Pages Menu
Categories Menu

Posted by on Dec 9, 2012 in The Notes | 0 comments

The Minor Second

The last three notes (b6, b3 and b7) are related to each other. They all contain a reciprocal third. There is a family resemblance of sound and function. (They also all happen to be a little flat in equal temperament. On a guitar it’s a nice trick to bend them a little to sweeten them.)

Here is another note in the family, farther out harmonically, the minor second:

That’s a dissonant interval. The b6 is already tense with reciprocal third energy. Now this b2- (The minus is an accidental to show its exact pitch; more later) is another reciprocal fifth beyond (below?) that note. Its ratio is 1/15, which expands to 16/15 — just above 1. See how the ratios show where the pitch of the note is? 1/1 is the tonic, 2/1 is the octave. 16/15 is just a little bit greater than 1, so it’s just a little sharper than the tonic.

It’s not pitch so much that makes consonance and dissonance. It’s harmonic relationship.

Music is all about tension and resolution. Here’s a very tense note. How to resolve it?

One answer is just a half step away, a drop to the tonic.

That’s a move in melodic space. The tonic is right next door and it’s an easy drop.

On the lattice, the 1 is not a next door neighbor. How about going home through harmonic space instead?

Going to the 4 is an interesting experience for me. There’s still reciprocal tension, but I’m much closer to home — I can smell the stables. It’s as though I felt a bit lost at the b2-, the harmonic distance was too great to really get my bearings. But moving to the 4 allows me to figure out where I am, and where the tonic is, so that the final move home sounds really right. The 4 says to me, “There is home, now go.”

Then the melody moves to the 5, and there is resolution. The 5 sends just as strong a signal as the 4, but of opposite polarity. The 5 says, “Here is home. Now stay.”

It’s a little story, a journey on a microcosmic landscape of attraction, repulsion and beauty.

Next: The Augmented Fourth

Read More

Posted by on Nov 19, 2012 in The Notes | 0 comments

The Major Seventh

The notes get more exotic as you move outward from the center. The ninth is quite consonant, but not nearly as consonant as the fifth. (Consonance and dissonance are descriptions of feelings; they are part of the flavor of an interval, and I don’t think the last word has been written on them yet. I’ll be taking my shot later in these pages.)

For very small ratios such as 3/2, the ear has no trouble perceiving where it is on the map. The signal given by 3/2 is so strong, in fact, that it’s the primary tool used in classical music to move the ear to a new key center.

As the numbers get bigger, the signal gets weaker, and the interval gets more dissonant. To get to the major second, you multiply by 3 twice. Then, using octave reduction, you can put it in any octave you want.  I chose 9:4 in yesterday’s example, giving an interval of a major ninth — an octave plus a major second.

Compounding a fifth and a third gives somewhat larger numbers (3×5 = 15, or a ratio of 15/8) and, sure enough, the note is more dissonant against the tonic. Yet it has its own unique beauty. Presenting the major seventh:

Tomorrow, another kind of flavor entirely, another primary color in the crayon box, if you will.

Next: A Reciprocal Note: The Fourth

Read More