170 



INTERVALS. 



Tntfrvil*. in our article I'AUI \ '- \':./ulioii, and exemplified under 

 """ " ' the names of all the intervals which have hitherto oc- 

 curred m our work. 



( Jreat ns were the number of intervals, or rather the 

 numbers of names by which the numerous writers on 

 nm-ic had denominated them, prior to the appearance 

 of the Rev. Henry Liston's Essay on perfect Intonation, 

 as we have endeavoured to explain them in the pro- 

 gress of our work, the numbers of well-defined and 

 perhaps of useful intervals, are, by Mr. Liston's la- 

 bours and discoveries, very greatly extended, even 

 to the number of 220 within the octave, as Mr. Farey 

 has recently shewn in a paper in the Philosophical 

 Magazine, vol. xlix. p. S6'2, wherein he has sketched 

 out the principles of Nomenclature, by which each 

 one of these Listonian intervals may be clearly deno- 

 minated. 



The NUMERALS major and minor, which practical 

 musicians use, as the common mode of expressing or 

 reckoning the intervals of the scale, viz. 1, I, 2, II, 3, 

 III, 4, IV, 5, V, 6, VI, 7, VII, 8 and VIII, furnish the 

 sixteen generic terms, whence, by means also of the 

 specific terms Comma and Diesis variously compound- 

 ed, Mr. Farey proposes to distinguish each of these 220 

 intervals. 



In practice, musicians use still more commonly ano- 

 ther mode of defining intervals, viz. by the LITERALS, 

 viz. F, C, G, D, A, E, B ; which thus arranged, .ire 

 each at the distance of a true fifth (V) apart, except 

 D and A, between which is a grave fifth (V ( ), each 

 of these 7 literals being at times (successively from F 

 upwards) raised a chromatic half note or sharp $, 

 (which sometimes is of the value , and sometimes 

 only iS ) ; and at other times these literals (successively 

 from B downwards) are lowered a chromatic half note 

 or flat ]) (Sorrf). 



Besides which, Mr. Listen occasionally raises each of 

 these 7 literals, and sharpened or flattened notes, (in the 

 succession above named,) a major comma (c) or acute 

 (') ; or lowers each of them, (in the reverse order,) a 

 major comma (c) or grave (), And when occasion 

 requires, these sharps and the flats, together with the 

 acutes and the graves, are by Mr. Listen and Mr. Fa- 

 rey respectively doubled, trebled, &c. ($$, $ 3 , $ 4 ; 

 bb, b 3 , b 4 ; " 'V 4 ; " V). in connection with the li- 

 terals in all their varieties of combinations : by which 

 means a literal notation isformed, comprehensive enough 

 for expressing each of the 220 notes above alluded to, 

 and even a much greater number, which are next to be 

 mentioned. 



Mr. Liston's scale of 59 notes in the octave, tuned by 

 means of perfect Vths, Illrds, and Vlllths, as describ- 

 ed in pages 7, 44, and 45 of his Essay, and to which 

 the most extended of his EUHARMONIC ORGANS yet 

 made have been adapted, contains no doubly acuted or 

 graved notes, and only four double sharps, viz. F, F', 

 C, and C', and two double flats, viz. 15, and B' ; but the 

 principles of his tuning process admit of being extend- 

 ed, as Mr. Farey has recently shewn, (in the Philosophi- 

 cal Magazine, vol. xlix. p. 443.) to produce 612 notes 

 in the octave, placed, as to acuteness and graveness, 

 nearly enough at equal distances from each other, to ad- 

 mit of being so considered, for all of the common pur- 

 poses of harmonics, or musical calculations, and accord- 

 ing to the artificial commas (S's) of Mr. Farcy's nota- 

 tion. 



Mr. Farey, in the paper last referred to, has minute- 

 ly described his extended Listonian Tuning Table, 

 5 



which contains each of the 612 notes above alluded to, 

 expressed in artificial commas above C. viz. 0, 1, 2, 3, 

 4, &c. to 6'12; and in literals, with their proper marks 

 or signatures, viz. C, B"$, D^b, C"$, B"*, &c. to c; 

 forming thus a more complete and systematic table of 

 musical intervals than was ever before communicated 

 to the public, or perhaps formed. 



We have been enabled, by another arrangement of 

 the materials of this Tuning Table into thirteen divi- 

 sions, to bring it within the compass of our pages, and 

 are happy in the opportunity of thus presenting our 

 musical readers with it as an important acquisition to 

 the science of harmonics. 



A Table of Lislonian Intervals, extended, by Mr. Farey, 

 to a nearly equal Scale o/6l2 Noles in the Octave. 



B 



574 



