus completing the octave. Using the interval of a tone, which he had found to be the difference between the intervals of a fourth and a fifth, as the unit of division, Pythagoras discovered that the interval of a fourth contained two tones and a fraction which as it was a little less than half a tone received the name of hemitone and which we now call semitone. The word tone as used here does not indicate the sound resulting from vibrations as it ordinarily does, but refers to the interval or step between two tones when the word is used to signify sound. The division of the tetrachord, as the interval of the fourth came to be called, into the lesser intervals of two tones and a semi-tone was designated as the diatonic system.
The tetrachord retained its prominence as the popular division of the Greek musical scale even after the establishment of the octave by Pythagoras, but the arrangement of the two tones and the semitone was not fixed and there appeared three varieties the Dorian, Phrygian and Lydian which differed as regards this point. The names were derived from the Greek nations bearing like names and it is believed that the arrangements corresponded with the traditions of the ancient scales belonging to them. The Dorian was considered the most orthodox and the entire interval of the octave was divided into lesser intervals according to that arrangement, that is, counting from the lowest upward the intervals occurred in this order : tone, tone, semitone, tone (marking the separation of two tetrachords), tone, tone, semitone. The seven intervals separated eight sounds, only seven of which differed from the others, the eighth being the repetition of the first, an octave higher in pitch. These different methods of dividing the interval of an octave are called modes.
After the octave had been established the scale could be extended with greater ease and after a time it was enlarged to two octaves by adding a tetrachord both above and below the original two. A record of this enlarged scale of Pythagoras, which derived the name of diatonic scale from the diatonic system of arranging the intervals, exists in a description left by the Greek mathematician Euclid, who lived about 300 B.C. He terms it the " Division of the Monochord " and gives the proportionate lengths of string capable of producing the various sounds in the scale.
At first the sounds of the Greek scale were denoted by names. Each sound included in the entire octaves and those designating the two extremes were given a separate name, there being in use fifteen different names. Later the names were discarded in favor of an equal number of arbitrary characters. When the Romans adopted the scale they discarded the Greek characters and invested the sounds with the names of the letters of their alphabet from A to P inclusive. During the latter part of the Fourth Century, A.D., Ambrose, (340-397), one of the Fathers of the Latin church, introduced music into the church, adopting the Greek diatonic scale. Many of the later developments in music were due to the work of churchmen attempting to perfect that employed in the church. Many of the hymns and chants were adaptations of popular melodies in no sense worthy of the use to which they were put. Although several authorities deny the claim, Pope Gregory the Great (540-604) is popularly credited with having done much toward the improvement of music. He is said to have gathered together all the hymns and melodies used in the service for all of the principal seasons of the church year and united them in such a manner that they were more easily preserved. He established schools for the education of choristers and would refuse to ordain a priest who did not possess a sufficient knowledge of church music. Perhaps as important as any of his works was the manner in which he simplified the nomenclature of the sounds of the scale. He was the first to recognize clearly the relationship which Pythagoras had established between tones situated at the distance of an octave apart and denoted them as they occurred in the course of the scale by the same Latin letter, only varying its character. For the first octave he used the capital letters A, B, C, D, E, F, G, for the second he used the small letters, and for the third the small letters doubled.
Guido d'Arezzo, an Italian Benedictine monk of the Tenth and Eleventh Centuries, has been falsely accredited with the invention of the staff or the series of five horizontal lines which are so arranged that when the signs or notes used to represent the musical tones are placed upon or between the lines, the pitch of the tones will be indicated by the position of the notes in respect to the lines. The etymology of the word refers to its function as a staff or assistant in determining pitch. At first the characters used to represent the tones were very crude. The neumes, as they are called, were irregular in outline and were doubtless derived from the hieroglyphics used by the old Jewish rabbis in indicating pitch in their chants. They possessed various shapes, resembling periods, commas, straight and curved lines, and were united to represent not single tones but groups of tones. They indicated where a melody was to rise and fall, and their arrangement showed the comparative rather than the actual pitch of any character. The neumes were placed immediately above the syllables to be sung, but it was impossible for them to enable a singer to read a new piece of music at sight. Doubtless they were employed to assist the singer's memory when attempting music which he had heard before. They were exceedingly inadequate and are unintelligible to present-day musicians.
About the year 900 a red line was added to indicate the actual pitch of one tone. This line was assumed to be F, and it naturally followed that the pitch of G and of E was likewise actually determined because of the position of the characters representing these tones immediately above and below the red line. Later a yellow line signifying C was added and the pitch of B and of D became actually designated because of their contiguity to C. Finally the colors were dispensed with and the letters F and G were written at the beginning of their respective lines. They acted as keys to the notation and thus acquired the name of claves or clefs from the Latin word clavis, meaning key. During the Eleventh Century two black lines were added, one situated above the yellow line and one situated between the red and yellow lines and designating E and A. Gradually the neumes were abandoned and the characters or notes became either square or lozenge shaped, the development into those now in use continuing gradually.
The fifth line of the staff was added about the time of Guido and a staff was produced very similar to the one now in use, although for a long time the number of lines which it contained varied. During the early Tenth Century a staff having a large number of lines was in use and the syllables to be sung were written between the lines at the proper pitch. The interval at which the voice was to proceed was denoted by the letters T and S placed at the beginning of the staff. They designated Tonus and Semitonum, the Latin words, meaning tone and semitone.
However, the mere five lines could not absolutely represent the pitch of a sound and the keys or clefs have been retained in use. Three principal ones are now employed. They are placed at the beginning of the staff and their position on the lines of the staff indicates the name and pitch of the notes standing on that line and relatively the names and pitches of all the notes on the lines and in the spaces above and below it. One clef indicates middle C and is not used in piano music nor much in vocal music, and hence is not familiar to many persons. Another clef indicates G, a fifth above middle C and is found in piano and organ music at the beginning of the staff in which are writ-ten the notes played by the right hand and in music sung by the soprano and alto voices. The third clef indicates F, a fifth below middle C and is found in piano and organ music at the beginning of the staff in which are written the notes played by the left hand and in music sung by the bass and tenor voices. These G and F clefs are also used in all instrumental music.
The ordinary staff of five lines can be increased by leger or added lines when necessary. These lines are employed when the range of notes used extends beyond the number which can be placed on or between the five lines. They are only the length of a note and can be added above or below the staff indefinitely, although when the number of added lines tends to be too great for ease in writing or interpreting the notes are written an octave lower than they are intended to be sounded and a dotted line drawn above them and marked 8va, denoting that the pitch should be an octave higher. Before the invention of the leger lines, the C clef was used almost exclusively and its position on the staff was changed whenever the change of notes used overstepped its limits. The positions of the clefs now in use are changed at times to avoid adding a very large number of leger lines. As has been seen the diatonic scale consists of a series of groups of seven sounds, for no matter what may be the extent of the scale it is merely made up of repetitions of seven sounds at the distance of an octave apart. One of the seven is selected and the other six are made subservient to it regarding certain relations which are of much importance in the structure of modern music. This important tone is called the key-note or tonic and the system of relations that hangs upon it is called tonality.
In the days of the Greeks the keynote was the mese or middle tone. Aristotle attributes to the middle string of the lyre an influence over the tuning of the other strings and a very frequent use in all compositions. It is a question as to what place in the octave the mese occupied and although one writer ascribes the position of fourth above the lowest, the more general belief is that it was the lowest, which naturally would be the more important as it designates one extremity of the octave. It is also believed that every composition ended in it. The tonality of the Greeks eventually became very complicated and has presented many difficulties to the investigator. Not until the middle of the Eighteenth Century were there presented any facts which might be considered authentic. The eight stringed lyre or double tetra-chord, an instrument which has previously been discussed, was in nearly all instances used in accompanying vocal music. It was tuned so that an interval of an octave existed between the highest and lowest strings. The diatonic system had decided that this interval of an octave should be divided into seven lesser intervals, five of them tones, and two semi-tones. Given these seven intervals there were possible seven methods of arranging them, each arrangement placing the semitone in new positions. The various arrangements are known as the Greek modes. The individual characteristics of each mode rested entirely upon the positions it gave the semitones. As time progressed changes were wrought in the modes, and their number was increased. Each addition that was gathered tended to make the Greek musical system more complex and less easy to understand. Furthermore, only vague and unsatisfying records have been left us of the conditions existing during the years preceding the rise of Christianity. Therefore, at this juncture a break occurs in the history of the structure of music.
With the coming of Christianity there was a very evident change in musical structure. Music as the expression of sentiments and belief in the Christ was productive of new sensations which sought expression. Furthermore, the believers were admonished to sound their praises by means of music, but it was only natural that the old music should serve as a foundation for the new, which grew from ideas borrowed from the ritual of the Jews, and from the temple and secular music of the Greeks.
Ambrose, in the Fourth Century, greatly simplified the modes by rearranging them until only four were retained. The tones of each mode were comprised within the interval of an octave counting upward from the keynote. The four modes of Ambrose are designated as the authentic modes and served as a foundation to four new ones which were added by Gregory two centuries later. These were called plagal or leaning modes, because of the relation which they bore to the authentic modes. The compass of the plagal modes was only an octave, as was that of the authentic, but the tones were limited to those between the fourth below the keynote and the fifth above the keynote. As an instance let the notes D, E, F, G, A, B, C, D, represent the first authentic mode. From this the first plagal mode was formed by using the notes A, B, C, D, E, F, G, A. In both cases D was the keynote. The compass of the mode had been increased down-ward by the interval of a fourth, but as it ascended had been decreased in the same degree. When a melody was written in any authentic or plagal mode the variety of notes which might be used was limited to the eight found within the interval of an octave and having positions as stated, either between the keynote and the octave or between the fourth note below the keynote and the fifth note above it. At times a mixture of the authentic and plagal modes was used, in which case the compass of both modes was employed and the range of notes was between the fourth note below the keynote (as in the original plagal mode) to the octave above the keynote (as in the original authentic mode). Again as time progressed the musical system became more complicated. In order to produce variety, which is always demanded by progress, several changes were made permissible and the simplicity which had been instituted by Ambrose was lost as had been the original simplicity of the Greek modes centuries before. Another reformation was necessary.
Tiring of the confusing authentic and plagal modes of Ambrose and Gregory, Glareanus, a writer of the Sixteenth Century and poet laureate to Emperor Maximilian, endeavored to create order. He made a diligent research among the old Greek modes and determined upon the use of six authentic modes and formed six plagal modes upon them. He attempted to give them the old Greek names, but became confused and did not bestow the correct ancient names upon the corresponding new modes. Nevertheless, his work was ignored to a great extent and the church modes remained in use in church music although two of those established by Glareanus, corresponding to our major and minor modes, were used in secular music.
When harmony began its growth it was found that the church modes were not suited to its use and they were discarded, leaving the two of Glareanus which had survived in secular music. One of these was especially abhorred by the pure-minded churchmen because of its incessant use by the Troubadours and other frivolous musicians. It was even called the modus lascivus, or wanton mode. However, it was the one most adaptable to harmony and has developed into our modern major mode, which has had such a general use that it has been employed in practically all the music written during the last two centuries. The older modes are some-times employed, and a decidedly powerful quality can be added to music when variety is obtained by the use of the church modes, the Dorian, the Phrygian, the Lydian, the Mixolydian, the Ionian and the AEolian. Handel shows his appreciation of this fact in the oratorio, " Israel in Egypt," where he employed the Phrygian in the chorus, " Egypt was glad," and the Dorian in the chorus, "And I will exalt Him?'
The intervals of the modern diatonic scale have been decided by tonality and harmony. Sounds may have the proper number of vibrations and may be perfect according to theory as based on the acoustical laws of Pythagoras, but when sounded together in the manner of harmony they are found to produce an effect which is not considered pleasant. As harmony has become the basis of our musical system this was a condition which could not be allowed to exist. It is true that harmony in a meager sense had already existed in melody where tones are sounded successively, for the same mutual relations are necessary in melody as in harmony. With the introduction of harmony in reality the laws governing these relations grew into greater importance until they formed the basis for fixing the exact positions of the tones in the scale. Notwithstanding the importance of harmony in solving this problem it must not overstep the bounds of its power, but at all times the importance of the tonic must be considered and reference must be made continually to the keynote when determining the other seven tones of an octave.
The intervals established by the Greeks did not allow the application of harmony and to satisfy the aesthetic sense of musicians the magnitude of some of the intervals was changed. The intervals of a tone between D and E and between G and A were lessened, or flattened, and the intervals of a semitone between E and F and between B and C were increased. Thus the scale as it now exists owes its intervals in a large degree to laws made by man.
The diatonic scale with C as a keynote is represented by the white keys of the piano or organ. The black keys represent notes which, when added to this diatonic scale, form the chromatic scale. Chromatic notes mark intervals of semitones, similar to the two which have always existed in the diatonic scale. They have been added owing to the natural desire of musicians to increase the available number of tones. A continuous succession of semitones is also a very natural arrangement, suggested by the two semitones already established. The semitones, like the tones, must have mutual relations with the keynote. They are generally considered as the tones of the diatonic scale changed by having been raised or by having been lowered half a tone, the name of the diatonic tone being retained. Nevertheless, this' is by no means the case, the chromatic semitones being entirely independent of the tones in this respect and being worthy of independent names if the simplicity of the notation would not then be detracted from by so doing.
The semitone of theory is not exactly half of a tone and when the distance it represents is counted upward from a given tone, say A, and then is counted downward from a tone above A, which is B, the new tones will not be identical, but the first, A sharp, will be a little below the second, B flat. This difference is called a Pythagorean comma and is of such minute magnitude that it is hardly distinguishable by the average ear and, though playing a somewhat important part in the mathematical consideration of the scale, is practically of no importance musically. The difference of opinion of physicists and musicians as to right and wrong on this subject has led to reciprocal concessions and a half-way point has been established, so that now the two tones are considered as sounding alike. This system of dividing the scale into almost equal intervals is termed equal temperament and its general use dates from the early part of the Eighteenth Century.
According to the more complicated and theoretically correct system having two chromatic tones between each two notes of the diatonic scale except when the interval is only a semitone, the chromatic scale would consist of seventeen tones instead of twelve as it now does. They would be C, C sharp, D flat, D, D sharp, E flat, E, F, F sharp, G flat, G, G sharp, A flat, A, A sharp, B flat, B. It is true that in order to simplify the scale into the twelve notes it was necessary to put many of the intervals out of tune, the interval of the octave remaining in its theoretical perfection. However, equal temperament distributes these unavoidable inaccuracies in tuning among the twelve chromatic tones in such a way that although no one of them is perfectly pure the deviations do not offend the ear.
Johann Sebastian Bach appreciated the great practicability of equal temperament and in 1722 there appeared his famous Wohltemperirte Clavier which contained twenty-four preludes and fugues, each one having been written in one of the major and minor keys of the twelve chromatic scales. It was a wonderful and most valuable demonstration of the manner in which the scales could be used after equal temperament had been applied to them. The new tuning opened opportunities for variety in composition that had hitherto been closed, for in the old theoretically correct tuning the music could only be written in the few keys in which a limited number of chromatic notes were employed.
It has so far been found impracticable to furnish key-board instruments with seventeen keys in the interval of an octave. If it were done the keyboard would be so extensive that the fingers of the performer could not cover a range of notes nearly as great as is now possible. Thus it is that equal temperament has made it possible for these instruments to become as generally useful as they now are. This tuning is as perfect as our musical system requires, as has been proved by the thorough test which it has undergone for the past two centuries.
Only an exceptionally trained ear can distinguish between equal tuning and theoretically correct tuning. The exactly pure tones can be produced only by the voice or with a flexible instrument such as the violin or the trombone. The vocalist and the performer upon these instruments have the power to determine the pitch of each note which is given, while the pitch of other instruments is previously determined by the tuner. The violinist decries equal temperament as improper, and objects to the piano, declaring that it is discordant. Nevertheless, as far as the piano and a host of other instruments are concerned, equal temperament is a necessary evil and the violin, the voice, or the trombone, must follow the newer tuning when used with the other instruments.
The divisions of half tones were noted by the Greeks, and because of their value in embellishing the diatonic scale were likened to coloring, and called chromatic tones. In church music the use of the chromatic tones was left to the dictates of tradition or to the taste of the singers until the Sixteenth Century, when the chromatic scale in its entirety was adopted.
Chromatic notes can be used to embellish melody with-out changing the key or can be introduced in the production of new diatonic scales by modulation. In the latter case variety is secured by adopting various notes of the diatonic scale as keynotes. It has been seen that in the diatonic scale the intervals of tones and semitones are arranged in ascending succession as follows : Tone, tone, semitone, tone, tone, tone, semitone. When C is the keynote and in the arrangement of the keyboards of the piano and organ, the semi-tones occur between E and F and between B and C. The intervals of tones and semitones must always follow the same sequence, and in order that this may be so when the key-note is changed it has been found necessary to add more notes to the scale, which can be done only by introducing chromatic tones. If G is determined upon for the keynote, it will be found that F, as it appears as a fourth in the key of C, is out of place and a new tone situated a semi-tone higher must be found to act as a seventh in the new scale so that the intervals may have the correct magnitude.
The new tone will be F sharp, a semitone above F and when it has been substituted the intervals will occur in their proper order. For the same reason tones must be flattened in a similar manner. If F is determined upon for the key-note it will be found that B as it appears as the seventh in the key of C is out of place and a tone situated a semitone lower must be found to act as a fourth in the new scale so that the intervals may have the correct magnitude. The new tone will be B flat, a semitone below B and by means of its substitution the intervals will occur in their proper order.
Every semitone may be a keynote. As the number of chromatic tones which must be substituted for those of the diatonic scale in order to maintain the proper succession of intervals, varies from one to seven, it is easily perceived that the array of chromatic signs in a piece of music would often be bewildering to the reader. To obviate the otherwise necessary repetition of the chromatic signs, a key signature is used. Just after the clef in the beginning of the staff the proper number of chromatic signs, sharps or flats, are placed upon the lines and spaces where the chromatic notes should occur during the entire piece, or until a new signature is inserted denoting a change of key.
The signs which indicate chromatic tones came into existence at various periods. That which marks the flat is of most ancient use and is found in the books of chant from about the year 927. Near the close of the Thirteenth Century there appeared the sign of the sharp in a slightly different form from that now used. The natural sign which destroys the effect was used in canceling the flat about the middle of the Seventeenth Century and has been employed in canceling the sharp since the Eighteenth Century.
As has been discussed heretofore, the arrangement of the intervals forming a scale has been in accordance with the major mode. In the minor mode the arrangement of intervals differs, wherein lies the distinguishing features of the mode. The original minor mode was the AEolian mode of Glareanus, but it is now not used exclusively. The succession of intervals in this mode is 12 345 678, which may be compared to the following succession as found in the major mode : 123 456-7 8. (The intervals of a tone are signified by and those of the semitone by .)
It is seen that the interval of a third, from 1 to 3, in the minor mode is less than the same interval of the major mode, and it is from these intervals that the modes derive their names. The third of the minor mode consists of but a tone and a semitone, hence, Lesser or Minor, while that of the major mode consists of two whole tones, hence, Greater or Major. In fact, the minor mode was at one time called the mode of the smaller third, and the major the mode of the greater third.
It is also to be seen that the interval between the seventh and eighth of the major mode is a semitone. The modern ear requires that the seventh degree be what is termed a leading tone, that is, it should possess such a marked relation to the eighth that when it is sounded we shall expect it to go to or lead up to the keynote. Hence. the interval of a tone was changed to a semitone which change, however, created an interval of a tone and a semitone between the sixth and seventh degrees so that the succession was thus: 12 345 6+7 8. The plus sign signifies the position of the interval of a tone and a half. (6 and 7 should be separated more than other degrees.) This succession filled all the requirements of music and is termed Harmonic, but the voice has no natural tendency to observe such a large interval as a tone and a semitone and it became advisable to overcome this difficult interval. This was done by increasing the interval of a semitone between the fifth and sixth degrees to that of a tone. The change brought about a new succession of intervals as follows : 1-2,34-5-6-7 8. As the scale descended it was also found well to change the succession thus :8-7-6 5-4-3 2-1 This scale is generally used in music for melodic construction for which reason it has received the name Melodic.
Rhythm is the idea of motion which is in music. Any succession of long and short tones contains a rhythm in that it possesses a complete motion peculiar to itself. In listening to music it is easy to observe the end-point of rhythmical divisions for at these points it is instinctively felt that a pause must occur and that a new motion must begin. Very similar is the instinctive realization that rhetorical pauses should occur at certain places in a literary composition.
Metre, the measure of music, is generally accepted as an essential feature of musical composition. It probably dates back almost to the beginning of music, when other voices joined that of the leader in the primitive chant. It was necessary that they be guided in some manner so that all would attempt the same tone at the same time. The most evident guide was the duration of the tones and when the length of duration had been determined upon the smallest definite measure in music had been selected. In poetry the syllables of words are arranged according to a measured form of some description, several syllables of varying lengths being contained in each division of the measure. When poetry was combined with music the metrical division which is the distinguishing feature of poetry made necessary similar metrical divisions in the music. The Greeks used a most elaborate system of metre which corresponded closely to that of their poetry. When music and poetry were combined the duration of the tones corresponded with the length of the syllables. Short syllables were sung to short tones and long syllables to long tones. This system of unequal length of the tones was also applied to the music when unaccompanied by poetry.
The writers on music of the early Christian era have maintained a bewildering silence in regard to measure and it is a matter of doubt as to its existence, but Fιtis in his History of Music shows the existence of signs of measure in church music of the Seventh Century. The method of regular uniform measure which runs throughout is of comparatively modern adoption and dates from the beginning of the use of the present system of notation. The system of placing the syllables to be sung between the lines of the staff in the place of the older neumes was followed by the use of angular periods or points placed on the lines of the staff instead of between them. The intervals to be observed were denoted by Greek letters placed at the beginning of each line of the staff.
This method in turn was followed by one in which notes of various values were employed. They were the Large, the Double Long, the Long, the Breve, the Semibreve, the Minim, the Greater Semiminim, the Lesser Semiminim or Fusa, the Semifusa and some of even smaller value, each note being equal to two of the next lesser denomination. The Semibreve is now known as the whole note, the Minim as the half, the Greater Semiminim as the quarter, the Lesser Semiminim as the eighth, and the Semifusa as the sixteenth. However, no exact length of duration had been determined for any of the notes and they merely represented proportionate duration. When independent melodies for several voices were arranged to be sung together the system of balancing two against one breve or two breves against one long was adopted. Owing to the absence of an exact measure or duration this system of notation proved inadequate and the necessary improvement gradually brought into existence the present notation and exact measure of duration.
Bars are the vertical lines which extend across the staff dividing the musical compositions into parts possessing equal duration and indicating the periodical occurrence of the accent. They may have originated in similar lines of varying lengths which extended across certain lines of the staff and at an early date indicated rests. The name bar has been incorrectly applied to the measure, which is that part of the staff found between the bars. At first music was not divided into measures, there being no necessity for it as the notes were all of one length. Later they were given various lengths and it became necessary for it to be measured, but bars were not employed, the value of the notes determining the metre. However, the values were changeable, depending upon the order in which the long and short notes followed each other. To overcome this deficiency the use of a mark called in Latin punctum divisionis, meaning point of division, was introduced. In appearance it resembled a period, but had no effect upon the value of the note it followed, only marking the rhythmic periods.
The bar began to make its appearance gradually and was used at times to mark the end of each verse. It was first used in music in which independent melodies for several voices had been arranged to be sung together. These parts were written under each other and the bars extended through the several staffs in which the notes were placed in order to aid the musicians in keeping together. A double bar marks the close of an entire composition or of any part of it which is complete in itself. This sign has nothing to do with marking the metre and does not need to occur at the end of a bar. The double bar preceded, succeeded, or it may be both, by a colon is the sign of repetition and is used when any theme is to be repeated for any reason.
The introduction of bars thus brought about the system of constant measurement known as metre. Each measure of music must contain a certain number of beats or time units. The number need not remain the same throughout an entire piece of music, but must continue through two measures, at least, until its regularity is apparent. Each beat or time unit need not be represented by an individual note, but one note may have the value of two or more beats and two or more notes the value of one beat. Furthermore, rests may occupy the positions otherwise held by notes and may possess various time values in the same manner as do notes. This, however, merely establishes a symmetrical order and the beats or time units may occur at various speeds, which are approximately indicated by words placed above the staff.
Medieval writers describe two kinds of time, perfect and imperfect. Perfect was that in which a breve was equal to three semibreves. The name was derived from the fact that the term perfect was always applied to the number three because of its association with the Ever Blessed Trinity. In imperfect time a breve was equal to two semibreves. At the beginning of every piece of music, immediately after the key signature, if there is one, there is placed a figure which indicates the metre and which is called a time signature. It is generally a fraction, the numerator of which indicates the number of beats to be found in a measure and the denominator the value of the notes representing each beat, although the values may be expressed in notes of other values. There result two general divisions of metre, duple and triple. In duple metre the number of beats which are contained in a measure is divisible by two and in triple metre the number is divisible by three.
About the Thirteenth Century time signatures made their appearance. To signify perfect metre the circle, as the most perfect of figures, was used. As the signature of imperfect metre the semicircle was employed, by token of its imperfection as a figure when compared with the circle. This sign has been retained and is used to indicate what is called " common time." Its form has changed until it bears a striking resemblance to a C which has led to the too-hasty sup-position that it referred to the word common, although the sign is used by nationalities who have no such word in their language. A horizontal bar through the sign denotes that each measure contains half as many beats.
There are innumerable methods of metrical measurement, but an explanation of a few signatures will give a general idea of their significance. The following for duple metre:
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The semicircle with the horizontal bar through it, or the fraction 2-2 denotes that each measure contains two beats, each one represented by a half note or its value in other notes.
4-2 denotes that each measure contains four beats, each one represented by a half note or its value in other notes.
The semicircle or fraction 4-4 denotes that each measure contains four beats, each one represented by a quarter note or its value in other notes.
6-8 denotes that each measure contains two beats, each one represented by a dotted quarter note or three eighth notes.
12-8 denotes that each measure contains four beats, each one represented by a dotted quarter note or its equivalent, three eighth notes.
12-16 denotes that each measure contains four beats, each one represented by a dotted eighth note or its equivalent, three sixteenth notes.
The following are triple metres :
3-2 denotes that each measure contains three beats, each one represented by a half note or its value in other notes.
3-4 denotes that each measure contains three beats, each one represented by a quarter note or its value in other notes.
9-8 denotes that each measure contains three beats, each one represented by a quarter note or its value in other notes.
9-16 denotes that each measure contains three beats, each one represented by a dotted eighth note or three sixteenth notes.
Modern composers have attempted irregular metres such as 5-4 and 7-4, 5-4 denoting that there are five beats in each measure, each beat represented by a quarter note, and 7-4 denoting that there are seven beats in each measure, each beat represented by a quarter note. A notable instance of the employment of 5-4 metre is by Arensky in his " Basso Ostinato," and Debussy has measured his " Nocturne " according to the 7-4 metre.
A system of metre is not followed without deviation, but the pleasure is increased and monotony avoided by occasional changes. The rate at which the music is to be interpreted may be quickened or retarded and any such changes are indicated by the Italian words, accelerando or rallentando. At times a pause is demanded when the motion is stopped altogether. The accent does not always fall upon the first note of the bar, but may be indicated for some other note, this system, termed syncopation, continuing for several measures. Another change is brought about by indicating emphasis of parts of the music after the same manner in which emphasis occurs in speaking. The success with which a composer varies the accent and emphasis constitutes in a great degree the success of his completed work.
We have now hastily traced the very gradual growth of the system of music, a system which doubtless has been changing with the ages and the races since the very beginning of the world, for we have no means of determining when or how the first music originated. We possess many conjectures founded upon observations of the methods employed in music-making by the most primitive peoples now in existence, but traces are found of the use of well-developed systems before the dawn of history. Except the most fundamental rules, those governing the system are founded upon no laws of nature but upon the changing basis of man's fancy, or more properly, his idea of the beautiful. This aesthetic sense changes with environment and training, and environment and the methods of training change with the years, so that coming generations will likely possess many additions to our varied history of music and its laws. We have, since the early Grecian period, authentic history of the changes that have been occurring in tonality, notation and rhythm and metre, but none of these changes has been based upon any scientific discovery but have occurred according to the dictates of musicians of the period in which they took place.
