•'Mi' Musical Intonation and Temperament. 



The reasons tor the precise intervals of the Diatonic scale can be 



best understood by examining the effect of hearing two or more 



pitches at the Bame time. These, when agreeable to each other, 



form Harmony. When Do, Mi and Sol, for instance, are heard at 



. their vibrations being as 4, 5, andG, must often coincide thus : — 



Sol 



n ' 



I! sre every other vibration of Do corresponds with one ofSol,and 

 every fourth pulsation of Do corresponds with one both of Sol and of 

 Mi Do is found to harmonize with .Mi 4:5, with Fa 3:4, with 

 So] 2:3, and with La 3:5. Ri harmonizes with Fa 35$: 42$ 



JO : 38 1 :: 5 i 6, with Fan 1 : 5, with La 354 : 53| :: -J : 3, and 

 with Sir 5 : B. Re harmonizes with Sol 3 : 4, and with Si :i : 5. Mi 

 harmonizes with Sol 5:6, with La 3:4, with Si 2 : :?. with Son 

 4:5, and with Do 7i ; •<. Fa harmonizes with La 4:5, with Sir 



. with Do 2:3, and with Re 3:5. Fan harmonizes with La 



. and with Re 5 : 8. Sol harmonizes with Si 4 : 5, with Do 3 : 4, 



with Re 'J : :'., and with Mi 3 : .">. Son harmonizes with Si .". : t;. and 



with Mi 5:8. La harmonizes with Do 5:6, with Re 3: l. with Mi 



'J : :f, with Fan :5 : :>. and with Fa 5:8. Sir harmonizes with Fa 



and with Re 1 : .">. Si harmonizes with Re "> : 6, with Mi 8 ; 1, 



With Sol ">: 8, and with Son :) : •">. 



It is obvious that the corresponding degrees of every other key 

 harm b other in the same way as those of Do. From 



this we see that the precise intervals of the Diatonic scale are not or- 

 bilrary t bu[ exactly such as will secure the greatest amount of harmonv, 



We see here onl) h'\ ratioB of vibration which produce harmony; 



'J:.-< called a Firm (Vth): :< : 1 a |\n urn (IVth)j 3 : 6 a MaJOB 

 Si mm (Vlth); 5:8 a Minob Sixth (nth): 4:5 a Majob Third 

 (Illrd); and ."):i; a Minor Thibd (3d). We need -ono farther 



into the subject of harmony — it constitutes a department of science 

 iratively well cultivated. 



Ill a composition one single train of sounds musl be Midi as to be 



of itself agreeable. This train is called the An;, and its agreeable 

 quality it Melody. The melody of pieces of a certain cast often 

 requires tlie Sharp 4th ami 5th. The harmony of these same pieces 



often contains minor thirds and sixths w here others would have major 



thirds and sixths. Hence the y are said to be in the Mikob Modi:, 



and o;her pieces are laid tO be in the Major Modi:. The Diatonic 



