Music is transmitted by sound, and sound is the result of the vibration of air (Benson, 2007). Take a wind instrument for example. When a player blows the wind instrument, the force first compresses the air molecules inside the instrument, which in turn causes the air outside of the instrument to vibrate. The form of vibration can be described mathematically by sine waves. When the energy that has traveled through the medium of air finally reaches the ear, the brain interprets it as sound (Bash the Trash, 2013).
We have said the mathematical representation of sound is sine wave. Let us look at the basic attributes of a sine wave.
A sine wave is periodic. The wavelength (λ) or period (T) is the distance or time from crest to crest or trough to trough. The number of times a sine wave repeats itself per second or per meter is frequency (f) = 1/T or 1/λ. The amplitude is the magnitude from the peak to the trough divided by 2. If we multiply λ with f, we get the speed of a wave. At room temperature, a sound wave travels at about 343 m/s (Giordano, 2010).
Here are music notes standard A (A4) and middle C (C4) and their respective waveforms (Austin, 1991).
Here are music notes standard A (A4) and middle C (C4) and their respective waveforms (Austin, 1991).
Fig.3 Pure wave forms form notes A4 and C4
We can see, standard A has a frequency of 440 Herz, and the frequency of middle C is 264 Hertz. The note one octave down from standard A has a frequency of 220 Hertz; whereas the note one octave above has a frequency of 880 Hertz (Rogers, 2004). All the other notes fall between the two octaves with their own corresponding frequencies. The full musical scale with its corresponding frequencies is given by (Elliott, 2006).