274 introduce a new note, which we shall call NE, a tonule below LAH. This note bears the same relation to LAH which TE bears to Doн. Musicians also think it necessary sometimes to introduce another new note, which they then use instead of FAH. It is a tone below NE, or a chromatic part-tone above FAH. We call it BAH. It bears the same relation to NE which LAY KEY G. LA MODE. bears to TE. BAH, NE, LAH, heard in succession, resemble, in mental effect, LAH, TE, DOH. The learner may sr metimes strike BAH more easily by thinking of it as TU. The note NE is in frequent use, but BAH is very seldom used in erdinary music. Tr the following Scottish tune :- c. Tunes of this kind are commonly called minor tunes, from their having the interval called a minor (smaller) third immediately above their predominating note LAH-(LAH, DOH), and in distinction from other tunes which have a major (larger) third above their predominating note DоH. They may be said to be in the LAK mode. It is advisable to take their pitch by means of DOH, is in other tunes. The signature may be written in this form, "LAH MODE, KEY A." Those who studied with us the modifications in the mental effect of the note LAH, will be quite prepared to understand how this kind of tune may be used in the serio-comic style, and how by quickening the speed they may even express a KEY D. LA MODE. lively careless abandonment. Of this we have several examples in the old English music. It will be a good vocal exercise for our pupils to learn to solfa them. What a pity that such fine music should have been set to the words of a foolish sentiment or a savage drinking-song! For the first, better words are given in Chappell's collection of "National English Airs." It To such words the tune must is entitled the Widow's Song. be sung more slowly. There is nothing comic in this sad wail. To the second we have adapted words from a poem of tragic truth, by James Russell Lowell. The third we have left as it is. : d'.,t Oh! 1.8 m.dr: m 1-1,t d' d'.,d't.r': d'.t 1:--:1.t d' d'.,d' t. r': d.t leave me to dream and weep, Or lift ye the church-yard stone, And send me my dead thro' the 1-1, ne, : bah, :m, care for no - bo d-til 1:-:ne, d: -: dit:- :r no, not 1 1 no · bo dy, The musical facts which are here ascribed simply to the common scale used in a peculiar manner, and admitting occasional variations are usually supposed to be founded on an entirely new scale, and that of a very remarkable structure. This new scale is described as having its "semitones" between its second and third, and fifth and sixth notes. (If you reckon from LAH, to LAH, in the common mode, you will find the tonules thus placed.) But the scale, it is said, only retains this form in descending, for in ascending the sixth and seventh are sharpened (making our occasional BAH and NE) so as to place the "semitones" between the second and third, and seventh and eighth. This is, in fact, two scales; and some teachers of the pianoforte have gone so far, Dr. Mainzer tells us, with this "illogical system," as to make their pupils play with the right hand ascending the scale-BAH and NE, at the same time that the left hand descending produced the sounds FAH and sоH! He justly remarks that "the simultaneous unison of notes so opposite, producing an effect so discordant, is more calculated to destroy than awaken the musical sentiments of the pupil." Let us examine facts and authorities on this subject. First, then, it appears that the common scale, even without any new note (NE or BAH), but simply allowing LAH to predominate and to be heard at the opening and at the close of a tune, is quite sufficient to produce a true "minor" tune- and that many fine melodies, manifestly minor, are formed on this model, using the ordinary notes of the common scale (from LAH to LAH) both ascending and descending, and not requiring the aid of any accidental note. No one can doubt that the first, second, third, fourth, and sixth of the examples given above are minor tunes, nor hesitate to allow that they are formed on the common scale, and are simply dis inguished by their making LAH, the proper mournful note, predominate. Accordingly we find Dr. Crotch describing his "ancient diatonic minor key (which corresponds with our common scale when you reckon from LAH to LAH1) as "the scale of the ancient Greek music, and found in the oldest national tunes, in psalms and cathedral music,”—Dr. Bryce speaking of this as the "proper" formula of minor tunes, in which are written "multitudes of exquisite melodies, especially among the ancient national music of different countries,"--and Dr. Mainzer maintaining that this is the only true and the only agreeable arrangement of notes for such tunes. By fact, then, and by competent authority, the comMON SCALE with LAH predominating is declared sufficient to produce a true minor tune. But still, it may be argued, are not BAH and NE the "sharp sixth and seventh" (reckoning from LAH, as though it were the key-note) always used in tunes of this kind (instead of FAH and soн) when the music ascends? Are they not, therefore, essential at least to every minor passage in which the music ascends from its sixth or seventh note? Must we not necessarily suppose a distinct scale in which these essential notes may find a place? We deny the proposition, and the conclusion falls, for Secondly, it appears that the now notes BAH and NE ("the sharp sixth and seventh ") are not essential even in ascending dy cares for me. passages, and that the use of them is entirely arbitrary. Nothing can prove this more clearly than the great discrepancy and disagreement among the best authorities on this subject. If there had been any fixed usage, long established by the requirement of good ears and the example of the best composers, such opposite statements of fact could not have existed. In reference to BAH (the "sharp sixth ") we find Dr. Callcott describing this note as "accidental," but rendered necessary for the sake of avoiding what he calls "the harsh chromatic interval," PAH NE, "from F natural to a sharp"-while M. Galin and M. Jeu de Berneval refer to this very interval as "a constitutive interval of the minor mode," full of "melancholy," "replete with anguish and tears," and speak indignantly of those who would "cancel" the very interval which is most "characteristic" of the "minor mode." Is it not evident from this, that the use of BAH is arbitrary-by some approved, by others disapproved? In reference to NE, Dr. Callcott declares that it is an "essential" part of the "minor scale" in ascending, but not to be used in descending. M. Galin and M. Jeu speak of NE as "invariable" and essential both in ascending and in descending, and M. Jeu gives examples of its use in descending. Schneider, in his "Elements of Harmony," maintains the same opinion. Marpurg, "one of the most influential theorists, who flourished during the latter half of the last century" (Mainzer, 77), declares that this custom (of using BAH and NE) by no means changes the essential nature of the tonality (key or mode reckoning from LAH to LAH1), and the two sharps which are prefixed to the sixth and seventh degree are purely accidental." Dr. Crotch says distinctly of both BAH and NE, these alterations are only occasional." Dr. Goss says, "The sixth and seventh (FAH and soн) are generally made accidentally major in ascending." Dr. Bryce ascribes the introduction of these notes to modern musicians, who prefer harmony to melody. Dr. Mainzer says that there are a very large number of compositions "in which the leading note (NE) does not appear at all in the minor keys, and this is the case with many composers of the fifteenth, sixteenth, and seventeenth centuries.' He then adduces examples from Gabrielis, from Palestrina, and from Morale, and also shows how, in the eighteenth century, along with professedly improved harmonies, NE was introduced as an occasional note, but not essential-Marcello, for example, introducing the following passage immediately after one in which NE had occurred. : S d1 f t m 1 ne S d d f ti m I 81 Sometimes in the course of a tune tor at the side will illustrate these ti-tu $1 d f1 Another "transition" into what is called the "minor of the same tonic" (DOH becoming LAH), is more proper to "tempered" musical instruments than to music itself or the unaided voice. You may treat it as transition into the key of ME flat, or, retaining the syllables of the original key, the new notes may be treated as chromatic. Thus you will have the oddlysounding notes Mow, Low, and Tow, as any one may perceive by drawing the two keys side by side, and bearing in mind the difference between the tonule and the chromatic part-tone. Our pupils will now be able to ransack the stores of classical music, and to take their "part" in fireside glees, at their pleasure. They will be very largely, and, we hope, very long, rewarded for all the patience and painstaking which we have demanded of them. ON PHYSICS OR NATURAL PHILOSOPHY. (Continued from page 261.) taste, and none the less so because he laboured generously to make music the property of the people, thus concludes:"Let any one sing the above scales one after the other (four varieties of the so-called "minor scale"), and assuredly he will not be long in discovering which of the four is the most agreeable and natural, and most in the character of the minor tonality (key). It is evident that the scales with leading notes (NE), instead of being pleasing, are disagreeable to the ear, and impracticable to the voice. The absence of the leading note (NE) on the contrary often gives to the melody something majestic and solemn. The Gregorian chant, so remarkable for melodious beauties, affords many proofs of this, and also the popular melodies of different countries, especially those of Ireland and Scotland, so much admired by the greatest musicians." Surely here is example and testimony enough to prove these noteswhether good or bad-at least non-essential and arbitrary. One question yet remains. Should not the scale on which minor tunes are framed be still treated as a distinct one, and something more than the common scale used in a peculiar manner? To which we answer-Yes, if it is distinct; but, if otherwise, why multiply difficulties and conceal the truth? But it clearly is not, in any particular, distinct. First, in reference to the "character" or musical effect of the notes-the most important particular of all-the notes of the so-called minor scale correspond precisely with those of the common one (reckoning from LAH to LAH) Not a single note of the common scale changes its character when used in a minor tune. LAH is still the sorrowful, TE the piercing, FAH the awe-inspiring note, &c., as before. Next, in reference to the exact intervals between the notes-they are precisely the same as those of the common scale (from LAH to LAH') with only this peculiarity, that the graver (flatter) position of the "variable note" RAY is ordinarily used in tunes of this character, whereas it is only occasionally used in other tunes. Premising that from DOH to DOH' is commonly called by musicians a major key (beginning with a major, or greater, third, DOH ME), and that a minor key beginning on a note in the position of our LAH would be called THE ELASTIC FORCE OF GASES. its relative minor, let us quote the following testimonies to the last point. Colonel Thompson says "The change to the rela-air increases in proportion to its density, was first proved by Experiments of Boyle.-The principle that the elastic force of tive (or, as it would more properly be called, the synonymous) minor reduces itself to avoiding the acute second of the old key (r) and using only the grave (r)." (See "Westminster Review," April, 1832). Dr. Crotch says "Some authors make it" (the first note of the principal minor key)" the same as the note LAH of the relative major key, viz., a in the key of c, a minor tone" (smaller tone-of eight degrees) "above G SOH). In that case all the natural notes excepting D (RAY) correspond with those of the major key of c." (See Crotch's "Elements"-Tuning, &c.) Turning to his illustrative plates, we find the scale of minor tunes requiring the smaller tone (eight degrees) between DOH RAY, and the larger tone (nine degrees) Letween RAY ME, while other tunes usually require a larger tone between DOH RAY and a smaller one between RAY ME. In fact the variable note assumes its grave position. But it sometimes does the same in the common scale. Is this, then, a peculiarity sufficient to establish a new scale? More over, is it not natural to suppose that the common scale, which is found to be essentially the musical scale of all nations, must hold a peculiar accordance with the ear and the sympathies of the human race? and is it not proper, therefore, to consider this as the one scale, and everything else that cannot establish a distinct and independent character as but a modification or a peculiar use of it? It is certain that great detriment must be done to the mind of our pupils, and great hindrance given to their progress, if we first cause them to study and practise our theory, of a new and self-contradictory minor scale, and then leave them to discover that, in music itself, instead of the artificial difficulties they have so laboriously mastered, there is only to be found the common scale, so used as to produce a peculiar effect and the merely occasional, non-essential, introduction of a new note! [We were present, in October last, at several choral performances of pupils who were taught to sing on the method developed in these lessons, some of which were attended by more than 3,000 people. We saw a choir of children who sang music at first sight, a thing quite new to us. The "Tonic Solfa Association" numbered 2,000 pupils in London alone last year, and the meetings referred to were the means of originating at once three new classes of about 200 pupils each. We may claim, for the POPULAR EDUCATOR, the credit of giving a cosmopolitan influence to these valuable efforts -ED. A Boyle in 1660, in the following manner :-He took a uniform These proportions clearly show that the pressures, and consequently the densities, are inversely as the spaces occupied by the same quantity of air; whence it follows that the elastic force of air is proportional to its density. Mariotte's Law. -Mariotte, a French philosopher, was the next experimenter who established the same principle in 1668, by the announcement of the following law, which has ever since borne his name, viz. :-"That the volume of any quantity of gas, at a given temperature, will diminish in the inverse ratio of the pressure to which it is subjected." This law is verified in the case of air by means of the following apparatus:-On a wooden board placed vertically, is fixed a glass tube bent Fig. 80. ever the level in both branches is not the same. Mercury is again poured into the larger branch until the pressure which arises from it reduces the air contained in the smaller branch to one-half its volume; that is, this volume, which was at first measured by 10 on the scale, is now reduced to 5, as shown in fig. 80. Now, measuring the difference of level ca between the mercury in the two branches, we find that it is exactly equal to the height of the barometer at the moment when the experiment is made. The pressure of the column c A is therefore equivalent to that of one atmosphere; by adding to it the atmospheric pressure which acts at c, at the top of the column, we see plainly that at the instant when the volume of air is reduced to one-half, the pressure is double of that which it was at first; which proves the truth of the law in this case. If the greater branch of the tube were long enough to admit of mercury being poured in till the volume of air in the smaller branch was reduced to a third of what it was at first, we should find that the difference of level in the two branches is equal to twice the height of the barometer; that is, it is equivalent to the pressure of two atmospheres, to which adding that which acts directly on the surface of the mercury in the greater branch, gives a pressure of three atmospheres. It is therefore under a triple pressure that the volume of air is reduced to one-third of its volume. The law of Mariotte has been experimentally verified in the case of air by MM. Dulong and Arago, as far as 27 atmospheres, by means of an apparatus similar to that now described. In order to demonstrate the truth of the law for any gas, the apparatus must be modified to admit of the introduction of the particular gas in question. The law of Mariotte has been verified also in the case of pressures less than that of the atmosphere. Thus, a barometric tube being filled only to about two-thirds of its length, the other third containing air, it is inverted and immersed in a deep jar or vessel full of mercury, fig. 81; the tube is then sunk in the vessel until the level of the mercury be the same within and without the tube; the volume of the air contained in the tube is determined by a scale fixed to the vessel, this air being now under a pressure exactly the same as that of the Fig. 81. upwards in the form of an inverted siphon; that is, having two unequal branches, see fig. 80. Alongside of the shorter branch, which is closed at the top, there is placed a scale indicating equal capacities or volumes in the parts of the tube corresponding to the parts of the scale; and alongside of the longer branch there is also placed a scale indicating equal altitudes in centimetres. The zeros. of the two scales are on the same horizontal line. In order to make the experiment, mercury is poured into the tube at the top of the longer branch, so that the level of this liquid may correspond to the zero of the scales of the two branches, a result which may be obtained by several trials. The air contained in the shorter branch is then subjected to the atmospheric pressure, which acts in the greater branch, when to the weight of the raised column, balances the pressure of the Till recently, it has been considered that the law of Mariotte was true for all gases and under all pressures. M. Despretz was the first who showed that this law ceases to be strictly true when the gases are subjected to a pressure nearly equal to that which produces their liquefaction. Lastly, M. Regnault has proved that this law does not apply equally to all gases. Thus, air and nitrogen are compressed a little more, and hydrogen a little less, than that which it indicates. In the case of carbonic acid, it does not even furnish an approximation to the truth when the pressure is considerable. Applications of Mariotte's Law.-The following examples of the application of this law may be useful to students of Chemistry and Physics. 1. A vessel in which air can be compressed contains 4:3 gallons of air, the pressure measure by the barometer being 29.6 inches; what will be the volume of air at the pressure of 30-4 inches? If denote the volume required, we have, 4.3 29.6: 30.4; whence, 29.6 X 4.3 x= 30.4 4.1865 gallons. 2. Having 20 gallons of gas under the pressure of one atmosphere; to what pressure must it be subjected, in order to reduce it to 8 gallons? If p denote the pressure required, we have, p: 1:20:8; whence, P= 20 X 1 The Manometer. The name manometer (from the Greek, raritymeasure) is generally applied to instruments employed in measuring the tension of gases or vapours when it is greater than the prossure of the atmosphere. There are various kinds, as the freeair manometer, the compressed-air manometer, and the metallic manometer. In these different kinds, the unit of measure which is employed is the atmospheric pressure, when the barometer stands at 30 inches. Now, we have seen that this pressure on a square inch is 14 lbs.; consequently, if we say that a gas has a tension of two or three atmospheres, we mean, that it acts on the sides of the vessel which contains it with a pressure of twice or thrice the weight of 143 lbs. per square inch. Free-air Manometer. This manometer is composed of a strong glass tube BD, fig. 82, about 5 yards long, and a cistern D, made of iron, containing the mercury in which the tube is immersed. This tube is cemented to the cistern and fixed on a board, along side of which is placed another tube A C, made of iron, and about 5 yards long; by means of this tube the pressure of the gas or of the vapour is transmitted to the mercury in the cistern. As manometers of this kind are most frequently used in cases where vapour of high temperature, or steam, would soften the cement which is employed to fix the glass tube to the cistern, the tube A c is filled with water; and it is by this means that the pressure of the vapour is transmitted to the mercury. In order to graduate the manometer, the orifice A is allowed to communicate with the atmosphere, and at the level where 82. the mercury becomes stationary in the glass tube, the figure Compressed-air Manometer. This manome- been attempted to be remedied by employing an apparatus of The inconvenience of both the preceding instruments has the following description, fig. 84, Nos. 1 and 2. This mano meter, invented by M. Richard, and of which No. 1 is the front view, and No. 2 the side view, is of the free-air description, indicates very high pressures, and is of a very moderate height. It consists of a tube doubled several times on itself, so as to present a series of vertical branches connected with one another by bent knees; that is, the instrument presents a continued series of siphons in the same vertical plane, altercolumns of mercury are separated by columns of water, which nating up and down and having the same vertical branches. The occupy the upper bent knees and the upper half of the height |