506 



Musical Intonation and Temperament. 



the same as from Do to Re. Compounding these, we have the inter- 

 val Mi to Sol, 5 : 6, as before. 



The interval between Sol and Si is still larger, 4 : 5, the same as 

 from Do to Mi. We will put in a sound La, the same as the Re be- 

 tween Do and Mi, making Sol : La :: 8 : 9, and La : Sr:: 9 : 10. La 1 , 

 then, makes 26a. vibrations a second 



We have now established 7 pitches between Do 1 and Do". They 

 are found in capitals in the table of Diatonic Scales. The ratios of 

 vibrations, and the intervals between them, are placed at the bottom. 

 We see there only 3 kinds of intervals, 8 : 9 and 9 : 10, both called a 

 Tone, (which we distinguish by calling one the greater Tone, and 

 the other the lesser Tone,) and 15 : 10, called in barbarous mixture of 

 Greek and Latin, Semitone, but more properly Hemitone. The in- 

 terval from any of these pitches to the next above or below is called 

 a Second ; to the next but one, a Third, &c. ; and to the eighth 

 above or below, an Octave. Thus from Fa 1 to FV is an octave ; 

 from Si' to Re a is a third, &c Every pitch resembles its octaves 

 more than it does any other pitch. Thus Fa" can be readily told 

 from Mi' or Sol', but is in one sense identical with Fa' and Fa'. 

 Hence they all bear the name of Fa. So of all the rest. 



Any series of 8 pitches whatever, having between them the seven 

 intervals, Tomes, Tone, Hemitone, Tone, Tone, Tonh, Hemitone, 

 is called a Diatonic Scale. Any Diatonic Scale beginning and 

 ending with Do, as that in the table, is called the Diatonic Scale 

 of Do ; and music composed of these pitches is said to be in the Key 

 of Do. The first and last note of any Diatonic scale is called Tonic, 

 the second Sufertonic, &c. We give the names at the head, of the 

 table. Four more notes are occasionally wanted in each octave. 

 These are a grave second, a flat seventh, a sharp fourth, and a sharp 

 fifth. They are accordingly added to the table. 



Furnished with these sounds, wo can produce the air of any un- 

 modulated piece of music we choose. Suppose, now, Archdalc were 

 written in the Key of Do, of which we have given the Diatonic 

 scale. It begins on the tonic. The highest note is an octave 

 above, and the lowest a fourth below. If the first sound were Do*, 

 the highest would be Do ; much higher than the female voice can 

 well reach. But if the first note bo taken on Do 4 , the lowest would 

 be Sol' ; too low for a lady's voice. Some other key, as of Sol, 

 must be used. 



