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Posted by on Dec 4, 2012 in The Notes | 0 comments

The Minor Seventh

The farther we get from the center, the less consonant the notes are, when played against the tonic. Consonance is a whole subject. It’s generally spoken of as though it could be plotted on a scale, from consonance to dissonance. I think this is a big mistake. Consonance has more than one dimension. Trying to force these independent dimensions of consonance onto a one-dimensional scale leads to unnecessary confusion.

Anywayy … The minor seventh is a pretty dissonant note in all dimensions. It’s three moves away from the tonic, down a third and up two fifths:

The ratio is 9/5.

This is some beautiful, exotic harmony.

Here’s a progression that shows off the flavor of the b7, in just intonation:

Hey, that’s beautiful! I worked it out as an illustration, with the idea of showcasing the minor seventh, and it turned out to be really nice music.

See why I’m in love with the lattice? It’s a beauty engine.

Next: Untempered Vs. Tempered

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Posted by on Nov 25, 2012 in The Lattice | 0 comments

The Major Scale

The notes 1, 2, 3, 4, 5, 6 and 7, clustered at the center of the lattice, constitute a major scale. This tuning uses the smallest ratios (the ones with the lowest numbers) available for each position in the scale. It goes back at least to Ptolemy in the 100’s AD.

I find it visually beautiful. It’s like a cat’s cradle.

Here it is again, with a drone on the tonic, to show how the notes resonate with the drone. Each one has its own flavor, its own harmonic character.

Notice how the melody never moves from a note to the note next door. It always moves two grid segments. This is a first look at the difference between harmonic space and melodic space.

Melodies “like” to move up and down on a linear scale. They want to go to a nearby note when they move — that is, near by in pitch. We hear, and sing, small movements in pitch better than we hear leaps.

Harmonies “like” to go to nearby notes too, but harmonic space is different than linear, melodic space. The 1 and the 5 are harmonic neighbors. In fact, they are as close together as notes can be, harmonically, without being the same note — a single factor of three. But they are far apart melodically — the 5 is almost at the midpoint of the scale.

1 and 2 are melodic neighbors, It’s easy to for the voice to move from one to the other. But they are far apart harmonically — two factors of three. A small move in pitch can produce a large harmonic jump.

Arranging a melody and chord progression involves interweaving the notes so they work in both spaces. The melody will tend to move up and down by small melodic steps, close together on the scale. The chords will tend to move by small harmonic steps, close together on the lattice.

It’s a bit like designing a crossword puzzle, working “up” against “down” until it all fits. The lattice is a wonderful tool for visualizing this dance.

Next: Reciprocal Thirds

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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

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