Line Art Project (Day 58)

Y EQUALS MX + B

1st Verse:

First! b's y-intercept,

That's the number without x.

On y, positive is up,

Negative is down, you're the best!

Chorus:

It's y equals mx + b. (Hook)

Linear? Yes! Equation? Yes!

It's y equals mx + b. (Hook)

Graphing lines easy, you'll see!

2nd Verse:

Next! m is just the slope.

That's the number with the x.

Rightward, positive goes up.

Negative goes down, you're the best!

(to Chorus)

This is the first song that I'm writing in 12EDL, our main scale for November and December. But there are several things I want to say about the new song and the new scale.

First of all, it's one of the songs that I wrote over the summer (and this was on the Stats blog) in anticipation of a Math 8 course at a charter school (where I obviously ended up not teaching). But once again, there is much overlap between Math 8 and Integrated Math I, so some of those will fit here. In that summer post, I labeled it as a "Song for November," which is why I wrote it in 12EDL as opposed to another EDL scale.

It was no sure thing that I'd still be in Chapter 2 in November. The official pacing guide has Chapter 2 ending last week and Chapter 3 starting this week. But some of the other Math I teachers have agreed to give a Chapter 2 Test either this week or next week. Thus the chapter material does indeed extend into November, which makes this song and its scale fit my plans.

As for the song itself, I wrote a tune for it in that same summer post. But this was back before I was thinking in terms of chords and riffs for our songs -- and I hadn't figured out how to chord 12EDL songs in the first place. Thus the Mocha code is a bit more complex than our ABAB songs for 10EDL (and it also contains sixteenth notes that I no longer include in my TI Mocha code generator):

https://www.haplessgenius.com/mocha/

10 N=8
20 FOR V=1 TO 2
30 FOR X=1 TO 59
40 READ A,T
50 SOUND 261-N*A,T*2
60 NEXT X
70 RESTORE

80 NEXT V

90 END

100 DATA 12,8,6,2,9,2,8,1

110 DATA 8,2,12,1,8,2,11,1

120 DATA 12,1,7,1,7,2,8,1

130 DATA 9,8,12,4,6,4,9,2

140 DATA 12,1,8,1,9,2,9,2

150 DATA 8,2,11,1,11,1,10,3

160 DATA 6,1,10,4,9,1,8,3

170 DATA 11,1,7,3,8,3,11,1

180 DATA 10,4,12,1,11,1,7,2

190 DATA 12,2,9,1,8,1,9,4

200 DATA 10,1,7,2,7,1,10,4

210 DATA 11,1,7,3,8,3,11,1

220 DATA 10,4,12,1,11,1,7,2

230 DATA 11,2,12,2,6,2,7,1

240 DATA 6,1,10,4,12,4 

As usual, click on Sound before you RUN the program.

While the 10EDL resembles a C major scale, 12EDL sounds more like A minor. But while we move from 10EDL into 12EDL, we must consider the new note at Degree 11 -- a note which lies about midway between Concert Bb and Concert B. When discussing 12EDL in previous posts, I've referred to this note as B in some posts and Bb in others. But now I must decide which note to play, now that I'm starting to perform 12EDL songs.

One possibility is to play it as B if it's followed by a higher note and Bb if followed by a lower note (which would usually be Degree 12, the low A). In some ways, this reminds us of "melodic minor" in the standard scale -- for example, C melodic minor has A and B natural when rising, but Bb and Ab when falling. Then again, note that A melodic minor uses B only, not Bb -- and remember that this is supposed to be an Am scale, not a Cm scale.

Another idea might be to notate Degree 11 as B -- but then leave it open whether this means the American B note or the German B, which is an American Bb. (The American B is German H.)

Most often for 12EDL, I'll interpret Degree 11 as B, since that's what we expect in an Am scale. Later on, we might see 15EDL scales based on F major -- then it's convenient to count Degree 11 as Bb.

And that takes us to possible chords for 12EDL songs. The scale goes A-B(b)-C-D-E-F#-A, so the root chord Am is fully represented in this scale. While the usual dominant chord for A minor -- namely E7 -- isn't completely part of this scale, at least the E is included. So I can still play E(7) on the guitar for many 12EDL songs (whereas G7 didn't work in most of our 10EDL songs).

In this song, since the sequence B-F# appears twice in the chorus line (the hook), I couldn't resist playing the double dominant chord B7 here, even though the B here is Degree 11, not a true B (and so B-F# is an 11/7 interval, not a perfect fifth). I'd have to rethink this if I ever had an instrument that played true EDL scales.

Thus the resulting riffs become Am-E7 in the verse and B7-E7-Am in the chorus. I decided to keep this Mocha code the way I originally wrote it over the summer, but as I play it more for the other class tomorrow, I'm likely to repeat riffs and smooth out the sixteenth notes, just as I did for the first few 10EDL songs that I wrote.

By the way, the title of this post refers to another Desmos activity in Math I -- the students write equations to generate art (including the logo of a fictitious company) in Desmos.

Meanwhile, Math III students are taking their District Benchmark Test today. I didn't want to sing the lyrics to today's song or have them posted on the wall during the test, and so I perform a different song in fifth period Math III. So instead, for them I return to Square One TV and play "One Billion Is Big":

ONE BILLION IS BIG

1st Verse:

Have you seen the headline? We did OK,

We sold a million records in just one day.

That's a thousand times a thousand sold,

That's plenty of vinyl, a million whole.

A million dollar bills reach for the sky,

Stack 'em about three hundred feet high.

A billion dollars is a thousand times more,

A lot more money than we bargained for.

Chorus:

One million is big,

One billion is bigger.

One thousand times one million,

That's one billion.

2nd Verse:

We're getting kinda hungry for our favorite food,

Hey, what do ya say? Are you in the mood?

Let's satisfy our special taste,

And get some lunch at the burger place.

See that sign? "One billion served!"

Beat box, that's a lot of hamburgers.

One thousand times, when ya order fries,

A million times one thousand apple pies.

(to Chorus)

3rd Verse:

If we multiply one million by ten, How close are we to one billion then?

If we take a look, we will see, We got a way to go, my friend Markie Dee.

If we multiply by one hundred this time, Let's take a look, and we will find,

That we're not even halfway there, We need a lot more to be a billionaire.

If we order one billion cheeseburgers, And eat one million cheeseburgers,

It would be enough to knock us off our feet,

'Cause we'd still have almost one billion burgers to eat.

One million's not even one percent of one billion. Wow!

(to Chorus)

Once again, I choose this song in honor of the Powerball jackpot reaching a billion dollars yesterday and surpassing it tomorrow. But I also performed it back at the old charter school around this time of year, and for the same reason as today -- during Benchmark Testing week, I wanted a song that was related to math, yet not directly related to the content of the Benchmarks.