Musical Intonation and Temperament. 511 



Scaio is the same, for both, though much mystery has been thrown on 

 this matter, and needless labor imposed on the student, by the so-called 

 Minor Scale. 



A few physical facts must now be stated before proceeding to the 

 •practical part of this .subject. 



First. — When a musical sound is produced near a siring of a mu- 

 sical instrument, if the sound harmonizes with the one the string will 

 produce, it causes the string to vibrate. Thus Do', Sol 4 , or Mi* will 

 produce vibrations in the Do 1 string ofa Piano Forte. 



Second. — When two strings, or two tubes, almost in harmony, 

 are near each other, they may influence each other's vibrations and 

 harmonize completely. 



Third. — When a string vibrates as a whole, and produces its 

 note, parts of the same string vibrate by themselves, and produce 

 higher pitches of sound. Thus, a string sounding Do*, may also pro- 

 duce Do', Sol", Do", Ali°, or Sol , or several or all of these, and per- 

 haps more. These secondary sounds are called Harmonics. Seve- 

 ral musical theories have been based on this fact — an unsafe founda- 

 tion, as some harmonics have no musical relation to any scale. Thus 

 a Do* string may give a harmonic of 890 vibrations between Sir' and 

 Sir". Tubes, as Trumpets and French Horns, &c, also give har- 

 monics — as also Bells, and, in fine, all musical instruments. The 

 lowest note of the tube, bell, or string, is called the Fundamental. 



Fourth. — When two pitches which are harmonics to the snmo 

 Fundamental are sounded together, the Fundamental itself may also 

 be heard. Thus, when Do", making 2">G vibrations, is sung with 

 Sol", making 38. r >, their pulsations coincide 12S times, and give the 

 impression of Do*, although it is not sounded. This fact, too, has 

 served as basis to ill-founded theories. 



These, things being thoroughly understood, we are prepared to 

 proceed to the practical application of them to our main problem. 

 This is to produce the tones indicated in musical compositions, which 

 is called Intonation ; or others near enough to them to answer in 

 their place, which is Temperament. 



Musical Instruments are divided into two classes. Perfect In- 

 strum hnts are those capable of producing pitches indefinitely near 

 each other, at the. will of the performer; as the Violin, the Trombone, 

 and the Human Voice. Imi'i-rekct Instruments can produce only 

 the fixed tones for which they are tuned. 



Of all perfect instruments invented by man, the Viol is by far the 



