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The musical facts which are here ascribed simply to the com#oon 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 LAHrto LAH, in the common mode, you will find the tonules thus placed.) But the scale, it is said, only retains

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 soH !
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 LAH1 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
$ones, nor hesitate to allow that they are formed on the com-
mon seale, and are simply distinguished by their making LAH,
the proper mournful note, predominate. Accordingly we find
Ijr. Crotch describing his “ancient diatonic minor key”
which corresponds with our-common scale when you reckon
from LAH to LAH') 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 musie of differ-
ent countries,”—and Dr. Mainzer maintaining that this is the
only true and the only agreeable arrangement of notes for such
tunes,
MON 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 soh) 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—
Seeondly, it appears that the new notes BAH and NE (“the
sharp sixth and seventh ") are not essentia; even in ascending

By fact, then, and by competent authority, the Cow

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 describ

'ing this note as “accidental,” but rendered necessary for the this form in descending, for in ascending the sixth and seventh 3. y

sake of avoiding what he calls “the harsh chromatic interval,” FA.H. NE, “from F natural to G 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. Calicott declares that it is an “essential” part of the “minor scale” in ascending, but not $9 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 LAH'), 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 soH) 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 avery 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, NR was intro: duced as an occasional note, but not essential—Marcello, for example, introducing the following passage immediately after one in which NE had occurred.

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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 mote (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 notes— whether 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 wised in other tunes. Premising that from DoR to Dołłł is commonly called by musicians a major key (beginning with a major, or greater, third, DoR ME), and that a minor key beginning on a note in the position of our LAH would be called its relative minor, let us quote the following testimonies to the last point. Colonel Thompson says—“The change to the relative (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 {so}). In that case all the natural notes excepting D (RAY) Sorrespond 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 Dołł RAY, and the larger tone (nine degrees) between 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 ; Moreover, 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 2 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 1 [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 cloir of children who sang music at first simht, 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 Imay claim, for the POPULAR F DUCATOR, the credit of giving a cosmopolitan influence to these valuable efforts.]—ED,

Sometimes in the course of a tune | the music takes the “minor ’’ charac- S dl f ter, introducing the new note NE, and t IIl returns again to the ordinary use of si –f the common scale. Occasionally, too, II]. l r the music passes into the minor of the In e SOH KEY, making a new note, a tonule Y S d below ME, which (to distinguish it tl—itti from NE of the original key) we call d f : NU ; and, not unfrequently, it enters tl In 11 the “minor” of the FAH KEY, origi- In 1–??/1 nating another note, atonule below RAY li I S1 (F), which we call NI...The modula- |mi,-n, tor at the side will illustrate these S1 d fi changes.

Another “transition ” into what is called the “minor of the same tonic ’’ (DoE 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 fiat, 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 hare demanded of them.

ON PHYSICS OR NATURAL PHILOSOPHY.
No. XIX.
(Continued from page 261.)

THE ELASTIC FORCE OF GASES.

Experiments of Boyle.—The principle that the elastic force of air increases in proportion to its density, was first proved by Boyle in 1660, in the following manner:—He took a uniform tube A B C, fig. 79, closed at C and open at A,

and bent upwards so that the part c N was Fig. 79. parallel to the part A. M. Mercury was poured A in at the open branch A until the level in both U7 branches of the tube stood at M and N respec- L

tively, and the air in the closed branch cn was of the same density as the external air in the branch AM. The distance CN was then measured and found to be 12 inches; the pressure in both branches was equal to 30 inches of mercury, being that of the atmospheric air; and the height of the mercury in the longer branch A M above the level of that in the shorter branch was 0. More mercury was poured in at A, until the distance C N was diminished to 10 inches, and the mercury stood in the longer branch 6 inches above that level; the pressure in both branches was now equal to the atmospheric pressure, 30 inches of mercury, and 6 inches of mercury additional, or 36 inches in all; more mercury was again poured in at A, until the distance CN was diminished to 8 inches, and the mercury stood in the longer branch 15 inches above that level; the pressure in both branches being now equal to the atmospheric pressure and 15 inches additional, or 45 inches in all. The experiment was repeated again and again, and the results tabulated as follows:— Distances from C

Heights of Mercury Pressures in both

to N in the shorter in A M above its branches of the branch. level in C N. tube. 12 inches 0 inches 30 inches 10 3, 6 , 36 , , § 1, 15 , , 45 , , 6 , 30 ,, \ 60 , , 4 ?? 60 22 90 35

The distances from C to N in the shorter branch diminishing

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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 plaeed 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

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 C A 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.

atmosphere. The tube is now raised, as shown in the figure, until, by the diminution of the pressure, the volume of air is doubled, as shown by the scale; it will then be found that the height of the mercury in the tube at A is the half of the true height of the barometer. The air of which the volume is thus doubled, is therefore submitted to a pressure of only half an atmosphere, for it is the elastic force of this air which, united to the weight of the raised column, balances the pressure of the exterior atmosphere. The volume of the air is therefore still in the inverse ratio of the pressure to which it is subjected. In the experiments just detailed, the mass of air in the tube remaining the same, its density becomes greater in proportion as its volume is reduced ; whence we deduce the following as a consequence of the law of Mariotte, that, “at a given temperature, the density of a gas is proportional to the pressure which it sustains.” Consequently, under the ordinary pressure of the atmosphere, the density of air being a 770th part of that of water, it follows that, under a pressure of 770 atmospheres, air would have the same density as water, if at such a pressure it would be still a gas. 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 nitro. gen 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 304 inches * : If z denote the volume required, we have,

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w : 20 :: 28 : 30 ; whence, w=*X*= 18% grains. 30 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 pressure 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 Jquare 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 14% lbs. per square inch.

| cistern, by means of a side tube A, fig. 83, is

which contains the gas or , vapour whose

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the mercury becomes stationary in the glass tube, the figure 1 is marked, signifying one atmosphere; then, proceeding from this point by 30, inches at a time, the figures 2, 3, 4, 5, and 6, which indicate the 82. number of atmospheres, are marked, because a column of mercury of the height of 30 inches, represents the pressure of the atmosphere. Then the intervals from 1 to 2, 2 to 3,. &c., are divided, into ten equal parts, which give the tenth parts of an atmosphere. If the tube A be now put in communication, for example, with a steam boiler, the mercury will rise in the tube B D to a height which measures the tension of the steam. In the figure, the manometer is shown as marking 4 atmospheres, which are represented by 3 times the height of 30 inches, besides the atmospheric pressure at the top of the column. This skind of manometer is only used for pressures which do not exceed 5 or 6 atmospheres. Beyond this point it would be necessary to make the tube so long that it would be easily broken. In this case, recourse must be had to such a construction as that explained in the next paragraph. Compressed-air Manometer.—This manometer, founded on the principle of Mariotte's law, is composed of a strong glass tube closed at its upper extremity and filled with dry air. This tube is immersed in a cistern partly filled with mercury, to which it is, cemented. The

put in communication with a close vessel,

elastic force is to be ascertained. As to the graduation of this manometer, the quantity of air contained in the tube is such, that when the orifice A communicates, with the atmosphere, the level of the mercury is the same in the tube and in the cistern. At this level, therefore, 1 is marked on the board to which the tube is attached. In continuing the graduation, it is necessary to observe that the pressure which is transmitted through the tube increasing, the mercury rises in the tube until its weight, added to the tension of the compressed air, balances the exterior pressure. If, therefore, we mark 2 atmospheres in the middle of the tube, we shall commit an error; for, when the volume of air in the tube is reduced to one-half, its tension, by the law of Mariotte, is that of two atmospheres; and, therefore, . when increased by the weight of the column of mercury which is elevated in the tube, it represents a pressure greater than two atmospheres. The number 2 must not therefore be marked in the middle of the tube, but a little lower, and at such a height that the elastic force of the compressed air, added to the weight of the column of mercury in the tube, shall be equal to two atmospheres. By such a calculation as this, the .exact position of the figures 2, 3, 4, &c. on the scale of the manometer is determined.” This in: strument is not yery.accurate when the pressures are great;

for the volume of air becoming less and less, the divisions of . the scale approach too near to each other. |

The inconvenience of both the preceding instruments has "

Free-air Manometer.—This manometer is composed of a strong glass tube B D, fig. 82, about 53 yards long, and a cisterm 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

been attempted, to be remedied by employing an apparatus of

the following description, fig. 84, Nos.1 and 2. This manometer, 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, alternating up and down and having the same vertical branches. The columns of mercury are separated by columns of water, which

occupy the upper bent knees and the upper hylf of the height

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This instrument, which is wholly metallic and without mercury, is constructed on the following principle, discovered by the inventor; when a tube having flexible sides and a slightly flattened or oval shape is wound up in the form of a spiral, in the direction of the less diameter, every interior pressure on the sides has a tendency to unwind the tube; and, on the contrary, eacterior pressure has a tegdency to wind it up. According to this principle, the manometer of M. Bourdon is composed of a brass tube, about 23 feet long, having its sides thin and flexible. A section across the tube, represented at s on the left in the figure, is an ellipse whose greater axis is about # of an inch, and smaller axis about or of an inch. The extremity a, which is open, is fixed to a tube with a stop-cock d, for the purpose of putting the apparatus in -communication with a steamboiler. The extremity b is closed, asid moveable like the rest of the tube. Now, when the stop-cock d is open, the pressure which is produced by the tension of the vapour of the interior sides of the tube causes it to unwind. The extremity b is then drawn from left to right, and with it an index e, attached to it, which indicates on a dial-plate the tension of the vapour in atmospheres. This dial-plate is previously graduated by means of a free-air manometer, by putting the apparatus in-Baotion with compressed air. This manometer has the great advantage above the preceding manometers, of being extreraely portable and not easily broken. It is now in operation in the locomotives upon several railroads in France. Metallic Barometer.— M. Bourdon is also the inventor of a metallic barometer founded on the same principle as his manometer. This apparatus, represented in fig. 86, is composed of a tube similar to that of the manometer, but shorter, hermetically closed, and fixed at its middle point; so that the vacuum having been made in it beforehand, whenever the atmospheric pressure diminishes, this tube unwinds itself in consequence of the principle above mentioned. The motion is thus communicated to an index which indicates the pressure of a dial-plate. As to the transmission of the motion, it is effected by means of two small wires b and a, which connect the extremities of the tubes with a lever fixed on the axis of the index. If the pressure increases instead of diminishing, the tube will close in upon itself, and there is a small-spiral spring at e, which then brings back the index from

|right to left, under the dial-plate. This barometer is of small

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