MUSIC THEORY FUNDAMENTALS - Chapter 2, Exercise 3 Solution
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How Many Sixteenth Notes Equal One Whole Note

PROBLEM
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How many sixteenth notes does it take to equal the duration of one whole
note? Show your reasoning using the real proportional relationships from
this chapter's own note-value table.

SOLUTION
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This chapter's own note-value table gives a sixteenth note's real
proportional duration as 1/16 of a whole note. To find how many
sixteenth notes fit into one whole note, take the reciprocal of that
fraction:

    number of sixteenth notes = 1 / (1/16) = 16

Alternatively, working step by step through the binary halving:

    1 whole note   = 2 half notes
    1 half note    = 2 quarter notes  ->  1 whole note = 4 quarter notes
    1 quarter note = 2 eighth notes   ->  1 whole note = 8 eighth notes
    1 eighth note  = 2 sixteenth notes -> 1 whole note = 16 sixteenth notes

ANSWER: It takes exactly 16 sixteenth notes to equal the duration of one
whole note.

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WHY THIS WORKS AS AN ANSWER

Both methods agree because they're really the same real, strict binary
relationship viewed two ways: the note-value table's own fractions (1,
1/2, 1/4, 1/8, 1/16) directly state each note's share of a whole note,
while the step-by-step doubling shows how those fractions actually
accumulate - each successive value in the system exactly doubles the
number of notes needed to fill the same duration, since each step is a
division by exactly 2.