Misic (Gr., a muse), an agreeable combination and arrangement of sounds, and the art of so combining and arranging sounds. It is indispensable to have some knowledge of the nature of sounds before we begin the consideration of the manner in which they are arranged and compounded in music. We here give only that information which is essential to the understanding of the subject of this article, referring the reader to the article Sound for a discussion of the nature of sonorous vibrations and of their properties. The more rapidly the sonorous pulses of the ear follow each other, the higher is the pitch of the sound perceived. Thus, the gravest sound which is really musical is caused by 40 vibrations a second, while the auditive sensation the highest in pitch is produced by about 40,000 a second. But the sounds employed in music have not so extended a range; they are practically embraced by about seven octaves, extending from 40 vibrations to about 5,000 a second. The gravest sound of an orchestral instrument is the E of the contra-bass, of 40 vibrations a second. Modern pianos and organs indeed give generally the C (of 33 vibrations) below the E of the contra-bass; and some recent grand pianos extend as low as the A (of 27 vibrations) in the next lower octave.

In the largest organs there is also sometimes a pipe which gives a sound that descends into the yet lower octave, reaching the C of 16Ż vibrations. Bnt-none of these grave sounds below the E of the contra-bass can be termed musical; for the separate pulses which compose them do not blend into smooth continuous sensations, but produce beats, corresponding in number to the rate of vibration indicated above. These grave sounds cannot be used alone, but are always sounded in unison with pipes or instruments giving their higher octaves and harmonics. Thus the latter are compounded with the harsh fundamental of the grave note, and at the same time blend with any harmonics which may accompany the fundamental of these grave sounds. In the higher regions of musical sounds, pianos give the notes A and even C, of 3,520 and 4,224 vibrations. The most acute sound of orchestral music is the D (of 4,752 vibrations) of the piccolo flute. - There are three distinctions to be made among sounds: their pitch, of which we have just spoken; their intensities, concerning which it is not necessary to enlarge; and their timbre, or that character by which we distinguish between sounds having the same pitch and intensity. All simple sounds, which we define as those having only one pitch, have the same timbre.

Such are the sounds given by flue organ pipes, or by tuning forks when mounted on resonant boxes. But the sounds employed in music are always composite, being formed of several simple sounds whose numbers of vibrations are to each other generally as 1, 2, 3, 4, etc. Simple sounds are unfit for musical expression by reason of their want of brilliancy; for this reason the notes of closed flue pipes are rarely sounded alone, but to invest their tones with feeling and life they are combined with other stops, giving the harmonics or furniture of their simple sounds. The sounds of the flute approach in character those given by closed organ pipes; but when associated with other instruments which bring out the sequence of the harmony, the flute, by reason of the perfect softness of its sounds and the facility with which it renders rapid movements, is charming, and cannot be replaced by any other instrument. It held a far more important place in ancient than in modern music; but even among the ancients the abler masters preferred the more thrilling sounds of stringed instruments.

The sounds of all other instruments, as well as the notes of the human voice, are composite, formed by the blending of several simple sounds, having different positions in the musical scale. (See Harmony.) Helm-holtz has proved that the distinctive timbre of any given sound is due to the number and relative intensities of its elementary sounds, or harmonics. - Stopped wooden flue pipes of large section give nearly simple sounds when blown with a feeble pressure. An increase of pressure in the blast develops the third harmonic, amd an excessive pressure may injure the timbre of the sound by giving to it too great an intensity compared with that of the funda-mental; it may even cause the latter to disappear, and then the whole sound will have risen in pitch by an octave and a fifth. Stopped organ pipes having small area of section compared with their lengths give the fifth harmonic as well as the first and third. In other words, closed pipes give the uneven harmonics; open and narrow pipes give the complete series of harmonics up to a certain number. Thus, if we close all the holes in a flute and blow gently, and then with increasing intensity, the instrument will successively give the first, second, third, and fourth harmonics.

In the case of the narrow open pipes in the organ (viola, principal, violoncello, contra-bass, viola-di-gamba), powerful pressure of wind gives the fundamental sounds of these pipes accompanied by the clear sounds of all the harmonics, including the sixth. It is quite otherwise in the case of the large open pipes. From the considerable mass of air which they contain, and from the fact that they do not readily jump in their pitch from the fundamental to one of the harmonics on increasing the wind pressure, these large pipes form the basis of the mass of sounds of the organ, and hence they have been called the principal register. In these pipes the fundamental sound is intense, and is accompanied by a few harmonics of feeble intensities. In the flute or chimney pipes, the timbre receives a brilliant character from a small open pipe adapted to the top of these closed pipes. By combining the stops on the organ, one can produce a great variety of timbre; and in this regard the organ has the advantage over all other musical instruments. Vibrating plates, or reeds, are used in the reed pipes of the organ, in themelodeon, and in the clarinet, hautboy, and bassoon; while in the horn, trumpet, trombone, and cornet the lips perform the office of the reed.

The sounds of all reed instruments are peculiarly rich in harmonics; it is not difficult to distinguish those even as high as the twentieth. The fundamental, or some powerful harmonic, is generally reenforced in reed organ pipes by surmounting them with open or partly closed tubes of various sizes and forms; and thus are obtained the various timbres of these instruments, such as the trumpet, vox Immana, etc. The clarinet gives only the odd series of harmonics, 1, 8, 5, 7, etc, while the hautboy and bassoon give the entire series, 1, 2, 3, 4, etc. If the hautboy takes one note of an interval and the clarinet another, some concords will sound best when the former instrument, others when the latter takes the upper note. Among stringed instruments those of the violin kind occupy the highest place. The tones of these are highly complex, containing the clear sounds of the higher harmonics from the sixth to the tenth; and as violins do not, like the piano, give fixed sounds evolved by a keyboard, they have great sonorous flexibility, giving the performer the power of playing in any mode or scale, and of gliding from one note to another without perceptibly breaking the continuity of the sound; and above all, he can obtain any note with varying intensity, and thus express his feelings by the most exquisite modulation.

When the violin is well played, the fundamental or lowest harmonic comes out with force, and the harmonics up to the sixth are feebler than in the cases of the guitar, harp, or piano; but the sixth and higher harmonics are stronger than in the case of the latter instruments. On examining with a vibration microscope the forms of the vibrations of the strings, Helm-holtz found that in instruments of the highest excellence these forms remained constant during the whole duration of the tone. To this great regularity in the vibrations he attributed the purity of the sounds of old instruments; and for the same reason the strings can be sounded with more force. In the piano the sounds are composite; the lower harmonics are relatively stronger than in the violin, but the harmonics above the sixth, which in the main form dissonant combinations with those below the sixth, are purposely prevented from appearing in the sounds of this instrument, by causing the hammers to strike the strings at points distant from the ends of the strings about one seventh of their length.

The sounds of the harp and guitar differ from those of the piano; for in these instruments we have catgut strings which are pulled aside from their positions of equilibrium, and then allowed to vibrate freely; in such circumstances the higher harmonics, which appear in the first swings of the cords, soon disappear from their sounds. But no instrument emits sounds so smooth, so clear, and so touching as those of the human voice. The voices of men are classed as bass, barytone, and tenor; those of women as contralto, mezzo-soprano, and soprano. The position on the musical scale and the range of these voices are given as follows in musical notation:

Misic 120033

We thus see that ordinary voices do not include two full octaves. The range from the lower F of the bass to the higher G of the soprano is a little more than three octaves. These limits, however, have been extended in exceptional cases. Praetorius, in his Syntagma Musicum, says that in the 16th century, in the time of Orlando di Lasso, there were at the court of Bavaria three basses, the brothers Fischer and one Gassner, who sang the F_i; while the highest note ever recorded is that attained by Lucrezia Ajugari, called La Bastardella.

Misic 120034

Mozart, who heard her at Parma in 1770, gives several passages which she sang for him. We copy the last of them, which ends in C8:

Misic 120035

She trilled on the D5 and performed other extraordinary feats. Mozart's father says that La Bastardella sang these passages with a little less force than the lower notes, but that her voice remained as pure as a flute. She could descend easily as far as G2. Kuhlau wrote for a songstress who astonished St. Petersburg in 1823 the part of Adelaide in his opera of Le chÔteau des Irigands. The dominant air in the third act reaches as high as A6. "At one representation, just as she was about to give the perilous note, the leader of the orchestra looked at her fixedly, which so disconcerted her that she gave C6." The voice of Gaspard Forster embraces three octaves, from A_1 to A.6; while that of the younger of the Sessi sisters extends through three octaves and a half, from C2 to F6. Catalani's voice had likewise a compass of three and a half octaves, as also had the voice of Farinelli, who went from A to D5.

Misic 120036

Very remarkable heights have likewise been reached by Nilsson and Carlotta Patti. At the age of puberty the glottis of man suddenly enlarges, and the voice ordinarily descends in pitch an octave. This change does not take place in castrates; their voices remain as in their childhood, and are distinguished by an indescribable flute-like quality. But cases are on record where the voice has never acquired the pitch characteristic of manhood; thus, M. Du-pont, who often sings at the celebration of high mass in Paris, has a remarkably tine soprano voice, vet he is 30 years old (1874), and is the father of several children. - In music we consider the ratios of the numbers of vibrations of definite sounds more than the absolute number of the vibrations, or pitch, of these sounds. From the most ancient times it has been known that the most harmonious concords are produced by means of the simultaneous sounding of strings whose lengths bear to each other simple ratios. Pythagoras, who probably derived the fact from the Egyptians, says that when the ratio of the lengths of the strings was as 1: 2, the grave note sounded in unison with its octave, while the ratio 2: 3 gave the quint, and 3: 4 gave the quart.

We now know that the numbers of vibrations of similar strings are inversely as their lengths, so that the existence of the above consonant intervals depends alone on the ratio of the vibrations of the strings, and not on the absolute number of vibrations of the fundamental note of the chord. (See Harmony.) When we double the number of vibrations corresponding to a note, we obtain the octave of this note, and the sensation caused by this higher octave seems to repeat that which corresponded to the lower. This interval of the octave, which includes all the notes of any musical system, is established by our physiological constitution, and was determined long before it was known that to obtain the octave of a note we had to double the number of its vibrations. Modern science has shown that the following musical consonances are only obtained when their constituent notes have the following vibration ratios: octave, 1:2; fifth, 2:3; fourth, 3:4; major third, 4:5; minor third, 5:0; major sixth, 3: 5; minor sixth, 5: 8. Within the compass of the octave are seven distinct steps of pitch, constituting the gamut. We here give the names of the notes of the natural gamut in English and German, and in Italian and French notation.

Under these names we give the relative numbers of their vibrations in whole numbers and in fractions; and in the succeeding line are the intervals between the notes of the gamut:

Names. -

C

D

E

F

G

A

B

c

ut

or

do

re

mi

fa

80l

la

si

do

Ratio of vibra-tions.

24

:

27:

30:

32:

36:

40:

45:

48

1

:

9/8:

5/4:

4/3:

3/2:

5/3:

15/8 :

2

Intervals be- twecn successive notes.

9/8

1 0/9

16/15

9/8

10/9

9/8

16/15

The gamut dors not suppose a knowledge of the absolute height of the notes; it only fixes the ratios. The first note, or tonic, can have any pitch; but once fixed upon, all the others must follow in the ratios of the above numbers; thus, if C makes 240 vibrations, then I) in the same time must give 270, E 300, F 320, and so on. One gamut is continued by a second, formed by simply doubling the numbers of vibrations constituting the first, and another by doubling the vibrations of the second, and so on. The ratios between the successive notes of the gamut and the first note, or tonic, are denominated their musical intervals. In the following table Ave give the names of the intervals preceded by the names of the notes. These intervals are designated by the position of the notes in the gamut:

C: C

Unison

1: 1

C: D

Second

8: 9

C: E

Third

4: 5

0: F

Fourth

3: 4

C: G

Fifth

2: 3

C: A

Sixth

3: 5

C: B

Seventh

8 : 15

C: C3

Octave

1: 2

C: D2

Ninth

4: 9

C: E2

Tenth

2: 5

C: F2

Eleventh

3: 8

C: G2

Twelfth

1: 3

....

C: C3

Double octave

1: 4

....

C: E3

Seventeenth

1: 5

etc.

etc.

etc.

The first six notes received their present Italian names from the Benedictine Guido Aretino in 1026. They are the first syllables of the words taken from the following stanza of the hymn to St. John the Baptist:

UT queant laxis REsonare fibris MIra gestoruin FAmvuli tuorum, SOLve polluti LAbii reatum, Sanete Johannes.

The air to which this hymn is now sung at Rome on St. John Baptist's day is altogether different from that used by Guido, for in ancient times the six syllables were sung to the notes which these syllables designated. The word si, derived from the fourth line (S and I), was first used by Francois Lemaire in 1684 to designate the seventh note of the gamut. The use of these words in solmization caused the Italians to change the ut into do. These names for the notes did not spread very rapidly, for during the time of Jean de Muris, in the 14th century, they still sang at Paris the syllables pro, to, no, do, tu, a; but finally Guido's names prevailed, except in Germany and England, where the notes are generally designated by the letters C, D, E, F, G, A, B (or II). The origin of the latter nomenclature is as follows: Before the 6th century, certainly during the time of Gregory the Great, they formed a series of gamuts corresponding to the ordinary range of the notes of the human voice, and of the principal musical instruments then in use. The notes were designated by the first seven letters of the alphabet, in this manner: A, B, C, D, E, F, G; a, b, c, d, e, f, g; aa, bb, cc, dd, ee.

Subsequently they added another note lower in pitch than those already embodied in their system, and this note was indicated by the Greek gamma (y), whence the name gamut. Others say that gamut comes from the fact that the letter y was placed on the lowest line of the staff. Guido replaced the letters by points which he wrote on parallel lines (the staff), each of which belonged to a certain letter, called the key or clef of that line. Thus when an F had been written at the beginning of a line, it indicated that all points on that line represented the note F. Afterward they enlarged these points, placed them between the lines, and increased the number of the lines and spaces as they were needed. In order to indicate a chord, or the simultaneous sounding of two or more notes, these notes were placed one below the other, and from this method of notation arose the name of counterpoint, or the science of accords. Musical notation at first only indicated the heights of the various notes on the musical scale; in 1338 De Muris invented squares to indicate their duration. This system was improved by Ottavio Petrucci (1470), who in 1502 was the first to print music by means of movable types.

The syllables do, re, mi, fa, sol, la did not originally stand for fixed notes, but simply the degrees of any gamut whatever. They stood for the hexachord of Guido, and were written below the letter which designated the fixed gamuts, beginning with C, with F, or with G:

C

D

E

F

G

A

B

c

d

e

f

• • • •

do

re

mi

fa

sol

la

do

re

mi

fa

sol

la

.

.

.

do

re

mi

fa

Thus the same note could occupy different positions in the movable gamut, which was often incompatible with the preservation of the established intervals of the notes, do, re, mi, fa, sol, la. Hence arose different modes, more or less harmonious, and a great confusion in the ancient system of music. They then felt the necessity of changing slightly the pitch of certain fixed notes when, by the transposition of the movable gamut, the intervals of the corresponding fixed notes did not give the intervals originally given to the series do, re, mi, fa, sol,, la. Thus, when do was written below F, and fa below B, the interval of F to B should have been a fourth; but as in reality it was greater, they diminished it by flattening B a semitone. The latter note was then called B molle, while it was B durum in the gamut which began in C. They indicated these changes by writing a b, round or square, and this is the origin of the signs b and. The origin of these signs is shown in the French language, in which they are respectively termed bemol and liecarre. By many modifications musical notation grew into the present system. - The signs now employed in music denote the length, pitch, and force of tones, or rhythm, melody, and expression. The length of a note is represented by its shape.

The notes are the breveMisic 120037 or |Misic 120038 |semibreveMisic 120039 , minimMisic 120040 , crotchetMisic 120041 , quaverMisic 120042 semiquaverMisic 120043 , demisemiquaver , and demiquaverMisic 120044 , but the first and lastMisic 120045 of these are little used. The breve is twice as long as the semibreve, the semibreve twice as long as the minim, and so on. A dot following a nute lengthens it one half, thus,Misic 120046 =Misic 120047 Rests, indicating silence, are:Misic 120048 , equal in length toMisic 120049 , or a whole bar;Misic 120050 =Misic 120051 ;Misic 120052 =Misic 120053 ;Misic 120054 =Misic 120055 ;Misic 120056 =Misic 120057 ' =;=. Rhythm is further marked by the division of time into measures of equal length indicated by vertical lines drawn across the staff. Measures again are divided into two, three, four, or six parts, and the first part of a measure is almost always accented. There are four measures in common use: double, triple, quadruple or common, with a secondary accent on the third part, and sextuple, with a secondary accent on the fourth part, each represented by figures placed at the beginning of the staff, as follows:

Misic 120062

Thus, taking the crotchet as a standard, in double time there must be two crotchets or their equivalent in every bar or measure, in triple three, in quadruple four, in sextuple six. There are exceptions to these rules, however, and even five crotchets to a bar have been used with eccentric effect. - The pitch of a tone is determined by its position on the staff, which consists of five parallel lines and the four intervening spaces, and by the clef, which indicates the pitch of all the notes on one line or space of the staff, whence the rest are easily found. In the early Italian school every kind of voice had its own clef, but at present only two are in general use, the treble or G clef of the violin,Misic 120063 , and the bass or F clef,Misic 120064 In some musical scores, however, particularly Italian, the C clef is retained for the tenor and alto parts. For the former it is placed on the fourth line,Misic 120065 , which thus becomes the position of 0, and for the latter on the third,Misic 120066 , The popular plan in writing music in four parts is to put the alto on the same staff with the treble, and the tenor with the bass or treble. With these staves, and the aid of short lines called leger lines above and below the staves, we are able to represent all the notes of the human voice, and even more. The following is the musical scale from the lowest bass note to the highest soprano:

Misic 120067

The pitch of any note may be raised half a tone by means of a sharp (#) placed before it, or lowered half a tone by a flat (b). When a sharp or flat is placed on a line or space at the beginning of a staff, it affects every note occurring on that line or space and its octaves throughout the piece. A natural (j) restores to its normal pitch a note affected by a flat or sharp. A note or passage may be raised or lowered an octavo by writing over or under it the sign 8va.-----...... Besides the words forte, fortissimo, piano, pianissimo, and their abbreviations,f..ff., p., pp., indicating that a note or passage is to be given loud, very loud, soft, or very soft, there are the signsMisic 120068 (crescendo), denoting a tone gradually increasing from soft to loud;Misic 120069 (diminuendo), the reverse of crescendo;Misic 120070 (sforzando), an explosive tone instantaneously diminished;Misic 120071 (staccato), a short articulate utterance as if each note were followed by a brief rest; andMisic 120072

(legato), a binding together of successive tones. The system of musical notation adopted indicates to the performer the pitch, the duration, and in an imperfect manner the intensity of musical sound, but conveys no idea of the timbre or composition of these sounds. A musical note, indeed, gives merely the pitch of the fundamental or first harmonic of a musical sou ml. This defect is unavoidable, and to the musician is generally of little consequence; for in concerted music the parts are written for special instruments, whose qualities of sound are well known to the musical ear. - It was only after ages of experience, and many changes, that the system of music reached its present condition. The principal problem was this: Whatever the note selected from the scale to begin the gamut, the other notes when combined with the former shall give the established musical intervals. In order to solve this problem, the fixed notes were altered, either by elevating them in pitch by a semitone, which operation is called sharpening a note, and is indicated by the sign ft, or by lowering them a semitone in pitch, which is to flatten a note, and is indicated by the sign b.

For the value of this semitone the interval 2/2 5/4- has been adopted, which is smaller than the ratio 1/1 6/5, the value of the interval E F. The notes C, D, E, etc., are given by the white keys of the piano and organ, while the black keys give the sharps and flats. The gamuts are always designated by the name of their first note, or tonic. All the gamuts called major are modelled on the primitive gamut of C, formed by the series of natural notes, C, D, E, etc. The gamut of G is formed of the notes G, A, B, 0, D, E, F#, G; that of F, of the notes F, G, A, B, 0, D, E, F. These gamuts constitute the major mode. Music, however, requires also a minor mode, formed of gamuts whose type is the gamut of A minor: A, B, C, D, E, F, G, A. The principal difference between the two modes consists in the introduction of the minor third, A - C (5: 6), in the place of the major third, C - E (4: 5). They are both characterized by a perfect accord, formed with the third and fifth of the tonic, as follows:

Perfect major accord, 0 E G.

" minor " A 0 E, or C E|- G.

The major and minor scales give us a series of 11 notes, which, severally combined with the tonic, form 10 distinct intervals. In musical notation they are as follows:

Misic 120073

In the minor mode we are often obliged to elevate by a semitone the seventh and also the sixth note of the gamut. To obtain absolute purity, all gamuts on an instrument of fixed sounds, like the organ or piano, would require an extraordinary, indeed an almost impracticable complication. Mr. A. J. Ellis has shown in a paper published in the " Proceedings of the Royal Society," vol. xiii., "On a perfect Musical Scale," that within the compass of an octave 72 notes would be required to give an absolutely perfect command of all the keys that are now used in music. It has therefore been found necessary to make a compromise, in perfect harmonious effects, in the construction of instruments with fixed sounds; and thus has come about the universal adoption of the musical scale known as that of "equal temperament," so called because between any two contiguous notes the same interval (called a semitone) exists throughout the whole scale. As the octave is divided into 12 equal intervals, it follows that each of these intervals is equal to 12, or to 1-05946. This scale being a compromise, the major triads are slightly dissonant.

Thus, in the natural scale the ratio of the vibrations of G: E: G are as 1: 1-25: 1-5; but on the scale of equal temperament these same notes bear to each other the vibration ratios of 1: 1.2599: 14983. Thus it follows that the interval of the major third is sharpened, while the fifth is flattened. If we take the middle octave of the piano for an example, we shall find that E and A are three vibrations a second too sharp, while the fourth and fifth are out of tune by one vibration a second. For convenience of comparison we here give the two scales. The natural scale is placed below the scale of equal temperament. The numbers of vibrations in a sound, correct to the nearest unit, are written under the notes. "When the vibration number is a fraction more or less than the number given, the sign + or - is respectively attached to the number. The notes belong to the middle octave of the piano.

c

c#

D

D#

E

F

F#

G

G#

A

A#

B

264

280-

296 +

314-

333-

352 +

373 +

395 +

419 +

444-

470 +

498 +

C

D

E

E

F

G

Ab

A

E

B

264

297

317-

330

352

396

422 +

440

469 +

495

The ratio of the semitones of the tempered scale is approximately 18/17, and a tone on this scale barely differs from the major tone of 9/8. This invention has been variously attributed to Neidhart and Werckmeister, to Sebastian Bach, and to Lambert the geometrician. This musical scale was first applied to the clavichord, and Emanuel Bach, son of Sebastian, said a well tuned clavichord was the most accurate of all instruments; this remark is readily understood when it is explained that, from the manner of production of the sounds on this instrument, the higher harmonics, even when evolved, are feeble and soon die out from the sounds, while the resultant tones appear only at the moment the chords are forcibly struck. But all organists know how harshly intervals are given on a stop of reed pipes, or on the furniture register, tuned to the equal-tempered scale. This harshness is due to the imperfect tuning causing the beating of harmonics and resultant tones. An excellent method of comparing the relative effects of natural and of tempered tuning is to listen to a few voices singing a series of sustained chords of three or four parts without accompaniment, and then listen to exactly the same chords with the accompaniment of a piano or melodeon.

In the latter case the harshness of the accompaniment is forcibly brought out. One naturally sings perfect intervals, and a violinist with a refined ear will involuntarily play on the natural scale; but if the voice is educated by the accompaniment of the piano instead of the violin, and if the violinist is always accompanying the fixed tones of an orchestra, then they will both have acquired the habit of rendering the false intervals of the tempered scale. - The vibration fraction of an interval expresses the ratio of the numbers of vibrations performed in the same time by the two notes which form the interval. Thus, the vibration fraction 5/4 means that while the lower of the two notes, forming a major third, makes four vibrations, the higher of these notes makes five. Therefore, while the lower makes one vibration, the higher makes five fourths of a vibration, or one vibration and a quarter. Conversely, while the higher note makes one vibration, the lower makes four fifths of a vibration. This reasoning is general, and hence follows this rule: Any fraction greater than unity denotes the number of vibrations, and fractions of a vibration, made by the higher of two notes forming a certain interval while the lower note is making a single vibration.

Similarly, any fraction less than unity indicates the proportion of a whole vibration performed by the lower note while the upper is making one complete vibration. The rules for adding and subtracting musical intervals are as follows: To find the vibration fraction for the sum of two intervals, multiply their separate vibration fractions together. To find the vibration fraction for the difference of two intervals, divide the vibration fraction of the wider by that of the narrower interval. Thus, a major third added to a fifth gives a major seventh; while a major third subtracted from a fifth leaves a minor third. One of the most common applications of the second rule is when an interval has to be inverted. The inversion of an interval less than an octaye is the difference between it and an octave; i. e., the interval which remains after the first has been subtracted from an octave. Thus, to invert the minor third we divide 2 by 6/5; or, in other words, we invert the vibration fraction of the interval and multiply by 2. This operation gives us 5/3; therefore, the inversion of the minor third is the major sixth. Evidently there exists a mutual relation between an interval and its inversion, so that each is the inversion of the other.

Thus, the inversion of the major sixth is the minor third. The following three pairs of consonant intervals, embraced within the compass of an octave, have to each other the mutual relation of inversions:

Minor third,

.

6/5

___

Major sixth,

.

.

5/3

Major third,

.

.

5/4

-----

Minor sixth,

.

.

8/5

Fourth,. .

.

.

4/3

----

Fifth, . .

.

.

3/2

Musical sounds of different pitch, simultaneously emitted, form, a chord. Chords formed of two notes are called binary chords; those of three notes are called triads. A binary chord is consonant when its two notes form a consonant interval. In a triad there are three intervals: one between its lowest note and its highest, and one between the middle and highest note. The triad is only consonant when all three of these intervals are concords. Therefore, to form consonant triads we select a note, then find the others, each of which forms with the bottom note a consonant interval. We then determine whether the interval between the two higher notes is a consonant one; if this be so, then the triad is consonant. To determine all of the consonant triads contained in an octave, above any selected bottom note, wo must assign to the middle and top notes every possible consonant position with respect to the fixed bottom note, and reject all such relative positions as give rise to dissonant intervals between those notes themselves. The remaining positions will constitute all the consonant triads which have for their lowest note that originally selected.

The intervals at our disposal are: for the middle note, from the minor third to the minor sixth; and for the upper note, from the major third to the major sixth. In the following table the possible positions of the middle note with respect to the bottom note are shown in the left-hand vertical column, the name of each interval being accompanied by its vibration fraction. The possible positions of the top note are similarly shown in the top horizontal line. Each space common to a horizontal and vertical line contains the vibration fraction of the interval formed between the simultaneous positions of the middle and upper notes named at the beginning of these lines. The intervals thus formed which are dissonant are designated by being enclosed in brackets. Whenever they are consonant the name of the interval is given.

Major third.

5/4

Fourth.

4/3

Fifth.

3/2

Minor sixth.

8/5

Major sixth.

5/3

Minor third.

6/5

[2/2 5/4]

[10/9]

5/4

Major third.

4/3

Fourth.

[25/9]

Major third.

5/4

[16/15]

6/5 Minor third.

[3/2 2/5]

4/3

Fourth.

Fourth.

4/3

[9/8]

Minor third.

5/4

Major third.

Fifth.

3/2

[16/15]

10/9

Minor sixth.

8/5

[2/2 5/4]

An examination of the above tables shows that the following are all the consonances:

Middle note. Minor third. Major third. Fourth.

Upper note. Fifth, or minor sixth. Fifth, or major sixth. Minor sixth, or major sixth.

The above consonances are thus expressed in musical notation:

Misic 120074

We thus obtain two groups of three major and three minor triads, which may be arranged thus:

(a)

Fifth.

(b)

Minor sixth.

(c)

Major sixth.

Major third.

Minor third.

Fourth.

(a)

Fifth.

(▀)

Major sixth.

(y)

Minor sixth.

Minor third.

Major third.

Fourth.

The above six consonant triads may be defined by the intervals separating the middle from the bottom note, and the top from the middle note, instead of defining these intervals, as we have done above, by the intervals formed by their middle and top notes with the bottom note. To bring about this change we perform on each one a subtraction of intervals. Thus, the difference between a fifth and a major third is 3/2X4/5=6/5, or a minor third. In this manner we find that the top and middle notes are separated by the following intervals:

a

b

c

a

V

Minor third.

Fourth.

Major third.

Major third.

Fourth.

Minor third.

Hence the two groups may be written as below:

(a')

Minor third.

(V)

Fourth.

(C)

Major third.

Major third.

Minor third.

Fourth.

(a')

Major third.

(▀')

Fourth.

Minor third.

Minor third.

Major third.

Fourth.

It can now be shown that the triads of each group are closely connected. Take (a), and form from it another triad, by causing its bottom note to ascend one octave, the other two remaining where they were. The middle will then become the bottom note, the top the middle note, and the octave of the former note the top note. Hence the lower interval of the new triad will be the upper interval of the old triad, i. e., a major third. The upper interval of the new triad will necessarily be the inversion of the interval which separated the extreme notes of the old triad. This interval is a fifth (see (a) ), and its inversion by the table already given is a fourth. Hence the new triad.

Fourth is Minor third , which is identical with (V). If we modify (b') in the same way, the new interval is the inversion of the minor sixth, i. e., the major third, and the resulting triad, viz, Major third, is identical with Fouth (c'). This triad, when similarly treated, brings us back to (a'), and the cycle of changes is complete. By an extension of the word' "inversion," it is usual to call the triads (b') and (c') the first and second inversions of the triad (a'). Exactly similar relations hold between the members of the second group of triads; (▀') and (y') are accordingly called the first and second inversions of the triad (a). The proof is exactly like that just given, and will be easily supplied by the reader. If we choose 0 as the bottom note of (a') and (a'), the major and minor groups will be expressed in musical notation byMisic 120075 .

They may also be defined in the language of thorough bass, which refers every chord to its lowest note, in accordance with the mode adopted in (a), (b), (c); (a), (▀), (y). Thus the triads (a'), (b'), (c') would be indicated by the figures 5/3, 6/3-, 6/4 respectively, and so would the triads (a'), (▀'), and (y); the differences between minor and major thirds and sixths being left to be indicated by the key signature. The positions (a') and (a!) are regarded as the fundamental ones of each group, (b'), (c'), and (▀'), (y') being treated as derived from them respectively by inversion. The fundamental triads bear the name of their lowest notes; thus (a') and (a'~) are called respectively the major and minor common chords of 0. The remaining members of each group are not named after their lowest note, but after that of their fundamental inversion; thus (V), (c'), and (▀'), (y') are respectively the major and minor common chords of G in their first and second inversions. The reason of this, as far as the major group is concerned, follows directly from Heimholtz's theory of consonance and dissonance.

The notes of the triads (a'), (b'), (c') are all coincident with individual harmonics of a composite sound whose fundamental tone is the low C Misic 120076 for (a') and (b'), and the octave above that note for (c'); hence they may be regarded as forming a part of the composite vibration of a 0 sound, and therefore each triad may be appropriately called by its name. With the minor triads this is not so completely true, because the E- in (a'), (▀'), and (y') is not coincident with an overtone of 0. The other two notes, however, are in each case leading harmonics of C, and therefore these triads belong at any rate more to 0 than to any other note-Common chords of more than three constituent sounds can only be formed by adding to the consonant triads notes which are exact octaves above or below those of the triads. The bright open character of the major and the gloomy veiled effects of minor chords are attributed by Helmholtz to the different way in which combination tones enter in the two cases. The positions of the first order of combination tones, for each of the six consonant triads, are shown in crotchets in the appended stave, the primaries being indicated by minims:

Misic 120077

Each interval gives rise to its own combination tone, but, in the cases of the fundamental position and second inversion of the C major triad, two combination tones happen to coin-ride. The reader will at once observe that in the major group no note extraneous to the harmony is brought in by the combination tones, In the minor group this is no longer the case. The fundamental position and the first inversion of the triad are both in an Abo which is foreign to the harmony, and the second inversion involves an additional extraneous note, Bb. The position of these adventitious sounds is not such as to produce dissonance, for which they are too far from each other and from the notes of the triad; but they cloud the transparency of the harmony, and so give rise to the effects characteristic of the minor mode. The unsatisfying character of minor compared with major triads comes out with peculiar distinctness on the melodeon; as indeed, from the powerful combination tones of that instrument, we should naturally have anticipated. - Sedley Taylor, from whose work "On Sound and Music" nearly all of the above passage on inversion is taken, says: " The musical notation in ordinary use evidently takes for granted a scale consisting of a limited number of fixed sounds.

Moreover, it indicates directly absolute pitch, and only indirectly relative pitch. In order to ascertain the interval between any two notes on the stave, we must go through a little calculation, involving the clef, the key signature, and perhaps, in addition, ' accidental ' sharps or flats. Now these complications, if necessary for pianoforte music, are perfectly gratuitous in the case of vocal music. The voice wants only to be told on what note to begin, and what intervals to sing afterward; i. e., it is concerned with absolute pitch only at its start, and needs to be troubled with it no further. Hence, to place the ordinary notation before a child who is to be taught to sing, is like presenting him with a manual for learning to dance, compiled on the theory that human feet can only move in twelve different ways. Not only does the established notation encumber the vocalist with information which he does not want; it fails to communicate the one special piece of information which he does want. It is essential to really good music that every note heard should stand in a definite relation-hip to its tonic or key note. Now there is nothing in the established notation to mark clearly and directly what the relation ought in such case to be.

Unless the vocalist, besides his own part, is provided with that of the accompaniment, and possesses some knowledge of harmony, he cannot ascertain how the notes set down for him are related to the keynote and to each other. The extreme inconvenience of this must have become painfully evident to any one who has frequently sung concerted music from a single part. A bass, we will suppose, after leaving off on F#, is directed to rest thirteen bars, and then come in fortissimo on his high Eb. It is impossible for him to keep the absolute pitch of F# in his head during this long interval, which is perhaps occupied by the other voices in modulating into some remote key; and his part vouchsafes no indication in what relation the Eb stands to the notes or chords immediately preceding it. There remains then nothing for him to do but to sing at a venture some note at the top of his voice, in the hope that it may prove to be Eb,, though with considerable dread, in the opposite event, of committing a conspicuous fortissimo blunder. The essential requisite for a system of musical notation, therefore, is that, whenever it specifies any sound, it shall indicate in a direct and simple manner the relation in which that sound stands to its tonic for the time being.

A method by which this criterion is very completely satisfied shall now be briefly described. The old Italian singing masters denoted the seven notes of the major scale, reckoned from the key note upward, by the syllables do, re, mi, fa, sol, la, si. As long as a melody moves only in the major mode, without modulation, it clearly admits of being written down, as far as relations of pitch only are concerned, by the use of these syllables. The opening phrase of 'Rule Britannia,' for instance, would stand thus: do, do, do, re, mi, fa, sol, do, re, re, mi, fa, mi. In order to abridge the notation, we may indicate each syllable by its initial consonant. The ambiguity which would thus arise between sol and si is got rid of by altering the latter syllable into ti. In order to distinguish a note from those of the same name in the adjacent octaves above and below it, an accent is added, either above or below the corresponding initial. Thus d' is an octave above d; dt an octave below d. When a modulation (i e., a change of tonic) occurs, it is shown in the following manner: A note necessarily stands in a twofold relation to the outgoing and incoming tonic. The interval it forms with the new tonic is different from that which it formed with the old one.

Each of these intervals can be denoted by a suitable syllable initial, and the displacement of one of these initials by the other represents in the aptest manner the supersession of the old by the new tonic. The old initial is written above and to the left of the new one. Thus rf indicates that the note re is to be sung, but its name changed to/a. As this is a somewhat difficult point, a few modulations are appended, expressed both in the established notation and in that now under consideration. The instances selected are from C to G, from C to F, from E to C, from G to F#.

Misic 120078Misic 120079

Immediately after a modulation, the ordinary syllable initials come into use again, and continue to be employed until a fresh modulation occurs. It will be seen at once that the difficulty of 'remote keys,' which is so serious in the established notation, thus altogether disappears. For instance, a vocal phrase occurring in Spohr's 'Last Judgment,' which in the established notation is represented in the following manner:

Misic 120080 takes, in the notation before us, the simple form:

S l t | d' m f s | s f I I I s | f m.

As another example, take the following, from the same work:

Misic 120081

The system of notation of which a cursory sketch has just been given originated, it is said, with two Norwich ladies named Glover, but has received its present form at the hands of Mr. J. Curwen, to whom it owes the name of 'tonic sol-fa,' by which it is now so widely known. No mention has been made of the notation for minor and chromatic intervals, nor of that for denoting the relations of time by measures appealing directly to the eye, instead of by mere symbols. On these and all other points connected with his system, Mr. Curwen's published works on tonic sol-fa give full and thoroughly lucid and intelligible explanations. Mr. Curwen has also created a very extensive literature of the best vocal music, printed in his own notation, which has given a most remarkable impulse to choral singing." Helmholtz gives his opinion in favor of the tonic sol-fa method. - Melody is a sequence of sounds of different heights and durations, producing an agreeable effect. In the development of music, melody preceded harmony; and Helmholtz traces the progress of musical theory through three distinct periods, viz.: 1, homophonous music of antiquity, to which belongs the music at present in use among oriental people; 2, polyphonic music of the middle ages, which allows of several parts, but without attaching any importance to the individual signification of musical accords; its period extends from the 10th to the 17th century, when it developed into: 3, harmonic or modern music, characterized by the importance given to harmony considered in itself.

This school of music began to develop in the 16th century. The best theory of melody, like that of harmony, is based on the existence of the harmonics in all musical sounds. The harmonics which exist in any two sounds determine the affinity of their sequence, just as the affinities existing between the notes of any chord depend on the harmonics which are common to them. It is necessary for the existence of a melody that the sounds composing it shall have definite intervals between them, or, in other words, steps in pitch, and that these sounds shall have definite durations. The measure of the music directs us in the division of time, while the sequence of the notes by definite numbers of tones and semitones gives us the means of making the steps in pitch; and thus we have the movement of the music from the rhythm and the melody. Such sounds as that made by the wind produce confused and unmusical impressions because of the absence of measure and of gradations in pitch; but music has a scale for measuring the ascending and descending movements of sounds, and this scale is the gamut. The foregoing considerations will lead to a rational explanation why, in the musical scale, we have the octave, the fifth, the third, and so on.

In the following table are given the tonic, and under it various musical intervals. Each interval is followed by those of its harmonics which it has in common with the tonic. The greater the number of such ties, the greater the affinity of the notes.

Tonic (1)

1

2

3

4

5

6

7

8

9

Octave (2)

-

2

-

4

-

6

-

8

-

Twelfth (3)

-

-

3

-

-

6

-

-----

9

Fifth (3/2)

-

-

3

-

-

6

-

-----

9

Fourth (4/3)

-

-

-

4

- .

-

8

-

Major third (5/4)

-

-

-

-

5

-

-

-

Minor third (6/5)

-

-

-

-

-

6

-

-

-

The octave has all of its even harmonics in common with the tonic; therefore the affinity between it and the tonic is greater than that between the notes forming any other interval. Hence, the octave is to a great extent the repetition of the tonic, and this is of course true of all the notes of any octave, referred to the same notes in the octave below. Thus we have a rational explanation of the fact that each succeeding octave repeats the impression made by the one which preceded it. The fundamental tone of the twelfth is really the third harmonic of the tonic, and its second and third harmonics coincide with the sixth and ninth harmonics of the tonic; but the affinity between the tonic and its twelfth is evidently far less than that existing between the tonic and its octave. In diminishing degrees of affinity follow the fifth, fourth, major third, and minor; third. The nearest affinities dominated in the earlier periods of music. Thus, in the polyphonic chanting of the middle ages the fifths were most in vogue, while the thirds and sixths are typical of modern music, and are characteristic of the early developments of harmony.

According to Helmholtz, there is an affinity of the first degree between two sounds when they have at least one harmonic in common; an affinity of the second degree when the two sounds have a harmonic in common with a third sound. From these premises he doduces the construction of the diatonic scale with notes which have for the tonic affinities of the first and second degrees. The immediate affinities of the tonic 0 are composed of the notes Ca, G, F, A, E, and Eb-. if we confine ourselves to the first six harmonics, the others being too feeble to determine an affinity. We thus have the gamuts: C__E_F_G_A__C2; or better, 0 _ _ E2J- _ F _ G _ A _ _ C2, for we cannot place in the same gamut notes so near to each other as E and E-. In this series there are two intervals which are too large, and in order to divide them we must recur to the affinities of G, which are C, D, E, B, C2. The D and the B are thus found to be related to C by an affinity of the second degree; on interpolating them in the above gamuts, we obtain the diatonic gamut C, D, E, F, G, A, B, C2; which becomes the minor ascending gamut if we place Eb in the place of E. The I) which we find in the affinity of F differs by a comma from D as determined by G. These examples will serve to show the method followed by Ilelmholtz. "In studying the rules of harmony we finally perceive that the accords, considered as complex sounds, contain the same relations of affinity as the notes of the gamut, by reason of the coincidence of some of their notes.

The important function of the tonic in modern music, or what M. FÚtis calls the principal of tonality, is also explained by the properties of the harmonica of the tonic. These principles, so clear and so simple, have afforded Helmholtz the means of deducing from considerations in some respects mathematical the fundamental rules of musical composition. Nevertheless, we cannot but be of the opinion that the last word on the theory of music has not been said, for all of the deductions of Helmholtz are not beyond criticism. Thus, Arthur von Oettingen has criticised with much reason the explanation which Helmholtz gives of the difference between the major and minor modes, for the phenomenon of the harmonics is sometimes barely perceptible. Yon Oettingen finds that difference in the reciprocal principles of tonicity and of phonicity. The tonicity of an interval or of an accord consists in the possibility of considering it as a group of harmonics of the same fundamental sound. It is thus that the major accord is formed by the fourth, fifth, and sixth harmonics of the tonic or fundamental. 1. Phonicity is the inverse property of having a harmonic in common; the minor accord 1/6, 1/5, ╝ has the sound 1 as common harmonic or phonic.

The major accord has the phonic 60; the minor accord has for tonic 1/60. These relations can be expressed as follows:

1/60

1/6 - 1/5 - ╝

1

4-5-6

60

Tonic.

Accord (minor).

Phonic.

Tonic.

Accord (major).

Phonic

F

A-C-E

E

0

C-E-G

B

Musicians call C the tonic and G the dominant of the gamut of 0 major, which can be written thus:

0

D

E

F

G

A

B

C

1

9

5/4

4

3/2

5

1 5

2

Yon Oettingen calls E the phonic and A the dominant of A minor, and writes the above gamut as follows:

E

F

G

A

B

c

D

E

Ż

8/15

3/5

2/3

3/4

4/5

8/9

1

By the development of this dualism he obtains the parallel construction of the major and minor modes." (Radau, Acoustique.) - Whenever music is written for parts, the laws of harmony necessarily come into play, and the skill of the composer is required, not only to have the harmonics correct, but that the parts shall be distinct and clear. This polyphonic style requires very intricate laws, and hence persons capable of creating lovely melodies, and writing them in combination with other themes, are as rare as great poets. In harmonious treatment of music, the following are a few of the radical laws. In the regular progression of harmonics the fundamental bass note falls a fifth to whatever note, or rises a fourth to the octave above it; but this law has many exceptions. If in the treble or soprano part the procession of notes is upward, say G D E G, the bass cannot give the same notes, but must use others, such iterations being intolerable to the musical ear. Accordingly, it is a rule in harmony or part writing that contrary motion is best between the extreme parts; or that when one goes upward the others go downward, and the reverse. The parallel motion, as it is called, is in use between extreme parts, but then the notes must bo different. Thirds or sixths move harmoniously together.

When the parts are in octaves, the law against identical notes moving up or down together ceases, for the effect of such unity supersedes harmony for the moment. There are certain keys which have a close alliance to others. Given a certain key or tonic, for example, on which it is proposed to write a piece, say C: the keys having the closest alliance to this are G major, the fourth below; A minor, the third below; F major, the fourth above; and E minor, the third above. Next in order of alliance to C are E major, E flat major, A major, and A flat major. The key of B major is widely dissociated from C; so too B flat major; and F sharp major is a distant musical shore only to be approached in a long musical voyage. D minor and D major in their relations to C can be used but transiently. D flat major can be reached readily through C minor. The passing to a new key without an intermediate chord is called a transition; when one or more chords are used, it is called a modulation. Transitions are among the brilliant effects of modern dramatic music. A great surprise, sudden and violent emotion, warrants a transition, and the change may be further enforced by an explosion of all the orchestral instruments. The transition is marked in proportion as the notes of the scale are changed.

A transition from C to G for the purpose named would be timid and feeble; but one from 0 to A flat or D flat would be effective. In the one case all the notes of the chord of G are found in the scale of C; in the others, two notes are changed; hence the shock. - We close this portion of the article with a few observations on the relations existing between the physical theory of consonance and dissonance and the aesthetics of music. Helmholtz founds his theory of consonance and dissonance on the fact that whenever a dissonance is perceived beats are produced by the constituent sounds of the chord, and that in consonance these beats are few or entirely wanting. On this physical basis the intervals are placed in the following order, according to their degree of freedom from dissonance. The octave stands first, then follow the fifth, the fourth, the major third, the major sixth, the minor third, the minor sixth. This classification, as stated, is based on the decreasing number of beating harmonics in the successive intervals; but it does not necessarily follow that the smoothest chords will always be those which are musically the most pleasing; for may there not be some other property which gives us greater satisfaction than mere consonance? "Esthetic considerations come in here, with the same right to be heard as mechanical considerations within their own domain.

Now unquestionably the ear's order of merit is not the same as the mechanical order. It places thirds and sixths first, then the fourth and fifth, and the octave last of all. The constant appearance of thirds and sixths in two-part music, compared with the infrequent employment of the remaining concords, leaves no doubt on this point. In fact these intervals have a peculiar richness and permanent charm about them, not possessed by the fourth or fifth to anything like the same extent, and by the octave not at all. The thin effect of the octave undoubtedly depends on the fact that every harmonic of the higher of two musical sounds forming that interval, coincides exactly with a harmonic of the lower sound. Thus no new sound is introduced by the higher note; the quality of that previously heard is merely modified by the alteration of relative intensity among the constituent harmonics. Major and minor thirds bring in a greater variety of pitch in the resultant mass of sound than does the fifth; but this can hardly be said of the major and minor sixths compared with the fourth.

On the whole, we are inclined to attribute the predilection of the ear for thirds and sixths, over the other concords, to circumstances connected with its perception of key relations, though we are not able to give a satisfactory account of them. The ear enjoys, in alternation with consonant chords, dissonances of so harsh a description as to be barely endurable when sustained by themselves. This constitutes a marked distinction between it and the other organs of sense. As instances of the kind of discords in which the ear can find delight, take the following. The chord marked * should in each case be played first by itself, and then in the place assigned to it by the composer. The effect of this isolated discord is so intensely harsh that it is at first difficult to understand how any preceding and succeeding concords can make it at all tolerable; yet the sequence, in both phases cited, is beautiful.

Misic 120082

Considerations such as those just alleged tend to show that, while physical science is absolutely authoritative in all that relates to the constitution of musical sounds, and the smoothness of their combinations, the composer's direct perception of what is musiestablished new ecclesiastical keys, founded and encouraged a system of musical training at Rome, wrote many hymns, and finally was the father of the Gregorian chant, upon the broad foundation of which the music of the church rested for several centuries. But as yet harmony, the most important element of music, did not exist. In chanting, the performers all sang the melody. The system of musical notation was also exceedingly imperfect, certain signs called numoe being used to designate the pitch and duration of notes, the lines and spaces of the staff not yet being invented. it was not until the discovery of harmony, and the invention of the staff and of a proper nomenclature for the notes of the scale, that the art of music began to free itself from its fetters. During the 7th, 8th, and 9th centuries there is little to be recorded in the way of musical progress.

At the close of the 9th century Hucbald, a Flemish monk, wrote a treatise on harmony, which had already begun to be practised after a rude fashion, the octave, fourth, and fifth only being used, and the parts progressing together. The following example, harsh enough to modern ears, will serve better than any description to show the condition of the science of harmony in those days:

Nos qui vi   vi mus be  ne   di   ci mus Do mi   num ex hoc nunc et us   que la sae  cu   lum.

Nos qui vi - vi-mus be- ne - di - ci-mus Do-mi - num ex hoc nunc et us - que la sae- cu - lum.

The notation is modern, for it was not till more than a century later that Guido Aretino, also a monk, added two lines to the staff, then consisting of two only, and originated the system of solmization on which his reputation rests. At the same time that progress was made in harmony within the church, the love of music, innate in human nature, found expression through the songs of the people. There is scarcely any nation whose traditions do not furnish examples of folk songs of a remote antiquity. The Celts made great progress in this direction; their bards were famous for their skill in poetry and song. They also possessed an instrument known as the crowth, which had several strings of different pitch; and many writers on music have asserted their belief that the secrets of harmony were known to them before they were to the Italians. The French also had their chansons, the Italians their canzonctti, and the Germans their Volkslieder. Nothing was more common than for the church composers to adopt some well known popular air as a theme for their masses.

Indeed, the masses were not infrequently named after the song which served as their basis, so that we find the mass " Farewell, my loves," that of "The Armed Man," that of " The Pale-faced Man," that of "The Red Noses," and many others similarly named. The minstrels, jongleurs, minnesingers, and troubadours played a very important part in the development of the music of the middle ages. From the close of the 11th to the commencement of the 14th century these musicians exercised a wide influence. Minstrelsy and warlike deeds were closely associated; many of the knights were also minstrels. Among those nobles who were distinguished troubadours were Thibaut, king of Navarre, the chevalier Raoul de Coney, and William IX., count of Poitou. Pierre Vidal of Toulouse accompanied Richard of England as minstrel on the third crusade. The troubadours cultivated various kinds of lyric compositions, such as the chanson or love song, the sirvente or satire, the ten son, or lyric contest, the halada or ballad, and the serena or serenade. On their return from the crusades they brought home various new musical forms caught in the East, which served to enlarge the domain of melody.

In the beginning of the 14th century the troubadours as a class disappeared; but in that century music received a fresh impetus from the Netherlanders, who suddenly took the lead of all European nations in the cultivation of the art, which supremacy they held for a century and a half, sending their musicians as teachers, leaders, and composers into all countries. The Netherlands at this time were rich and prosperous; their cities were in a condition almost of republican freedom; the government under the house of Burgundy was liberal, and fostered with especial care the arts of painting and music. Counterpoint received great attention during the period of the Dutch supremacy, and in the course of the 15th century the Netherlanders became the most learned contrapuntists in Europe. The first of their composers who came into notice was Guillaume Dufay, born in Hainaut, in the latter part of the 14th century. His masses, which are to be found in manuscript in the papal chapel, are the oldest known in contrapuntal form. Dufay is credited with having emancipated music from the harsh succession of fourths, fifths, octaves, and unisons, which constituted the harmony of preceding composers.

The next Flemish composer of eminence was Jan Okeghem, who exerted great influence not only as a composer, but also as a teacher. Among his pupils was Josquin des Pres (died about 1530), the most famous composer of his day. He did not strive, as did many of his time, to construct impossible fugues and ingenious contrapuntal puzzles, written simply to display his technical knowledge, but sought to infuse intelligence and soul into all the parts, and to give sympathy and expression to music. His influence was felt in Italy, where for a time he was attached to the pontifical choir of Sixtus IV., and in France, where he was composer and chief singer in the chapel of Louis XII. Among his celebrated pupils were Jannequin Arcadelt and Willaert. With the last named of these composers (died about 1563) the ascendancy of the Dutch in musical composition began to decline. The application of movable metal types to the printing of notes in 1502 served to cheapen and diffuse published music. Willaert's greatest distinction rests on the fact that he was the first celebrated composer who gave his attention to the composition of madrigals, from which fact he was called "the father of the madrigal." While still a young man he went to Venice, and he became the head of the Venetian school.

During the 16th century, and contemporary with Willaert, lived many notable composers: in Italy, Palestrina, Constanzo Festa, Luca Marenzio (one of the greatest of madrigalists, surnamed the Sweet Swan), and Cypriano de Rore, called by the Italians il Divino; in the Netherlands, Orlando di Lasso, Clemens non Papa, and Christian and Sebastian Hollander; in Spain, Cris-tofano Morales; in England, Marbeck, Tallis, Bird, Morley, Weelkes, and Wilbye. Nearly all of these distinguished themselves as composers of madrigals; the English cultivated this form of composition with so much success that the practice of madrigals became during that century the delight of refined society; sight reading was at that time even more than in our own day a common accomplishment among the educated. The madrigals of Wilbye, Weelkes, and Morley have never been surpassed in beauty of melody and form, or in the freedom with which the different parts move. In 1601 Thomas Morley published a collection of madrigals in fulsome praise of Queen Elizabeth, entitled " The Triumphs of Oriana," to which 20 English composers contributed.

Of the composers of other nations whom we have named, the two most famous were Palestrina and Orlando di Lasso. The latter was the last of the great Netherlands school, and after his death the ascendancy passed over to the Italians. As to Palestrina, it is difficult to overestimate the talent of the man or his influence over the art in his day. In his compositions the solemn words of the mass found their highest and noblest musical expression. He was truly regarded as the great reformer of church music. So fully was his genius recognized by the composers of his own time, that 14 of the most celebrated combined to compose and dedicate to him a collection of psalms in five parts. He used only the ecclesiastical modes, and avoided all straining after effect by strange harmonies; but his knowledge of counterpoint, and the elevation and nobility of his style, made his masses and his other compositions, of which he wrote a vast number, examples for all time of what true church music should be. During this century the keyed instruments in use were the organ, the virginal, the spinet, the clavichord, and the harpischord. The viol, the guitar, and the flute were also used. Between 1550 and 1600 instruments were first introduced into churches for the purpose of accompanying voices.

No such thing as independent accompaniment was known at this time, the instruments being used only to reŰnforce the voice and playing from the vocal score. The violin now began to assume new importance, and in the hands of the Amati family and their immediate successors it was brought with wonderful rapidity to a beauty of form and color and sweetness of tone that have not since been excelled. It is the only example in history of an instrument which at once attained its perfection, and which the inventors of two centuries and a half have not been able to improve upon. (See Amati.) - The closing year of the 16th century witnessed the birth both of opera and of oratorio. In the year 1600 was performed at Florence a work entitled Euri-dice, una tragedia per musica. The words were by Rinuccini, the music by Peri. This work possessed after a rude fashion the charac-. teristics of the modern opera. In the same year was performed at Rome Emilio del Cava-liere's religious drama L'Anima e corpo, which may be considered the forerunner of the oratorio, as Peri's work was of the opera.

The way had been long preparing for both opera and oratorio, through the miracle plays and the performances representing the passion of Christ. These sacred musical dramas were often performed in a hall, called by the Italians oratorio, adjoining the church, and hence came to be called by that name. Cavaliere's work was first represented on the stage of the church of La Vallicella, with appropriate scenery and action. The personages were Time, Pleasure, the Body, the World, and Human Life. There was also a chorus that commented, after the manner of the Greek tragedies, upon the events narrated. The instruments of accompaniment were placed behind the scenes, and were as follows: una lira doppia, a double lyre; un clavicembalo, a harpsichord; un cliitarone, a large guitar; due flauti, two flutes. Instead of overture, a madrigal with all the voice parts doubled was recommended by the composer. The example thus set by Cavaliere was speedily followed by other composers. Among the most distinguished of those who contributed to this form of composition during the 17th century were Carissimi, Stradella, Scarlatti, and Caldara. Another element combined with that of the miracle plays to give form to the opera; this was Greek tragedy.

With the revival of letters a new impetus had been given, especially in Italy, to the study of the Greek authors. At the house of Giovanni Bardi, count of Vernico, in Florence, a small musical and literary circle was accustomed to meet to discuss the probable forms of Greek music, and the method in which they could be made available. Vincenzo Galilei, father of the astronomer, was one of this number. From theory they advanced to practice, established new ecclesiastical keys, founded and encouraged a system of musical training at Rome, wrote many hymns, and finally was the father of the Gregorian chant, upon the broad foundation of which the music of the church rested for several centuries. But as yet harmony, the most important element of music, did not exist. In chanting, the performers all sang the melody. The system of musical notation was also exceedingly imperfect, certain signs called numoe being used to designate the pitch and duration of notes, the lines and spaces of the staff not yet being invented. It was not until the discovery of harmonv, and the invention of the staff and of a proper nomenclature for the notes of the scale, that the art of music began to free itself from its fetters.

During the 7th, 8th, and 9th centuries there is little to be recorded in the way of musical progress. At the close of the 9th century Hucbald, a Flemish monk, wrote a treatise on harmony, which had already begun to be practised after a rude fashion, the octave, fourth, and fifth only being used, and the parts progressing together. The following example, harsh enough to modern ears, will serve better than any description to show the condition of the science of harmony in those days:

Nos qui vi   vi mus be ne   di   ci mus Do mi   num ex hoc nunc et us   que m sa3 cu lum.

Nos qui vi - vi-mus be-ne - di - ci-mus Do-mi - num ex hoc nunc et us - que m sa3-cu-lum.

The notation is modern, for it was not till more than a century later that Guido Aretino, also a monk, added two lines to the staff, then consisting of two only, and originated the system of solmization on which his reputation rests. At the same time that progress was made in harmony within the church, the love of music, innate in human nature, found expression through the songs of the people. There is scarcely any nation whose traditions do not furnish examples of folk songs of a remote antiquity. The Celts made great progress in this direction; their bards were famous for their skill in poetry and song. They also possessed an instrument known as the crowth, which had several strings of different pitch; and many writers on music have asserted their belief that the secrets of harmony were known to them before they were to the Italians. The French also had their chansons, the Italians their canzonctti, and the Germans their Vollcslieder. Nothing was more common than for the church composers to adopt some well known popular air as a theme for their masses.

Indeed, the masses were not infrequently named after the song which served as their basis, so that we find the mass '. Farewell, my loves," that of " The Armed Man," that of " The Pale-faced Man," that of "The Red Noses," and many others similarly named. The minstrels, jongleurs, minnesingers, and troubadours played a very important part in the development of the music of the middle ages. From the close of the 11th to the commencement of the 14th century these musicians exercised a wide influence. Minstrelsy and warlike deeds were closely associated; many of the knights were also minstrels. Among those nobles who were distinguished troubadours were Thibaut, king of Navarre, the chevalier Raoul de Coucy, and William IX., count of Poitou. Pierre Vidal of Toulouse accompanied Richard of England as minstrel on the third crusade. The troubadours cultivated various kinds of lyric compositions, such as the chanson or love song, the sirvente or satire, the tenson or lyric contest, the halada or ballad, and the serena or serenade. On their return from the crusades they brought home various new musical forms caught in the East, which served to enlarge the domain of melody.

In the beginning of the 14th century the troubadours as a class disappeared; but in that century music received a fresh impetus from the Netherlander, who suddenly took the lead of all European nations in the cultivation of the art, which supremacy they held for a century and a half, sending their musicians as teachers, leaders, and composers into all countries. The Netherlands at this time were rich and prosperous; their cities were in a condition almost of republican freedom; the government under the house of Burgundy was liberal, and fostered with especial care the arts of painting and music. Counterpoint received great attention during the period of the Dutch supremacy, and in the course of the 15th century the Netherlanders became the most learned contrapuntists in Europe. The first of their composers who came into notice was Guillaume Dufay, born in Hainaut, in the latter part of the 14th century. His masses, which are to be found in manuscript in the papal chapel, are the oldest known in contrapuntal form. Dufay is credited with having emancipated music from the harsh succession of fourths, fifths, octaves, and unisons, which constituted the harmony of preceding composers.

The next Flemish composer of eminence was Jan Okeghem, who exerted great influence not only as a composer, but also as a teacher. Among his pupils was Josquin des PrÚs (died about 1530), the most famous composer of his day. He did not strive, as did many of his time, to construct impossible fugues and ingenious contrapuntal puzzles, written simply to display his technical knowledge, but sought to infuse intelligence and soul into all the parts, and to give sympathy and expression to music. His influence was felt in Italy, where for a time he was attached to the pontifical choir of Sixtus IV., and in France, where he was composer and chief singer in the chapel of Louis XII. Among his celebrated pupils were Jannequin Arcadelt and Willaert. With the last named of these composers (died about 1563) the ascendancy of the Dutch in musical composition began to decline. The application of movable metal types to the printing of notes in 1502 served to cheapen and diffuse published music. Willaert's greatest distinction rests on the fact that he was the first celebrated composer who gave his attention to the composition of madrigals, from which fact he was called "the father of the madrigal." While still a young man he went to Venice, and he became the head of the Venetian school.

During the 16th century, and contemporary with Willaert, lived many notable composers: in Italy, Pa-lestrina, Constanzo Festa, Luca Marenzio (one of the greatest of madrigalists, surnamed the Sweet Swan), and Cypriano de Rore, called by the Italians il Divino; in the Netherlands, Orlando di Lasso, Clemens non Papa, and Christian and Sebastian Hollander; in Spain, Cris-tofano Morales; in England, Marbeck, Tallis, Bird, Morley, Weelkes, and Wilbye. Nearly all of these distinguished themselves as composers of madrigals; the English cultivated this form of composition with so much success that the practice of madrigals became during that century the delight of refined society; sight readiug was at that time even more than in our own day a common accomplishment among the educated. The madrigals of Wilbye, Weelkes, and Morley have never been surpassed in beauty of melody and form, or in the freedom with which the different parts move. In 1601 Thomas Morley published a collection of madrigals in fulsome praise of Queen Elizabeth, entitled " The Triumphs of Oriana," to which 20 English composers contributed.

Of the composers of other nations whom we have named, the two most famous were Palestrina and Orlando di Lasso. The latter was the last of the great Netherlands school, and after his death the ascendancy passed over to the Italians. As to Palestrina, it is difficult to overestimate the talent of the man or his influence over the art in his day. In his compositions the solemn words of the mass found their highest and noblest musical expression. He was truly regarded as the great reformer of church music. So fully was his genius recognized by the composers of his own time, that 14 of the most celebrated combined to compose and dedicate to him a collection of psalms in five parts. He used only the ecclesiastical modes, and avoided all straining after effect by strange harmonies; but his knowledge of counterpoint, and the elevation and nobility of his style, made his masses and his other compositions, of which he wrote a vast number, examples for all time of what true church music should be. During this century the keyed instruments in use were the organ, the virginal, the spinet, the clavichord, and the harpischord. The viol, the guitar, and the flute were also used. Between 1550 and 1600 instruments were first introduced into churches for the purpose of accompanying voices.

No such thing as independent accompaniment was known at this time, the instruments being used only to reŰnforce the voice and playing from the vocal score. The violin now began to assume new importance, and in the hands of the Amati family and their immediate successors it was brought with wonderful rapidity to a beauty of form and color and sweetness of tone that have not since been excelled. It is the only example in history of an instrument which at once attained its perfection, and which the inventors of two centuries and a half have not been able to improve upon. (See Amati.) - The closing year of the 16th century witnessed the birth both of opera and of oratorio. In the year 1600 was performed at Florence a work entitled Euri-dice, una tragedia per mnsica. The words were by Rinuccini, the music by Peri. This work possessed after a rude fashion the characteristics of the modern opera. In the same year was performed at Rome Emilio del Cava-liere's religious drama L'Anima e corpo, which may be considered the forerunner of the oratorio, as Peri's work was of the opera.

The way had been long preparing for both opera and oratorio, through the miracle plays and the performances representing the passion of Christ. These sacred musical dramas were often performed in a hall, called by the Italians oratorio, adjoining the church, and hence came to be called by that name. Cavaliere's work was first represented on the stage of the church of La Vallicella, with appropriate scenery and action. The personages were Time, Pleasure, the Body, the World, and Human Life. There was also a chorus that commented, after the manner of the Greek tragedies, upon the events narrated. The instruments of accompaniment were placed behind the scenes, and were as follows: una lira doppia, a double lyre; un clavicembalo, a harpsichord; un cliitarone, a large guitar; due flauti, two flutes. Instead of overture, a madrigal with all the voice parts doubled was recommended by the composer. The example thus set by Cavaliere was speedily followed by other composers. Among the most distinguished of those who contributed to this form of composition during the 17th century were Carissimi, Stradella, Scarlatti, and Caldara. Another element combined with that of the miracle plays to give form to the opera; this was Greek tragedy.

With the revival of letters a new impetus had been given, especially in Italy, to the study of the Greek authors. At the house of Giovanni Bardi, count of Vernico, in Florence, a small musical and literary circle was accustomed to meet to discuss the probable forms of Greek music, and the method in which they could be made available. Vincenzo Galilei, father of the astronomer, was one of this number. From theory they advanced to practice, and Galilei was the first to write music for a single voice. Among the members of this circle were the poet Rinuccini and the musician Peri. Their efforts to reproduce the musical declamation of the Greeks resulted finally in the musical setting to Rimiccini's Euridiee, in which appeared what they called the stilo rappresen-tatho, which in a somewhat altered form we now know as recitative. The opera of Euridiee was called by its authors a drama per mu-sie-j, the term opera not being applied to this kind of composition till 1(556. The scenery represented first green fields, then the ocean, afterward the abodes of the blest, and finally the torments of the infernal regions. The language was bombastic, and the music awkward and affected. The solos were in the style of recitative, and the choruses in madrigal form.

The instruments were the same as those mentioned above in the oratorio. The next Italian operatic composer of eminence was Claudio Monteverde. His Orfeo, composed in 1607, was an advance upon Peri's music. The orchestration was better, the recitative more dramatic, and suggestions appeared of the aria, which was yet to be invented. The opera quickly spread over Italy, and finally crossed the Alps, Cardinal Mazarin introducing it in 1615 into France. The first opera there performed was La Jinta pazza, winch was given in the presence of Louis XIV. The first French opera was called Alcebar rol de Mogol; the words and music were by the abbe Mailly, and it was performed in 1616. The first French operatic composer of any note was Cambert, who however was speedily supplanted in the favor of the king by the Italian Lulli. This composer for many years controlled the French lyric stage, more by his sense of dramatic situations than by the merit of his musical forms, He was the first to elaborate and give prominence to the overture.

The first of his operas performed in France was Les fetes de l'Amour et de Bacchus, which was represented in 1672. The principal Italian composers during the last half of the 17th century were Cesti, Alessan-dro Scarlatti, and Carissimi. The last did not write for the stage. Henry Purcell (1658-'95) was at this time one of the few native composers on whom the English could look with pride. He had been a close student, almost an imitator, of the style of Carissimi, and did much, both through his operas and church compositions, for the elevation of his art, - The 18th century was the age of great orchestral writers, operatic and oratorio composers, and performers. It would be impossible to name all of the illustrious musicians of that century; among those of most conspicuous talent were (in the order of their birth) Marcello, Domeni-co Scarlatti, Rameau, Handel, Bach, Porpora, Hasse, Martini, Pergolesi, Jomelli, Cluck, Pic-cini, Haydn, GrÚtry, Paisiello, Clementi, Cima-rosa, Mozart, Cherubini, MÚhul, Beethoven, and Spontini. Auber, Schubert, Rossini, Meyerbeer, Donizetti, and others, though born in the 18th century, belong rather to the 19th, in which their genius began to manifest itself.

We can only refer with any detail to such of those whom we have named as exercised a marked and lasting influence upon the art. First among them was Johann Sebastian Bach. Though he was only cantor at St. Thomas's church in Leipsic, and undertook no works that were not in the simple line of his duty, he has given to the world organ and vocal compositions unrivalled in their way. The art of fugue writing, so steadfastly cultivated during the so-called Dutch period, he perfected. Taking the German chorals for his themes, he wrought upon them his great work, the passion music, the sublimest ever composed for the Protestant church. Though Bach produced also delightful compositions for the stringed orchestra, such as his suite in D, his fame must rest upon his passion music and his organ and pianoforte works. While Bach was elevating the church music of Protestantism, his great contemporary Handel was working out that mighty chain of oratorios that have since been the delight of the world. For many years he had devoted himself to the composition of Italian operas; more than 40 of these exist, but never will be placed upon the stage again.

From them, however, have been selected many arias, such as the Lascia ch'io pianga from the opera of Binaldo, that are still among the greatest favorites of the concert room. It was fortunate for the world that Handel failed in his operatic enterprises, otherwise such works as " Saul," " Samson," "Judas Maccabfeus," "Israel in Egypt," and the "Messiah" would never have existed. In the century and a quarter that has elapsed since they were created, no greater works of their kind have been produced. From Haydn composition for the 'orchestra received its greatest development. This illustrious composer when a boy had the benefit of instruction from Porpora, the great Italian composer, from whom he derived his knowledge of vocal writing; and he learned the art of setting words to music from Metastasio the poet. But with all these advantages he failed as an operatic composer, while he succeeded in orchestral music and oratorios. His genius for melody was so great that, although he was nearly contemporary with Handel, his melodies are in advance of Handel's in grace, symmetry, and essential beauty.

His muse was kindred with Mozart's. In symphonic writing, in many respects, he has not been excelled; in breadth and depth, however, the palm for that department has been awarded to his successor Beethoven. The form of the symphony, as developed by Haydn, is derived from that of the piano sonato or violin quartet; generally it is composed of four movements: an allegro, usually the principal movement; then a slow movement; then a minuet, or old dance tune; then a rondo, or finale, of quick movement. There is no organic completeness in this design, so far as the number of movements is concerned; they are all distinct, and there might as well be one movement, or 40, if so many could be compassed; but symphonies and quartets were composed according to this method as though under an irrefragable law. Their structure is: a theme or melody in a given key, say 0 major; a passage leading to another key, G major, the most closely related to the first, with a strong assertion of the chord of the seventh or the fifth of G, which is D, before the second theme or melody' is taken; then follows some accessory and climacteric matter, and we arrive at the end of the exposition of the primary ideas.

The second part is taken up, generally after the first is repeated, but without stopping; and now begins what is called the development of ideas, in which the primary ones are set off in various ways, by new harmonies or accessories of melody, by double counterpoints (that is to say, placing phrases indifferently as the bass or treble), by modulations, by instrumentation, etc.; and this runs into a repetition of the original melody, to which the second melody is added, but this time in the same key with the original, and the whole is crowned with a musical peroration in which appear the most ambitious flights and climaxes. The second movement of the symphony is a clear melody, with accessory and developed matter, and the melody repeated with a short peroration. The third is a minuet, measured and somewhat developed. In Beethoven's symphonies the minuet is set aside for the scherzo, or playful movement, in which piquancy is aimed at. The last movement of the symphony is a melody or theme with accessories, its repetition, and a peroration. Sometimes the last movement is the most important. In the choral symphony of Beethoven the voices are added.

The quartets and" sonatas of Haydn, as well as those of later composers, are on the same plan as symphonies, but generally briefer, as the variety of instrumental coloring in an orchestra warrants greater length. In the course of 50 years Haydn produced more than 500 instrumental compositions. A remarkable trait of the composer was his unerring sense of orchestral color, and of the precise instrument or combination of instruments that best produced the effects he had in mind. "While Haydn was developing the instrumentation of his time, Gluck was working with equal zeal and success in the domain of opera. He was a great reformer, and was the first to announce in clear and unmistakable language the true principles upon which opera should be composed. Much that he then said has since been reiterated by Richard Wagner. Even now the world is slow to accept the theories then advanced; what wonder then that Gluck in his day excited the liveliest antagonism, and that a contention arose between his adherents and those of Piccini (the Gluckists and the Piccinists) which enlisted on one side or the other all the literary and fashionable people of Paris? In the preface to an edition of three of his operas (Paris, 1769) Gluck expounded his theories of operatic composition, the pith of which is that the legitimate purpose of music is to second poetry in order to strengthen the expression of the sentiments and the interest of the drama, without interrupting the action or weakening it by superfluous embellishments. (See Gluck, vol. viii., p. 43.) These maxims the composer exemplified by his works.

The subjects were mostly from Greek classical literature, as the names of his principal operas indicate, such as "Orpheus," "Alcestis," "Iphigenia in Aulis," "Paris and Helen," and "Iphigenia in Tauris." In spite of the fierce opposition of the Piccini faction, France gave its adherence with enthusiasm to Gluck and his works, and from that day the false and artificial methods of the earlier composers were laid aside, and a new era began for the opera. The dramatic and poetic element found its true position by the side of melody and harmony. The next great composer to exert a wide influence upon operatic and other forms of composition was Mozart. He was a man of universal musical genius, and was distinguished as a waiter of chamber music and symphonies and as an operatic composer. His pianoforte compositions "were also numerous; but his influence was not marked in that direction, since he adhered to the forms given him by his predecessors, without effecting in them any great change or improvement. To this generation he is best known through his operas. He was a thorough master of the Italian art of singing, and brought to the support of the voice and the enriching of his scores his profound knowledge of treatment.

What Gluck had begun in the way of sweeping aside the formalism and artificiality of the earlier Italian operatic composers, Mozart completed. Their works together gave a new direction to art, which has had its effect on all subsequent composers for the lyric stage. While the "Orpheus," "Alcestis," and "Iphigenia" of Gluck, and the Don Giomnni, "Marriage of Figaro," and " Magic Flute " of Mozart still keep the stage, the works of their contemporaries have mostly passed into oblivion. Cimarosa's Matrimonio segreto is still occasionally heard, but we look in vain in the modern operatic repertoire for the works of Paisiello, Salieri, Sarti, Paer, Zingarelli, Hasse, or Righini, all prominent composers in Mozart's time. But the 18th century was distinguished also by many illustrious performers. The more extended knowledge of harmony and the constantly increasing technical ability of instrumental players pushed on the musical instrument makers to improvements and new inventions. The violins, violas, violoncellos, and double basses, as we have seen, had already attained their perfection at the hands of the Amati, Stradi-varius, the Guarneri, Stainer, and other great makers.

Yet much remained to be done for keyed instruments, and the efforts for improvement made in this direction resulted in the substitution of hammers for the quills that were used in the harpsichord, and the instrument so constructed took the name of forte piano. The invention has been ascribed to several different men, and by some authorities it is carried back to Bartolommeo Cristofali of Padua, harpsichord player to the court of Tuscany. Improvements were made by Schr÷-ter of Bohemia, Silbermann of Strasburg, and Stein of Augsburg; but the progress was quite slow. The piano used by Gluck was made by Pohlmann in 1772, and is still in existence. It is a small square instrument, 4Ż ft. long and 2 ft. wide, the wires being little more than threads, and so thin that a moderately hard blow would break them. The action is imperfect, and the hammers are a few thicknesses of leather glued over the head of a horizontal jack working on a hinge. John Broadwood and sons became the leading English makers of pianofortes in the latter part of the century, and about the same time the house of Erard was founded in Paris; and Pleyel soon after established himself also in Paris as a pianoforte maker.

John Broadwood's first patent bears date July 17, 1773. Among the celebrated performers of this time were Tartini, Farinelli, and Dragonetti. - Among composers born in the last century who came to their maturity and exerted their influence mainly in the present, maybe named Spontini, Cherubini, Beethoven, Bo´eldieu, Hummel, Herold, Spohr, Weber, Auber, Schubert, Moscheles, Rossini, Meyerbeer, Mercadante, and Donizetti. Of the men born within the present century who have distinguished themselves in the art, either as composers or executants, are Bellini, Adam, Mendelssohn, Thalberg, Paganini, Balfe, Bennett, Bishop, Wallace, Berlioz, Chopin, Ernst, David, Hiller, Schumann, Gade, Verdi, Gounod, Halevy, Ole Bull, Vieuxtemps, Thomas, Liszt, Herz, Joachim, Wagner, Franz, Raff, and Rubinstein. Among these Beethoven beyond a doubt occupies the loftiest position in his art; with him instrumental music reached its highest point of development. Whatever form of music he touched he enlarged and ennobled; under his hand the sonata was perfected and the symphony rose to its grandest proportions, culminating in the ninth, concerning which Wagner has said that with it " the last of symphonies had been written and the domain of instrumental music exhausted." His two masses and his single opera Fidelio are also among the noblest accomplishments of German art.

A few years later than Beethoven, Spontini was born. Among the immediate successors of Mozart he holds an illustrious place. His style was noble and vigorous, his orchestral treatment admirable, and his dramatic instincts correct. In his Vestate and Fernando Cortes are many passages of true genius. Cherubini may be cited as a composer who particularly linked the styles of the close of the last century with those of this. He produced operas which are still represented, and he was equally successful in his sublime church music. He competed with Reicha, moreover, in his profound treatises on the fugue. In brilliant fluency Rossini excels all others who have written for the Italian opera; but then it must be remembered that he was preceded by Mozart, whose operas were written to Italian words, and with melodies identical in shape, in caecsu-ral pauses, in syllabication, and in relation to the chords, with the Italian school of Paisiello, Piccini, and Cimarosa. Whatever tendency there may have been to avoid excessive ornamentation in singing, and to maintain the theory of Gluck, was set aside for many years by Rossini. Mozart, who indulged occasionally in ultra-florid music, or several notes rapidly sung to a syllable, was not brilliant in that department.

Rossini was, and his ornate arabesque work not being of the old pattern, that is to say, merely roulades following a plain melody, but being integrated with the melody itself, he struck the secret of popularity, and swayed Europe musically. The voices, whether bass, tenor, contralto, or soprano, were made to do this ornate work, lavished on serious and comic scenes alike; but with all this profusion of notes, there are ever present touches of severe simplicity. This was exemplified when he wrote for the French Grand Opera, and produced Guillaurne Tell. Among Rossini's Italian contemporaries were Bellini and Donizetti. The romantic, tender, and impassioned strains of the former gave a new impulse to the Italian music, and established a greater popularity for it than it had hitherto enjoyed. The directness of his melodies, and his use of a few notes instead of many for masculine voices, enabled amateurs to seize hold of them who were unable to cope with the floridities of Rossini. In this new school Donizetti was the peer of Bellini, and the author of Lucia and Lucrezia Borgia, with all his shortcomings, has never been surpassed in popularity. It remains only to speak of Verdi, and all the Italian composers of any decided influence in the art will have been referred to.

This composer exhibits a perfect apprehension of climax, intuitive knowledge of stage business, and strong dramatic perception. His melodies are clear, strong, and well defined. In his earlier works his merits stood in strong contrast with certain vices of style, such as overstraining the voice for effect, and noisy and empty unison passages. In his later works, such as the Aula and the "Requiem Mass," he has profited by the example of more painstaking composers, and produced works more carefully considered and of higher merit than his previous compositions. Many of the operas produced by composers for the French stage combine grace, brilliancy, breadth, and grandeur. Among these the works of Meyerbeer are conspicuous. The Huguenots contains some of the finest music ever written for the operatic stage. It has been objected to Meyerbeer that his was too much the music of effect, that he sacrificed the higher form of art to the spectacle, that years of labor were devoted to the careful study of form, and that the soul escaped; in a word, that while his operas evinced a prodigious talent and industry, the genius was lacking. However this may be, the world has had reason to admire the splendid results of the patient labor which this composer bestowed on his operas.

Among the French composers Halevy holds an honorable place. His opera La June, produced 40 years ago, has maintained its place with undiminished effect, though in his later compositions he was less successful. The most popular of recent French composers are Gounod and Ambroise Thomas. The Faust of the former and Mignon of the latter are performed wherever French or Italian opera has a foothold. In Germany the modern composers wielding the greatest influence have been Von Weber, Mendelssohn, Schumann, and Wagner. Von Weber, grasping all the extensions and improvements in orchestration, wrote overtures of a larger texture and clearer dramatic form than any predecessor, and infused into his operas qualities which placed him at the head of the new school, the romantic. His vocal writing often wants fluency, though this is less apparent in Der FreischŘtz than in Euryanthe; had his metres been better, his music would not have been amenable to this charge. But the transcendentalism of his music was the most daring ever attempted.

In a certain class of passionate expression he was without a rival; certainly no such intense portraiture of womanly love was drawn in music before his Agatha. The influence of Mendelssohn was exercised partly through his orchestral works, but mainly through his two great oratorios "St. Paul" and "Elijah." Schumann manifested his strength in the vigor and novel form of his pianoforte works, and in the intensely poetic feeling, the dramatic fervor, and the variety of color of his compositions for orchestra; while Wagner has made his power felt through the earnestness with which he has put forth his ideas in his critical writings and through his great works based upon those ideas. The opposition and discussion that have been aroused by the theories broached by him are far greater even than those that were excited when Gluck propounded somewhat similar ones a century ago. But Wagner has gone much further than Gluck dared in carrying out his ideas. As briefly stated by himself, his objection to previous methods upon which operatic composition has proceeded is this: "The error of opera as a form of art has consisted in the fact that music, which is only a means of expression, has been made the end, while the drama, which is the true end of expression, has been made the means; and thus the actual lyric drama has been made to rest upon the basis of absolute music." If this theory is accepted and acted upon by future composers in the same spirit in which it is carried out by its promulgator, it will revolutionize the art of operatic composition.

Among its immediate consequences is the subordination of the composer to the poet. The drama is the thing first to be considered, the music being only a means through which the emotion excited by the dramatic situation is deepened and intensified. In the opera the aria has always been one of the principal means, through which the music found expression; but the aria being a formal thing, constructed according to certain fixed rules and centring attention on itself and its own melodic beauty, this retarded the action and distracted the auditor from the thing sung about, to the thing sung. Accordingly, this could find no place under the new theory, and Wagner cast it aside, putting in its place the melos or " endless melody," a kind of musical declamation springing naturally out of the sentiment of the words that are being sung. The orchestra also ceases to be a mere instrument of accompaniment, and is made by Wagner to enter into the dramatic situation and express it with every variety of tone and harmonic combination. The operas, or rather musical dramas as Wagner prefers to call them, written upon these theories, he avers should have a poetical basis; and he finds the proper subjects in the myths of his own country, making the Nibeluvgenlied the text of his later works.

He has deemed it essential for the true exposition of his ideas that his latest operas should not be brought out in any of the German opera houses, but should have a building constructed expressly with a view to their fit and complete presentation, Such a building is now in course of erection at Baireuth, Bavaria, and there in the spring of 1876 Wagner proposes to put his theories to the final test. The four dramas composing the tetralogy, Der Ring der Nibe-lungen, will there be produced, each on a separate day. They consist of Das Rheingold, Die Wal1clire, Siegfried, and G÷tterd÷mmerung. Upon the success or failure of the magnificent and costly experiment there to be made, the future of the opera will in a measure depend. - A very decided influence has been exercised upon the musical art of our own day by the composers for the pianoforte. The extensions and improvements of that instrument, now carried so far as to make it the epitome of the orchestra, have been of great use to composers of every class. Through the grand piano and the organ the intricacies of the science of harmony have been explored, chords analyzed, the relations of keys made clear, and melody developed.

About 1840 Thalberg began to write dramatic music for the piano, in which he gave the precise vocal pitch of the airs, and at the same time surrounded and embellished them with an arabesque of brilliant execution. Then came Liszt, remarkable as a conductor and composer, but chiefly as a pianist, he carried the difficulties of pianoforte playing to their utmost limit, and placed himself by his astonishing powers at the head of modern pianists.

Chopin was a composer of the greatest sensibility.' Using the rhythms and characteristic traits of the music of his native country, he treated his themes with a passionate and dramatic fervor and grace that have made him the poet of the instrument, Rubinstein, Clara Schumann, and Von Bulow are also to ho ranked as virtuosos of the first order. The pianists whom wo have named have seemingly thoroughly explored the capacities of the pianoforte as it at present exists, both as an instrument of expression and of execution. Every technical difficulty has been presented and every form of sentiment expressed, and in this department of the art at least there would seem to be but slight room for further progress. - See Hawkins, " A General History of the Science and Practice of Music" (5 vols. 4to, London, 177G; new ed., 2 vols. 4to, 1853); Burney's "General History of Music from the Earliest Ages to the present Period " (4 vols. 4to, London, 1776-'89); Forkel, Allgemeine OescJiichte der Musih (2 vols., Leipsic, 1788); Ilullah, "History of Modern Music" (London, 18G2); Fetis, Histoire generate de la musique depute les temps Us plus anciens jusqiu'a nos jours (4 vols., Paris, unfinished); Bitter, " History of Music, in the Form of Lectures " (2 vols., Boston, 1871-'4); and Chappell, "The History of Music " (4 vols., London, 1874 et seq.).