the relative pitch of all the keys or fixed tones of any musical instrument, so as 

 to distribute the four wolves which are in the major thirds, and likewise the 

 quint wolf, according to some given systematic proportions. And the object 

 of temperament is to adjust the relative pitch of all the keys or fixed 

 tones in such a due proportion as to render the instrument harmonious and 

 melodious in the highest degree possible. This is an object of very great con- 

 sequence to the musical world. For, the finest keyed instrument, even if it be 

 played upon in the most capital manner, loses, either when out of tune, or when 

 tuned according to an improper temperament, the power of producing those 

 delightful and exquisite sensations which the very same instrument becomes 

 capable of producing when it is tuned scientifically and correctly. 



There are a great number of different modes of temperament, which 

 maybe classed as follows, viz. the equal temperament, and the unequal 

 temperaments. 



That mode of temperament in which the quint wolf is distributed in an equal 

 proportion amongst all the twelve quints of an instrument is that which is called 

 THE EQUAL TEMPERAMENT. And every other mode of temperament, 

 without exception, is called an UNEQUAL TEMPERAMENT. 



In that mode of tuning which is called THE EQUAL TEMPERAMENT, all 

 the twelve quints are made imperfect ; for, every one of them is tuned flatter 

 than perfect. But, in my mode of tuning, for example, which is one of the 

 UNEQUAL temperaments, there are, as will be explained in the sequel, 

 seven quints quite perfect, and five quints flatter than perfect. 



The consequence of an equal distribution of the QUINT WOLF, in the 

 EQUAL temperament, is, that the C wolf will become, of necessity, 

 equally distributed amongst the three major thirds jn the C column ; and that 

 the G, D, and A wolves will become equally distributed amongst the three 

 major thirds in the G, D, and A columns respectively. 



The equal temperament is, however, a mode of tuning which I very 

 much disapprove. According to that erroneous system, there is not a single 

 perfect third, nor a single perfect fourth, nor a single perfect quint, in the whole 

 instrument. That charming and delightful harmony and melody which a proper 

 mode of tuning enables fine players to produce, is thus rendered, in every case, 

 impossible. All those chords, which nature has rendered perfect, are, by this 

 objectionable contrivance, rendered imperfect. And in those instruments where 

 chords are made to sound for a considerable time, such for instance as organs, 

 the imperfection of the equal temperament is most striking. Perfect 

 chords are pleasing to the ear, they strike to the heart, and they are founded in 

 the very nature of musical sounds. But, by that mode of tuning which is called 

 THE equal temperament, all those regular coincidences of those duly 

 proportioned vibrations which produce true concords are destroyed, and every 

 thing is discord. Let us take a quint, as an example explanatory of this fact. 

 We have already seen, that, when the wire in a well constructed inonochord is 



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