Music and mathematics – if you happen to be involved in both of them, and there’s a high chance that anyone reading this has a background in both – then you sure have at least once heard of this pair. While neither originates from nor is a requirement for understanding the other, researching into the relationship between them has given quite some interesting results. However, today I will limit my discussion to a very basic overview of the frequencies of the notes you often hear.
- Why is frequency important?
As you all know, piano emits sounds when being played. Being a wave, sound has two properties: frequency and amplitude. The frequency affects the pitch of the sound, and the amplitude affects the volume. In the figure below we see the amplitude and wavelength of a typical sound wave, and the frequency value would equal the inversion of the wavelength value:
There are many different notes, or pitches, and each of them comes with a different frequency. These frequencies, however, are strict, and it is important that the musical instrument follow it exactly in order to produce the sound needed. Therefore, knowing the frequency can greatly assist in tuning the instruments to its correct pitch.
- Frequency for Piano:
The modern piano people often see is based on the twelve-tone equal temperament system, containing the notes C, D♭, D, E♭, E, F, G♭, G, A♭, A, B♭, and B in that exact order, after which we will return back to C but one octave higher. This follows the octave rule, in which for every octave risen up, even though the note is the same, the frequency will be doubled, thus making it higher-pitched. Moreover, since the distance between the notes are geometrically (not arithmetically) equal, the frequency of each note will be a twelfth root of two higher than the previous note.
Crash on Maths 