1864.] 



of Insti'uments with Fixed Tories^ 



421 



^ ^% ff% 9 9^> ^ 9% ^ ^S* Hence it is easy to compare the different effects 

 of the two systems as applied to the same quahty of tone, for harmonies 

 which are common to both. Having two concertinas so tuned, and a third 

 tuned to just intervals, I have been able to make this comparison, and my 

 own feeling is that the Mesotonic is but slightly, though unmistakeably, 

 inferior to the Just, and greatly superior to the Hemitonic. 



There are two other points in which the complete Mesotonic system 

 possesses advantages over the Hemitonic. The Mesotonic Vllth is rather 

 flat, but by using the flat VTIIth in its place, when the harmony will allow, 

 the effect of an extremely sharp Vllth is produced, which is sometimes de- 

 sirable in melodies. Thus log Mesotonic Vlllb = '28195, which is sharper 

 even than log Pythagorean VII = '27840, The ordinary and flatter Vllth 

 can be used when necessary for the harmony, ilgain, by using the 

 German sharp Vlth in place of the dominant 7th, that is, by using the 

 chords (^7 B7 e, Db F A9 h. Ah C F9 f% G B\f c^, Bb D F gi, 

 FA GEO a^, G B D e% I) F^ A bj^, A E f x , E B c x , 

 BBj^ F^ g X, in place of G? ^> Z)> fi. By F A) c>, A7 C E\? fj9, 

 EQGB^ch, ^QDEa^, FACeh, CEGdy, G B D f, DF^Ac, 

 A Eg, E G^ B d, B F^ a, when the progression of parts will allow, 

 an almost perfect natural seventh, better than that obtained by using the 

 corresponding just tones, will result, producing beautiful harmony ; for 

 log Mesotonic VIg='24228, log 1= '24304, and log Just VIj ='24497. 

 The ordinar}^ sharper 7th can be used when necessary. Neither of these 

 effective substitutions is possible on the Hemitonic system. 



Considering that singers and violinists naturally intone justly (Delezenne^ 

 loc. cit.)y and that the interval errors of the Mesotonic system seldom 

 exceed the natural errors of intonation which may be expected from the 

 inability of the ear to appreciate minute distinctions of pitch, it appears 

 desirable to tune harmoniums at least, and perhaps organs, mesotonically. 

 Except as an instrument for practising singers, however (for which purpose 

 it would be superseded by a Mesotonic harmonium), it would be unnecessary 

 to alter the Hemitonic tuning and arrangement of the piano. But it would 

 be best to teach the Mesotonic intonation on the violin in preference to the 

 Hemitonic, as proposed by Spohr*. As, however, it would be useless to 

 tune mesotonically with only 1 2 tones to the octave, it is necessary to have 

 some practical arrangement for 27, 24, or 21 tones at least. I propose the 

 following plan for 24 tones, and as these are exactly twice as many as on 

 pianos, &c. of the usual construction, I call my arrangement the 



* " Unter reiner Intonation wird natiirlich die der gieichschwebenden [Hemi- 

 tonic] Temperatur verstanden^ da es fiir moderne Musik keine andere giebt. Der 

 angehende Geiger braucht aiich nur diese eine zu kennen ; es ist deshalb in dieser 

 Schule von einer ungleichschwebenden [defective equal, or unequal] Temperatiu* 

 eben so wenig die Rede, wie von kleinen und grossen halben Tonen [c c^Si c d\? = 

 B c, that is, :|f = T], well durch beides die Lehre von der voUig gleichen Grosse 

 aller 12 halben Tone nur in Verwirrung gebracht wird."-— Violinschule, p. 3. 



