Frequency
Sound is created through air pressure waves--concentric circular regions emanating from the sound-creating object of high pressure and low pressure. In music, the frequency of a sound is equal to the frequency of the sine wave that represents the same pitch, where the frequency of the sine wave is measured in the number of times per second the object emanating it generates high pressure. Notes with high frequency sound high, and notes with low frequency sound low. Middle C, roughly in the center of the piano, has a frequency of about 255 Hertz (abbreviated Hz), or oscillations per second, while human hearing range is from about 20 to 20,000 Hz.
If an instrument generates a single note, when pressure at a given point near the instrument is graphed, the resulting graph[1] is a sum of sine waves of various levels of frequency and amplitude. The frequency of the lowest sine wave is generally perceived as the frequency of a sound, even if this sine wave does not have the largest amplitude. The entire list of frequencies is called the frequency spectrum. Frequency is different from pitch, because multiplications in frequency translate to additions in pitch; successive octaves are equally spaced in pitch, but exponentially increasing in frequency.
Intervals
When two notes have frequencies a:b where b/a is rational, the interval between the two notes is within Just intonation and denoted b/a. If the two notes have frequency spectra where all non-negligible frequencies are multiples of the lowest frequency (as is the case with most methods of sound production, including the human voice, most instruments, and square/saw/triangle waves) the two notes will sound concordant when played at once.
- ↑ By taking the Fourier transform.