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Musical Notation by Marie Howland


Why is it that the knowledge of music is not more common?—that is, why is it that there are so few people in this and every other country who are able to read and write music as they read and write their mother-tongue? Is it that the musical ear is a rare gift? Evidently not, for music is composed of a small number of elements, which are found for the most part in any popular air, and almost every person can sing one or more of these airs correctly. It is not, then, the musical ear nor the sense of time which is wanting. Neither is the cause to be attributed to the fact that few study music; for, although the teaching of music is by no means so general as it should be, still it is taught in our schools, public and private, singing-schools are common even in our small villages, and there is no lack of teachers both of vocal and instrumental music. And yet out of every hundred who take up the study of music, it is safe to say that about ninety abandon it after a short time, discouraged by the almost insurmountable difficulties presented at every turn. Only those succeed who are endowed with rare natural aptitude, an indomitable will, and time—four or five years at least—to devote to an art which is as yet a luxury to the masses of the people.

M. Galin, his pupil M. Chevé and other advocates of reform in musical notation declare that the people are deprived of this grand source of culture because of the blind, inconsistent and wholly unscientific nature of the ordinary musical notation. At first this seems incredible, but one has only to compare this notation with that elaborated by Émile Chevé after Galin's theory to become convinced that the statement is true. People are apt to say, "Why, it cannot be that our system of writing music is so defective: in this age of improvements and scientific precision gross inconsistencies would have been eliminated long ago." And so, indeed, they would have been but for the fact that the very basis of the system is altogether at fault. How are the Chinese, for example, to "improve" their system of writing? It is simply impossible. They have some thousands of abstract characters, hieroglyphs standing for things or thoughts. All these must be swept away, and in their place must come an alphabet where each letter stands for an elementary sound. These elementary sounds are few in number in any language. So of our musical notation. It is doubtful if it can be materially improved; it must be discarded for a system of fewer elements and a more clear and precise combination of them.

No, it is not strange that we have not adopted a better method of musical notation before this. Think how long a struggle it required to abandon the cumbersome Roman notation for the short, clear and precise Arabic—how many centuries of feeble infancy the science of mathematics passed before the invention of logarithms rendered the most tedious calculations rapid and easy. Most people take things as they seem, giving but little thought to their meanings and relations to each other; and so an awkward method may be followed a long time without protest. People are blamed for their devotion to routine, but devotion to routine is perfectly natural. It is mental inertia, and corresponds to that property in physics—the inability of a body of itself to start when at rest, or stop or change its course when in motion. And then the general distrust of new things—"new-fangled notions," as contempt terms them—retards the examination and adoption of improved and labor-saving methods.

It is more than fifty years since Pierre Galin, professor of mathematics in the institute for deaf mutes at Bordeaux, published his Exposition d'une nouvelle Méthode pour l'Enseignement de la Musique, and more than thirty since his distinguished disciple, Émile Chevé, demonstrated practically, in the military gymnasium at Lyons, the immeasurable superiority of that method; and yet such is the repugnance of teachers of music to any change in their routine that they have paid little or no attention to the work of Galin and his followers. The Méthode élémentaire de la Musique vocale, by M. and Mme. Émile Chevé, has never been translated into English. It was published in Paris by the authors in 1851—a work of over five hundred pages in royal octavo, and a most clear and exhaustive exposition of the method which they followed with such success.

In proof of the superiority of that method, an account of M. Chevé's test-experiment at the military gymnasium at Lyons in 1843 will be interesting. The gymnasium was at that time under the direction of two officers of the French army, Captain d'Argy and Lieutenant Grenier. The facts are taken from their official report of the experiment.

By order of Lieutenant-General Lascours the soldiers of the gymnasium were placed at the disposition of M. Chevé, that he might make a trial of his method. General Lascours further ordered that the officers in charge of the gymnasium should be present at every lesson, and report carefully the progress of the pupils and the final results of the course.

The members of the class were taken at large from the twelfth, sixteenth and twenty-ninth regiments of the line, fifty from each. M. Chevé accepted all as they came, and agreed formally to bring eight-tenths of the class of one hundred and fifty in one year to the following results: (1) To understand the theory of music analytically; (2) To sing alone and without any instrument any piece of music within the compass of ordinary voices; (3) To write improvised airs from dictation.

"Candor compels us to admit," says the report, "that nearly all of the soldiers showed the greatest repugnance to attending the course, and did so only because they were ordered to do so. Several months elapsed before this bad spirit could be conquered, and before the majority of them could be brought to practise the vocal exercises. Some even refused to try to sing, on the ground that they were old, that they had no voice, that they could not read, etc."

The first lesson took place October 1, 1842. There were five a week, of an hour and a half each. At the end of the month the professor wished to classify the voices, and required each pupil to sing alone. The experiment was rather discouraging. More than two-thirds were unable to sing the scale: twelve refused to utter a sound, and declared that nothing would induce them to try. These twelve were immediately dismissed. The rest remained, though some confessed that they had not sung a note since the beginning of the course. These, however, now promised to practise all the exercises in future. Under these unfavorable circumstances the professor engaged anew to fulfil his contract, on condition that the pupils would submit to practise the exercises conscientiously and attend regularly. From this time, with the exception of three or four rebellious spirits, none were rejected.

The month of October was not very profitable to the pupils, on account of continual absences necessitated by military reviews. April and May of the following year (1843) also brought many interruptions through the various demands of the service. Sickness, promotions, punishments, mutations, and the disbanding of the class of 1836, which took away several under-officers, gradually reduced the class, so that in July only a little over fifty were left. This falling off greatly troubled Professor Chevé, especially when the army at Lyons went into camp and left him with only twenty-eight pupils. This reduction of the class could not have been foreseen or prevented. M. Chevé could not be held responsible for the fulfilment of his promise, except to eight-tenths of those that remained.

Two months after the opening of the course M. Chevé printed at his own expense a collection of one hundred and forty pieces of music from the best composers, and gave a copy to each of his pupils, that they might read from the printed page instead of the blackboard. Three months after the opening of the course General Lascours visited the gymnasium and was present during one of the lessons. He was struck, as were all the visitors on that occasion, by the progress obtained. The pupils were already far advanced in intonation and in time: they read easily in all the keys, and sung pieces together with great spirit and correctness.

On April 25, 1843, the general returned, accompanied by Madame Lascours and all the officers of his staff. The following was the programme of the occasion: (1) A quartette from Webbe; (2) A Languedoc air in three parts, from Desrues; (3) A trio from the opera of Œdipus in Colonna, by Sacchini; (4) Singing at sight intervals of all kinds, major and minor; (5) Singing at sight in eight different keys; (6) Two rounds in three voices from Siller; (7) A quartette from the Clemenza di Tito of Mozart; (8) A quartette from the Iphigenia of Gluck; (9) A trio from the Corysander, or the Magic Rose of Berton; (10) Exercise upon the tonic in all the keys, major and minor; (11) Exercise in naming notes vocalized; (12) Singing at sight a trio from the Magic Flute of Mozart; (13) Ave Regina, by Choron—three voices; (14) The Gondolier, a round in three parts, by Desrues; (15) A quartette from the Magic Flute; (16) Chorus from the Tancredi of Rossini; (17) The "Prayer" from Joseph, by Méhul.

This is certainly a remarkable programme to be filled by illiterate soldiers with only six months' training. "It would be difficult," says the official report, "to paint the astonishment of the spectators upon this occasion. The confidence and readiness with which these soldier-students of music sang at sight the most difficult intonations, major and minor, the facility with which they read in all the keys, and, finally, the certainty and spontaneity with which they all, without exception, recognized and named various sounds vocalized, showed clearly that they possessed a very superior knowledge of intonation. All the pieces which they sung were rendered with irreproachable correctness, though the professor did not beat the time, except through the first bar to indicate the movement.

"With the consent of General Lascours, all the teachers and professors in the city, including the members of the Royal College, were on one occasion admitted to a private rehearsal of M. Chevé's class. The result was the same—admiration and astonishment. The professor received on all sides well-merited praise for a success gained in so short a time and with such unfavorable conditions.

"These soldiers have at this moment (September 1, 1843) reached a degree of power in intonation and in reading music at sight which is fairly wonderful. They can sing together at sight any new piece in three or four parts, the music being written, after the new method, in figures. If the piece be written in the ordinary musical character, no matter what the key, they can also sing it at sight together after they have together sung each part by itself. All the members of the class understand thoroughly the theory of music, and are able to write from dictation a vocalized air never heard before, no matter what the modulations may be.

"Such are the results obtained by Professor Chevé from a mass of men taken at hazard and against their will. The experiment to-day has had eleven months of duration, seventeen or eighteen lessons being given every month. The pupils have never studied at all between the lessons, and those who remain at the present time have lost many lessons from punishments, illness, leave of absence, etc.

"As to the method pursued by M. Chevé, it is as follows: In theory he demonstrates de facto the inequality of major and minor seconds, and from this he deduces the theory of the gamut. Here he follows in the footsteps of his master, Galin. The theory of time he takes from the same source. In practice, he employs the Arabic figures for the musical notes, as proposed by J. J. Rousseau and modified by Galin, using a series of exercises created by Madame Chevé. To these exercises especially does M. Chevé owe his ability to make his pupils masters of intonation in an incredibly short time. He teaches time by itself, using a language of durations invented by the father of Madame Chevé, M. Aimé Paris, and tables of exercises in time made by Madame Chevé. Transposition is also taught separately, and never does M. Chevé require his pupils to execute two things simultaneously until they understand perfectly how to do them separately.

"In this way M. Chevé leads his pupils through every step of the theory of music until they are able to read in the ordinary notation every kind of music, and to execute during any piece all the possible changes of mode or key."

The report—which is duly signed by the officers having charge of the gymnasium—ends with the expression of their "profound conviction that the method of teaching music employed by Professor Chevé is faultless, if it may be judged by its practical results."

There is a very common impression, in this country at least, that the best new method of writing music has been tried and abandoned, weighed in the balance and found wanting. This is far from the fact. It is doubtful if there is one person in a hundred in this country who ever heard even the name of Galin or Chevé. Some twenty years ago there was a little interest excited in a new method of musical notation. A class was formed in Lowell, Massachusetts, and a "singing-book" was used there with the notes written with numerals on the staff instead of the usual characters. But it could not have been the Chevé method that the Lowell professor used, for he employed no new system of teaching time—a prime characteristic of that method.

Those who examine the subject fairly will be compelled to take the position held by Galin, Chevé and their school, that a new method of writing music is imperatively needed, because that now in use lacks the essential elements of a scientific system: it is neither simple, clear nor concise. There are certain elementary principles which must be observed in the exposition of any science, and especially in that of music, which is addressed to all classes of intelligence. Among these principles are the following, as stated by M. Chevé: 1st. Every idea should be presented to the mind by a clear and precise symbol. 2d. The same idea should always be presented by the same sign: the same sign should always represent the same idea. 3d. Elementary textbooks or methods should never present two difficulties to the mind at the same time; and such textbooks or methods should be an assemblage of means adapted to aid ordinary intelligences to gain the object proposed. 4th. The memory should never be drawn upon except where reasoning is impossible.

Let us test the exposition of the ordinary musical notation, and also that of the school of Galin, by these principles and compare the results.

First. Is every idea presented by a clear and precise symbol?

In the ordinary method, certainly not. The musical sounds or notes are represented by elliptical curves with or without stems; by spots or dots with plain stems, or with stems having from one to four appendages, or with these appendages united, forming bars across the stems. These curves and dots are placed on the five parallel lines of a staff, as it is called, or between the lines of this staff, or on or between added or "ledger" lines above and below the staff. Certainly, these cannot be called precise symbols, especially when we reflect that any one of them placed upon any given line or space may represent successively do, ré, mi, fa, sol, la, si, or the flats or sharps of these notes. The notes, indeed, have no names, being all alike for the various notes; but names are given to the lines and spaces of the staff; and, alas! the names of these lines and spaces change continually with the change of key or pitch. For example: if we commence a scale with C, our do will be on the first added line below the staff, and its octave, do, on the third space counting  from the lowest. If we commence a scale with G, our do will be on the second line from the bottom, and the octave on the first space above the staff; and so on for all the other scales except those which commence a semitone below or above. For example: the scales of the key of G and of G flat would be placed exactly the same upon the staff, though the signature of G would be one sharp upon the staff at the beginning, and that of G flat would be six flats. The same may be said of the keys of D and D flat, F and F sharp, etc.

Again: the scales of the keys of G flat and of F sharp are the same—are played on precisely the same keys of the organ or piano—yet they are placed on different lines and spaces of the staff, and the signature of the first is six flats, and of the second six sharps.

Think of the disheartened state of the victim of this notation when he has learned to read comfortably in one key, and then, taking up a piece of music written in another key, finds that he has all the lines and spaces to relearn! The wonder is that he does not lose his wits altogether.

Compare this maze of notes and lines and spaces, for ever changing like a will-o'-the wisp, with the following:

Low Octave.
Middle Octave.
High Octave.



Here everything is as clear as day. Take any note—as 5, for example. This is sol—always sol, and never by any chance anything else. If it has a dot under, it is sol of the octave below the middle; if it has no dot, it belongs to the middle octave; and if it has a dot above, it belongs to the octave above the middle. These three octaves are amply sufficient for all the purposes of vocal music, which alone is considered here. For instrumental music, where many octaves are used, the system is modified without losing its simplicity and conciseness. To represent the flats, Galin crosses the numerals with a line like the grave accent, and marks the sharps by a line like the acute accent.
For example, flats represent do flat, flat, mi flat, etc.: sharps represent do sharp, sharp, mi sharp, etc.

A score of music in the new style of notation has no signature—that is, no flats or sharps at the beginning. Above the line of numerals is written simply "Key of G," "Key of A flat," etc. The pitch, of course, must be taken from the tuning-fork or a musical instrument, as it is in all cases.

Second. The same idea should always be presented by the same sign: the same sign should always represent the same idea.

It has already been shown how this principle is disregarded; but take, for further illustration, the symbols indicating silence. There are seven different kinds of rests, and there is no need of more than one. These signs are:

Illustration of music rest symbols.

Again: these rests may be followed by one or two dots, which increase their duration. For example: an eighth-note rest dotted equals an eighth note and a sixteenth; and followed by two dots it equals an eighth, a sixteenth and a thirty-second note in time. That is, the first dot prolongs the rest one-half or a sixteenth, and the second dot prolongs the value of the first dot one-half or a thirty-second.

To a disciple of Galin it is really amazing that such a bungling, unscientific way of expressing silence should have been tolerated so long. Compare these "pot-hooks and trammels," dotted and double-dotted, with Galin's symbol of silence, the cipher (0)! This is all, and yet it expresses every length of rest, as will be shown presently.

Let us now examine the symbols representing the prolongation of a sound. There are three ways by the common notation, where there should be but one. First, by the form of the note itself, as—

Illustration of musical note symbols.

Second, by one or more dots after a note, the first dot prolonging the note one-half, and the second dot prolonging the first in the same ratio. Third, by the repetition of the note with a vinculum or tie, the second note not being sung or played. Galin uses simply a dot. It may be repeated, as a rest or a note may, but then its value is not changed, any more than in the case of notes or rests repeated. For example:


     1|3556|5•31| 7143|3•21|

Here are the first measures of a well-known hymn in common time, four beats to the measure. As all isolated signs, whether notes, prolongations or rests, fill a unit of time, or beat, it follows that the dots following sol and mi prolong these through an entire beat, for the dots are isolated signs. Whatever the time, each unit of it appears separate and distinct to the eye at a glance; and all the notes, rests or prolongations that fill a beat are always united in a special way. This will be more fully shown hereafter.

Third. Elementary textbooks or methods should never present two difficulties to the mind at the same time; and such textbooks or methods should be an assemblage of means adapted to aid ordinary intelligences to gain the object proposed.

The first thing that the student of music encounters is a staff of five lines, armed with flats or sharps, the signature of the key, or with no signature, which shows that the music upon it is in the key of C. On this staff he sees notes which are of different pitch, and probably of different length. In any case, there are at least three difficulties presented in a breath—to find the name of the note, give it its proper sound, and then its proper length; and these difficulties are still greater because the ideas, as we have seen, are hidden under defective symbols.

Take all the teachers of vocal music, says M. Chevé, place them upon their honor, and let them answer the following question: "How many readers of music can you guarantee by your method, out of a hundred pupils taken at random and entirely ignorant of music, by one hour of study a day during one year?" The reply, he thinks, will be: "Not many." And if you tell them that by another method you will agree in the same time to teach eighty in a hundred to read music currently, and also to write music, new to them, dictated by an instrument placed out of sight or from the voice "vocalizing," they will all declare that the thing is impossible.

The great composers and renowned performers are cited as examples of what the ordinary methods have accomplished. No, replies Chevé: they are exceptional organizations. The methods have not produced them. They have, on the contrary, arrived at their proficiency despite the methods, while thousands fail who might reach a high degree of excellence but for the obstacles presented by a false system to a clear understanding of the theory of music, which in itself is so simple and precise. In the study of harmony especially, says the same authority, does the want of a clear presentation of the theory produce the most deplorable results. It has made the science of harmony wellnigh unintelligible even to those called musicians. Ask them why flats and sharps are introduced into the scales; why there is one sharp in the key of G major and five in B major; why you spoil the minor scale by making it one thing in ascending and another in descending—that is, by robbing it of its modal superior in ascending and of its sensible in descending. They will in most cases be unable to answer, for neither teachers nor textbooks explain. The catechisms found in most of the elementary works upon music are replete with stumbling-blocks to the young musician. Mr. R. H. Palmer, author of Elements of Musical Composition, Rudimental Class-Teaching and several other works, says in one of his catechisms that "there are two ways of representing each intermediate tone. If its tendency is upward, it is represented upon the lower of two degrees, and is called sharp; if its tendency is downward, it is represented upon the higher of two degrees, and is called flat. There are exceptions to this, as to all rules." This is deplorable. Music is a mathematical science, and in mathematics there is no such thing as an exception to a rule. But to quote further from the same catechism: "A natural is used to cancel the effect of a previous sharp or flat. If the tendency from the restored tone is upward, the natural has the capacity of a sharp; if downward, the capacity of a flat. A tone is said to resolve when it is followed by a tone to which it naturally tends." How long would novices in the science of music rack their brains before they would comprehend what the teacher meant by a tone tending somewhere "naturally," or by the tendency of a restored tone being destroyed by the "capacity of a flat"? The same writer, speaking of the scale of G flat, says it is a "remarkable feature of this scale that it is produced upon the organ and piano by pressing the same keys which are required to produce the scale of F sharp." This is precisely equivalent to saying that it is a remarkable feature that the notes C, D, E, F are produced by pressing the same keys which are required to produce do, , mi, fa.

One more citation from the same author. Speaking of the formation of scales, he says: "Thus we have another perfectly natural scale by making use of two sharps." This vicious use of the term "natural" is deplorable, because it is apt to give the pupil the notion that some scales are more natural than others. A certain note is called "C natural," and it is not uncommon for learners to suppose that it is easier or more natural to sing in that key, as it is easier on the piano to play anything in it because only the white keys are used, while in any other at least one black key is required. Indeed, a pupil may study music a long time before he finds out that there is no difference between flats and sharps, as such, and other notes—that all notes are flats and sharps of the notes a semitone above and below. Seeing the staff of a piece of music armed with half a dozen sharps or flats, the first thought of the pupil is that it will be rather hard to sing. And many really suppose that flats and sharps in themselves are different from other notes—a little "flatter" or "sharper" in sound perhaps—and secretly wonder why their ear cannot detect it. Of course it may be said that there is no necessity for pupils to have such absurd notions, but it is inevitable where the theory of music is made so difficult for the beginner. No doubt the ambitious and naturally studious will delve and dig among the rubbish of imperfect textbooks, analyzing and comparing the explanations of different teachers, until order takes the place of chaos; but textbooks should be adapted to ordinary capacities, and thereby they will better serve the needs of the most brilliant.

Fourth. The memory should never be drawn upon except where reasoning is impossible.

In science you have general laws, and from these deduce particular facts depending upon them, but collections of facts and phenomena without connection you must learn by heart. The extensive and involved nomenclature of music, added to the complicated and inconsistent system of notation, is a continual and exhausting strain upon the memory. Teachers commence their drill in vocalization, as a rule, with the scale of the key of C, and the pupils, fired with a noble ambition to become musicians, make a strenuous effort to remember where do, , mi and the other notes are placed on the lines and spaces of the staff. Presently the "key is changed," and with that change comes chaos. All the notes are now on a different series of lines and spaces. The confusion continues until the series of seven notes is exhausted. Then come scales with new names, commencing upon different notes (flats and sharps), but with places on the staff identically the same as others having different names!

Long before this point is reached by the pupil his courage flags, his ambition cools, and in the greater number of cases dies out altogether. To be sure, if he has the rare courage to persist he will come to recognize the notes of any key, not by the number of lines or spaces intervening between them and some landmark, but by their relative distances from each other measured by the eye. But this requires long practice. At first he must remember if he can, and when he cannot he must count up to his unknown note from some remembered one. It is, at best, a labor of Sisyphus. With many people—bright and intelligent people, too—it requires years of practice to read new music at sight even tolerably readily; for it is not simply a question of learning the notes, difficult as that may be: there is a further difficulty, and to many even a greater difficulty—that of the measure. Not the number of beats in a measure or bar and their proper accentuation—this is but the alphabet of time—but to group correctly and rapidly the fractional notes, rests and prolongations in their proper place in time. In very rapid music this becomes an herculean task, requiring long-continued and arduous practice. It is not simply a question of nice appreciation of rhythm, but of mathematical calculation, to know instantly and unhesitatingly, for example, that one-sixteenth, one half of one-sixteenth and one thirty-second added together equal one-eighth—that is, one-third of the unit of time or beat in six-eighths time.

Any one can see that such mental feats, ever varying as they are in music, and demanding instant solution at the same time the attention is given to the intonation, style, etc., must require an exceptional temperament and natural capacity. The fact is, it is beyond the power of most musicians. They must practise their instrumental and vocal music, and learn it nearly "by heart," before they attempt to perform it for others.

The writer of this has attended a class taught by one of Chevé's pupils, and can testify to the efficiency of the method, though the lessons were a very modest attempt to exemplify the perfection of the system. The lessons of M. and Mme. Chevé were divided into three parts: first, a drill in the principles of the theory of music; second, singing scales and exercises; third, drills in "reading time," beating time, analyzing time, etc., ending with some diverting "round" or "catch" or some exercise in vocal harmonies. On their method of teaching time, more than on any other part of their system perhaps, did the grand success of the Chevés depend. Rhythm was always taught separately from intonation, it being contrary to their principle to present two difficulties together before each had been mastered alone.

The first grand law of Galin's system is that every isolated symbol represents a unit of time or beat, whatever the measure. For example:

5 , unit of sound articulated.
, unit of sound prolonged.
0 , unit of silence.

The second law is that the various divisions of the unit of time are always united in a group under a principal bar, and such a bar always contains the unit of time—never more, never less. To illustrate:


Here the units of time—the numeral, the dot and the cipher—are divided first into two equal parts, and then into three. In both cases the groups represent units of time—one beat of a measure—according to the rule. It will be noticed that the form of the notes is the same whether whole or divided into fractions; that is, there are no different forms for "crotchets," "quavers," "semiquavers," etc., the expression of time being better provided for. Thus, halves or thirds are indicated to the eye by a single bar surmounting two signs for halves, three for thirds. If the halves or thirds have in their turn been divided by two, then the principal bar covers two little groups of two signs each; if the halves or thirds have been divided by three, then each principal bar covers two or three little groups of three signs each.

Nothing could be more simple than this. The eye has always before it, separate and distinct, the unit of time or beat; and the mind apprehends instantly the number of articulated sounds, prolongations or silences (rests) that must be sung or played during that beat. The eye has no hesitation, the mind no calculation, as to what note commences or ends a beat. Even the most modest student of music will see the immense advantage of this. Nor is there any need for the multiplicity of fractions to express different kinds of time. The moment the eye rests upon the score the student knows the measure as definitely and certainly as he knows the letters of the alphabet.

"And is this all there is in this system of notation?" some one will ask. Practically, Yes. There are the symbols of intonation, the numerals and the dot—the dot below or above the notes showing the octave ( octave ); the two diagonal lines indicating flats or sharps ( flats or sharps ); the horizontal bar indicating the time ( time ); and the vertical line or bar dividing the measures ( 1 2 3  | 4 3 2  | ).

The following is the air "God Save the Queen!" or, as we call it, "America," written in this method. The lower line, of course, is the alto:


                     'God Save the Queen', or 'America'

It will be noticed that the dot in the second measure which prolongs the note si ( 7 ) is not placed against it, as we are accustomed to see it. It is carried forward into the second beat, where it belongs. There it is grouped with the note do ( 1 ), and occupies one half of that unit of time; for all the signs grouped under a line or under the same number of lines are equal in time to each other, the same as all isolated signs are. In the sixth measure the dot is isolated; therefore it fills the whole beat, while the following beat is represented by a rest ( 0 ). In two of the measures there are groups of two notes. Each of the notes in these groups of course equals in time half of an isolated note, for each occupies half the time of one beat.

The French say déchiffrer la musique—to puzzle it out, to decipher it, as one would say of hieroglyphs on an Egyptian sarcophagus. The term is well chosen. The causes of the obscurity of musical notation are numerous, but the most prolific is undoubtedly expressing time by the form of the symbols of sound. In slow movements, and where only few modulations occur, this does not seem to be a serious objection; but in the rapid movements of compound time it becomes insupportable—at least after one has learned that there is a better way. An example in 68 time—six eighth-notes to the measure—will illustrate this:

music example

Here each triplet fills the time of one-third of a beat; that is, three-sixteenths equal one-eighth, according to the sublime precision of the old notation! But then no such thing as a twenty-fourth note is in use: three twenty-fourths would just do it! This is a part of a vocal exercise. The learner would have to divide each beat into three parts each, unless very familiar with such exercises; and one of these divisions would fall on a rest, another in a prolongation, another in the middle of an eighth note. In the new method see how the crooked places are straightened:

_______________      _______________
      _____   _____           _____    _____
1  0 2 3  4 3 2   1  • 2 3  • 4 5

It "sings itself" the moment you look at it, after a little study of this rational notation. Note also that there is no mathematical absurdity here: the division is logical, and yet the air is perfectly expressed in every particular.

The mastery of time in music is at best an arduous task, yet teachers of music, as a rule, expect their pupils to learn it incidentally while studying intonation. They give no special drill in pure time at every lesson; and the result is that army of mediocre singers and players who never become able to execute any but the very simplest music at sight. They may know the theory of time, may be able to explain to you clearly the divisions of every measure, but this is not sufficient for the musician: he must decipher his measures with great readiness, precision and rapidity, or he never rises above the mediocre. The ambition to excel without hard labor is the bane of students of the piano especially. It leads them to muddle over music too difficult for them; finally, to learn it after a fashion, so that they may be able to "rattle and bang" through it to the delight of fond relatives and the amazement and pity of severe culture. Not that we should have consideration for all that passes for severe culture and exquisite sensitiveness among musical dilettanti. In no field of art is there so much affectation, assumption and charlatanry as in music. Some years ago a musician in New York of considerable reputation refused to play on a friend's piano because, as he said, it was a little out of tune and his ear was excruciated by the slightest discord. The lady wondered that the instrument should be out of tune, as it was new and of a celebrated manufacturer. She sent to the establishment where it was made, however, and a tuner promptly appeared. He tried the A string with his tuning-fork, ran his fingers over the keyboard, declared the piano in perfect tune, and left. That evening the musician called, and was informed that a tuner had "been exercising his skill" upon the instrument. Thereupon he graciously condescended to play for his hostess, and the sensitiveness of his ear was no longer shocked. She never dared to undeceive him, but mentioned the fact to another musician, a violinist, who exclaimed, greatly amused, "The idea of a pianist pretending to be fastidious about concord in music! Why, the instrument at its best is a bundle of discords." Both of these musicians were guilty of affectation; for, although the piano's chords are slightly dissonant, the intervals of the chromatic scale are made the same by the violin-player as by the pianist. What right, then, has the former to complain? To be sure, the violinist can make his intervals absolutely correct: he can play the enharmonic scale, which one using any of the instruments with fixed notes cannot do. But does he, practically? Does he not also make the same note for C sharp and D flat? The violinist mentioned of course alluded to the process called equal temperament, by which piano-makers, to avoid an impracticable extent of keyboard, divide the scale into eleven notes at equal intervals, each one being the twelfth root of 2, or 1.05946. This destroys the distinction between the semitones, and C sharp and D flat become the same note. Scientists show us that they are different notes, easily distinguished by the ear. Representing the vibrations for C as 1, we shall have—

C C# D¨ D D# E¨ E etc.
1 25

each note being increased by one twenty-fourth of itself, or in absolute vibrations—

C C# D¨ D D# E¨ E etc.
261 271 271 293 305 303 326 etc.

This is the enharmonic scale, having twenty-one notes. The chromatic has eleven, and the name—it may be remarked in passing—is from the Greek word for "color" χρωμα because the old composers wrote these notes in colors, and had them so printed. Not a bad idea, surely: many a learner on the piano would be overjoyed to see all the ugly flats and sharps on the staff in brilliant holiday dress.

There is no reason at this day, when science in all fields is making such progress, why the ordinary music-teacher should have so limited a knowledge of his subject. He should be able to explain the fundamental principles of the different scales upon the theory of vibration, and to so educate the apprehension of his pupils that they will not be content with the imperfect catechisms of the music-books in vogue. And with the adoption of a rational system of writing music, which will reduce the time and labor of learning it to one half, there will be time for the niceties of a science of such vast importance to the culture—and, indirectly, to the moral progress—of the world.