Peterik Chapter 10: Using Chords in Songwriting
Table of Contents
Introduction
We're now ready to move on to the next Peterik chapter on chords. Then we'll try to figure out how to add chords to our EDL songs.
More on Interactive Notebooks
It's been a long time since I've discussed the traditionalist debates. One website were traditionalists tend to post (and I used to link to all the time from the old blog) is the Joanne Jacobs site.
The reason I'm returning to Jacobs today is that one commenter appears to attack interactive notebooks in math classes. All summer, I've written about interactive notebooks -- how I should have used them in past classes, and how I plan on using them in future classes.
Here's the link and the comment:
https://www.joannejacobs.com/post/grading-reforms-teach-kids-they-can-do-nothing-get-something
Notice that this anonymous guest refers to a "notebook check," which doesn't necessarily mean that it's an interactive notebook. But that reference to "coloring skills" suggests that these are indeed interactive notebooks after all.
I cut the comment off here after the "college professors" justification, but if you read the rest of the guest's comment, he (or she) goes on to distinguish between education classes (that is, those for teachers working for a credential) and all other classes (like Calculus classes). Education classes often model K-12 teaching methods, and thus might use interactive notebooks in a way that, say, a college Calculus class wouldn't.
It appear that the guest's teacher had interactive notebooks be worth say 20-25% of the grade, so even if the test component is almost 100%, the notebook would drop the grade to below 80%, hence a C. That this teacher only collects the notebooks once, right at the end of the semester, is unusual. If the teacher had checked notebooks throughout the term, the guest would have only lost the points for the final check, and so it's possible that after losing, say 5%, the final grade would still be above 90%. So one quick solution to this problem is to collect the notebooks more often.
But the first line of the comment gives the whole game away:
"These reforms may be a problem for kids who only do the work when forced..."
That, of course, is why interactive notebooks exist in the first place. Some students won't take notes or do homework unless they are forced to do so. But for students like the guest, the notes and HW are only the means to an end -- passing the tests. Such students are mature enough to take notes, finish HW, and do whatever it takes to prepare for the tests.
Recall that this current discussion all started when, at the end of last year, one of my junior Ethnostats students said that more students would have done the work if there had been interactive notebooks. I did have a form of notebook, but only some projects were done in there -- not regular notes/HW. (And noting that this student earned one of the lowest grades in the class -- managing to scrape by with a C+ on the strength of said notebook projects -- she's clearly including herself in this group.)
My original reluctance to implement interactive notebooks was because I was afraid that some students would lose their notebooks -- yes, just like the guest here, except that they'd lose them early in the year (or never buy one at all) and then use that as an excuse not to do the work. This past year, I still wasn't sure whether I should collect notebooks during COVID, but the fact that the other math teacher (my partner teacher) had interactive notebooks showed me that I could still have them despite the pandemic.
The guest at the link above is anonymous. Joanne Jacobs changed her website recently, and many commenters haven't figured out how to log in with their names yet, so most are anonymous. The one poster who does post with a name is Bruce Smith -- yes, it's the traditionalist who encourages students to take Calculus as juniors. (To this day, I still refer to junior-year Calculus as "Bruce level" -- so, for example, the youngest girl in my Calculus class last year was working at Bruce level math.) Anyway, Bruce posted in this thread to express strong agreement with the notebook-losing guest.
In another post, the author -- whom I assume is the same as the original guest (though I can't be sure due to anonymity), uses the phrase "teachers acting like tin pot dictators" -- the implication being that grading notebooks is dictatorship while grading only tests is freedom. But in a test-only high school class where only 10% is mature enough to take notes/pass tests and the other 90% fail, the teacher will be thought a "dictator" for failing 90% of the class, no matter how much (the other 10% believe) that those F's are deserved.
Posters like Bruce and the original guest believe that high school students should be mature enough to take notes on their own like college students, so that they wouldn't need to be graded. My counterclaim, of course, is that most high school students aren't mature enough, so notebooks are needed. Based on the discussion I had with my Ethnostats junior and my partner teacher, I believe that more students learn more math with the interactive notebooks -- and this outweighs the inconvenience suffered when mature students are asked to make them too.
(Case in point -- in many classes, including those I've subbed in -- students at the start of class ask whether they must take notes, hoping the answer is "no" so that they won't have to. Again, in a class of mature students, this question wouldn't even be asked -- you take notes because doing so helps you learn and pass the upcoming test, not because you "have to.")
If we have a class full of immature students, I'm sure that the traditionalists would have no problem explicitly teaching them to take notes and become mature students -- they'd argue that such instruction should take place well before high school -- for example, in the last year of elementary school (that it, around fifth grade). The guest, who lost the notebook in high school when math is one of six classes, is more likely to keep the notebook when it's a single teacher the entire day -- and of course, there's no spot in the National Honor Society on the line in fifth grade.
And of course, someone like Bruce might argue that students are more likely to reach his level of math (that is, Calculus in Grades 11-12) if they are learning notetaking in fifth grade, as opposed until waiting until high school to learn it.
So what is my decision on notebooks? I said I'm going to do notebooks, and I still will. As I wrote earlier, we can mitigate some of the problems the guest had, simply by collecting notebooks more often so that a single lost notebook isn't detrimental to the grade.
As for students who never buy notebooks in the first place, I'll probably purchase a few extra notebooks for those who don't intend on ever going to the store to get one. The first assignment will be to purchase the notebook, and so those who depend on me to give them one will already lose points on the first notebook check.
How many assignments will the notebook ultimately contain? Well, much of what about notebooks pertains to the old charter school, where I taught math and science (so, for example, one side of the notebook is math and the other side is science). Since I'm only teaching math, that's now irrelevant.
A typical one-subject notebook contains 70 sheets, each with a front and back, so the entire notebook contains 140 pages. I might use slightly less than 140 pages, though -- I know how easy it is for two pages to stick together, and so a student might count the pages and get 138 if two pages cling to each other, or 136 if another pair sticks. Indeed, that 67 assignments that I assigned my Calculus class each semester will fit almost perfectly here -- 134 assignments for the year. Note that these will be labeled as Pages and not as Assignments.
But not all of these pages are considered homework. Some of these pages are for notes. And this is what makes it tricky. One page per day is 180 pages -- but of course, there will be some weeks when there are no pages, such as the first few weeks of school (giving the students time to buy the notebooks), finals week, and so on. Yet on other days there will be two pages, if one page is for notes and the other for an assignment. So I must make sure to budget the pages throughout the semester -- the 67 system, if you recall, assumes four pages per regular week, three if there's a holiday or test.
Of course, I might still give some online assignments (DeltaMath, Desmos, and so on). In order for students to receive credit, they must do at least some of the work inside the notebook. (This is like the "IXL accountability form" that I suggested for the old charter school.)
The 67 pages are worth three points each, so that's 201 (rounded to 200) points. But once again, this is assuming that homework (or the notebook) is still worth 20% of the grade (with notebooks collected four times, so each check is worth 5%, not 20%). The 10% classwork component will still consist of the Warm-Up and Exit Pass sheet (which is separate from the notebook), and then it's still 30% for the quizzes and 40% for tests.
But this is assuming that there isn't automatic grade weighting in Google Classroom or Aeries. As the only one teaching my subjects at my school, I could control my own grade percentages. But I might be joining a larger department this upcoming year. (As you've probably guessed by now, no, I still don't know where I'm working -- and at this point, I'm assuming I won't know until just barely before the first day of school.) That department might already have grade weights programmed in. So I'll come up with exact percentages once those are known.
Is there anything else I can do to protect mature students like the Jacobs guest? Perhaps I could have something like, if an A is earned on the final exam, then the student automatically gets full credit for all missing notebooks. This is an extension of my extra credit policy where the students can get points if they show that they know the math that is missing from their grade (and of course, an A on the final shows that they know that math in their notebook). Then again, getting an A on a math final is quite difficult (even for the top students, who usually scored 25 out of 30 on my finals last year). Thus I hope to protect the grades of mature but unlucky students who lose their notebooks, yet still motivate the immature students to learn.
Rapoport Question of the Day
On her Daily Epsilon of Math, Rebecca Rapoport writes:
What percentage, rounded down, of a 10000-year-old sample of carbon-14 (which has a half-life of 5730 years) would be remaining today?
Well, since there are 10000/5730 half-lives in 10K years, and each half-life reduces the amount of C14 by a factor of 1/2. Thus the remaining percentage is 1/2^(10000/5730) = 0.298. Normally we'd want to round 29.8% up to 30%, but we were asked to round it down. So the desired percentage is 29% -- and of course, today's date is the 29th.
Carbon-14 dating is used to determine the age of ancient objects. But notice that this problem also has an interpretation in music -- in 5730EDO, go down one EDO step per year. Then after 10000 steps, by what interval have we descended? Well, 1/4 would be two octaves, but 0.298 is closer to 3/10, which would be a major 13th (a octave plus a major sixth).
Peterik Chapter 10: Using Chords in Songwriting
Chapter 10 of Jim Peterik's Songwriting for Dummies is called "Using Chords in Songwriting." Here's how it begins:
"Given the fact that you're reading this book, you may already have a basic grasp of chords on the instrument of your choice."
We learn here why chord structure forms the foundation of our songs:
"If the chord structure is solid, you can build a masterpiece on top of it; if it's weak, everything you lay on top of this foundation runs the risk of collapsing. So what is a chord?"
Yes, we should already know what a chord is -- a combination of notes played simultaneously. Peterik tells us how we can get started with chords:
"Songwriters start as fans of different songs, and then as they learn those progressions, they start to adapt and modify them to their own style."
And he quotes Don Barnes of 38 Special here:
"The first song I ever learned on the guitar when I was nine years old was the hit 'Tom Dooley' by the Kingston Trio."
And this is a simple song with just two chords repeated, so it's perfect for a beginner. The author tells us how the chords we choose depends on the genre:
"What blues and some rock do is make each chord a dominant seventh chord. Your A will become an A seventh -- an A major chord with a G natural on top of it to give it that grindy or bluesy sound."
Other genres, such as pop-rock, have their own preferred progressions, such as 1, 4, 7, 3, 6, 5:
"Each of these chord pairs is all a fourth apart, just down one step from the previous pair. In jazz, instead of the 1, 4, 5 progression that you find so often in pop, rock, and blues, you might use a repeating back and forth cycle of the 1, 6, 2, 5 chord progression."
In order to move forward with chords, we should practice on the two main chordal instruments -- keyboard and guitar:
"A good suggestion would be a piano setting combined with a touch of strings to give it a little cushion and grandeur. Now play a nice big C major chord."
Peterik tells us how he sometimes fools around with chords to make his songs sound unique -- for example, he placed the third on the bottom in his "I Can't Hold Back":
"The last of three times the E major, A major, B major chord progression is repeated, the root of the chord is used for that extra solidity the last time around."
We should learn as many chords as possible on our chosen instrument:
"The more chords you have in your arsenal, the more options you give yourself. Many writers will find interesting ways of linking chords together by keeping certain notes within the chords the same whether they are at the bottom of the chord or the top of the chord -- keeping the main note of the key common to at least two or three of the chords."
The author starts out with some tips for picking -- at the guitar:
"For Latin songs, a nylon stringed guitar (also called a classical or flamenco) may be your ticket to inspiration. Using a capo on the neck of your guitar can be a useful technique while writing a song."
Then he moves on to pecking -- at the keyboard, which can simulate other instruments besides piano:
"In addition, you'll find synthesized brass patches -- useful when writing '80s style rock -- listen to 'Heat of the Moment' (written by John Wetton and Geoff Downes; performed by Asia for reference), woodwinds, and a vast collection of strange and wacky synthesizer and bass sounds, R&B, gospel, jazz, new age, urban, and dance pop are all primarily the divinity of the keyboard."
This takes us to the next "Practice Makes Perfect" section.
Chords in Mocha EDL Scales
Before we start with my own music here, let me point out that when I wrote about 28EDO in my Pi Approximation Day post, one of the 28EDO composers changed his video to private. In deference to his wishes, I have edited that post and deleted the video.
Oh, and by the way, last night someone from Illinois won a billion dollars in the lottery. Whenever the jackpot gets that high, I think about the song "One Billion is Big" from Square One TV. If we analyze this song according to what we learned in Peterik's chapter today, we notice that this song is considered rap/hip-hop (old school '80s style, yes, but hip-hop nonetheless) -- and so, like most songs of that genre, it's not chordally complex. For most of the song, only two chords repeat -- D minor and C major. The chorus, however, is melodic and in the key of F major, hence F (and a few other chords) appear here.
OK, now let's get to the main topic here -- chords in our EDL songs. There are a few things to say here about EDL's and chords:
- The simpler EDL scales may be considered part of just intonation. Just intonation means that it's based on simple ratios of whole numbers (though how low depends on the musician). Most just intonation theorists count prime numbers up to 7 as just intonation, so 10EDL counts -- but most don't count prime numbers 17 or larger, so 18EDL rarely counts as just intonation. The EDL's in between might be consider just to some musicians and non-just to others.
- The advantage of just intonation is that chords sound more in tune when they are just. So we would expect chords in the lower EDL's to sound great, except for one problem...
- Our one instrument that plays EDL scales -- the Mocha emulator -- doesn't play chords!
And this is a shame. Why Mocha (or the '80s computer on which it's based) uses EDL scales which are good for just intonation yet can't play chords is a mystery. Still, if we want to give the songs produced by the EDL generator a strong backing, then we should look at what chords go well with EDL music.
Let's start with our simplest EDL scale, 10EDL, C-D-E-F#-A-C. This is a pentatonic scale that's quite similar to the established C major pentatonic scale C-D-E-G-A-C, so this is a great place to begin. So suppose we have a song whose melody is in C major pentatonic -- what chords might it use? Well, this song contains one major chord, C-E-G, and one minor chord, A-C-E.
But in practice, a C major pentatonic song will contain chords besides C and Am. Indeed, the song will likely contain the three major chords associated with C major -- C, F, G (that is, 1, 4, 5). The G chord contains a B, even though there's no B in C pentatonic. And the 4 chord is rooted on F -- a note which itself doesn't appear in C major pentatonic. In other words, there exist two notes (F, B) that appear in the chords of the song, yet not in the melody. (For a simple example, consider the simple tunes "Farmer in the Dell" or "Old Macdonald" -- both have pentatonic melodies, both use the 5, and possibly the 4, chords that include notes not in the pentatonic scale.)
Thus, returning to 10EDL, we note that we don't need to be bound to the pentatonic 10EDL scale when looking for chords to play with the melody. Looking at the notes C-D-E-F#-A-C, we see that it has the same minor chord A-C-E as C pentatonic. It contains one major chord, D-F#-A (a supermajor chord, since it's based on the 9/7 supermajor third), which can even be extended to a dominant seventh. But what it lacks is a chord on the tonic C. So perhaps we can add an extra note to our chord that doesn't appear in melody. (The most obvious note to add is a G, to complete the C major chord C-E-G.)
On the other hand, 18EDL already has plenty of notes. The fundamental note of 18EDL is a D, so the 18EDL scale is D-D#-E-F-F#-G13-A-B11-C-D. (Degrees 11 and 13 are often irregular -- Degree 11 can be written Bb or B, while 13 can be written G or G#.) We can already build both a minor chord (D-F-A) and a major chord (D-F#-A, which is the same supermajor chord from earlier) on the tonic D, and so it appears that we should be able to make enough chords using only the notes of 18EDL, without having to add any extra notes missing from the melodic scale.
In previous posts, I've referred to a hypothetical chordal instrument that could play chords that fit with our EDL scales. According to Peterik, both keyboards and guitarlike instruments are chordal. The best possibility for an EDL scale would be a string instrument similar to a guitar, where the frets are equally spaced on the fretboard. Then it would truly be equal divisions of length, as the name EDL implies.
And I've always been fascinated with dividing the string into 18 frets for 18EDL. That's because the first fret would be 18/17 above the open string -- an interval called "Arabic lute index finger." This name implies that there was once an ancient string instrument -- a "lute" (or "oud," the Arabic name) whose fretboard was divided into 18 frets as 18EDL. Then when the index finger is placed on the first fret, the interval 18/17 is played. The Arabic lute "middle," "ring" and "little" fingers would then correspond to the intervals 18/16, 18/15, and 18/14, except that these already have established names (major tone, minor third, and supermajor third), so only 18/17 needs a special name.
Of course, I won't play an actual Arabic lute in class -- I'll be playing the guitar. So instead, the idea is to play the songs on the real guitar, but note that these correspond to intervals on our hypothetical lute that is fretted to 18EDL. The real guitar is tuned to standard EADGBE, so our hypothetical lute will also be tuned to EADGBE (though we don't know whether the real Arabic lute even had six strings).
A key difference between standard (equal temperament) and just intonation is that standard tuning matches all scales equally well (or equally poorly), while just intonation is tuned to one scale exactly, and the other scales not at all. Since D is the fundamental of 18EDL, our goal will be to tune to the D scale exactly. In particular, the D string should be tuned to (white or wa) D. Now we're thinking in terms of Kite's colors -- we want to know what color the other strings should be tuned to in order to play the important chords of D major (at least the 1, 4, 5 chords -- D, G, A).
Here is a justly tuned D major scale:
wa D, wa E, yo F#, wa G, wa A, yo B, yo C#, wa D
If we play the 1, 4, 5 chords in this scale, for all three of them the root and fifth are both white/wa, while the third is yellow/yo. (In general, roots and fifths should be the same color in order for the chord to sound in tune, while the third should be a different color.)
Let's start with our 1 chord. In standard tuning, the open D chord is:
D: xx0232
The open D string is already colored wa. The G is fretted at the second fret to mark A, which we want to be wa. Thus the open G must also be wa, as 18 and 16 are always the same color. But the B string can't be wa, because fretted at the third fret it becomes green/gu (18/15). Instead, the open B should be yo (the opposite of gu), so that the fretted D becomes wa (to match the open D below). The E string should also be yo, since fretted at the second fret it because yo F# (which we want to be yo).
Now let's try the 5 chord, which is A:
A: x02220
And we already have a problem here. The wa D string is fretted at the second fret to give wa E, but this doesn't match the open yo E string. (Octaves, like fifths, also need to be matching colors.) One way to solve this is to make it a dominant seventh chord:
A7: x02223
Then the top yo E string is fretted at the third fret to produce G (which is also wa, just like the wa D produced at the third fret of the yo B string earlier). The open A string must also be wa, in order to match the wa A produced at the second fret of the wa G.
That leaves us with the 4 chord, which is G:
G: 320003
Both the top and bottom E strings are both yo, so that both third fret G's become wa. But that leads to a new problem -- the B at the second fret of the wa A string must also be wa -- which then doesn't match the open yo B string (and since thirds aren't suppose to match the root, the yo B is desired). And this is fatal -- there's no dominant seventh trick to avoid the differently-colored B's.
And starting with a key other than D leads to the same problems. It's impossible to play the 1, 4, 5 major chords in any key so that all three chords are colored properly. (And it could be pointed out that the correct D chord shouldn't even use yo F# in the first place -- the 18EDL scale contains not a yo F#, but a red/ru F#. So perhaps the top string should be ru E, not yo E.)
Of course, if we can't play three chords in Arabic lute tuning, what good is Arabic lute tuning? Once again, we don't know how many strings the ancient ouds even had. It's easier to have only four or five strings be justly tuned than six. If the oud did have six strings, then it was unlikely to use EADGBE tuning -- instead, we might have an extra D string (which would make tuning to the D scale easier), or perhaps omit one of the other string (for example, an A string is problematic because our desired major scale both wa A and yo B, which can't both be playable on the same A string).
We could try to work out what the best tuning other than EADGBE for the Arabic lute might be -- but then, do I really want to tune my guitar to this other tuning (of a hypothetical EDL instrument)? In the classroom, I'm likely just to stick to EADGBE tuning and just forget about the Arabic lute (even if it doesn't truly fit the 18EDL scale).
I might continue to work on this problem. Once again, our first songs won't even be in 18EDL but 10EDL, and we still didn't even begin to answer what chords we'd want for 10EDL. (Since 10EDL is further along the fretboard than 18EDL, the true answer is to take our 18EDL lute and figure out which chords are playable on the higher frets near 10EDL -- but we never completed the 18EDL lute.)
And once again, the most important for music is that it should sound good. What might happen is that I perform a few 10EDL songs, figure out what chords sound good with them, and then declare those chords to be the "proper" chords for 10EDL.
Conclusion
As I've already mentioned traditionalists in this post, I've been thinking about the tracking controversy, and whether there's a possible solution. Since any solution to the tracking problem is controversial, I'm burying this in the bottom of the post (as I always do with the tracking debate).
Again, the idea behind tracking is that students feel most comfortable when the math they see in their class is neither too hard nor too easy -- and one way to accomplish this is tracking, which places strong math kids in higher math classes and weaker students in lower classes. The problem is that tracking inevitably leads to racial segregation -- when the parents see that most of their students' classmates are of the same race, while those in the other class are of a different race, the parents then object to the whole tracking system.
And so here's a controversial solution to the tracking problem -- track the students, not by math level (nor by ELA level, as the "path plan" mentioned on the old blog does), but by history class.
First of all, parents get to choose which history curriculum to enroll their students in -- for simplicity, let's label the two history curricula "1619" and "1776." (I mentioned 1619 in another recent post. This is an oversimplification to be sure, but the labels 1619 and 1776 are instantly recognizable as two very different historical paradigms.)
Presumably most black parents would choose to enroll their students in the 1619 curriculum, while most white parents would choose the 1776 curriculum. (Other races can have specialized curricula -- for example, my district has a Hispanic majority, so its history class might have a Mexican-American perspective distinct from either 1619 or 1776.)
The 1619 and 1776 curricula then divide the school into two tracks -- and then on each track, math can be taught however you like. Perhaps the capstone math class for the 1619 track might be an Ethnostats class (similar to what I taught last year but focused on the majority race of the class), while the 1776 track might be dominated by traditionalists who prefer that type of math.
This does avoid some problems -- no parent should complain about the history curriculum since the parents chose to place the students in that class. And likewise, there should be no complaints about the math, since the math matches the history paradigm that was chosen.
This isn't a perfect solution, of course. One problem is that 1619 and 1776 clearly refer to two types of US History -- but US History isn't taught until fifth grade here in California (and different grades in other states). So the tracks can't even begin until fifth grade. But I believe that there is no perfect solution to the tracking problem.
Here in California, the tracking debate has resurfaced because a new set of standards is being proposed and discussed. Originally, the standards were to discourage separating the students into different math classes through sophomore Geometry -- at which point, a combined Algebra II/Precalculus class for juniors would prepare the students for senior Calculus.
But for this, I have no simple solution. (Under an Integrated Math program, I'd argue that the best year to branch into tracks is Grade 8, not 11 -- Math 8 and Integrated Math I are similar enough that they can be combined into a single class without too many issues, unlike Algebra II/Precalculus.)
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