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Posted by on Sep 10, 2013 in Background, Equal Temperament, Just Intonation, Recordings, Septimal Harmony, The Lattice | 2 comments

Premature Nostalgia: Making Friends With Equal Temperament

I just recorded a new song, and it’s a perfect example of how equal temperament and just intonation can get along together.

Here’s the cut:

 

Reading this blog might give you the impression that I’m “against” equal temperament and “for” just intonation, or untempered music.

True, discovering untempered music has been like sailing to a new world. It’s delicious to have 20 or more notes to work with instead of 12, each with its own individual personality.

Equal temperament, however, is a fabulous invention. The lattice of fifths and thirds does not quite repeat. If you start with any note and go in any direction, you will soon encounter almost the same note again, but it will be off by a comma, a small interval, from the original note.

There are no two notes tuned exactly alike on the entire infinite lattice.

Equal temperament flattens out the lattice just a hair so it does repeat. Now there are only twelve notes to work with, and they imply the untempered ones in the ear. This innovation makes lots of things possible in music. Beethoven and Mozart could not exist without it.

It’s sometimes said that equal temperament and just intonation are incompatible with each other, because the notes will be out of tune. I say they can get along fine, you just have to show ’em who’s boss.

I submit for your consideration: Ray Charles.

Ray Charles’ piano is an equal tempered instrument. Ray Charles’ voice is most certainly not. He is singing the exact resonant notes, those blue notes, all tuned just like a gospel choir, which is what he grew up loving. Ray is boss. His voice establishes the tonality of the song. The backup singers, the horns and the standup bass all agree, this song is in the harmonic pocket, and it resonates.

That leaves the piano slightly out of tune, but who cares?

Notes that are slightly out of tune don’t necessarily sound bad — that’s the basis of the “chorus effect.” No two singers in a choir are exactly in tune with each other, and the resulting complexity is a huge part of the sound of the choir.

So if the tonality is established in the ear, maybe the equal tempered notes, which are only a bit off after all, will just enrich the sound a bit.

Listen to how “Hit the Road, Jack” starts off. First the piano intro. ET. Then the horns kick in, and they start to establish the soul of the tune. Then come the backup singers, that gospel choir. When Ray’s voice finally joins them, the pocket is waiting for him, and he proceeds to own it. The piano is now a background instrument.

I think that’s the secret. Put untempered instruments up front, and ET instruments more in the background. This asserts the untempered tonality in the ear.

Playing acoustic guitar and singing is a great playground for this. The acoustic guitar is, in its bones, an equally tempered instrument. Fretted instruments drove the adoption of ET in Europe, even before keyboards did. The voice is the archetypal untempered instrument. It can do anything.

If the guitar is boss, the song will be in equal temperament. If the voice is boss, you can establish any tonality you want (blues, Gypsy, whatever), and the guitar will tag along. You can retune it in the ear, just like Ray retunes his piano.

Here are some tricks for making friends with acoustic guitar (or any tempered instrument):

1) Sing solidly in tune, with the tonality coming from you, and not from the guitar. Don’t follow the guitar, lead it. The song is the melody, it is your voice, and you are accompanying that voice with guitar notes.

I like to think of the guitar as playing the grid lines on the map. The guitar notes are perfectly equally spaced, and are excellent reference points. The guitar tells me where I am. We completely agree on one note, the tonic. I use the tonic on the guitar as my true home base.

My voice is playing the actual territory.

2) Sing louder than the guitar.

This isn’t all that easy. The guitar is projecting outward, so it sounds louder to the audience than it does to me. The voice is right there in my head, so it sounds quieter to the audience than it does to me. If I sound balanced to myself, the audience will hear way more guitar than vocal. I hear this all the time at open mics.

I’ve found that in an acoustic setting, I have to sing twice as loud as my guitar (from my own point of view) for it to sound balanced out in front of me.

It gets easier with more JI instruments. In “Premature Nostalgia,” the fretless bass and backing vocals are all in strict just intonation. The guitar is truly a backing instrument, and the tonality of the song feels secure.

3) There is a third, more subtle thing you can do to bring the guitar closer to just intonation. The most clearly out-of-tune note on acoustic guitar is the major third. It’s already 14 cents sharp even when perfectly tuned, and the slightest unintentional string bend will take it into some really grating territory. Choose chord voicings that de-emphasize major thirds, and your guitar will sound a lot sweeter. I wrote an article illustrating this effect, here.

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Posted by on Aug 26, 2013 in Consonance, Just Intonation, Recordings, The Lattice | 0 comments

100 Girlfriends, Part 2

My new song video, Real Girl, contains many examples of consonance and dissonance, tension and resolution. In my last post, I extracted a phrase from the song and slowed it way down to illustrate how the bass and melody dance, creating and resolving tension in several different ways. Here is the last half of that analysis.

When we last left our heroes, they were on the 4 and b6, quite consonant relative to each other, but still unresolved because the ear remembers where the tonic is. Here is that clip:

Now the melody moves back to the 7. This interval, against the 4, is the dreaded tritone, the devil’s interval, and it’s dissonant indeed.

Then the bass moves up to the 1, lessening the dissonance, and the melody soon joins it, and all is consonant.

But there is still a sense of incompleteness, even though both the bass and melody are smack on the tonic, the most consonant interval of all. What’s up?

The answer is that the ear remembers that the root is still the 4, and we aren’t quite home yet. Getting there requires a cadence, or final resolution. Notice that in this next clip the bass note never moves, but the harmonies and the melody signal that the root has now moved to the 1 and we are home. The bass note has magically changed character.

Here is the complete sequence, annotated.

Next: The Blue Tritone

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Posted by on Aug 22, 2013 in Consonance, Recordings, The Lattice, Tonal Gravity | 0 comments

100 Girlfriends

There is a passage, in my song Real Girl, that clearly showcases both kinds of dissonance — the kind that comes from harmonic distance, and the kind that comes from reverse polarity.

This melodic passage occurs many times in the song, and it contains a rather dizzying series of tensions and resolutions. My friend Jody Mulgrew, who has an exquisite sense of pitch, experienced actual nausea the first time he heard the song. He told me, “I was wondering how to tell my friend Gary that I didn’t like his new song. Then, before the chorus, it started to sweeten up, and when the song was over I immediately hit the ‘replay’ button. I realized it was just tension and resolution.”

I think my friend was experiencing what I call tonal vertigo. His comment spurred some of my thinking on the nature of harmony, how it may be a byproduct of our orientation software. The “100 girlfriends” section is a roller coaster ride in the tonal gravity field. Here it is in its original form:

Now to slow it way down and take it apart.

The first dissonant melody move is to the 7. The interval is a major seventh, down a half step in pitch, and the harmonic distance is great enough (3×5=15) that the note is quite dissonant. But the bass, alternating between 1 and 5 as so many bass lines do, quickly moves to resolve the dissonance.

Note that there is still an unresolved, unfinished feeling. Even though everything you can hear is beautifully consonant, the ear still remembers that the real root of the chord is the 1. This memory is crucial to tonal music.

The next move creates a different kind of dissonance. This is the tension of reverse polarity.

First the melody moves to the 1. This note is right next to that 5 in the bass, and beautifully harmonious. But there is tension, because it’s a reciprocal note. The way to get from a 5 to a 1 is to divide by 3 — it’s one move to the left on the lattice.

Then it makes a crazy move, to the b6, that gives me vertigo. Not only is this note distant from the bass note (a factor of 15), but it’s the reciprocal version of the major seventh, its mirror twin, the minor second. You’re dividing by 15, rather than multiplying. Here’s the article that explains why this is such an important difference.

If this weren’t enough, the b6 is also a reciprocal of the root. Remember, even though the bass is the 5, the root is still the 1. The b6 is the mirror twin of the 3, an intensely reciprocal note. So the tension is very high.

And, in two moves, the melody has covered a lot of harmonic territory, all in the reciprocal, Southwest direction. No wonder Jody felt nausea! It’s an E-ticket ride.

DisneyETicket_wbelf

Once again, the bass moves to save the day. The chord changes too — that 4 in the bass is the new root. The melody note magically becomes a minor third, not fully consonant, not fully resolved, but a lot better.

In the next post, the famous tritone! Then full resolution.

Next: 100 Girlfriends, Part 2

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Posted by on Aug 20, 2013 in Just Intonation, Recordings, The Lattice | 1 comment

Real Girl, Animated

Here is my third stop-motion animation of a full song.

Real Girl uses a custom nine-note scale. It occupies the Southeast quadrant of the lattice, the zone of the natural minor, with two added notes — the 7, which allows for a major V chord in the progression, and the 7b5, a blue note that is showcased often in the melody.

This scale contains a sharp dissonance, between the b6 and the 7.  I go back and forth between those two notes a lot, with a stop on the 1 in between to help ease the transition.

Watch how the melody and bass chase each other around. In the next few blog posts, I’ll slow this dance down, and show how the polarity flips create tension and resolution. When the melody is below and to the left of the bass, the energy is reciprocal, tense. Then one or the other moves so that the melody is above and to the right, the energy becomes overtonal, and the tension resolves.

Another fun thing to watch is the alternating bass. Roots and fifths are right next to each other on the lattice. The red lens swings like a pendulum throughout the verses.

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Posted by on Jun 22, 2013 in Just Intonation, Recordings, The Lattice, The Notes, Tonal Gravity |

To the Far Northwest

The chorus of Be Love is solidly in major territory. The chords are I, V, IV, the classic backbone chords of the major scale.

The verse, however, is going to be back in the Northwest — I, bVII-, IV. I have to get back over there somehow, and I want to lead the ear strongly so that the move feels right.

Once again I’ll use a dominant seventh type chord. Here’s the shape again:

P1080225

The ear expects a I chord to come after this. Perhaps it’s one of those “nature abhors a vacuum” things. All the notes have tonal gravity that is pointing at the center, yet there’s nothing there. It’s as though the planets are orbiting the sun, and the sun is missing. The ear wants to put it there.

This “dominant seventh” shape is named after the dominant chord, the V7, where it shows up so often. It can be used elsewhere, and is the main tool used in classical music to change keys.

When I started to work this out, I already had a climax in mind for the chorus. In the last line, I wanted to leap all the way to the far Northwest, the ii- chord (lower case roman numerals mean it’s a minor chord), and have the melody sit still while the chords revolve around it. Here’s the ii-:

P1080430

 

It’s a long leap, but I can make it with one transition chord, the I7.

P1080421

Adding a seventh to the I chord sends a strong signal to the ear: “We’re going west!” Normally the next chord would be a IV.

This move is used all the time in music. It’s common for the bridge of a song to start on a IV chord — it’s a shift on the lattice that makes the bridge sound different from the rest of the music, much like my shift to major for the chorus of Be Love. Putting a I7 right before the bridge tells the ear to expect this shift.

I do something a little different, though. There is also a huge vacuum where the ii- ought to be — look how the two chord shapes fit into each other. Sure enough, going to the ii- after the I7 is satisfying and dramatic. Here’s how the sequence looks and sounds.

Notice how the melody leads the way again, by going to the 4. There’s another lovely passing chord, a stack of perfect fifths, right before the change.

P1080425

 

Next: The Septimal Minor Third

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