4 On Earl Stanhope^ two Systems of 



Columns 5, 6, 7, 8, and 9, arc intended to explain the 

 Equal- beating System of his Lordship (see vol. xxv. 

 pp.301, 302; xxvii. p. 2035 and xxviii. p. 150) : the 5lh 

 contains the complete vibrations (which Earl S. would call 

 Beats) made in one second of time ; wherein 2-10 is assumed 

 as the pitch of 'C on the Tenor Clift' line (a ledger line be- 

 low the Treble, or the same above the Bass stave in music), 

 on the authorities quoted in the article Concert pitch, in 

 vol. ix. part 1. of Dr, Rees's New Cyclopaedia, lately pub- 

 lished. 



I am aware that Earl Stanhope, (vol. xxv. p. 303,) refers, 

 in his Tuning Table, to the Octave below, my C instead of 

 above it, at least for tuning of some of his notes, but 

 I have preferred this Octave, and added to my calculation, 

 vol. xxvii. p. 203 ; extending the same to the equally heat- 

 ing Thirds in this his Lordship's System. 



If the Third E bA in his Lordship's Table be tempered 

 sharp 1-066 commas, and the Third bAc, also sharp '843 

 parts of a comma, both of these will beat 10*00 times per 

 second ; and his three successive Fifths GD, DA and Ae, 

 if tempered flat -4721, -3163 and -21 16 parts of a comma 

 respectively, will each be found to beat 3*158 times per 

 second nearly. The half of the number of Vibrations in 

 columns 4 or 5, or of Beats in this Octave, will answer to the 

 first Bass Octave, and twice these numbers to the first 

 Treble Octave respectively; and the half or double of these 

 again, will express the next descending or ascending Octave 

 respectively, and so on, throughout the whole scale. 



Columns 6 and 7 contain the logarithms and lengths of 

 strings in this System, for comparison with the notes in his 

 Lordship's Monochord System, vol. xxvii. p. 195; as co- 

 lumn 8 is intended, to compare with vol. xxviii. p. 141 ; 

 in which column, I have preserved the terms f and m, 

 the same, and thrown all the differences between this and 

 the monochord system, into the term 2, as the same are 

 expressed in column 9 : from whence it appears, that half 

 the notes differ more than l^- Schismas from each other re- 

 spectively, in these two Stanhopian Systems. 



A Table 



