« ΠροηγούμενηΣυνέχεια »
The musical facts which are here ascribed simply to the con- passages, and that the use of them is entirely arbitrary. Nothing second scale used in a peculiar manner, and admitting occasional can prove this more clearly than the great discrepancy and variations are usually supposed to be founded on an entirely disagreement among the best authorities on this subject. If new scale, and that of a very remarkable structure. This new there had been any fixed usage, long established by the requirescale is described as having its “semitones" between its ment of good ears and the example of the best composers, such second and third, and fifth and sixth notes. (If you reckon opposite statements of fact could not have existed. In referfrom LAH/. to LAE, in the common mode, you will find the ence to Bar (the "sharp sixth”) we find Dr. Callcott describtonules thus placed.) But the scale, it is said, only retains ing this note as "accidental," but rendered necessary for the this form in descending, for in ascending the sixth and seventh sake of avoiding what be calls the harsh chromatic interval," are sharpened (making our occasional Bak and ne) so as to place PAH NE, "from r natural to G sharp”-while M. Galin and M, the " semitones” between the second and third, and seventh Jeu de Berneval refer to this very interval as a constitutive and eighth. This is, in fact, two scales; and some teachers of interval of the minor mode,'' full of “melancholy," "replete the pianoforte have gone so far, Dr. Mainzer tells us, with this with anguish and tears," and speak indignantly of those who o illogical system," as to make their pupils play with the right would "cancel" the very interval which is most “ characterhand ascending the scale--BAH and Ne, at the same time that istic of the “minor mode." Is it not evident from this, that the left hand descending produced the sounds Far and son! | the use of Bah is arbitrary--by some approved, by others dis He justly remarks that "the simultaneous unison of notes so approved ?
approred ? In reference to Ne, Dr. Callcott declares that it is opposite, producing an effect so discordant, is more calculated an essential” part of the “minor scale" in ascending, but not to destroy than awaken the musical- sentiments of the pupil.” to be used in descending. M. Galin and M. Jeu speak of NE 28 Let us examine facts and authorities on this subject.
“invariable" and essential both in ascending and in descending, First, then, it appears that the common scale, even without any and M. Jeu gives examples of its use in descending. Schneider, new note (NE or BAH), but simply allowing Lau to predominate in his “Elements of Harmony,” maintains the same opinion. and to be heard at the opening and at the close of a tune, is Marpurg; "one of the most influential theorists, who flourished quite sufficient to produce a true " minore tuns- and that many during the latter half of the last century" (Mainzer, 77), declares fine melodies, manifestly minor, are formed on this model, using the that this custom (of using BAH and xe) by no means ordinary notes of the common scale (from LAHI LO LAR) both changes the essential nature of the tonalitý (key or mode ascending and descending, and not requiring the aid of any reckoning from LAH TO LAH?), and the two sharps which are accidental note, No one can doubt that the first, second, prefixed to the sixth and seventh degree are purely accidental." third, fourth, and sixth of the examples. given above are minor | Dr. Crotch says distinctly of both Bay and NB, "these altera tunes, nor hesitate to allow that they are formed on the com- tions are only occasional." Dr. Goss says, “ The sixth and mon scale, and are simply distinguished by their making LAH, seventh (Fan and sow) are generally made accidentally major in the proper mournful note, predominate: Aecordingly we find ascending." Dr. Bryce ascribes the introduction of these Dir. Crotch describing his : " ancient diatonic minor key notes to modern musicians, who prefer harmony to melody. (which corresponds with our common scale when you reckon Dr. Mainzer says that there are a very large number of comfrom LAH to LA#4) ag.“the scale of the ancient Greek music, positions " in which the leading note (NE) does not appear at all and found in the oldest national tunes, in psalms and cathedral in the minor keys, and this is the case with many composers music," _Dr. Bryce speaking of this as the proper" formula of the fifteenth, sixteenth, and seventeenth centuries. He of minor tunes, in which are written" multitudes of exquisite then adduces examples from Gabrielis, from Palestrina, and melodies, especially among the ancient national music of differ from Morale, and also shows how, in the eighteenth century, ent countries,”—and Dr. Mainzer maintaining that this is the along with professedly improved harmonies, Ne was intro only true and the only agreeable arrangement of notes for such duced as an occasional note, but not essential Marcello, for tunes. By fact, then, and by competent authority, the com- ; example, introducing the following passage immediately after NON SOALE with LAH predominating is declared sufficient to one in which Ne had occurred. produce a true minor tune. But still, it may be argued, are not Bar and NE the “sharp sixth and seventh" (reckoning
KEI B fiat. from LAH, as though it were the key-note) always used in tunes of this kind (instead of Far and son) when the music uscends? 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
1, : Si.fi Isi :S 1,: essential notes may find a place! We deny the proposition, and the conclusion falls, for
pul Seeondly, it appears that the new notes BAH and NE (" the sharp sixth and seventh") are not essential even in ascending Dr. Mainzer, who is a high authority on subjects of musical
taste, and none the less so because he laboured generously to Sometimes in the course of a tune make music the property of the people, thus concludes :- the music takes the " minor” charac
f “Let any one sing the above scales one after the other (four ter, introducing the new note NE, and varieties of the so-called “minor scale"), and assuredly he will returns again to the ordinary use of ii-f not be long in discovering which of the four is the most the common scale. Occasionally, too, agreeable and natural, and most in the character of the minor the music passes into the minor of the tonality (key). It is evident that the scales with leading notes SOH KEY, making a new note, a tonule (Ne), instead of being pleasing, are disagreeable to the ear, and below Me, which (to distinguish it
tz-tula impracticable to the voice. The absence of the leading note from ne of the original key) we call d (NE) on the contrary often gives to the melody something majestic NU; and, not unfrequently, it enters
ti and solemn. The Gregorian chant, so remarkable for melodious the “minor" of the rau KEY, origi
na-9286 beauties, affords many proofs of this, and also the popular nating another note, a tonule below RAY melodies of different countries, especially those of Ireland and| (r'), which we call'NI. The modula. nii-ny Scotland, so much admired by the greatest musicians.” Surely tor at the side will illustrate these
fy here is example and testimony enough to prove these notes-changes. whether good or bad-at least non-essential and arbitrary. One question yet remains. Should not the scale on which
Another " transition" into what is called the " minor of the minor tunes are framed be still treated as a distinct one, and same tonic” (pou becoming LAH), is more proper to “temsomething more than the common scale used in a peculiar pered” musical instruments than to music itself or the unaided manner? To which we answer--Yes, if it is distinct, but, if voice. You may treat it as transition into the key of Me flat, otherwise, why multiply difficulties and conceal the truth or, retaining the syllables of the original key, the new notes But it clearly is not, in any particular, distinct. First, in refer- may be treated as chromatic. Thus you will have the oddlyence to the character or musical effect of the notes--the most sounding notes MOW, Low, and now, as any one may perceive important particular of all--the notes of the so-called minor by drawing the two keys side by side, and bearing in mind the scale correspond precisely with those of the common one (rec- difference between the tonule and the chromatic part-tone. koning from LAH to Lan) Not a single note of the common
Our pupils will now be able to ransack the stores of classical scale changes its character when used in a minor tune, LAF is music, and to take their "part' in fireside glees, at there
pleastill the sorrowful, Te the piercing, FAĦ the awe-inspiring note, sure, They will be very largely, and, we hope, very long, re&c., as before. Next, in reference to the exact intervals be warded for all the patience and painstaking which we ha e tween the notes--they are precisely the same as those of the demanded of them. common scale (from LaH TO LAR') with only this peculiarity, that the graver (flatter) position of the “variable note ordinarily used in tunes of this character, whereas it is only ON PHYSICS OR NATURAL PHILOSOPHY. occasionally used in other tunes. Premising that from dou to
No. XIX. Doh' is conimonly called by musicians a major key (beginning with a major, or greater, third, DOH ME), and that a minor key
(Continued from page 261.) 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
Experiments of Boyle.—The principle that the elastic force of tive (or, as it would more properly be called, the synonymous) air increases in proportion to its density, was first proved by minor reduces itself to avoiding the acute second of the old Boyle in 1660, in the following manner :He took a uniform key (r”) and using only the grave (r')." (See “ Westminster
tube A B C, fig. 79, closed at c and open at A,
Fig. 79. Review,” April, 1832). Dr. Crotch says "Some authors and bent upwards so that the part c n was make it” (the first note of the principal minor key) “ the same parallel to the part Am. Mercury was poured А. as the note Law of the relative major key, viz., A in the key of in at the open branch a until the level in both
branches of the tube stood at M and n respecc, a minor tone (smaller tone of eight degrees) “above G (sou). In that case all the natural notes excepting D (RAY) | tively, and the air in the closed branch on was Correspond with those of the major key of c.' (See Crotch's
of the same density as the external air in the « Elements ” —Tuning, &c.) Turning to his illustrative plates, sured and found to be 12 inches; the pressure
The distance Cr was then mea. we find the scale of minor tunes requiring the smaller tone in both branches was equal to 30 inches of degrees) Letween RAY ME, while other tunes usually require mercury, being that of the atmospheric air ; a larger tone between DOH Ray and a smaller one between and the height of the mercury in the longer In fact the variable note assumes its grave position. branch A N above the level of that in the shorter
branch was 0. Bat it sometimes does the same in the common scale. “Is this,
More mercury was poured in then, a peculiarity sufficient to establish a new scale? More at A, until the distance c n was diminished to 10 over, is it not natural to suppose that the common scale, which inches, and the mercury stood in the longer
C is found to be essentially the musical scale of all nations, must branch 6 inches above that level; the pressure hold a peculiar accordance with the ear and the sympathies of in both branches was now equal to the atmothe human race ? and is it not proper, therefore, to consider spheric pressure, 30 inches of mercury, and 6 this as the one scale, and everything else that cannot establish a all; more mercury was again poured in at a,
inches of mercury additional, or 36 inches in distinct and independent character as but a modification or a all; more mercury was again poured in at A, peculiar use of it? It is certain that great detriment must be until the distance cn
B done to the mind of our pupils, and great hindrance given to inches, and the mercury stood in the longer their progress, if we first cause them to study and practise our ! branch 15 inches above that level; the pressure theory, of a new and self-contradictory minor scale, and then in both branches being now equal to the atmospheric pressure leave them to discover that, in music itself
, instead of the arti- and 15 inches additional, or 45 inches in all. The experiment ficial difficulties they have so laboriously mastered, there is only was repeated again and again, and the results tabúlated as
follows: to be found the common scolc, so used as to produce a peculiar effect and the merely occasional, non-cssential, introduction of a new note!
Heights of Meroury [We were present, in October last, at several choral performances of pupils who were taught to sing on the meti:od developed in these lessons some of which were attended by more than 3,000 people. We
30 inches saw a cloir of children who sang music at first sight, it thing quite new
6 The Tonic Solta Association " numbered 2,000 pupils in London alone last year, and the incetings referred to were the means of originating at once three new classes of about 200 pupils tach. may claim, for the POPULAR EDUCATOR, the crcdit of giving a cosnopolitan influence to these valuable eľorts.)-ED.
The distances from c to n in the shorter pranch diminishing
8 6 4
30 36 45 60
as the heights of the mercury in the longer branch, and conse- | ever the level in both branches is not the same. Mercury is quently the pressures in both branches, increase, proves that again poured into the larger branch until the pressure which the densities of the air in the shorter branch increase as the arises from it reduces the air contained in the smaller branch spaces diminish; and that the elastic force of the air, mea- to one-half its volume; that is, this volume, which was at first sured by the pressures, is proportional to its density; for we measured by 10 on the scale, is now reduced to 5, as shown in have, by comparing the distances in the first column with the fig. 80. Now, measuring the difference of level c A between pressures in the third column, the following inverse pro- the mercury in the two branches, we find that it is actly portions :
equal to the height of the barometer at the moment when the 10
experiment is made. The pressure of the column ca 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 These proportions clearly show that the pressures, and conse- it was at first; which proves the truth of the law in this case. quently the densities, are inversely as the spaces occupied by
If the greater branch of the tube were long enough to admit the same quantity of air ; whence it follows that the elastic of mercury being poured in till the volume of air in the smaller force of air is proportional to its density.
branch was reduced to a third of what it was at first, we should Mariotte's Law. - Mariotte, a French philosopher, was the find that the difference
of level in the two branches is equal to next experimenter who established the same principle in 1668, twice the height of the barometer ; that is, it is equivalent to by the announcement of the following law, which has ever the pressure of two atmospheres, to which adding that which since borne his name, viz. :-"That the volume of any quantity acts directly on the surface of the mercury in the greater of gas, at a given temperature, will diminish in the inverse ratio branch, gives a pressure
of three atmospheres. It is therefore of the pressure to which it is subjected.” This law is verified under a triple pressure that the volume of air is reduced to in the case of air by means of the following apparatus: On one-third of its volume. The law of Mariotte has been experi2 wooden board placed vertically, is fixed å glass tube bent mentally 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
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.
atmosphere. The tube is now raised, as shown in the figure, In order to make the experiment, mercury is poured into the until, by the diminution of the pressure, the volume of air is tuve at the top of the longer branch, so that the level of this doubled, as shown by the scale; it will then be found that the liquid may correspond to the zero of the scales of the two height of the mercury in the tube at A is the half of the true eranches, a result which may be obtained by several trials. height of the barometer. The air of which the volume is thus The air contained in the shorter branch is then subjected to the doubled, is therefore submitted to a pressure of only half an atmospheric pressure, which acts in the greater branch, when- / atmosphere, for it is the elastic force of this air which, united
to the weight of the raised column, balances the pressure of the the mercury becomes - stationary in the glass tube, the figure exterior atmosphere. The volume of the air is therefore still 1 is marked, signifying one atmosphere; then, proceeding in the inverse ratio of the pressure to which it is subjected. from this point by 30. inches at a time, the
In the experiments just detailed, the mass of air in the tube figures 2, 3, 4, 5, and 6, which indicate the remaining the same, its density becomes greater in proportion number of atmospheres, are marked, because as its volume is reduced; whence we deduce the following as a column of mercury of the height of 30 a consequence of the law of Mariotte, that, “at a given tem- inches, represents the pressure of the atmoperature, the density of a gas is proportional to the pressure sphere. Then the intervals from 1 to 2, 2 to which it sustains.” Consequently, under the ordinary pres- 3, &c., are divided into ten equal parts, sure of the atmosphere, the density of air being a 770th part which give the tenth parts of an atmosphere, of that of water, it follows that, under a pressure of 770 atmo- If the tube A be now put in communication, spheres, air would have the same density as water, if at such a for example, with a steam boiler, the mercury pressure it would be-still a gas.
will rise in the tube BD to a height which Till recently, it has been considered that the law of Mariotte measures the tension of the steam. In the was true for all gases and under all.pressures. M. Despretz. was figure, the manometer is shown as marking 4 the first who showed that this law ceases to be strictly true when atmospheres, which are represented by 3 the gases are subjected to a pressure nearly equal to that which times the height of 30 inches, besides the produces their liquefaction. Lastly, M. Regnault has proved that atmospheric pressure at the top of the this law does not apply equally to all gases. Thus, air and nitro column. This kind of manometer is only gen are compressed a little more, and hydrogea a little less, th
and hydrogea a little less, than used for pressures which do not exceed 5 or 6 that which it indicates. In the case of carbonic acid, it does not atmospheres. Beyond this point it would be even furnish: an approximation to the truth when the pressure is necessary to make the tube so long that it considerable.
would be easily broken. In this case, recourse Applications of Mariotte's Law,—The following examples of must be had to such a construction as that the application of this law.may be useful to students of Chemistry explained in the next paragraph. and Physics.
Compressed-air Manometer --This manome1.- A vessel in which air. can be compressed contains 4:3.gal-ter, founded on the principle of Mariotte's lons of air, the pressure measures by the barometer being 29•6 law, is composed of a strong glass tube closed inches ; what will be the volume of air at the pressure of 30:4 at its upper extremity and filled with dry air. inches? If a denote. the polume required, we have,
This tube is immersed in a cistern partly filled
with mercury, to which it is.cemented. The
cistern, by means of a side tube A, fig. 83, is
put in communication with a close vessel,
which contains the gas .or · vapour whose sphere; to what pressure must it be subjected, in order to reduce it of air contained in the tube is such, that 2. Having 20. gallons of gas under the pressure of one atmo- elastic force is to be ascertained. As to the
graduation of this manometer, the quantity to 8 gallons!
when the orifice A communicates . with the If p denote the pressure required, we have,
atmosphere, the level of the mercury is the P:1::20:8; whence,
same in the tube and in the cistern. At this 20 X 1
level, therefore, 1 is marked on the board to -2} atmospherese
which the tube is attached. In continuing
the graduation, it is necessary to observe 3. A gallon of air weighs 20 grains at 32° Fahrenheit, the that the pressure which is transmitted through barometric pressure being 30 inches; what will be its weight at the tube increasing, the mercury rises in the the same temperature, when the pressure is 28 inches?
tube until its weight, added to the tension If w denote the weight required, we have,
of the compressed air, balances the exterior
pressure. If, therefore, we mark 2 atmo-
spheres 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 The Manometer.--The name manometer (from the Greek, rarity- tension, by the law of Mariotte, is that of two measure) is generally applied to instruments employed in measu- atmospheres; and, therefore, when increased ring the tension of gases or vapours, when it is greater than the by the weight of the column of mercury which pressure of the atmosphere. There are various kinds, as the free- is elevated in the tube, it represents a pressure greater than air manometer, the compressed-air manometer, and the metallic two atmospheres. The number 2 must not therefore be manometer. In these different kinds, the unit of measure which marked in the middle of the tube, but a little lower, and is employed is the atmospheric pressure, when the barometer at such a height that the elastic force of the compressed stands at 30 inches. Now, we have seen that this pressure on a air, added to the weight of the column of mercury in the square inch is 144 lbs.; consequently, if we say that a gas has tube, shall be equal to two atmospheres. By such a calcua tension of two or three atmospheres, we mean, that it acts on the lation as this
exact position of the figures 2, 3, 4, &c., sides of the vessel which contains it with a pressure of twice or
on the scale of the manometer is determined. This inthrice the weight of 14 lbs. per square inch.
strument is not very accurate when the pressures are great; Free-air Manometer. This manometer is composed of a strong for the volume of air becoming less and less, the divisions of glass tube B D, fig. 82, about 51 yards long, and a cistern | the scale approach too near to each other. D, made of iron, containing the mercury in which the tube is The inconvenience of both the: preceding instruments has immersed. This tube is cemented to the cistern and fixed on a been attempted to be remedied by employing an apparatus of board, along side of which is placed another tube A C, made of ), the following description, fig. 84, Nos. 1 and 2. This manoiron, and about 5 yards long; by means of this tube the pressure meter, invented by M. Richard, and of which No. 1 is the of the gas or of the vapour is transmitted to the mercury in the front view, and No. 2 the side view, is of the free-air descripcistern. As manometers of this kind are most frequently tion, indicates very high pressures, and is of a very moderate used in cases where vapour of high temperature, or steam, "height. It consists of a tube doubled several times on itself, would soften the cement which is employed to fix the glass so as to present a series of vertical branches connected with tube to the cistern, the tube A c is filled with water; and it one another by bent knees; that is, the instrument presents a is by this means that the pressure of the vapour is transmitted continued series of siphons in the same verticai plane, alterto the mercury.
.nating up and down and having the same vertical branches. The In order to graduate the manometer, the orifice A is allowed .columns of mercury are separated by columns of water, which to communicate with the atmosphere, and at the level where occupy the upper bent knees and the upper hilf of the height
of the branches. The apparatus being completely filled with the columns of mercury. This correction will be made by columns of mercury and water, if one of the extremities of the multiplying the preceding product by the fraction in which tube be put in communication with the vessel of gas or vapour represents the ratio of the excess of the density of mercury whose tension is to be ascertained, the other extremity remaining above that of water, to the dersity of mercury. The donbled open to the free-air, the excess of the pressure in the vessel over tube is made of iron; the second' vertical branch open io the
air is mounted with a glass tube to show the extremity of the Fig. 83.
column of mercury; and the scale, which is made of brass, is graduated to atmospheres.
Metallic Manometer.-M. Bourdon, a mechanician of Paris, has recently invented a new manometer, represented in fig. 85
that of the atmosphere will produce the elevation of the level of the mercury in all the branches; these elevations will be of This instrument, which is wholly metallic and without mercury, equal height if the tube be of the same bore throughout; and is constructed on the following principle, discovered by the in this case, the effective pressure of the gas in the vessel will inventor; when a tube having sexible sides and a slightly flat
tened or oval shape is wound up in the form of a spiral, in the Fig. 84.-Nos. 1 and 2.
direction of the less diameter, crery interior pressure on the sides has a tendency to unwind the tube; and, on the contrary, exterior pressure has a tendency to zind it up.
According to this principle, the manometer of M. Bourdon is composed of a brass tube, about 2. feet long, having its sides thin and flexible. A section across the tube, represented at 8 on the left in the figure, is an ellipse whose greater axis is about it of an inch, and smaller axis about of an inch. The extremity a, which is op'en, is fixed to a tube with a stop-cock d, for the purpose of putting the appara:us in communication with a steamboiler,
The extremity b is closed, and moreable 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 on 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 rapour in atmospheres. This dial-plate is previously graduated by means of a free-air manometer, by putting the apparatus in-buition with compressed air. This manometer has the great advantage above the preceding manometers, of being extremely portable and not easily broken. It is now in operation in the locomotives upon sereral railroads in France.
Metallic Barometer, M, Bourdon is also the inventor of a metallic barometer founded on the same principle as his mano.
This apparatus, represented in ig. 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 pressuro 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 be given by the height to which the mercury is raised above fixed on the axis of the index. If the pressure increases instead the point of departure in the open branch of the tube, multiplied of diminishing, the tube will close in upon itself, and there is a by the number of vertical branches, minus the correction due to small-spiral spring at e, which then brings back the index from the influence of the weight of the intermediate water between ( right to left, under the dial-plate. This barometer is of small