252 Professor Edwin H. Barton [Marcb 8, 



instruments that a note called by tbem a low " F " can Ije sometimes 

 obtained. This note would have on the foregoing scheme the fre- 

 quency lS'd}i. At first the possibility of this '• F " seems scarcely 

 crediljle to the theoretician. But after hearing and producing the 

 note, the necessity of accounting for its possibility was forced home. 



And really the explanation proves very simple. It usually 

 depends upon two points ; (a) the spread or diffused resonance of 

 of the pedal ; and {h) its intentional mistuning with respect to the 

 other notes of the instrument. These are taken in order. 



(«) For theory shows that, other things being equal, the lower 

 the note of such an instrumei>t, the easier it is to force its vibrations 

 out of tune, sharper or flatter. Thus, with the pedal the range of 



Table II. — Spread Resonance of Lower Open Notes on Brass Instruments. 



resonance is such that the note may be sounded nt any pitch what- 

 ever over a range of five or six semitones. 



(Jb) Since the law of frequencies 1(>(>, 2<io, 'MX), 4U(>, etc., is only 

 approximately true for these instruments, in order to secure good 

 relative tuning of the higher notes which are in constant use the 

 pedal (which is not used musically) is purposely mistuned. On some 

 instruments it may be say, D or E flat, instead of C. 



Hence, if the central pitch of the pedal is sharpened two or 

 three semitones, and it is possible to force this note both up and 

 dow^n two or three semitones, it becomes possible to sound the pedal 

 of true pitch C, to sound the low " F," and to sound notes of every 



