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Posted by on Nov 4, 2013 in Recordings, The Lattice | 0 comments

The Flying Dream Video (etc.)

Here is the video that started this blog. It is a stop-motion animation of my song Flying Dream, as it moves in harmonic space. It’s a preview of what the blog is all about. Red = bass, yellow = melody, and orange = the harmonies.

Be Love is the second full song video I did. While Flying Dream is all over the lattice, Be Love occupies a small space, moving left and right between Major and Mixolydian modes.

Real Girl lives in the lower right quadrant, minor and dominant.

I’m posting these again so they will be close to the top of the front page. Anjalisa Aitken and The Harmony People have come into my life, and I’m shifting my focus from study and writing to performing and creativity.

I think I’ve pretty well said what I have to say about the lattice for now. The videos are explained, and I’ve brought you pretty much up to speed with my lattice explorations so far. I’ll still be learning, and I’ll keep you posted, but I’m content with this particular yearlong blurt. Time to get out there and put all this cool stuff to use!

There is plenty to find here. A random approach might work best — find a recent article that catches your eye, click links to go deeper, and use the back button to get back up the chain. I’m especially fond of the posts in the Septimal Harmony category.

Enjoy, I’ll be back. Contact with fellow lattice-heads is welcome.

PS I have other presences on the Web. Here are some links:

 

YouTube

The Harmony People (duo with Anjalisa) Beautiful, uplifting, interesting original music.

Facebook
Hotel Utah Artist Page — lots of live recordings.

 

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Posted by on Oct 2, 2013 in Recordings | 0 comments

Be Love at Sacred Grounds

I love open mics. I have two favorites in San Francisco that I make every time I’m in town — Hotel Utah on Mondays, and Sacred Grounds on Thursdays.

It is in places like Sacred Grounds that the culture begins, where it wells up right from the ground, not manufactured or corporate or in service of any agenda but the beauty of human creativity.

Last week I sang Be Love at Sacred Grounds, and my dear friend Claudia took a video. Here it is. I hope you enjoy it. It really gets the flavor of the place.

 

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Posted by on Jul 18, 2013 in Just Intonation, The Lattice, The Notes |

Mixolydian Mode

I’ve been quiet lately because I’ve been working on an animation of my song Real Girl. It’s a complicated one, a dance of harmonic tension and resolution. The bass and melody chase each other around the lattice like courting butterflies.

Meanwhile, there’s more to be extracted from the Be Love video.

A mode is a type of scale, characterized by the pattern of intervals between its notes. The note spacings stay the same no matter what key it’s in. When we say a song is in A major, we mean the tonic is A, and the mode is major. The major mode, also called Ionian, is the familiar Do-re-mi-fa-sol-la-ti-do.

Any combination of notes, covering an octave and organized in pitch order, can be a mode. There is a particular set of modes, often called church modes, that can be played on the white keys of the piano. The different modes start on different notes. The major mode goes from C to C; Aeolian, or minor mode, runs from A to A. Stick to the white keys, and the notes will be right for that mode.

Ionian and Aeolian are the commonest modes in modern Western music, but Dorian (D to D) and Mixolydian (G to G) are popular too.

I wrote the chorus of Be Love first. It’s in major mode. I wanted the verse to have a different feel, so I decided to make it Mixolydian — a favorite for several reasons. I love the name. And, as Mathieu points out in his book Harmonic Experience, it’s particularly easy to improvise over. It’s common in rock music from the seventies on — see the BTO clip in this post. My song Driving is mostly in Mixolydian mode.

The big reason I wanted the change was to make the chorus more of an anthem, by contrast. Mixolydian has a dark, beefy quality to me, and when the chorus comes around it sounds like the sun is coming out.

In equal temperament, there is only one difference between major and Mixolydian scales. The seventh degree is minor instead of major. Starting with G, and going up the white keys, you get G-A-B-C-D-E-F-G. The G major scale goes G-A-B-C-D-E-F#-G. Only the seventh is different.

In just intonation, the situation is a bit different. There are three b7s in the inner lattice:  b7, b7-, and 7b7. Which to choose?

Here is the major scale.

P1110316c

One possibility is to just drop the 7 to the b7:

P1110316d

I like the interpretation below. It uses the b7-, and also changes the 2 to a 2-.

P1110316b

This gives me an in-tune major flatted seventh chord, which I love. In the key of G that’s F major — lots of rock music uses this chord.

The notes of this scale (Western Mixolydian?) are in the same relationship to each other as the notes of the major scale, shifted one space to the left. The intervals are just as consonant as the major scale ones, only arranged in a different order.

It’s easy to write chord progressions in this mode. Major and minor triads form triangles on the lattice (major triads point up, and minor ones point down) and there are five in-tune triads, just like the major scale. Since the triangles are all connected, moving from one to another feels natural and is easy for the ear to follow.

Again I refer to Mathieu’s book. Have I lately? In Harmonic Experience he writes about “matchstick harmony.” Cool stuff.

Here is the scale, animated against a drone.

Next: Mixolydian Matchsticks

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Posted by on Jun 23, 2013 in Equal Temperament, Just Intonation, Septimal Harmony, The Lattice, The Notes |

The Septimal Minor Third

At the very end of the chorusBe Love showcases one of my favorite notes, the 7b3.

Most of the notes of the inner lattice can be approximated on the piano, but not the septimal minor third. It’s in between the keys. Blues pianists can evoke it by trilling between 2 and b3, but only variable-pitch instruments can actually hit the note.

Here it is in context:

It’s fun to sing this part of the song, stretching out that septimal note and tasting its flavor.

The passage illustrates the harmonic function of the note. It’s the septimal flatted seventh of the 4, also called the harmonic seventh or barbershop seventh. This is a beautifully consonant note, a great addition to a major chord. It’s generated by multiplying by seven. I use it here as a harmonic seventh over the IV.

Relative to the 1, the 7b3 is a compound note. To get there, you divide by 3, and then multiply by 7. The ratio is 7/6, octave reduced. The pitch is 267 cents, between the 2 and the b3. Here it is on the scale. The colored notes are in just intonation, the black ones are in equal temperament.

Scale with 7b3

Over a I chord, the 7b3 sounds bluesy, restless, gutsy — it’s the insistent melody note in Taking Care of Business. It’s at the heart of the guitar riff in Dizzy Miss Lizzy (George often bends it up to the major third), it’s Jagger’s haunting first “ooooh” of Gimme Shelter. Gimme Shelter

The Stones’ music is a feast of 7b3’s. So is Led Zeppelin’s. These septimal notes are found everywhere the blues has left its impression.

There’s an old question: why do the minor melody notes of the blues sound good over major chords? The web is full of discussions as to why this is so.

I think it’s because the blue minor third is not the b3, but the 7b3. The regular minor third is a reciprocal third, and harmonically it doesn’t fit with major chords — it’s in a different part of the lattice.

But the 7b3 is an overtonal 7th, built on the 4, generated by multiplication. The major notes are made by multiplying by 5. Times 5 and times 7 go together very well. The harmonic seventh chord is a thing of beauty.

There’s an implication for blues guitar. You can’t play this note in the classic minor pentatonic blues box. You can play a b3 (bend it a little to tune it up), or a 3 (bend it harder), but not a 7b3, it’s flat of the b3, and you can’t bend down.

minor pentatonic

You can play a 7b3 by grabbing the 2, one fret below, and gently bending up to it. The following box works great for septimal notes. They’re all laid out under the ring finger. Bend them by less than a half step.

major pentatonic

This box makes it easy to play the classic bit of melody, 7b3 – 2 – 1. All three songs I linked to earlier have this melody in their bones — BTO, the Stones, the Beatles. It’s everywhere. Here it is in Be Love.

Next: Mixolydian Mode

 

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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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