Wednesday, October 5, 2022

Lesson 2.1.3: Slope (Days 39-42)

GROWTH SLOPE

First Verse:
Nine minus three is six. Growth!
Three minus zero's three. Growth!
Six over three is two. Growth!
That's how you find the growth!

Pre-Chorus:
Find the change in y. Slope!
Find the change in x. Slope!
y change o'er x change. Slope!
That's how you find the slope!

Chorus:
Almost all lines have growth,
Almost all lines have slope.
Once you have found the growth,
Then you have found the slope.

Second Verse:
Three minus zero's three. Growth!
Six minus zero's six. Growth!
Three over six, one half. Growth!
That's how you find the growth!
(to Pre-Chorus)

This is the eighth song that I'm writing in 10EDL, our main scale for September and October. The next few 10EDL songs will be written in ABC format, with verses, a pre-chorus, and a chorus.

This song is influenced by another Desmos lesson, where students are asked to find the "growth" of a linear graph, just as they can from a tile pattern or table. Of course, "growth" in this lesson is just a euphemism for "slope." Interestingly enough, the students find this growth using "slope triangles," as opposed to "growth triangles." (Oh, and I also used "delta" for change -- the Greek letter appears in this CPM lesson, but not in this Desmos lesson.)

Here's a link to the Mocha code for the song:


10 N=8
20 FOR V=1 TO 76
30 FOR X=1 TO 2
40 READ A,T
50 SOUND 261-N*A,T
60 NEXT V
70 RESTORE
80 NEXT X
90 END
100 DATA 7,2,9,2,9,2,7,2,7,4,10,4,9,16
110 DATA 7,2,9,2,9,2,7,2,7,4,10,4,9,16
120 DATA 7,2,9,2,9,2,7,2,7,4,10,4,9,16
130 DATA 7,2,9,2,9,2,7,2,7,4,10,4,9,16
140 DATA 5,4,5,2,7,2,6,4,5,4,7,16
150 DATA 5,4,5,2,7,2,6,4,5,4,7,16
160 DATA 5,4,5,2,7,2,6,4,5,4,7,16
170 DATA 5,4,5,2,7,2,6,4,5,4,7,16
180 DATA 9,6,10,6,10,4,7,2,9,2,9,12
190 DATA 9,6,10,6,10,4,7,2,9,2,9,12
200 DATA 9,6,10,6,10,4,7,2,9,2,9,12
210 DATA 9,6,10,6,10,4,7,2,9,2,9,12

Don't forget to click Sound before you RUN the program.

This is the most complex 10EDL song yet, with no short lines in the chorus or any other part. At this point, I start to wonder whether there's an easy way to make Mocha repeat each line four times without having to type in the corresponding DATA line that many times. (Perhaps we might dispense with DATA and use GOSUB subroutines, but each subroutine would still be long.)

As for the guitar riffs, I use D7-G7 in the verse, C-D7 in the pre-chorus, and C-G7 in the chorus. Since there is no G in 10EDL, I've been avoiding the G7 chord (even though the tonic is C). The only 10EDL note that fits in the G7 chord is D, so I play it over the long D notes, including the dotted half note at the end of the chorus melody, D-(low)C-C-F#-D-D.

This is the second of two Chapter 2 lessons to be given before the Chapter 1 DeltaMath Test.

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