=344. Overtones.=--The _quality_ of the tone produced by a vibrating string is affected by its vibration in parts when it is also vibrating as a whole. (See Fig. 336.) The tones produced by the vibration in parts are called _overtones_ or _partial_ tones. The presence of these overtones may often be detected by the sympathetic vibration of other wires near-by. What is called the _first_ overtone is produced by a string vibrating in _two_ parts, the _second_ overtone by a string vibrating in _three parts_, the _third_ overtone by its vibration in _four_ parts and so on. In any overtone, the number of the parts or vibrating segments of the string is one more than the number of the overtone. For example, gently press down the key of middle C of a piano. This will leave the string free to vibrate. Now strongly strike the C an octave lower and then remove the finger from this key. The middle C string will be heard giving its tone. In like manner try E¹ and G¹, with C. This experiment shows that the sound of the C string contains these tones as overtones. It also illustrates sympathetic vibration. Important Topics 1. Interference, beats, production, effects. 2. Vibration of strings, three laws. 3. Three classes of musical instruments. 4. Fundamental and overtones, nodes, segments, how produced? Results. Exercises 1. What different means are employed to produce variation of the pitch of piano strings? For violin strings? 2. How many beats per second will be produced by two tuning forks having 512 and 509 vibrations per second respectively? 3. A wire 180 cm. long produces middle C. Show by a diagram, using numbers, where a bridge would have to be placed to cause the string to emit each tone of the major scale. 4. How can a violinist play a tune on a single string? 5. What are the frequencies of the first 5 overtones of a string whose fundamental gives 256 vibrations per second? 6. One person takes 112 steps a minute and another 116. How many times a minute will the two walkers be in step? How many times a minute will one be advancing the left foot just when the other advances the right? 7. Why is it necessary to have a standard pitch? 8. How can the pitch of the sounds given by a phonograph be lowered? 9. How many beats per second will occur when two tuning forks having frequencies of 512 and 515 respectively, are sounded together? 10. Which wires of a piano give the highest pitch? Why? (6) TONE QUALITY, VIBRATING AIR COLUMNS, PLATES