192 0?i the Stanhope Temperament: 



the results of his calculations, which, however convenient it 

 may prove in using his monochord (which ra|)prehend is rather 

 a costly instrument), whereon the length of wire for sounding 

 C is divided into 1 20 parts, and the decimals of those parts, the 

 same is not readily adapted for repeating his experiments on 

 the monochords more commonly in use, whereon the length 

 for C, or the key note, is made unity, or l-OOOOO, and the 

 same is divided decimally : therefore in column 8 of Table I. 

 following, and column 6 of Table 11. (pages 193, I96, and 

 197,) I have reduced his lordship's numbers (xxv. 309.) to 

 this scale, the numbers herein being the numbers answering 

 to the logarithms in the preceding columns. It appears, how- 

 ever, necessary here to remark, that musical intervals are of 

 that peculiar species of magnitude v/hich cannot he numeri- 

 cally defined lij the lengths of the strings which yield the 

 sounds; and that every attempt of that kind is as futile, as 

 it would be to attempt the definition of a plane surface, or 

 of a solid body, by one of its lineal dimensions. 



For the purposes of comparing the magnitudes of musical 

 intervals, the intervals of sounds themselves may be added 

 to each other, or deducted, at pleasure, on an instrument fur- 

 nished with a sufficient number of adjustable strings, as 

 our noble author has shown (p. 292, &c.): thus any number 

 of the conchords called ffths (V) can be added upwards to 

 each other with accuracy, the point of acuteness, or interval 

 from the fundamental or key note thus obtained, can be 

 compared with that obtained by adding in ascent a number 

 oi octaves (VIII) or other conchords; or we can, from those 

 points accurately descend by deducting (or adding in de- 

 scent) any other of the conchords, as major or minor thirds 

 (III or 3rd), major or minor sixths (VI or 6th), or of minor 

 fourths (4th), to any fresh points in the scale, from whence 

 we may wish to make accurate comparisons with the key 

 note, and thence with any other notes in the scale. 



Notwlthstandina that this mode of composing intervals 

 of sound is well known, and is in constant use by tuners of 

 keyed instruments, as organs, harpsichords, piano-fortes, 

 &c. ; yet no author that I. have read has yet adopted this 

 simple, accurate, and convenient mode of notation or ex- 

 pressing, 



