All sounds, including music, that we hear are actually vibrations in the air that propagate through as a wave. This wave can be represented as a signal transmitted to the ear over time. Through Fourier analysis, this signal can be represented as a sum of different frequency waves each weighted with its own "strength". These different frequencies cause one noise to sound "higher" or "lower" than another. In fact, the pitch of a noise, or how high or low it sounds, is determined entirely by its frequencies and their strengths.
Every musical note is a noise that is concentrated at a particular frequency. In typical musical formats, all musical notes are divided up into octaves, or repeating sets of notes that sound like a higher or lower version of the octaves around it. Each octave contains 12 different notes denoted C, C#, D, D#, E, F, F#, G, G#, A, A#, and B, in increasing order. The notes denoted with a sharp (#) symbol are so denoted because they are slightly higher than the note sharing the same letter. However, the same set of notes can be denoted using flats (b). This indicates that a note is slightly lower than the note that shares the same letter. Thus F# and Gb are the same note, and because they sound the same, they are indistinguishable by sound alone. These notes will be denoted as F#/Gb for the rest of this project. On a piano, the white keys are the unaltered letter notes, while the black keys are the notes with sharps or flats. Finally, every note has a number on the end denoting which octave it is in, with higher numbers meaning higher pitch. For example, middle C is C4.
Mathematically, the frequency of each note is exactly
Every song has a tempo, or a speed at which the music is to be played. Tempo is defined as beats per minute, where a beat is usually defined to be a particular length of note. All notes lengths are then given a value, such as a quarter or a half. This value determines how many beats that note should last. Interestingly enough, a beat is usually defined to be one quarter note, and thus a quarter note is 1 beat, a half note is 2 beats, and an eighth note is half a beat. Additionally, a dot can be added to a note to add half its length to it. So a dotted quarter note is 1.5 beats, a dotted eighth note is .75 beats, and a dotted half note is 3 beats.






