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Try the applet!
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Sample submitted solutions:
From: Mark, age 13
School: Issaquah Middle School, Issaquah,
Washington
1. What is the ratio of the mystery
polyrhythm? Explain how you know.
The ratio of the mystery polyrhythm is 3:4.
When I built the same song on the composite
panel, the notes match with the two ratios
at 1:3 and 1:4. To find a ratio of two speeds,
you take the smallest number on the right
side of the ratio and add the bigger number
on that side from the other number. Therefore,
1:3 and 1:4 equal 3:4.
2. Create a polyrhythm of your own using
two of the rhythms in the applet. What is
the ratio of the polyrhythm and its phrase
length? Explain how you know.
My composite rhythm has a ratio of 2:6.(One
bar is 1:2, the other is 1:6). The phrase
length of this rhythm is 6. This is because
you count how many note slots it takes before
the rhythm of sound repeats itself.
3. A complicated polyrhythm has the
ratio 2:3:4:5:6:7. What is its phrase length?
How do you know?
To find the phrase length of this rhythm,
you must find the least common denominator
of all the numbers. Since 5 was one of the
numbers, the number would have to end in
a 5 or 0. Since 7 was the biggest number,
I decided to check by sets of 70's. I went
up till I got to 420, which all the numbers
go into. So the phrase length of that song
is 420.
From: Andy, age 14
School: Issaquah Middle School, Issaquah,
Washington
1. What is the ratio of the mystery
polyrhythm? Explain how you know.
The ratio of the mystery polyrhythm is 3:4.
I found this by positioning the squares
on the beat boxes of the composite polyrhythm
so they coincided with the beat box X's
of the mystery. I them took into account
the number of beats for each polyrhythm
and noticed it took 12 beats in order for
the beats to be simultaneous, or 3 sets
of the 4 original beats. 12 is also the
LCM of the latter numbers in the two combinations
of two(1:3, 1:4), to which we could conclude
produced the phrase length in other cases.
2. Create a polyrythm of your own using
two of the rhythms in the applet. What is
the ratio of the polyrhythm and its phrase
length? Explain how you know.
I made a polyrhythm with the beats 1:3 and
1:5. The result was a polyrhythm that has
a phrase length of 15 and a ratio of 3:5.
The ratio was the smaller of the latter
of the two beat ratios in direct relation
to the other beat. The phrase length was
the least common multiple of the digits
of that ratio
3. A complicated polyrhythm has the
ratio 2:3:4:5:6:7. What is its phrase length?
How do you know?
The phrase length is 420. I found this by
obtaining the least common multiple of the
six digits contained in the ratio.
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