id: 06618962
dt: j
an: 2016e.00964
au: Ludwick, Kurt
ti: Counting melodies: recursion through music for a liberal arts audience.
so: PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 26, No. 4, 325-333
(2016).
py: 2016
pu: Taylor \& Francis, Philadelphia, PA
la: EN
cc: M85 K25 N75
ut: counting; Fibonacci sequence; liberal arts mathematics; mathematics and
arts; music and mathematics; recursion
ci:
li: doi:10.1080/10511970.2015.1122689
ab: Summary: In the study of music from a mathematical perspective, several
types of counting problems naturally arise. For example, how many
different rhythms of a specified length (in beats) can be written if we
restrict ourselves to only quarter notes (one beat) and half notes (two
beats)? What if we allow whole notes, dotted half notes, etc.? Or, what
if we allow each note to be selected from some specified set of tones
(e.g., C, C$\sharp$, D, etc.)? In my course on music and mathematics
for the liberal arts, I use these questions as a method of introducing
students to the concept of recursion, as it turns out that such
questions lead naturally to sequences (indexed based on the length of
the rhythms or melodies being considered) defined by recurrence
relations, such as the Fibonacci sequence.
rv: