Noticing Things

This is what I wanted to say when I was talking about Kim's Game!  But I got sidetracked.  (Happens every few hours.)

Thinking back to my teaching days (i.e, before 2017), I realize that I missed a lot of good opportunities.  One of the basic tricks (it's not really a trick, but kids pay attention if you call it a trick) is: to notice things. 

One of the major things I taught was techniques of integration.  If you don't know what integration is, it's a little like being a doctor.  You have an integration problem (which is a math problem that has to be solved), which is your patient.  You first have to assess what kind of integration it is, because what you do next depends on that assessment.  It's like a diagnosis, get it?  You need to find out which way to go.  In math (unlike in medicine) if you go the wrong way, nobody gets sick or dies; you just have to back up, and start again in a different direction. 

Classifying your problem--- the diagnosis--- depends on noticing various little things, just as in medical diagnostics.  Once the doctor notices one thing, there are other related things he or she could look for.  It's exactly the same in mathematics!  Is there a radical of a certain sort?  Is there a logarithm?  An exponential?  A fraction?  A simple substitution you could do?

The good students are already hot on the trail of these critters.  At the time I was teaching, I was so annoyed with the typical students, that I thought: oh let them go screw themselves; they should have picked up a lot of this in Grade 10.

But a lot of things could have gone wrong in Grade 10: athletics---even if the kid was hopeless at it; hormones; a marginal high school teacher; a home environment where there was nobody to help with studying; all sorts of problems.  If I had gone just a tiny bit outside my lane, and helped my students with the FOIL rule, for instance,  which is something they learn in 6th or 7th Grade, they might have kissed the ground I walked on!  Well, that's going too far; I walked on some pretty dirty ground.

When I was thinking about this post, I wondered whether the whole concept of noticing things might be a pretty universal performance aid.  Does critical reading require noticing certain things?  Does debugging faulty code in a program involve noticing certain things?  It seem to me that even getting the benefit of a video clip a teacher shows a class requires noticing things.  This is huge. 

Notice things, young people.  No pressure. 

Arch

Harmonica Harmony

When I was a kid, I was given a so- called "mouth organ", which was the term, where I grew up, for the gadgets known in these parts as a harmonica.  These things were everywhere, at one time, but they're getting to be a curiosity.  Bob Dylan played one, so did John Lennon. 

When I learned to play one, it was considered a great achievement---briefly.  After a while, the constant racket of the thing got on my family's nerves, until I went off to boarding school---a humble school, not at all the same thing as the luxury institutions we find around here---and it became the responsibility of the school authorities to moderate my explorations with the harmonica.  Then, along came A Hard Day's Night, that miraculous introduction to the Beatles and their music. 

I lost no time learning to play I should have known better, a lovely soft rock song that featured the harmonica, and my friends and I sang it all the time, for a year.

It's time to get into the meat of this post. 

You can either Blow into a harmonica, or Suck.  Blowing produces a nice chord, in the key of the harmonica; mine was in C, and you'd get a bold, brassy C chord:

C E G C E G ...

and so on, depending on how many octaves your harmonica had.  A typical kid harmonica had three. 

If you sucked in, you also got a chord, but not one of the common (major or minor) chords, but a more sophisticated chord.  Rather than give you its name, I'll give you the notes:

B D F A B D F A ...

When I first learned music theory, I learned a whole lot of major chords, which I and my fellow-students played on a piano. Then I learned a whole lot of minor chords. Then, on certain (root) notes, I learned seventh chords. The most heavily-used one was the dominant seventh, GBDF.  In a pop song in the key of C major, you could do quite well if you just knew C major, F major,  G major, and G major dominant seventh.  In the quest for brevity, pop musicians called that last chord G^7th, but there are many seventh chords on the root of G.  Pop musicians don't need to know those, so they don't; it is The Way, as the Mandaloreans would say.  But if you were Elton John, you'd know all the chords on the root of G. 

The peculiar chord you get by sucking in on a harmonica is also a seventh, but not one of the common ones.  Since you can only either blow into the harmonica, or suck on the thing, there are only two chords, and this sucking chord is actually quite a clever choice, and in fact the only possible choice.  You could play a huge number of tunes with those two chords, and of course that's what we did.

In smaller harmonicas, all the way at the left end, if you blew, you would actually get a low G.  Oddly enough, if you sucked, guess what?  You would also get a G!  So, for complete disclosure, the chord you get if you blew is actually

G C E G C E G C E G C,

and if you sucked, instead, you'd get

G B D F A B D F A B D F A.

You would think that this would give you a horrible discord!  In fact, though, you get one of the most glorious chords of all, called a chord of the ninth.  This chord of the ninth on G,  GBDFA, is an important chord in 19th- century music; in fact you hear it all the time in Strauss waltzes!  In The Beautiful Blue Danube, in the introduction, it is the third chord you hear.  (Not on G, but the key of the piece.  The introduction is in A, if I remember right.)

Now, once that low G is added, we can call this chord of which I speak, the ninth on G, or the dominant ninth of C major.  But even without the G, the chord is the seventh on the chord BDF, which is a diminished chord.  We do not call it a diminished seventh, which is the name of a significantly different chord (OK, I'll tell you what it is, since you might not be able to sleep if I didn't: it's B D F FlatA.  The extra Flat makes it a note not strictly in the key of C major.)  Honestly, I don't know the common name for that chord---BDFA---in popular music.

OK, I  need to take a nap now.