51G Musical Intonation and TcmpcramcAt. 



that it is more difficult than the old way. Experience alone can an- 

 swer tliis objection, and the results will a little surprise those who, 

 knowing it to be better, expect to find it also slower than the old modes. 



But some of our best teachers are firmly of the opinion that any 

 system of names used in singing will prove a serious impediment to 

 vocalization, and compel the singer who has once used it to apply 

 names in every difficult place, before he can apply the words. This 

 »s a necessary consequence of names transposed with the change of 

 key, and it is barely possible that the inconvenience might result 

 from a rigid perseverance in the use of fixed names long after the oc- 

 casion for them had passed, but their moderate use by beginners, 

 like spelling words to learn to pronounce them, or beating in order 

 to keeping time, will prove a great aid at first, and, if duly discon- 

 tinued, of not the least inconvenience afterwards. 



The other perfect instruments need no further notice. We pass 

 to imperfect instruments, and first to Keyed Instruments, as the Organ 

 and Piano Forte. These instruments almost universally have 12 

 fixed sounds in each octave. These sounds supply imperfectly the 

 various pitches of all the scales in which we play. The difference 

 between the true pitch and that used lor it is Temperament. To 

 examine this subject, we will Buppose the 12 intervals to be exactly 

 equal. This is called EauAL Temperament. To divide the oc- 

 tave into 12 equal intervals, we must find a ratio which multiplied 12 

 tines into itself, will produce the ratio of 1:2. This ratio is' 

 'V': 'V2, or 1 : 'V-'. To extract the 12th root of 2, we begin 

 by extracting its square root. This, we know, cannot be expressed 

 in figures, and of the 12th root is equally incommensurable. If two 

 Strings, ,'. of an octave apart, vibrated once together at the Creation, 

 their vibrations would not again coincide till the Resurrection Morn ! 

 The problem, however, like squaring the circle, can be solved near 

 enough for all practical purposes, and the vibrations will be 

 1:1.059463. To Bee how these intervals will lit our purpose, we 

 will call the lowesl of 12 pitches I>o, the second Don and Rer, the 

 third Re, dec. When we first look at the 62 sounds in the IS scales 

 we have given, we are ready to despair of any accommodation ofthem 



to I 'J fixed pitches, bul we know, as the intervals of every scale are 



exactly similar, that an instrument of equal temperament will lit one 

 kej ai well as another, since it matters not with which ofthe twelve 

 Bounds you begin. By comparing the scale of the key of Do with the 



