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Costume 1 · musicWed 16 September1 / 4
Chords and string length
This week's common denominators, turned into sound
NameDate
Think about this
Stop a guitar string exactly halfway and you hear the same note an octave higher, because the length became 1⁄2.
So what happens if you make the length 2⁄3 instead?
1Write down what you think.
Stop the string at a different point and the note changes. The notes that sound good together are the ones whose lengths make simple fractions. Pythagoras found this 2,500 years ago, and this week's common denominators fall straight out of it.
Costume 1 · musicWed 16 September2 / 4
Chords and string length
NameDate
Now you — the string is 60 cm, and that note is C
2How long must the string be to sound C one octave higher?
3How long for G? (the length is 2⁄3)
4How long for F? (the length is 3⁄4)
5Which string is shorter, G or F? Compare using a common denominator.
2⁄3 and 3⁄4 cannot be compared as they stand.
Costume 1 · musicWed 16 September3 / 4
Chords and string length
NameDate
6A shorter string gives a higher note. Which is higher, G or F?
7On a 90 cm string, what length gives G?
8Explain in words why 2⁄3 and 3⁄4 cannot be compared as they are.
Put them in order
9E has length 4⁄5. On the 60 cm string, how long is that?
Costume 1 · musicWed 16 September4 / 4
Chords and string length
NameDate
10Put 2⁄3 (G), 3⁄4 (F) and 4⁄5 (E) in order, longest first.
Put them over 60 and the answer is the lengths in cm.
11Are the three you just ordered going from high notes to low, or low to high?
12Length 1⁄2 was C an octave up and 2⁄3 was G. What note is length 1⁄3 ?
1⁄3 is 2⁄3 of 1⁄2.
Extra · you may skip this
A 40 cm string sounded G. Halve it to 20 cm — what note do you get?
kids/learn — weekly worksheet. The answers have a page of their own.