Pages Menu
Categories Menu

Posted by on Jun 21, 2013 in The Lattice, The Notes, Tonal Gravity |

The Power of the Seventh Chord

The V chord, the major chord based on the 5, is a powerful compositional tool. It points, very clearly and with a lot of tension, directly at the tonic. If you want to lead the ear to the I, the V chord is the top-of-the-line triad.

Why this is so is still a bit mysterious to me. It’s been discussed a lot. It seems to have both melodic and harmonic elements.

Melodies “like” to move short distances in pitch, and the move from the V to the I is elegant melodically. The 7, or major seventh, resolves up a half step to the 1. The major seventh is called a leading tone because of this very property. The 2 drops a whole step, also to the 1, and the 5 stays put.

In harmonic space, voices, especially roots, “like” to move short distances too. The shortest move of all is a fifth, and when the V goes to the I, the root moves down by a fifth. It seems natural that if the ear is anticipating the next chord, it will place its bet on the change that expends the least energy. All three notes could be seen as moving that same short distance, the easiest possible move.

I like to think of it in terms of tonal gravity. The tonic, the 1, is like a sun at the center of a solar system, and it exerts a gravitational pull. Moving away from it creates tension, collapsing into it creates resolution. Just as with gravity, the closer in you are, the stronger the force. The V is right next to the I, harmonically, so the tension is very strong.

The V chord isn’t the last word, however. It’s possible to crank it up, by adding another tense note.

P1080225

The 4 and the 5 are the closest notes to the 1, in harmonic space. These two notes have the strongest tonal gravity of all. Their effect is different — 5 is the strongest overtonal note, and 4 is the strongest reciprocal note. Both point straight at the tonic.

Melodically, the 4 is two half steps below the 5. This makes it a flatted or minor seventh, added to the V chord. So the final chord is called a V7.

Of all the notes we could add to the V chord, the 4 creates the most tension, and it’s pointed directly at the tonic. I say this is the source of the power of the dominant 7th chord.

In Be Love, I add even more tension before I’m through. The melody dances around, and right before the final resolution, it lands on the 6.

P1080237

I’ve added yet another tense note to the mix. It’s not as strong as the 4, but it jacks up the gravity another notch. The root is on 5, so the 6 is two half steps up from it melodically. This makes it a ninth chord — start with the basic major triad, and add a seventh and a ninth.

Now I’m set up as strongly as possible for a return to the tonic, and sure enough when the drop happens it lands with authority. I’m in major land now, and the chorus will feel entirely different from the verse.

Here’s the whole effect:

Next: To the Far Northwest

Read More

Posted by on Jun 10, 2013 in Just Intonation, The Lattice, The Notes, Tonal Gravity |

Home

Tonal music is music that has a particular key center, or home note. Not all music is tonal, but most is, worldwide.

The key note is at the center of the lattice of fifths and thirds. All other notes are generated from this one. I call it the 1. It’s also called the tonic. When we say a song is “in the key of A,” we mean that A is the tonic.

This isn’t any particular A. In the key of A, every one of the ten or so A’s within the range of human hearing is a tonic, or perhaps more accurately some octave of the tonic. The tonic itself is an abstract concept, of “A-ness.”  In concert pitch, A is defined as a vibration of 440 cycles per second (called Hertz, or Hz), and any octave of this, up or down, is also a tonic. Thanks to a remarkable (and handy) quirk of human perception, multiplying or dividing a pitch by 2 does not change its essential character. So 220Hz is also an A, as are 110, 55, 27.5 — and 880, 1760 and so on forever.

The tonic doesn’t even have to be one of the 12 equal-tempered notes — it can be halfway between A and A#, and it will still work just as well. The rest of the notes are simply calculated from that home note. The resulting music will be in tune with itself, and will sound fine, even though it has no relation to concert (A=440) tuning. In learning songs from old recordings, I’ve found that many are in between two official keys. The instruments are tuned to each other, but not to any outside reference. They sound great.

The tonic sounds like home. The great driver of tonal music is the sense of departure from, and return to, home.

Be Love, like many tonal songs, starts right off with the tonic. It makes a statement, with the very first note: “This is where home is.”

Again and again throughout the song, the music departs from home, creating tension, and then returns to it, relieving the tension. The following clip contains two such homecomings, at 0:07 and again right at the end.

Then, finally, the song ends with the tonic. Ahhhh. Journey complete, the lattice has been explored, and after many adventures Sam Gamgee is back in Hobbiton.

Not all songs begin and end on the tonic. If you want the song to sound resolved, finished, end it on the tonic. If you want it to sound unresolved, unfinished, end it on another note. It’s a powerful tool. Listen to the end of Cream’s Sunshine of Your Love.

Have you ever had the experience of the audience clapping at the wrong time, in the middle of a song? It’s embarrassing!

Usually it happens when you pause for dramatic effect, and the audience thinks you are finished. You can send a strong signal that the song is not over by pausing on a chord that is clearly not the tonic. Then, when you do want the audience to clap, give them a big tonic chord and they’ll know what to do.

Next: The Compass Points

Read More

Posted by on Jun 6, 2013 in Just Intonation, Recordings, The Lattice, Tonal Gravity |

Be Love

After two years of working mostly with existing material, I’m happy to be writing songs again. This one took me over completely for a few days, and then I spent another couple of weeks recording it and animating it on the lattice.

Be Love is a simpler song than Flying Dream, and I think it does a better job of illustrating what the lattice is all about. A couple of notable moments:

  • Several times, all the notes suddenly collapse to the 1, the note in the center. Check out the feeling of arrival, or homecoming in the music when it happens. It’s especially powerful going into the first chorus at 1:12. This is a real-time demo of tonal gravity.
  • During the verse, the song hangs out in the left part of the lattice, and then for the chorus it moves to the right. This is an example of a change in mode — the song stays in the same key (1 is still the center) but two of the scale notes change. The language of pure music doesn’t translate literally to English, or to emotion, but it evokes its own sensations that can support, or contradict, the words and feelings in the lyrics.

Next: Home

Read More

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

Cadences

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

Read More

Posted by on Mar 11, 2013 in Consonance, Just Intonation, The Lattice, Tonal Gravity | 1 comment

Tonal Gravity

I believe that the great driving force in tonal music, that creates the drama and story of the music itself (independently of any lyrics), is the longing for home.

Home is the tonic. If a song is in the key of A, all the A’s in their various octaves will sound like home.

Although there are many exceptions, most music begins on the tonic, to show the ear what key the piece is in, and ends on the tonic, to bring the listener home again. In between, the music wanders, out and back again, creating tension and resolution.

One of the beauties of the lattice is that it shows a clear graphical display of this tension.

It’s as though the tonic creates a sort of gravitational field around itself. It acts a lot like real gravity. The chords and notes move in this gravitational field, like planets and moons around a sun. The gravitational field follows a few basic rules:

  1. Movement away from the center creates tension; movement toward the center gives a sense of resolution.
  2. Notes that are overtonal from the center, generated by multiplying, located to the right and up, will feel more resolved. Notes that are reciprocal, generated by dividing, to the left and down, will feel unresolved.
  3. 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.
  4. The closer together two notes are, the more consonant, or harmonious, they will be when sounded together. The farther apart they are, the more dissonant they will be, the more they will clash.

Roots generate local gravitational fields. I think of them as Jupiter to the tonic’s Sun. When the root is on the 5, for example, it shifts the gravity field to the east on the lattice, and the 2 and 7 become harmonious, consonant notes, rather than dissonant ones. The tonic still has great influence, so the entire chord feels unresolved — a 5 chord pulls very strongly toward the 1 chord, a property that is heavily relied upon in Western music. As long as the 5 is the root, though, the 2 and 7 will be consonant harmonies, because they are close to the 5 on the lattice.

Here is a movie to show how that works. The music starts with a tonic chord. Then, one at a time, the 2 and 7 are introduced. These notes are dissonant, and create a sense of tension against the tonic.

Then the root moves to the 5, and the character of the 2 and 7 changes. Now they form a major chord based on the 5, a harmonious configuration. They have become moons of Jupiter. Hear how the dissonance goes away? But there is still plenty of tension, as now there are three notes venturing away from the center, pulling the ear back toward home.

Then the root moves back to the 1, and the 2 and 7 collapse back in toward the center. There is a sense of arrival.

This movie illustrates another observation: consonance / dissonance and tension / resolution are not the same thing. They both relate to distance on the lattice, but they do not necessarily track together. When the root moves to the 5, the dissonance goes away, but there is a new tension, a drive to resolve toward the center. The ear remembers where home is, and longs for it.

These principles can be consciously used to create desired effects when writing and arranging. Resolution and consonance give the music beauty, and tension and dissonance give it teeth.

Next: Cadences

Read More