Music

Given the sheet music for a composition (see some choices below), analyze its mathematical structure. What is the key and time signature of the piece? How do those choices affect the piece? How might a change in the key or time signature affect the piece? Does the composer only use scale tones from the given key, or are there accidentals? If there are accidentals, how does their presence affect the tone or sound of the piece? What range of frequencies would be produced by someone playing the piece? What intervals show up frequently (address both by name and by ratio r)? What melodic transformations are used (transposition, retrogression, etc.)? What kind of chords are used most often (triads? I chords, IV chords, etc.? major/minor?) and how does the choice to use those chords frequently contribute to the tone or sound of the piece? If you were the composer, what choices might you make to cause the piece to sound more interesting? More upbeat? More haunting? More unstable-sounding? More (anything else you can think of