Last year on Mole Day, I wrote about the old charter school from the previous year, and how I'd blown an opportunity to teach science on Mole Day that year. But this year I already have plans for today -- intelligence, music, and rainbows. None of this has anything to do with chemistry. Again, if you wish to read about how to teach chemistry on Mole Day, please refer to last year's post.
Let's start with Sue Teele's text. Then we'll move on to music, and I'll introduce the original Mocha song that I played while subbing yesterday.
Chapter 5 of Sue Teele's Rainbows of Intelligence is called "Rainbows of Intelligence Model." It begins as follows:
"The rainbows of intelligence model has been created to build upon multiple intelligences and to address the complex pathways that enable individuals to process information."
In today's chapter, Teele begins with the science of rainbows. So I guess I'll be writing about science today after all, though not chemistry or moles. Let's define "rainbow" or "spectrum":
"A spectrum contains the seven distinct colors we can see, red, orange, yellow, green, blue, indigo, and violet, as well as other kinds of light, including ultraviolet and infrared, which we cannot see."
Teele highlights the following statement:
"A rainbow is produced by sunlight passing through a collection of raindrops that spread the sunlight out into a spectrum of colors."
And believe it or not:
"Every rainbow is a full circle, but is seen as a bow or arc."
According to the author, white light is an optical illusion:
"Sunlight appears colorless and is commonly called white light. However, it really comprises a mixture of different colors."
It takes a prism to separate this colors -- and as it turns out, raindrops serve as a prism:
"When a light ray enters or leaves a raindrop, it changes direction and the change is different for each color."
By the way, let's sneak a little Geometry into this conversation:
"A rainbow cannot be seen when the altitude of the sun is greater than 42 degrees because no part of it is above the horizon. A typical raindrop is spherical."
Now here's the most important part for Teele's rainbow metaphor:
"Only one color of light can be seen from each raindrop. It requires many raindrops to see the colors in the rainbow."
She explains this in more detail:
"Raindrops lower in the sky contribute blue and green light; drops higher in the sky contribute red and yellow light."
Here we already note the similarity between Teele's rainbow and Kite's musical rainbow. Lower raindrops are blue and green, while lower (minor) intervals are blue and green. And higher raindrops are red and yellow, while higher (major) intervals are red and yellow.
Teele continues:
"White light is composed of all the wavelengths of visible light. The waves that make up sunlight and incandescent light are a mixture of all the colors of the spectrum."
Of course, the author's idea is to connect these colors to multiple intelligences. She highlights the following statement:
"When our students are given the opportunity to let their 'lights shine,' they reveal a full prism of colors or abilities that may never be discovered if they are not allowed to use their full spectrum of intelligences."
And using the rainbow analogy:
"If each area of the brain represents a different raindrop, then it is necessary to combine different parts of the brain to reach the full spectrum of human processing."
At this point, Teele writes about a secondary rainbow, which we may see outside the first one:
"A secondary rainbow occurs when raindrops high in the atmosphere refract and reflect light back to the viewer. These raindrops are higher than those that cause the primary rainbow and are different because they internally reflect the incoming sunlight twice rather than just once."
But when it comes to rainbows of intelligence:
"Each rainbow is your own. Each eye sees a unique, individualized rainbow."
And Teele highlights the following statement:
"Each individual is unique and has the potential to develop each color of the rainbow or all of the intelligences by reflecting off several different raindrops or ways of learning."
She explains:
"If we consider the human potential as the entire spectrum of the rainbow with seven different colors or seven different intelligences that can be seen and infinite combinations of colors that cannot always be seen by the human eye, then we realize that each individual is unique and has the potential to develop all of the intelligences by reflecting off several different raindrops or ways of learning."
And this is a warning to all teachers:
"If we do not tap into the correct angle or manner or processing for each individual, we cannot see the total rainbow of colors or the potential for each individual."
At this point, the author writes about how different colors are related:
"To completely understand this model for multiple intelligences, we need to examine the relationship of primary, secondary, and complementary colors to learning."
Most of the pictures in this book are black-and-white. But obviously color is very relevant to this chapter, and so the only colored images in Teele's book are in this chapter. Her first colored picture shows a color wheel (or star) containing primary, secondary, and complementary colors.
Teele describes two different ways to analyze colors. The first is called additive or RGB, and this is how colors of light combine. Colors on computer monitors are based on RGB. Here she shows us how primary colors of light combine to form secondary colors:
green + blue = cyan,
red + blue = magenta,
red + green = yellow.
The other way is called subtractive or CMYK, and this is how colors of ink combine. Colors on computer printers are based on CMYK. Here she shows us how primary colors of printing and paint combine to form secondary colors -- these are the opposite of RGB:
yellow + magenta = red,
cyan + yellow = green,
cyan + magenta = blue.
The K stands for black, as Teele explains:
"A fourth color, black, is generally added to reinforce the detail of the picture, enhance the modeling, and improve the reproduction of gray or neutral colors."
Teele moves on to complementary colors -- these colors of light combine to form white, and these colors of printing and paint combine to form black:
"Red and cyan, green and magenta, and blue and yellow are complementary colors of both light and printing and paint."
Notice that Kite's complementary colors in music are slightly different. First of all, these colors combine only to make white -- there is no black in his notation. One pair of complementary colors is yellow (5-otonal) and green (5-utonal), while another is blue (7-otonal) and red (7-utonal). Kite's idea is for the complementary colors to oppose each other on the rainbow, not a wheel. So blue and red are complementary because blue is on the bottom of the rainbow with red on the top. Green and yellow oppose each other for the same reason, with these two colors closer to the middle.
In the original Kite thread, one poster, Joseph C. Ruhf, actually proposed using the complementary colors of light to music. His idea is for red/cyan to denote the 3-limit, green/magenta for the 5-limit, and blue/yellow for the 7-limit. But Kite rejects this as being more difficult to remember.
Returning to intelligence, Teele's model of intelligence is like a spiral of color, with each color representing an intelligence:
"There are gradations within each color. The seven colors spiral both in and out, signifying infinite possibilities for individuals to process information."
The seven colors of the rainbow correspond to the seven intelligences -- but what happens to the eighth intelligence?
"Because the naturalist intelligence appears to possess overlapping characteristics of several of the primary intelligences, it can be viewed as a secondary intelligence."
As Teele points out, learning often requires combining the intelligences:
"Learning geometry requires logical-mathematical and spatial intelligences. Playing the piano blends musical, linguistic, logical-mathematical, spatial, and bodily-kinesthetic intelligences and may additionally use both of the personal intelligences."
Here is a suggestion for us teachers:
"Teachers can provide the sunlight that assists students' colors to shine through each raindrop and combine to form the rainbow. The core of the spiral of colors is well balanced and strong."
Intelligences develop, just as a caterpillar develops into a butterfly:
"Individuals are always changing through these developmental stages. Sometimes they become more like a cocoon and, although to the outside world nothing is happening, changes are occurring on the inside."
Teele concludes the chapter with the following:
"By providing a rainbow of opportunities for all students, all students can develop to their full potential. They can reveal their prism of colors when they are allowed to use the full spectrum of intelligences."
And her final picture in the chapter is of a panda with colorful butterfly wings.
Notice that Teele never makes a one-to-one correspondence between colors and intelligences. But we can if we use Kite's colors. To Kite, the old common-practice music never really progressed beyond the 5-limit, of yellow (major) and green (minor). I like the idea of using yellow and green to represent the two traditional intelligences of linguistic and logical-mathematical. For both traditional music and traditional education, there's too much yellow and green and not enough of the other colors. And so both Teele and Kite are showing us how to progress to full rainbows for both intelligence and music.
Before we get to my new Mocha song, let's return to Kite's color website. In the past month or so, he was stuck on colors for the 11-limit -- perhaps topaz (11-otonal) and fuchsia (11-under). But he found these colors too hard to remember, and so he's come up with another color that fits the rainbow better.
Kite's new color for the 11-limit is "lavender." The first syllable, "lav," sounds like "lev" as in the number eleven. (The dozenal website sometimes uses "levimal" to mean base 11, and "lev" is often used to mean digit-eleven in base 12.) There is only one color for the 11-limit, since 11-otonal and 11-utonal both sound neutral (that is, between major and minor). If we really need to distinguish between otonal and utonal, then we can use "lo" (or "lova") and "lu."
Here is a link to Kite's website. Scroll down for his "lavender" proposal:
http://www.tallkite.com/forum/index.php?topic=86.195
According to Kite, lavender actually fits the rainbow better than topaz or fuchsia (or even his old colors jade or amber). But how can this be? Lavender is a shade of violet, while lavender intervals are neutral, between minor (green) and major (yellow). How can violet fit between green and yellow? It would appear that his old jade and amber fit the rainbow better.
Well, Kite's explanation is that is goes back to his old color "purple" for 7-limit neutral intervals. In his old purple notation, purple is equivalent to both "reddish-red" (ruruyo) and "bluish-blue" (zozogu, where "zo" means "azure" or blue). Indeed, a neutral purple third was considered equivalent to both the ruruyo super-augmented 2nd and the zozogu sub-diminished 4th. This means that "purple" is actually between red and blue, where it belongs on the rainbow. The purple 3rd marks the end of the rainbow of 2nds and the start of the rainbow of 4ths. The rainbow of 3rds overlaps both of these. We think back to Teele's secondary and overlapping rainbows.
And now "lavender" is the 11-limit interval that fits where the old purple 7-limit interals were.
Meanwhile, Kite is still torn on whether to have colors for the 13-limit. He finds that too many colors difficult to remember. Even though "tho" and "thu" can be used for 13-otonal and 13-utonal, there are no good colors for 13 that logically fit the rainbow. (Hmm -- two color names that start with "th" are "thistle (purple)" and "thulian pink," and the second even starts with "thu.")
Kite finds that colors for the 17-limit and above are unnecessary -- he still uses "so" and "su" for 17 and "no" and "nu" for 19. There's no shorter name for 23 than "twenty-tho" and "twenty-thu," but by this point we're reaching into the obscure primes. Kite was originally hoping for a color for 13 in order to distinguish between 13th chords and the 13-limit by using a color for the latter. There are no 17th chords in music and so there's no need for a 17-limit color.
Now let's get to the music. After sixth period music class left yesterday, first period was conference and so my day of teaching was complete. But I knew that some students would come back after school to pick up their instruments to take home. So I wanted to prepare a song for the students quickly during first period so that they could hear it playing when they returned after school.
http://www.haplessgenius.com/mocha/
In the past, I pointed out that Mocha music is based on EDL scales, which are utonal. This means that it's easier to play minor scales than major scales. To illustrate this, let's start with a simple triad and gradually add more notes until we obtain the full scale. The chart shows us the simplest EDL in which the just form of the scale is playable:
Subset of Scale Minor EDL Major EDL
Triad (Root-3-5) 6EDL 15EDL
Root-3-5-8 6EDL 30EDL
Root-3-4-5-8 12EDL 60EDL
Root-2-3-5-7-8 18EDL 90EDL
Root-3-4-5-6-8 24EDL 60EDL
Pentatonic 36EDL 90EDL
Lawrence's Scale 36EDL 180EDL
Full Natural Scale 72EDL 180EDL
In every case, the minor scale is playable in a simpler EDL than the major scale. The utonal EDL's of Mocha are better aligned to the minor scale than the major scale.
Meanwhile, last year I posted Mocha songs on Thanksgiving and Christmas. But Mocha plays minor scales more easily than major scales -- and the gloomy, sad-sounding minor scale sounds better on Halloween than for Thanksgiving and Christmas. Therefore Mocha's EDL scales fit Halloween like a glove, more so than the happier holidays.
In the list above, "Lawrence's Scale" refers to musician Kristen Lawrence. On YouTube, she's posted many songs that can be played at Halloween, including "The Ghost of John":
"Ghost of John" is a traditional song written using the natural minor scale. But Lawrence plays a slightly different version that avoids the minor sixth. By omitting the green 6th, the song is playable in 36EDL -- with the 6th, we'd have to go up to 72EDL instead. (Lawrence includes the traditional green 6th in her final verse, when she sings "John once said 'I lost my head.'") Another song played in the minor key without the 6th is her "Souling Song."
So now let me describe my original song. We see above that 6EDL is the simplest "scale" which contains the minor triad -- unfortunately, it contains that triad and no other notes. The simplest EDL that actually sounds like a full scale is 12EDL.
I wanted to create yesterday's song in 12EDL, but I chose 18EDL instead. This is because I couldn't find my old 12EDL post quickly enough. It was easier to find 18EDL -- I wrote about this scale on May 31st (so it pops up first when I click on the "May" archives), and on the next day, June 1st, I wrote the program that creates a song in 18EDL (so I just click on "Newer Post"). Time was of the essence since I had less than an hour to create the whole song.
As a reminder, here is the 18EDL scale again, except with Kite's newest colors:
The 18EDL scale:
Degree Ratio Note
18 1/1 white D
17 18/17 17u D# (su D#)
16 9/8 white E
15 6/5 green F
14 9/7 red F#
13 18/13 13u G (thu G)
12 3/2 white A
11 18/11 lavender B (lu B)
10 9/5 green C
9 2/1 white D
I coded and ran the 18EDL program. I like to run the program twice, so that the resulting song can contain both a verse and a bridge (AABA format). This is the song that it randomly created:
10 CLS
20 PRINT "NOW PLAYING HALLOWEEN"
30 PRINT "MUSIC RANDOMLY GENERATED"
40 N=8
50 FOR V=1 TO 3
60 IF V=2 THEN Z=29 ELSE Z=13
70 FOR X=1 TO Z
80 READ D,T
90 SOUND 261-N*D,T
100 NEXT X
110 RESTORE
120 NEXT V
130 GOTO 50
140 DATA 18,12,10,4,17,8,17,8
150 DATA 18,8,16,8,17,12,14,4
160 DATA 18,16,17,16,18,12,12,4,18,16
170 DATA 18,16,17,8,10,4,14,4
180 DATA 18,16,17,4,9,4,10,4
190 DATA 18,4,18,12,10,4,17,12
200 DATA 10,4,18,8,9,8,12,16
Don't forget to check off the Sound box on the lower-left before you RUN the program!
As I explained in my June 1st post, the generating code is based on alternating between the first two notes of the scale (Degrees 18 and 17) and then adding quarter, half, dotted half, and whole notes. But as it turned out, by luck of the random draw, the song avoids both 11 and 13, as well as 15 -- and 15 is the minor third (18/15 = 6/5).
Despite lacking the minor third, the song still sounds eerie for Halloween. The use of Degree 17 -- the Arabic lute index finger -- makes up for the lack of a minor third. Here is the subset of the 18EDL scale that I actually used in class:
The 18EDL scale:
Degree Ratio Note
18 1/1 white D
17 18/17 17u D# (su D#)
16 9/8 white E
14 9/7 red F#
12 3/2 white A
10 9/5 green C
9 2/1 white D
This scale contains only six notes (plus the octave), the same as both 12EDL (the scale I was originally trying to play) and Lawrence's minor scale.
Later on I ran the randomizer again and obtained another song containing Degrees 11, 13, and 15, but the first one is what I played. We change the above lines for the second song, the one I didn't play:
60 IF V=2 THEN Z=29 ELSE Z=15
140 DATA 18,16,17,4,9,4,15
150 DATA 18,8,18,4,15,4,17,8
160 DATA 13,8,18,16,17,12,11,4
170 DATA 18,4,18,12,18,16,18,12,17,4
180 DATA 14,12,11,4,18,8,17,8
190 DATA 17,12,12,4,18,12,16,4
200 DATA 17,12,9,4,18,16,12,16
As the students came in to pick up their instruments, I had Mocha continue to play the song. The GOTO in line 50 is supposed to make the song run forever in an infinite loop, but for some reason something was wrong and the song would stop unless I click in the box and scroll up/down. I think the students enjoyed this Halloween song.
I also had the notes of the song written on the board (except I used Eb for D#). Notice that 5-limit music plus 17 are all easy to notate in our usual notation (12EDO) -- only 11 and 13 fall between the usual notes of 12EDO. On one hand, avoiding 11 and 13 makes it easy to convert to 12EDO, but on the other, if I wanted a song in 12EDO, I would have just composed in 12EDO. The second song, which contains 11, 13, and 15, demonstrates the full power of 18EDL (and thus can't be converted as readily to 12EDO).
As often happens in middle schools, the regular teacher is scheduled for ten minutes of yard duty right after school. This made it tricky for the students to pick up their instruments! A few students convinced their first period teachers to let them out early, and so they were able to get the instruments before I leave for yard duty. I placed a note on the door for the others to wait until after duty. It would have been great if I could have the song playing inside while they waited outside (and it was loud enough for them to hear), but as I said earlier, the infinite loop wasn't working.
After the student picked up the instruments, the regular teacher returned. I told her that I had come up with a song on the computer to inspire the students, and she smiled.
The root note of this song was supposed to be white D. But when I tried to play along on the piano in the classroom, the root note actually sounded more like middle C. It's either this, or maybe I made a mistake and wrote 40 N=9 instead of N=8 (which would change the root note to white C). I'll need to check again how to convert Mocha notes to concert pitch.
Notice this means that the note I wrote on the board as C actually sounded more like Concert Bb. In other words, my song was written in tune with transposing instruments in Bb (such as trumpets, or even certain clarinets).
By the way, whenever I sub in a music class, I usually report on the songs that the students actually played in class (and then convert the songs to EDL scales). But I was so excited about finally being able to create and play my own song that I didn't try to convert any songs. (Once again, keep in mind that EDL scales are for composing new music, not converting old songs to the new scales.)
At the least, I should convert one song the students played to EDL -- "When the Saints Go Marching In" -- as I parodied that song at the old charter ("When the Scientists Go Marching In"). Another simple song that might be easy to convert is "Scarborough Fair." Other students were practicing a medley of patriotic music, and there was an interesting-sounding song played on the strings with a piano accompaniment that I don't remember much about today.
Here is today's review worksheet for Chapter 4. Oh, and since tonight's Mega Millions jackpot is still over a billion dollars, I might as well post the Square One TV "One Billion Is Big" song again:
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