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Posted by on Mar 14, 2014 in Equal Temperament, Just Intonation, The Lattice | 3 comments

A Harmonic Journey: ET and JI Compared

The Harmonic Lattice can be viewed as a map of harmonic space. Music moves in harmonic space, just as it moves in melodic space (the world of scales and keyboards). The two spaces are very different from each other.

In melodic space, such as a piano keyboard, when two notes are close together, it means they are close in pitch.

In a harmonic space, such as the lattice, when two notes are close together, it means they are harmonically related.

“Harmonically related” means that one note can be converted into the other note by multiplying and dividing by small whole numbers. A note vibrating at 100 cycles per second is closely related to a note at 300 cycles per second. In melodic space, these two notes are far apart, but in harmonic terms they are right next door to each other — they harmonize.

In my video, Flying Dream, I animated the movement of one of my songs on the lattice. Now I’ve animated a composition of W. A. Mathieu’s.

Mathieu is the author of Harmonic Experience, an astonishing book that takes music back to its origins in resonance and pure harmony, and then uses the lattice concept to bring that harmonic understanding forward into the world of equal temperament. For me, the book opened the study of music like a flower.

The lattice, and my stop-motion animations, have given me a sort of musical oscilloscope. Instead of the music being some sort of black box, I can see inside it, get a visual image of what is going on harmonically. The new tool has made songwriting, improvising and arranging much easier.

I’ve animated Example 22.10 from the book. It’s intended to be an illustration of unambiguous harmony — the chord progression moves by short distances on the lattice, so it is clear to the eye and ear where you are. I think it’s a beautiful piece of music in its own right, a one-minute tour of a huge area of the lattice. It uses 28 different notes!

There are two versions of the video. The first one, in ET, has a soundtrack of Allaudin Mathieu playing the piece on his beautifully tuned piano. This is perfect equal temperament. It uses twelve notes to approximate the twenty-eight notes that the piece visits.

For the second one, in JI, I retuned the piano to the actual pitches of the lattice notes. Now, magically, the piano has all 28 notes. There is a whole new dimension to the music. In the JI version, I feel:

  • Slight vertigo when the music moves quickly
  • Satisfaction when a spread-out (tense) pattern collapses to a compact (resolved) one
  • A great sense of homecoming at the end
  • Stronger consonance and dissonance than in the ET version.

The four voices, from lowest to highest, are red, green, orange and yellow. It’s fun to follow one voice at a time.

This lattice is notated differently. It’s my usual system, but with letters instead of numbers. C is the tonic.

 

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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 27, 2013 in Consonance, Just Intonation, The Lattice, Tonal Gravity | 2 comments

Tonal Gravity and the Major Scale

In my last post, I proposed a simple way to graph tonal gravity against the octave.

Overtonal notes, generated by multiplying, are restful, stable — they have positive polarity, pulling toward the center. Reciprocal notes, generated by division, are restless, unstable — they push. I call this negative polarity. Mixed-polarity notes have both, and I’ve chosen to simply add their overtonal and reciprocal components together to get the total polarity.

Here again is the graph of the 13 most central notes of the lattice.

Tonal Gravity 13-01

The stable notes are gravity wells, and the unstable ones are peaks. Melodies and harmonies dance in this gravity field. Higher points represent tension, lower ones resolution, and the lower they are, the more resolved and stable. The tonic major triad, most stable of all, occupies the lowest spots — 1, 3 and 5.

The polarity map of the major scale looks like this:

Tonal Gravity Major Scale-01The notes are all overtonal except the 4, which is strongly reciprocal, and the 6, which is mixed and slightly unstable.

Here’s a split screen video showing the major scale, against a tonic drone, on both the lattice and the octave. This is an example of how the lattice serves as a Rosetta Stone, a translator between harmonic and melodic space.

Can you hear the push/pull quality of the notes? Each note has its own feeling against the steady 1.

 

 

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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 Aug 15, 2013 in Consonance, The Lattice, The Notes, Tonal Gravity | 0 comments

One More Mirror Pair

I’m almost done with the next full-song video. In the meantime, here’s one more pair of mirror twins for consideration.

The 2- is a common melody note in my songs, and in the blues. It goes well with the blue note 7b3 — there is an extremely common melody that goes 7b3, 2-, 1. It’s a darker, more dissonant note than its comma sibling, the 2.

The b7 is dissonant and gorgeous — check out the sequence at the end of this post.

Each note is a compound of three legs on the lattice — two fifths, or a factor of 9, and a major third, a factor of 5. By the logic of the last post, the short leg should predominate, which would make the 2- slightly overtonal and stable, and the b7 slightly reciprocal and unstable.

This proves out when I listen to the video. Even though the 2- is distant from the center, and quite dissonant, it still feels stable. The tonal gravity field is “pulling” rather than “pushing.”

I’m setting up here for a map of the tonal gravity field. I think I can put some numbers on this stuff. Coming soon. I’ll use that new song animation as a basis — it’s full of fleeting dissonances and polarity flips.

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