Texas Mathematics Teacher Spring/Summer 2022 - 23

On the Cover: Find the Mathematics... in Musical Instruments!
Continued from page 16
Pre-K to 2nd Grade
Instruments that make sounds by . . .
. . . strings being plucked or pulled: cello, guitar
. . . air being blown over or through them: flute,
saxophone, tuba
. . . being tapped or hit: drum, piano, triangle
You can make sound with a guitar by plucking the strings
or tapping on the body of the guitar. You can make sound
with a piano by tapping the keys which taps the strings,
but you can also reach inside and pluck the strings.
There are many other instruments that fit into these
categories! Check with a friendly music teacher for more
ideas.
The guitarrón and sitar are string instruments.
The bawu and shofar are wind instruments.
The djembe and mbira are percussion instruments
Bawu:
https://www.youtube.com/watch?v=Im6JQ_aQk_s
Djembe:
https://www.youtube.com/watch?v=FMs3LTtgwY8
Guitarrón:
https://www.youtube.com/watch?v=SQ6Ot3twpSU
Mbira:
https://www.youtube.com/watch?v=HA0y_oZO7Dc
Shofar:
https://www.youtube.com/watch?v=n5FcH5hKGqs
Sitar:
https://www.youtube.com/watch?v=tTbY_EeC9Wg
3rd to 5th Grade
The 6th key is C. You can count six notes beginning with
E: E, F, G, A, B, C.
The 45th key is G. Counting up is not the most efficient
method, but it works. There are 7 notes from A to G, and
there are 6 groups of 7 in 45 with 3 remaining. Because
6 x 7 = 42, the 43rd key will be E, the 44th F, and the 45th
will be G.
Seven of the 45 keys will play C. Eight of the keys will
play an F.
There are 7 full octaves on a standard piano. Using all the
keys, there are 7 groups of 12 in 88; using the white keys,
there are 7 groups of 7 in 52; using the black keys, there
are 7 groups of 5 in 36.
The highest note on a standard piano is C. The 7 octaves
will use 84 keys. The 85th key will be A. The 86th key is
a black key - the last black key - that is known as both
A-sharp or B-flat. The 87th and 88th keys are both white,
and therefore the 88th key is C.
www.tctmonline.org
From the table, I would estimate the distance that would
give a frequency of 150 Hertz to be about 20 cm, because
150 is about halfway between 155 and 146, the distances
that correspond to those frequencies are 15 and 25 cm, and
20 is halfway between 15 and 25. Using the line of best fit
equation, I get an estimate of 23.8 cm.
It doesn't make sense to extrapolate based on this data
because the slide can't be extended less than 0 cm, and the
slide would come off the trombone if it were extended a
little further than 59.5 cm.
Spring/Summer 2022 | 23
6th to 8th Grade
Let's denote a valve is pressed by the letter P, and not
pressed by the letter N. There is 1 way to press all 3 valves
(PPP), 3 ways to press exactly 2 valves (PPN, PNP, NPP),
3 ways to press exactly 1 valve (PNN, NPN, NNP), and
1 way to press 0 valves (NNN). There are 8 total ways to
press the 3 valves of a French horn. This comes from
1 + 3 + 3 + 1, and also from 2×2×2, because every valve has
2 possible positions.
For a tuba, there is 1 way to press 4 valves (PPPP), 4 ways
to press exactly 3 valves (PPPN, PPNP, PNPP, NPPP),
6 ways to press exactly 2 valves (PPNN, PNPN, PNNP,
NPPN, NPNP, NNPP), 4 ways to press exactly 1 valve
(PNNN, NPNN, NNPN, NNNP), and 1 way to press
0 valves (NNNN). There are a total of 16 ways to press the
4 valves of a tuba. Notice that 1 + 4 + 6 + 4 + 1 and 2×2×2×2
both equal 16.
You may notice a connection to Pascal's triangle and the
binomial theorem with the above problems. For a recorder
with 8 holes, there are 256 ways to cover the holes. There
is 1 way to cover all 8, 8 ways to cover exactly 7, and so on.
9th to 12th Grade
For the trombone, the relationship between the distance
and the frequency of the sound appears to be linear. The
correlation is negative, because an increase in the distance
leads to a decrease in the frequency. The correlation is
strong, because the r-squared value is very close to 1, and
also because the points are very close to a straight line.
https://www.youtube.com/watch?v=Im6JQ_aQk_s https://www.youtube.com/watch?v=FMs3LTtgwY8 https://www.youtube.com/watch?v=SQ6Ot3twpSU https://www.youtube.com/watch?v=HA0y_oZO7Dc https://www.youtube.com/watch?v=n5FcH5hKGqs https://www.youtube.com/watch?v=tTbY_EeC9Wg https://www.tctmonline.org/

Texas Mathematics Teacher Spring/Summer 2022

Table of Contents for the Digital Edition of Texas Mathematics Teacher Spring/Summer 2022

Texas Mathematics Teacher Spring/Summer 2022 - 1
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Texas Mathematics Teacher Spring/Summer 2022 - 36
http://www.brightcopy.net/allen/txmt/68-01
http://www.brightcopy.net/allen/txmt/67-01
http://www.brightcopy.net/allen/txmt/66-02
http://www.brightcopy.net/allen/txmt/66-01
http://www.brightcopy.net/allen/txmt/65-02
http://www.brightcopy.net/allen/txmt/65-01
http://www.brightcopy.net/allen/txmt/64-02
https://www.nxtbook.com/allen/txmt/64-1
https://www.nxtbookmedia.com