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THE

PHILOSOPHICAL MAGAZINE.

I. On the two Systems of Musical Temperament recommended by Earl Stanhope,-Mr. Hawkes's System, &c. By Mr. JOHN FAREY.

SIR,

To Mr. Tilloch.

HAVING bestowed some pains to illustrate the System of Musical Temperament described by Earl Stanhope in your xxvth volume, as applicable to keyed Instruments, by the help of a Monochord, whose divisions are according to geometric mean proportionals, I beg now to present to your readers, the notes of the other System, described by his Lordship in the same Essay, to be effected by making three successive tempered Fifths, and two successive major Thirds, in different parts of the scale, beat equally quick respectively.

The table accompanying this, is divided into 10 columns, entitled at the bottom, as has usually been done.

Column 4 contains the number of complete vibrations made by a musical string or other sounding body in o one second of time, when the intervals are agreeable to Earl Stanhope's Monochord System; whose logarithms, lengths of strings, and other particulars for comparison herewith, will be found vol. xxvii. p. 195*, and vol. xxviii. p. 141.

* I beg here to correct an unfortunate error in the length of string which I have in this page assigned to Lord Stanhope's 6th, owing to my having taken out the number answering to the logarithm 8100300 (instead of ⚫8010300) viz. 6456987 instead of '6324554; for which correction I wish to acknowledge my obligation to Mr. J. Barraud, a gentleman engaged in these inquiries, who has verified the numbers in this column, except in some of their last places, independent of the logarithms in the preceding column.

Vol. 30. No. 117. Feb. 1808.

A 2

Columns