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- Musical Instruments
- Instrument Groups are: String, Keyboard, Woodwind, Brass and
Percussion instruments
- All instruments have primary resonators and secondary resonators
and often resonating cavities.
- What determines the sounds of the different instrument groups?
- String vibrations, Pipes
- The speed of sound is constant, so the wavelength is inversely
proportional to the frequency:
- If a string that sounds a certain note is shortened by 1/2, then an
octave higher will be heard
- If a string is shortened to 2/3 of its length, then a fifth
higher will be heard
- If a string is shortened to 1/3 of its length, then a octave
above the fifth will be heard
- A shortened pipe will behave in a similar manner; if shortened
(usually by opening a hole)
by 2/3 of its length, a fifth higher will be heard.
- Harmonics
- A string can vibrate in any of the usual standing wave patterns
where 2L = n and n can be 1, or 2, or 3, etc.
- The harmonics are heard from the number of different ways that a
string can vibrate
The lowest harmonic is the fundamental, where one-half wavelength
stretches across the string length L
- The second harmonics fits one full wavelength across L; each half of
L vibrates independently, as if L were split into two parts.
The second harmonics sounds one octave
higher, just like the string that was shortened by 1/2
- Music Intervals
- The higher the pitch, the larger the frequency
- The frequency change across one octave is a factor of 2
- The frequency change from the fundamental to the fifth is a factor of 3/2
- The frequency change from the fundamental to the third is a factor of 5/4
- A major chord is a fundamental, third, and fifth sounded simultaneously
- The musical keys
- We can use the piano key called middle C as a reference note; it
has a frequency of 261.6 Hz
- The note 'A' above middle C is known as concert A; it has a
frequency of exactly 440.0 Hz (North America).
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