446 M): Farey's extended Scale of Musical Intervals. 



bearing ^D^rare or ora/e Marks, except 7 of them in the centre, 

 will be found to traverse the Table diagonally, from the top 

 left-hand corner to the bottom right-hand corner*: and the^ 

 Notes without acute or grave Marks, but bearing Sharps or Flats, 

 (except ill the centre, the 7 above-mentioned) will be found to 

 cross diagonally, from the top right-hand corner to the left-hand 

 lower corner, of the large manuscript Table T am describing. 



I beg to recommend to Musical Students, the useful exercise, 

 of filling up a Table of these 612 equal Notes, from what is here 

 said: by the study of which, a more perfect insight into the 

 true relation of the Musical Scale, will be had, than by any other 

 means: especially that which is usually resorted to by Teachers 

 and Professors of Music, for explaining the derivation and nature 

 of the general Scale, by means of the major and minor Tones 

 and Semitone, or T(l()4), t(93), and S or H(57); v.'hich, (in 

 common with almost any other three Intervals) are certainly 

 capable, of correctly expressing musical values, when negative 

 sig7is are used, yet this mode is pernlexingly intricate, and in- 

 deed, unnatural ; because, the progress of Modulation, and the 

 tuning of all Instruments, is conducted by means of the Concords, 

 the Fifths, Octaves, or major Thirds, the Notes of the com- 

 mon Chord : and in no instance is it practicable to use T, t or 

 S, for the purpose of Tuning: why then should they be used in 

 deriving or explaining the general Scale, instead of III, V and 

 VIII ?, by which it is in fact produced, and whereby (when ne- 

 gative signs are admitted)every Note may as readily be expressed, 

 as by means of S, t and T. 



I heartily wish that Mr. Flight of St. Martin's Lane, the Or- 

 gan Builder, who is himself a good Musician, and a very in- 

 genious Mechanic, were encouraged, by a Subscription among 



Musical 



* In the like direction, througliout tlie Table, the same Note, as to the 

 Letter and Flats and Sharps it bears, but always lessening a grave or in- 

 creasing an acute Mark, in proceeding one step diaKonaily downwards, will 

 b« found to range: and the number of artificial Commus will, each one, 

 increa^, eleven from the last one, in this same direction; — and this pro- 

 perly of the Scale, when thus tabulated, forms by far the best and easiest 

 mode of examining the accuracy, of a Table, of the extent mentioned ; or 

 of increasing this, all around, to any required degree. But the Student is 

 to be apprised, that although every Note thus obtained, beyond the limits 

 oftheTalile, will, by the artificial Commas belonging to it, appear to be 

 eqval to some one other Note, within the Table: yet, that very small dif- 

 ferences will still always be found : — it being no more possible, for the same 

 exact value of Interval in 2, f and m, to return, than for this tuning pro- 

 cess, again to reproduce any Note whatever, exactly. 



.Around the border of my Table there are, if the artificial Commas only 

 ■*verc considered, 108 repeated Notes; but these Notes, when strictly calcu- 

 lated in X, f and m, are found to differ from those within the Table, re- 

 spectively, by Uirce different, exceedingly small Intervals; viz. 34 of them 



differ 



