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Posted by on Mar 12, 2013 in The Lattice, The Notes, Tonal Gravity | 2 comments


A cadence is a chord progression that gives a sense of arrival or resolution.

One particular cadence, the V-I (or V7-I) is especially powerful. In classical music, a V-I cadence is practically mandatory at the end of a piece, and it is the biggest gun in the composer’s arsenal when changing keys, or modulating.

The following movie shows a I-V-I progression. It starts on the I to establish the tonic, then there’s tension, then resolution. The V-I cadence draws the ear back to the tonic chord.

Here’s a cadence that visits the V7 first:

To me it looks like the V chord tosses out a rope, lassos the tonic and pulls.

It’s interesting to look at the notes in light of tonal gravity. In yesterday’s post, I laid out two rules of gravity on the lattice:

  1. Movement away from the center creates tension; movement toward the center gives a sense of resolution.
  2. The closer you are to the center in your journey, the stronger the sensations of tension and resolution are. The field is stronger closer in, just like real gravity.

There are four notes in the V7 chord.

  • The 5 is as close as you can get to the 1 (in harmonic space), so it creates a lot of tension. It is an overtonal note — that is, it appears in the overtone series of the 1. Pluck a string tuned to the tonic frequency, and the 5 will tend to be strongly present in the timbre of the sound. The way I see it, the ear is always searching for home. Every note gives it two clues — which direction is home, and how far away is it? The 5 gives a very strong signal, pulling the ear toward the tonic: “Home is this way, and it’s close! Come on!”
  • P1060030The 2 reinforces this conclusion. It’s farther out, so the signal is weaker, but it is still in the harmonic series of the 1, and it’s pretty close in. The little detective in the ear gets another clue.
  • Same with the 7, although now the effect is weaker. In traditional theory, the 7 is called a leading tone, and it’s thought to pull melodically toward the 1 — a sort of gravity in melodic space. It “wants” to resolve a half step upward. I feel this too, and I think the harmonic pull reinforces it further.
  • Then there’s the 4, which is what makes it a seventh chord (the 4 is a minor seventh of the 5). This is a reciprocal note, that is, it’s generated by division rather than multiplication. Like the 5, it points directly at the 1, from point-blank range. Reciprocal energy is different from overtonal energy. To me, it feels as though reciprocal notes are pushing toward the tonic — the message feels more like “Home is that way, now go!”

For the detective in the ear, the 4 slam dunks the case. The only reasonable conclusion is that home is located in that empty space between the 4 and the 5 on the lattice. Any other interpretation is much weaker. Every note in the V7 chord is pointing strongly to the 1, and when the notes collapse inward to the I chord, the resolution is completely satisfying.

I’ve heard a charming story about Beethoven. Apparently the composer was depressed and wouldn’t get out of bed. A friend came by and played some music, ended on a dramatic V7 chord, and sat down to wait. Beethoven finally had to get out of bed and play the tonic chord. Tough love! Don’t know if the story is true, but it certainly could be. The V7 is strong medicine.

When this particular chord shape appears somewhere else on the lattice, it can point so hard to its own center that the ear believes the tonic has moved. It’s as though the gravity of the planets is so strong that it can move the sun.

Next: Intervals


  1. Dear Garry,

    i’m so happy for found such a helpful and informative article u wrote while have experimenting and discovery for helping me to trace the musical knowledge particularly there are many good innovative ideas-easier for me to follow as well as get to know more and understand well the system of tonality,conception of sound based on nature Acoustic phenomenon by showing how the music function through the hierarchy of the musical polar by tonic-subdominant-dominant. it was presentable, comprehensive, practical, accessible guide and engaging through using non-music subjects for it help in interpretation musical and providing even more supplementary materials for pedagogical tool. another hand, your writings sparkle with the wit and wisdom of man eager to share your intellectual passions. i just cannot wait to continue for further reading and learning more by this discussion and hope if you answer yes-so that to be accepted and joining was part of your reader and able browsing your website. looking forward your reply and more articles.

    thank you!

    peter ngu

  2. Thanks Peter! Have fun with the blog — do be sure to read that book I talk about all the time, “Harmonic Experience.” I owe a great deal to Mr. Mathieu. And I love to discuss this stuff, you may write me any time through the website’s contact page. All the best!

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