Music Related to Math
...octave higher, it would double again. Consider the note A. The ratio from A to C would be 4:5. The ratio from A to D would be 3:4. The ratio from A to E would be 2:3. The ratio from A to F would be 3:5. Also to take into consideration is half steps and whole steps. Going from one note to the next is called a half step. This includes the notes without sharps or flats. For example, going from A to A#/Bb is considered one half step. Two half steps equal one whole step. Going from A to B is considered one whole step. When wanting to make length of notes different, one may simply add a dot to a note. By doing this, it adds half of the original value to the note. For example, if one takes a quarter note which is worth one beat, and adds a dot to it, it because one and a half beats creating the ratio 3:2. When taking a half note and adding a dot to it, it becomes two and a half beats again creating the ratio 3:2. Adding a flag to the end of a note divides the value of the original note by two. For example, apply a flag to a quarter note, and it becomes half the length of a quarter note creating the ratio 1:2. Also, time signature resembles a fraction at the beginning of the piece of music. In four-four time (4/4), there are four beats in a measure and each note gets one beat. In two-four time (2/4), there are two beats in a measure and the quarter note gets one beat. As one most likely knows, when music is made, sound is produced. Sound comes in waves just like sine graphs and cosine graphs. A French heat engineer, Fourier, discovered that any sound waves can be written in terms of sine and cosine if the wave is smooth and consis...