Tuesday, September 6, 2022

Lesson 1.3.1: Simplifying Exponential Expressions (Day 19)

EXPONENTIAL EXPRESSION

First Verse:
When John's saying 1, Mia's saying 1.
When John's saying 1 times 3, Mia's saying 3 to first.
When John's saying 1 times 3 times 3, Mia's saying 3 to second.
Rule: Multiply powers, add little numbers.

Second Verse:
When John's saying 5 to fourth, Lauren's saying 5 to fourth.
When John's saying 5 to fourth o'er five, Lauren's saying 5 to third.
When John's saying 5 to fourth o'er five o'er five, Lauren's saying 5 to second.
Rule: Divide powers, subtract little numbers.

Third Verse:
When John's saying 2 squared, Lachlan's saying 2 to second.
When John's saying 2 squared squared, Lachlan's saying 2 to fourth.
When John's saying 2 squared cubed, Lachlan's saying 2 to sixth.
Rule: Power of powers, multiply little numbers.

Fourth Verse:
When John's saying 2 squared times 3, Kelly's saying 2 squared times 3.
When John's saying 2 squared times 3 all squared, Kelly's saying 2 fourth 3 squared.
When John's saying 2 squared times 3 all cubed, Kelly's saying 2 sixth 3 cubed.
Rule: Power of product, distribute little numbers.

The names in this song come from the Desmos activity on which this is based. In particular, John and Lachlan are the names of the activity creators. (I don't know where the girls' names come from.)

This is the first song that I'm writing in 10EDL, our main scale for September and October. The first few 10EDL songs will be written in AAAA format, with verses only.

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


10 N=8
20 FOR V=1 TO 4
30 FOR X=1 TO 25
40 READ A,T
50 SOUND 261-N*A,T
60 NEXT X
70 RESTORE
80 NEXT V
90 END
100 DATA 5,4,9,4,5,4,6,4,9,2
110 DATA 8,2,9,8,9,2,7,2,5,2
120 DATA 9,2,7,6,9,6,10,8,9,4
130 DATA 9,4,9,16,10,12,8,2,8,2
140 DATA 8,4,6,4,8,4,8,4,10,16

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

This is also the first song for which I play guitar chords. The 10EDL scale goes C-D-E-F#-A-C, but I was wondering whether we should change F# to G to make a traditional pentatonic scale. Well, for this song I retain the F# note. The F#'s are surrounding by D's, suggesting the D(7) chord in addition to G(7) and C chords. For the eight bars, the chord pattern is C-G7-D7-G7-G7-C-G7-C.

The tricky part is making the lyrics fit the tune here. I consider making each of the first three lines fit the first four bars, and then the last line of each stanza fitting the last four bars. The problem is that there are both short lines ("When John's saying 1, Mia's saying 1") and long lines (such as all the "2 squared times 3" lines), and no single line of music fits both easily.

Thus there is room for improvement in this song. I might consider going back and changing some of the lines in the verses in order to make both mathematical and musical sense.

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