in autumn) in pastures, orchards, vineyards, etc. Its pileus is regularly convex, becom ing almost flat when old; fleshy, dry, white with a tinge of yellow or brown; of a silky smoothness on the upper surface, or somewhat scaly, but never warty; thickly set on the under side with very unequal gills, which in a young state are pink, and afterwards become dark brown. The pileus is attached by its center to the top of the stem. The stem is of a firm fleshy texture, and towards the top is surrounded by a more or less distinct white membranous ring, the remains of the curtain or vail (indusium), which in a young state extends to the pileus, and covers the gills. This mushroom is gathered for the table when young, being preferred when the vail is still unbroken, and the unexpanded pileus has the form of a ball or button; but both in this state, and afterwards, whilst it shows no symptoms of decay, it is used for making ketchup (q.v.). It has a very pleasant smell and taste, and the flesh, when bruised, assumes a reddishbrown color.-Very similar to it, and often sold instead of it in London and elsewhere, but rejected by all skillful houskeepers as unfit even for making ketchup, is the ST. GEORGE'S AGARIC (A. Georgi), sometimes called whitecaps, frequent in moist pastures and near buildings in all parts of Britain. This species is easily distinguished by its larger size the pileus being sometimes 18 in. broad-its coarser appearance, its rather disagreeable smell, the yellow color which its flesh assumes when bruised, and the lighter color of its gills.-Care must be taken not to confound the common mushroom with the white variety of agaricus phalloides, a species not uncommon in Britain, chiefly in woods and on the borders of woods, which is very poisonous. Perhaps it is the possibility of this mistake which has led to the prohibition of the common mushroom in Rome, where many kinds of esculent fungi are brought in great abundance to the market, and where a special officer superintends the sale of them. A. phalloides is, however, easily distinguished by the ring at the bottom of the stem, the white color of the gills, the warts on the upper surface of the pileus, and the powerful smell, which becomes extremely disagreeable as the mushroom grows old.-Another species of mushroom much in use for the table is the FAIRY-RING MUSHROOM (A. oreades), sometimes called Scotch bonnets-the Champignon of the French. It is common in pastures in the U. S., Britain and most parts of Europe, often forming fairy rings (q.v.). It is much smaller than the common mushroom, the pileus being seldom more than an inch broad, the stem taller in proportion. The stem is solid, fibrous, and tough, with no ring; the pileus smooth, fleshy, tough, convex, with a more or less distinct boss (umbo) in the center, of a watery brown color; the flesh white. The odor is strong, but agreeable. This mushroom is used for ketchup, and is also dried and powdered for use at table as a savory addition to sauces and stews. It is constantly brought to market in England. It is liable, however, to be confounded with several poisonous species; but only one of them, A. dealbatus, forms fairy rings, and this may be readily distinguished by its disagreeable odor, by its becoming grayishbrown in zones when soaked in water, by the margin of the pileus being at first rolled inwards, and by its very fine dingy whitish gills.-The other edible species of mushroom or agaric are numerous, but they are chiefly used on the continent of Europe, and scarcely at all in Britain, although some of them are common British plants.-The ORANGE-MILKED AGARIC (A. deliciosus), which grows chiefly in fir-woods and among junipers, has a viscid pileus, 4 in. or more broad, at first orange, afterwards pale, the gills and juice orange, the gills running down the stem, the smell and taste agreeable.— The MOUSSERON (A. prunulus) is common in woods and pastures, particularly on sandy soils. It has a pileus about 2 to 4 in. broad, convex, yellowish-white when young, the gills at first white, and afterwards flesh-colored. The odor is agreeable. It is much esteemed on the continent as an article of food.-The PARASOL AGARIC (A. procerus) is found in pastures, especially under trees. It loves sandy soils. It is remarkable for its long stem, 8 to 12 in. high, with a thick spongy ring. The pileus is 3 to 7 in. broad, at first obtusely conic, then bell-shaped, covered with brown scales. The taste and smell are pleasant.The WHITE FIELD AGARIC (A. virgineus) is one of the most common of British species, growing in pastures, with viscid or satiny white or whitish convex pileus, fully an inch broad, stem nearly 2 in. long, and light chocolate-colored distant gills, which run down the stem. It grows either singly or in groups.-The ANISE MUSHROOM, or SWEETSCENTED AGARIC (A. odorus), grows in shady woods and dells among moss and decaying leaves. It has a slightly convex pileus, about 3 in. broad, with pale gills. The odor is like that of anise.-The IVORY MUSHROOM (A. eburneus) is found in woods, with pileus 2 to 3 in. broad, of a grayish-yellow color, broad gills, and a rather long and somewhat scaly stem. The SMOKY MUSHROOM (A. fumosus), with pileus smoke gray above, the gills and stalk yellowish, is common in fir-woods: -All these are edible, and more or less pleasant and nutritious. Finer than most of them is the IMPERIAL MUSHROOM (4. cæsarius), the Kaiserling of the Germans, a species found in loamy soils in some parts of Europe, with orange pileus and lighter yellow stem and gills; but, unhappily, it is apt to be confounded with the very poisonous amanita (q.v.) muscaria.

The common mushroom is frequently cultivated both in the open garden and in houses or sheds. To grow it in the open garden, beds are prepared, generally of earth mixed with horse-dung, partly fresh and partly from old hotbeds, and are raised into ridges almost as high as broad. To grow it in houses, boxes are filled with alternate layers of half-rotten horse-dung and of straw, with a surface layer of fine mold. But of each of these methods there are many different modifications, none of which can here

be detailed. In both, the production of mushrooms is sometimes left to the chanceoften almost a certainty-of spawn (mycelium) or spores existing in the dung or earth; sometimes, to increase the probability of a speedy and abundant crop, earth is introduced into the bed or box from a pasture known to be rich in mushrooms, and mushroom spawn is also frequently planted, which is either collected where mushrooms grow, or produced by artificial means, often appearing and being propagated extensively without the development of the mushroom itself. The almost certain production of mushroom spawn in heaps of slightly fermenting horse-dung, straw, and earth, has been often urged as an argument in favor of the equivocal generation of fungi, but the minutenes☛ and multitude of the spores may more reasonably be urged. See illus., MOSSES, ETC.

MUSIC (Gr, mousike, from mousa, muse: Lat. musica), a combination or succession of sounds having the property of pitch, so arranged as to please the ear. The pleasure derived from music arises from its exciting agreeable sensations, and raising pleasing mental images and emotions. Apart from words, it expresses passion and sentiment, and linked to words, it loses its vagueness, and becomes a beautiful illustration of language.

The doctrine of musical sounds is based on the principles of acoustics (q.v.). Sound is conveyed through elastic media by waves, not of alternate elevation and depression, but of alternate condensation and rarefaction; in which it is the form, the condition of the groups of particles that progresses, not each individual particle. When a series of vibrations recur on the ear at precisely equal intervals of time, following each other so closely that each cannot be separately distinguished, the result is a musical sound or note. The sound ceases to have a musical character when each pulsation is individually audible, as is the case when there are fewer than about sixteen beats in a second. The gravity or sharpness of the sound is called its pitch, and depends on the number of vibrations in a given time. A succession or progression of musical sounds following each other constitutes melody; the difference in pitch between any two of them is called an interval. Where two or more musical sounds, whose relative pitch is properly proportioned, are heard simultaneously, the result is a chord, and a succession of chords constitutes harmony.

When a vibration is communicated to a string stretched between two points, the result is a musical note, whose pitch is dependent on the length of the string and the degree of tension applied to it: the shorter the string, and the greater the tension, the higher is the pitch. If the string be divided in the middle, the tension remaining the same, the note produced is twice as high in pitch, and is called the octave to the note produced by the whole string. Every vibration of the one corresponds to two of the other, and there is between a note and its octave a far closer relation than between any two other notes; they go together almost as one sound, and are considered to a great extent as one musical sound. In the diatonic scale, familiar to every correct ear, there are six notes, bearing certain harmonic relations to the fundamental note, interposed between it and its octave; and as we ascend, the notes arrange themselves in similar successions of sevens, each set an octave higher, or double the pitch of that which preceded it. The seven notes are designated by the names of the first seven letters of the alaphabet, the same letter being used for any note and its octave. For another notation also in use, see SOLFEGGIO. Taking C for the fundamental note, we have for our scale

CDEFGABCDEFGAB Ċ, etc.

The scale may be extended up or down indefinitely, so long as the sounds obtained continue to be musical. The satisfaction and sense of completeness which the diatonic scale gives the ear, arise from its being founded on correct harmonic principles. The quality called harmony is produced by a coincidence of vibrations; notes are more harmonious the oftener their waves coincide. Besides the octave, two of whose waves coincide with one of the fundamental, there are other intervals harmonious, though in a less degree. Dividing our string into three parts instead of two, we have a note higher than the octave, which may be lowered by an octave by making the string two thirds of the original length, and produces a wave of which three coincide with two of the fundamental. Next to the octave, this note stands in the most intimate relation to the fundamental; it is called the dominant. Dividing the string by five, and lowering the note two octaves, another harmonic is got, called the mediant. In contradistinction from both these, the fundamental note (or any of its octaves) is called the tonic or key-note. Cbeing taken as the key-note, E is the mediant, and G the dominant. These three notes, when struck simultaneously, form the harmonic triad, and stand to each other in the relation of 1, 4, (numbers indicating the number of vibrations, which are inversely as the length of the string), or, reducing fractions to integers, in the relation of 4, 5, 6. When a musical string is vibrating, these sounds are heard on close observation more or less distinctly vibrating along with it, the cause being a spontaneous division of the string into aliquot parts, producing subordinate vibrations simultaneously with the principal vibrations. But the dominant may in its turn be the tonic from which another triad of tonic, mediant, and dominant is taken, forming a scale of triads extending indefinitely up and down, and it is from three such adjacent triads that the diatonic scale originates. Its elements

are the triad of the tonic united with the triads which stand in the most intimate relation to it-viz., those immediately above and below it

FAC, CEG, GBD.

F is the note whose dominant is C (the tonic), and therefore, in respect of C, it is called the subdominant. A is the mediant of the subdominant F, and therefore called the submediant. D is the dominant of the dominant, and is called the super-tonic. B, the mediant of the dominant, is called the leading note. We have seen that the notes of each triad stand to each other in the relation of 4, 5, 6. Preserving this proportion, and multiplying to avoid fractions, we have

FACE GB D

as 16, 20, 24, 30, 36, 45, 54

We must multiply F and A by 2, and divide D by 2, to bring them within the compass of an octave, and then we have

CDEFGAB C

as 24, 27, 30, 32, 36, 40, 45, 48

These are the degrees of the diatonic scale, which are indicated by the white keys of the pianoforte, as in the figure represented below.

The interval CD is commonly called a second; CE, a third; CF, a fourth; CG, a fifth: CA, a sixth; and CB, a seventh; CC being, as already seen, an eighth or octave-names corresponding to the position of the notes on the key-board or in the diatonic scale, but having no relation to the proper proportional numbers already given. The intervals of the third, fifth, and sixth (counting from the key-note), owing to the more intimate harmonic relation of the notes between which they lie, afford more satisfaction to the ear than the others, or are, as it is called, the most perfectly consonant intervals. Intervals may be counted from any note as well as the tonic. DF is called a third as well as CE, although these intervals are unequal. We may have intervals beyond the octave; they are, however, substantially but repetitions of those below, CD, a ninth, being also a second, and so on.

It is often desirable in the course of a musical composition to change the key-note, which involves the formation of a diatonic scale on some other note than C, in which case we are said to modulate from one key into another. As the intervals CD, DE, EF, etc., are by no means all equal, the notes which we have already got will not do for a scale founded on any other tonic than C. The ratios of the intervals in the diatonic scale, expressed in numbers by logarithms, are:

C D E F G A B с

51 46 28 51 46 51 28

At first sight it would appear that in keyed instruments there must be a separate row of keys for each tonic, but practically this is found not to be necessary. If D instead of C be taken as key-note, E, G, and A are some approach to the correct second, fourth, and fifth, but F and C are greatly too low in pitch for a proper third and seventh. With some notes taken as key-note, the correspondence is greater, with others it is less. The difficulty is overcome by a system of compromises called temperament (q.v.). Roughly speaking, we have in the diatonic scale an alternation of two long intervals, a short

interval, three long intervals, and a short interval. The long intervals 51 and 46 are styled tones, and the short interval 28 a semitone. Were the tones all equal, and the semitone exactly half a tone, a note interposed in the middle of each tone, dividing the seven intervals into twelve, would make it immaterial where the scale began. A system founded on this supposition is the remedy actually adopted in most keyed instruments, and the inaccuracy produced by this compromise is not sufficiently great to offend the ear. The interposed notes, indicated by the black keys of the pianoforte (see fig.), complete what is called the chromatic scale, consisting of twelve intervals approximately equal.

The notes of music are represented in ordinary notation on a series of five parallel lines, called the staff. On these lines, and in the four spaces between them, marks are placed indicating the notes, which are counted upwards, beginning with the lowest line. Every line or space is called a degree, the staff consisting of nine degrees.

When more than nine notes are required, the spaces below and above the staff are used, and the scale is extended by means of short added lines, called leger lines. The pitch of the notes on the scale is determined by a figure called a clef (clavis, a key),

placed at the beginning of the staff on a particular note, from which all the others are counted. The clefs most in use are the bass, tenor, and treble clefs, represented on the notes F, C, and G respectively (see CLEF). The treble and bass clefs only are used in music for keyed instruments, and when a staff is required for each hand they are joined together by a brace, the upper staff for the right hand, the lower for the left. The ascending scale in these clefs is as follows:

Treble.

CDEFGABCDEFG A B C

Base.

CDEFGA BCDEFG ABC

These notes correspond with the white keys of the pianoforte or the diatonic scale when C is key-note, no allowance being made for the black keys, which, as we have seen, divide the tones into semitones. Those semitones which do not occur with C as key-note are represented by the signs # (sharp) and (flat). The sign, prefixed to a note, elevates it a semitone in the scale, raising, for example, F to F sharp. b lowers the note by a semitone, depressing B to B flat. When a note which has been elevated by a sharp, or depressed by a flat, is to be restored to its original place, the character ↳ (natural) is prefixed to it.

The names of the intervals correspond to the degrees of the staff, but it has been seen that intervals of the same name are not necessarily equal. If the sign of a flat or a sharp be prefixed to either note of an interval, it still preserves its name of a third, a fifth, etc.; but to distinguish intervals of the same degree, the qualifying epithets of major and minor, augmented and diminished, are used.

The different keys in music are best understood by reverting to the scale of triads, on which the diatonic scale is founded. Taking a series of triads, of which the dominant of each is the key-note of the next, we obtain the following scale, extended both upwards and downwards from C:

ĊI

O E G B D F A C EG BDFACE G B D F A C E G B DI FI AI CI EI ĢI

Each triad is composed of the key-note, its mediant, and dominant, and the scale of each key is composed of the triad of the key-note, with the triad immediately preceding and that immediately following it. Each key is succeeded by the key of its dominant, and if we begin with the key of C (in the middle of the scale), each key acquires an additional sharp until we reach the key of F with six sharps. These are the sharp keys. If, beginning again with the key of C, we go back instead of forwards in the scale of triads, we obtain the flat keys; each key has an additional flat to that above it, till we come down to the key of Go with six flats. This key in instruments with temperament is exactly the same with that of F, and on this account it is not generally found convenient to extend the keys beyond six, or at most seven, sharps or flats. G with seven sharps is the same as Do with five flats, and Co with seven flats is the same as B with five sharps. In music written in these keys, double sharps and double flats occur, which are indicated by the characters X and respectively. In writing music in any key with sharps or flats, it is usual, instead of prefixing the sharp or flat to each note when required, to place the sharps and flats belonging to the key together after the clef, on the degree to which they belong, and such collections of sharps or flats are called the signa

nature.

A sharp or flat introduced in a composition which does not appear in the signature, is prefixed to the note, and called an accidental.

The diatonic scale and keys above described belong to what is called the major mode there is also another mode in use called the minor mode. In the minor, as in the major mode, the diatonic scale and the keys are based on the scale of triads. Each of the triads already considered consists of two unequal intervals, called a major third and minor third. Supposing we begin with the minor instead of the major third, we have a succession of chords taking their minor third from one triad and their major third from another. These compound chords are called minor triads. Their proportion is as 10, 12, 15, and out of three such consecutive minor triads the scale of the minor mode is constructed.

D F Å C EG B

80, 96, 120, 144, 180, 216, 270

Multiplying D and F by 2, and dividing B by 2, to bring the whole within the compass of an octave, we have:

A B C Ꭰ E F G A

120, 135, 144, 160, 180, 192, 216, 240.

The scale here represented is what is known as the descending scale of the minor mode. When the seventh of the scale ascends to the eighth, it becomes sharp, as the proper leading note or sharp seventh to the tonic. This sharp is, however, always omitted from the signature, and placed accidentally before the seventh which it is to elevate. In order to avoid the harsh interval of the augmented second (from F to G), it is usual in the ascending scale to make the sixth sharp also, in order to accommodate the seventh; thus the ascending or accidental scale of the minor mode has two notes altered from the signature. 1 DESCENDING SCALE.

ASCENDING SCALE.

Each minor scale is called the relative minor to the major scale on its right hand in the scale of triads, with which it has the same signature: thus the relative minor scale to C major is that of A minor.

Each minor scale is also called the tonic minor to the major scale on the same key-note, from which it differs in flattening the third of its tonic, and in the descending scale also the third of its subdominant and dominant. The tonic minor scale to C major is C minor.

As the descending scale regulates the signature, each tonic minor has three flats more or three sharps less in its signature than its tonic major.