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)?
Answer these questions in whatever order you like (along with any other
commentary you might find interesting) in a typed essay of at least 3 pages
(that is, at least two full pages and at least half of a third page). If you
have the ability to process math symbols (say, using LaTeX or Lyx) into a
typed format, that would be preferred, but if not, any equations you feel
are important to include may be handwritten if they are clear and legible.
If you use any sources other than the textbook, your classroom notes, and
the sheet music of the piece in question, you must cite it properly in some
format. MLA, APA, AMA, etc. is irrelevant to me. Some of these pieces
contain notation we have not covered in class. Feel free to ignore such notation
in your analysis, unless you have a particular desire to address it. Your
choices (the sheet music to which you can find under files on Canvas):
1) Invention 3, BVW 774, Johann Sebastian Bach
2) Original Rags, Scott Joplin
3) I Cannot Sing the Old Songs, Claribel
4) Lied Ohne Worte – Opus 53 No. 5 – Volkslied, Felix Mendelssohn
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