Pages Menu
Facebook
Categories Menu

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.

 

 

Read More

Posted by on Nov 14, 2012 in The Lattice | 0 comments

Harmonic Space

Now to relate all this to the lattice in the video.

Listening to music is like going on a journey. Most tonal music starts by establishing a center, or basic note, and a basic harmonic framework for the song, such as a major or minor mode. A few melody notes, and a beginning chord, and you have some idea of the space in which the journey will be occurring. Strauss’ Also Sprach Zarathustra (of 2001 fame) is a great example. The famous opening section, called “Sunrise,” gives an extremely clear sense of home. You know exactly where you are, sonically.

By the way, it’s fun to hum this while using an electric toothbrush.

The piece goes on to travel away from this home, and back again, many times. The journey takes place in a space of some sort, an auditory environment.

But what might this space look like? One way to visualize music is staff notation:

It’s beautiful, and if I know how to read it, it will tell me what the music sounds like. It doesn’t do such a good job of showing me why music sounds the way it does. Neither staff notation, nor the 12-tone scale, gives me a particularly clear idea of how music works. Why would this be restful and sonorous:

major

While this, though beautiful in a different way, has tremendous tension? Sounds like the villain (or the cat) is about to pop out and scare you.

aug

Okay, okay, here’s the resolution:major

Aaahh.

If I know a lot about music theory, I can interpret the notation and come up with explanations. The second example is an augmented chord, and yes it sounds like that. But why, Mom, wh-wh-why?

Next: The Lattice

Read More

Posted by on Nov 7, 2012 in Just Intonation, The Lattice | 0 comments

The Tonic

The heart of the lattice is the note called 1. This note is the tonic.

Almost all the music you hear — pop, rock, classical — has one note that is at the center, a master note against which all other notes are measured. That note is the tonic. It’s the Do of Do Re Mi. When you call a scale “G Major,” or say that a song is in the key of G, the G is the tonic.

A single note means little by itself. But when it’s considered in relation to the tonic, it acquires meaning. The examples in yesterday’s post show how a note changes character when played against different tonics.

The tonic establishes the framework for the rest of the notes in a piece. It’s the anvil on which the music is forged.

The tonic can be any note. When you tune your guitar by the campfire, without a tuner, just tuning it to itself, you’ve chosen a reference frame that will make perfect sense, regardless of whether it’s the same frame as a piano or orchestra back home. You can happily play great music in the key of G-and-a-half, if you’re playing solo.

Once you’ve established the tonic, the rest of the notes are tuned, and named, relative to that note. The tonic is the center, the Big Bang of that particular musical universe. The rest of the structure comes from the interplay between the tonic and small, whole numbers — mainly 2, 3, 5 and 7.

The tonic is Home. The lattice shows how music is a journey, away from home and back again, through different lands, each with its own scenery and feeling.

Next: Harmonic Experience

Read More

Posted by on Nov 6, 2012 in Just Intonation, The Notes | 0 comments

Notes and Intervals

A note, in music, is a sound with a particular pitch. Pitch is frequency, measured in cycles per second, or Hertz (Hz). The faster the vibration, the higher the pitch.

A vibration, at, say, 220 Hz, all by itself is a note by that general definition. But the note doesn’t acquire its distinct personality until it’s considered in relation to some other note. That relationship is called an interval.

Here is that 220 Hz note, played on a cello, all by itself: 220 Hz

Here it is in relation to a note an octave below, vibrating half as fast, at 110 Hz: 220 and 110

It still sounds like the same note. But now play it with a note vibrating at 1/3 of its frequency, or 73.33 Hz. The 220 Hz note acquires a very different character: 220 and 73

And now with a note at 1/5 its frequency, 44 Hz: 220 and 44

Even though the 220 Hz note always has the same pitch, in a different context it has a different personality and function.

The lattice of the Flying Dream video does not show absolute pitch. Each intersection, or node, represents a note, named according to its relationship to one special note: the Tonic.

Next: The Tonic

Read More