Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

this, we know that the octave is known by this fraction; and as there are 12 half notes in the octave, all melody and harmony are compofed of thefe 12 notes; for the octave above or below are but the replicatives of the fame founds in an higher or lower tone. Therefore the following table is the meafure of the distance to any particular half tone required in the octave; and they are alfo factors to find the dimenfions of mufical chords and other inftruments.

[blocks in formation]

To apply the factors in the table to the confiruction of organ-pipes.

Here you are to obferve that the dimenfions of the cavity of fome one pipe must be given; and each particular dimenfion must be multiplied by the factor in the table, and the product gives the like dimenfion of that pipe that will found the note belonging to that factor. Thus

for

for example, fuppofe C the key-note, and the given dimenfions of the pipe to be 1.57 by 1.46, and 20.9 inches long. Now fuppofe I would have the dimenfions of that pipe to found G, viz. 7 half tones higher than the given pipe. Then 1.57 multiplied by .66742 gives 1.0478; 1.46 multiplied by .66742 gives .9744; and 20.9 multiplied by .66742 gives 13.9491; and thus you have the dimenfions of the pipe required.

The dimenfions for all the femitones in the above octave are as follow.

[blocks in formation]

If you would have an octave below, multiply the dimenfions of any pipe by 2 and it gives the dimenfions of that pipe an octave below; and take the dimenfions it gives an octave above: Proceed in this manner for double octaves either above or below.

In

In conftructing round pipes of a cylindrical form, the fame rules must be obferved as with thofe which are fquared, and the given length and diameter only made ufe of in the opera

tions.

To apply the factors in the table in conftructing of musical strings.

In this cafe, multiply the length of the given ftring by any of the factors in the table, and the refult is the length of the ftring that will found the note belonging the factor made ufe of if the thickness and tenfion are the fame.

What must be the length of that string to found 4 half tones above another that is 40 inches long?

.7937
40

Anfwer 31 7480 inches.

What must be the length of thofe ftrings to found the notes D, E, F, G, A, B, C, if the key-note C is 40 inches long?

[blocks in formation]

Suppofe it is required to find the, weight that any string must be ftretched with to found any particular note, by having given the weight requifite to found the key-note.

RULE. Divide the given weight by the fquare of the factor in the table, the quotient will give the weight required to found any note above the key-note, if the ftrings are of equal lengths.

What must be the weight to ftretch a ftring 40 inches long that it may found an octave above the key-note, if the key-note is ftretched with 7 pounds, and is 40 inches long alfo?

.5000
.5000

.25)7.00(28 pounds, the weight required.

50

200
200

From whence we find, that if the diameters and lengths of mufical ftrings are equal, the times of the vibrations (and confequently the note founded) will be inverfly as the fquare roots of the weights which stretch them; for if the weights are as 1 to 4, whofe fquare roots are I and 2, then the times of vibration will be as 2 to 1, and confequently they will found octaves to each other. Hence in conftructing ftringed inftruments, as fpinets, harpfichords, &c. a skilful artift will compound thefe proportions of the length, diameter, and tenfion of ftrings, to very great advantage.

FINI S.

Page. Line.

4

6

10

29

35

50

ΤΙΟ 118

138

147 175 237

242

[merged small][merged small][merged small][ocr errors]

[ocr errors]
[ocr errors]
[ocr errors]

ERRAT A.

To for underneatth read underneath.
22 for number read numbers.

24 for 4790x64 read 4790384, &c.
9 for .92916 read 02916.

8 for factots read factors.

30 for gains of each read gains or loffes of each.

3 for exttact read extract.

5 for of tower read of the tower.
31 for term read terms.

26 for what read what is.
17 for

readj.

12 for measure read go.
31 for one one read one.

273 2 for may read many.
290 29 for ine read line.
30 for line read moft.

ibid.

[ocr errors]
[ocr errors]
« ΠροηγούμενηΣυνέχεια »