Thursday, June 7, 2018

Seventh Chords

What are seventh chords? Chords that contain the seventh note in a scale starting from the root of the chord! That's not a very practical answer, though, when experimenting with microtonality, where scales are not clearly defined. Here is an alternate definition: a seventh chord is a four note chord constructed by stacking thirds. The root note is the foundation. The next note is a third above the root. Another third above that is some sort of fifth note. Another third above that is some sort of seventh note. Typically the interval of a third is composed of two steps of a scale. So a seventh chord looks like 1-3-5-7 in terms of steps of a scale. But intervals are more fundamental than scales. The notion of a sequence of three intervals, each a third, makes sense even without any scale.

There are two different intervals of a third: a major third and a minor third. This gives eight different types of seventh chords, built from sequences of these different thirds, e.g. major-major-major, major-major-minor, major-minor-major, etc.

To find out how these seventh chords sound in the microtonal system where an octave is divided into 53 equal steps (rather than the conventional 12 steps), I wrote a little program that uses simulated annealing to construct a fractal pattern near a phase transition. The program builds a 12x12x12 toroidal mesh and places a seventh chord at each vertex. The total number of possible chords is 8x53=424. Each vertex can have any one of these 424 chords. Chords at neighboring vertices are probabilistically selected to be similar to each other. Chords are more similar the more notes they have in common.

The result, so far at least, is not very musical! But it's a lot of seventh chords! 1728 sevenths

Wednesday, February 21, 2018

Good and Evil

Some years ago I was on an airplane and sat next to a person who was a life coach of some kind. I think we could all use a bit of help in leading better lives, so I was keen to find out what kind of approaches she used. I don’t remember exactly what I was struggling with myself at that time, but I asked this life coach how she helped people think through ethical dilemmas, situations where it was difficult to see which action was best.

This life coach said that she really didn’t think there was any such thing as an ethical dilemma. A good person would just know in their heart what the right thing to do would be. If a person doesn’t know right from wrong, then coaching isn’t going to help them anyway.

I was completely shocked by this answer. The idea that some people just inherently know the right thing to do where other people don’t… the idea that in the real world there is generally a choice between a right thing versus a wrong thing, rather than a choice where every option available has negative aspects… these ideas strike me as so utterly simplistic! And this woman was a life coach! These were the ideas she was encouraging in her clients. I have to admit, I let her know that I thought her approach to ethics was na├»ve to the point of being delusory and destructive. We did not disembark that flight with warm friendly feelings!

This idea, that people can be divided neatly into good people and not-good people, clearly has well established roots in American culture. It has roots in Calvin’s theology and the Puritans, the folks who came over on the Mayflower. This idea seems to be alive and well today. I hear strong echoes of it when I hear gun advocates contrasting law-abiding citizens versus criminals.

Recognizing the Puritan roots of today’s political conflicts certainly doesn’t solve any problems. John Calvin was no fool. I suspect one difficulty is that his theology was too subtle for most of his followers, so what we’re stuck with is a crude distortion. Perhaps some kind of return to Calvin, learning to dig deeper into his ideas, could be a way to help folks out of their simplistic Manichean trap. Anyway, I hope that a more accurate diagnosis of the problem can help lead us into a healthier way of living.