Counterpoint

In this section of the book Society Changed, Don Walker discusses the idea of the Harmony School with people from the Green School System and those planning the Social Tech Schools.

Sally Aston of Social Tech comments on the Harmony School proposal:

“I didn’t understand it at all. Yours is the Harmony Match Project, but you don’t like the idea of too much harmony. You stress counterpoint.”

“That’s right. It was Helen’s idea.  My wife isa fabulous musician, as you’ve heard.”

“Amazing. Could you give me the short and sweet version of the counterpoint argument?”

“Sure. You have eight students in a class, I understand. Suppose it was four. In typical songs with four note harmony, the top line carries the melody, which is the most interesting sequence of notes. The middle lines are less interesting sequences, used basically to fill out the harmonies. The bass line on the bottom is the usually quite boring, just a few notes in a simple rhythm.”

“I guess that’s true.”

“Well, in Bach and the other great composers of the baroque period, each of the four lines would have a distinct melody. They would be related, variations on some basic one, but each would be an interesting sequence of notes. No performer plays something boring. The harmonies are there, alright, but many are inverted in various ways, to create melodic differences. That’s counterpoint.”

“OK, and this applies to schools because …, ah, wait, I think I’m getting it …, yes, I see. You don’t want one student to carry the melody while the others just harmonize, you want each student to play a part which is interesting in its own right.”

“Exactly. In music it is hard to extend this very far, but not impossible. Eight different instruments playing pure counterpart would be extraordinary. But eight students could hold a discussion in which none of them were unequal participants.”

“What a wonderful idea, Don. So you care mostly for counterpoint, despite the work harmony in your project name?”

“Not at all. Harmony is very important, but it does not mean just sounding good together. True harmony is based on the idea of a harmonic progression, or chord progression, whereby tension is created then relaxed by mild or strong discords followed by mild or strong concords. A chord progression must be carefully designed so that the changes in tension tell some kind of story, usually not an intelligible story about real world events, except in movie music.”

“Fascinating. So in place of a carefully planned chord progression, you want a carefully planned classroom lesson?”

“Let’s say a lesson skeleton, which the teachers and students can flesh out with improvisations, just as great performers do.”

Sarah understood Don’s explanation, well enough, then the next day Helen gave a brilliant exposition of it at the keyboard of her lovely little portatif organ, providing musical illustrations of each concept. The others were overwhelmed. What stunning concepts! Ken resolved at once to get some people to research how they could be applied in the Green school system. The Tech Fantasies trio immediately decided to incorporate as much as possible their school — somehow.

Don said, “I don’t think our goals are compatible. You want as much networking within the classroom, Sally and friends. More important than overall compatibility is networking. Ideally, each grade is fully connected, in the graph theoretic sense of the term: not isolated individuals and no cliques. Isn’t that right?”

“Yes, insofar as this is possible in a class by itself. We are also concerned with overall school networking. That’s our primary goal, much more so than actual class compatibility. The class might contain two highly incompatible people, but as long as they are linked by a chain of highly compatible individuals, that’s OK. Better, maybe.”

“An interesting idea. I’d like to see where it leads. Now, Ken and Sarah, you just divide people into the best possible classes, based on compatibility.”

“That’s right, Don”, Ken said, “though it took us a while to get the right definition of compatibility. The teachers on our committee suggested an overall class compatibility metric. The fewer conflicts the class had due to incompatibility, the better. It was Beth who pointed out that everyone on our committee was a complete idiot.”

“Not an idiot, Daddy, just biased. Most of the people on the committee were teachers like Annette, who liked the idea of a manageable class of kids who got along. All I did was argue the case of my cousin Miri, who wanted to be in a class which contained one good friend, just one. She didn’t care about the rest of the class.”

“Yes, Beth set us on the right path, although we did a little better than Miri wanted. We matched each child in a specific grade with one other, forming pairs of probably friends. Then we matched each pair with some other pair, forming a foursome, who usually sat together at one table for lunch, as it turned out. Then we matched two foursomes into a single class of eight.”

“That is an attractive approach, Ken”, Sally said. “I still prefer our networking idea, but I can see the merit in yours.”

“Well, this is where we differ from both of you, I’m afraid”, Don said. “The existing Green schools have too much compatibility within them. It would be hard for a class to have sufficient discord in it. Resolution of discords is essential to the use of chord progressions. The same is true of the proposed Social Tech school. Your networked people would tend to drag one another into unwanted concords.”

The others were clearly mulling this over.

Beth had remained quiet throughout this discussion. Then she spoke out, taking charge, “I don’t see your approaches as orthogonal, because classes can be taken apart and reformed as necessary. If all of your classes are completely connected, then your school probably is too. That big network could be divided into subnetworks in many many different ways. Not nearly as many as in our Green Schools, but a lot. Do you agree?”

“I do”, Sally looked at Ann and Drake for confirmation. They nodded.

“Good. Now, Mr. Walker, your approach could be used on any small class. Classes capable of sufficient discord and concord would work best, but unless I am mistaken, there are several acceptable ways of selecting a set of 8 pitches from the 12 distinct notes within an octave. Isn’t that correct, Mrs. Walker.”

“Yes it is, Beth.”

“Good. Just as sec while I do a quick calculation in my head. Ah, yes, there are 495 ways of picking 8 notes out of 12. I imagine all would be interesting and useful.”

Ken asked if Don or Helen could be more specific.

“If I paid for a school right away, how would you do it? Let me pick a number. We use 64 students per grade. How would you divide them into classes, Helen? Don?”

Don responded. “I think I would cluster the 64 students into 8 clusters, based on worldview, attitudes, preferences and all of that. We might end up with a group of people who are conservative, libertarian and love music, for example. Another group might be socialist and love sports. Then I’d slice those clusters the other way, putting one person from each cluster in each class of eight. That plus lessons based on Helen’s theory should do it.”