Background

Most people can hum a variety of melodies, from tunes learned in childhood, such as “Mary Had a Little Lamb,” to Christmas songs to famous classical melodies, such as Beethoven’s Ode to Joy, to the melody of the current hot songs on the Top 40. Women and men often sing these melodies at different pitches. Well, it turns out that to change a melody from one octave to the next you have to double all of the frequencies of the tone. Thus, since changing from one octave to the next means doubling frequencies the distance between any two notes in the higher octave is twice as far in frequency than the lower frequency, even though the pitch change is the same in each case.

Go to the next tab. You can play either the melody from Beethoven's Ode to Joy or Mary had a little lamb. You can play both tunes at a moderate octave or shift the melody up an octave, with the 'Ratio: Double' button or shift all the notes up a the same amount in frequency ('Add 246.94' button). This latter shift doubles the frequency of the first tone, but adds just the same frequency change to all other tones. Which change preserves the melody?