The Real Parallel Galaxy

an "Offset Modal System" theory put into musical practice, by Emmett Chapman ©2004

Emmett's video of "Parallel Galaxy" from Hands Across the Board


Emmett's original sheet music

In July 1980 I first devised a network of "offset scales" as I referred to them at the time. I improvised on the colorful seven-tone scales with one altered tone, then drew circular charts that related the scales to each other in a modal network, a process of synthesis that revealed lush new modes as I rotated the chart to put different scale degrees at a key center reference point.

The following month I composed "Parallel Galaxy" using this system, but called it "Starry Night". In 1984 my brother Dan and I finalized the graphic art for the circular charts depicting my discovery, which I renamed "Offset Modal System". In 1985 I recorded "Parallel Galaxy" on The Stick? in duo with vocalist Josh Hanna and this became the title track for my first album, an LP released that year (now re-mastered to CD).


Triple Wheel™ chart delineating the traditional
Greek modes (inner Wheel), the Offset Modal System
(middle Wheel), and Double Offset Modes (outer Wheel).

The unique modal theory became "crystallized" in the "Galaxy" song, but it also opened up a "galaxy" of improvisation leading to ever new compositions and novel song arrangements. I also expressed the complete discovery on two unique charts which illustrate in seed form this music theory put into practice. One chart was a triple "Wheel™" with twelve divisions patterned after astrology charts. The other was a "Stone™" chart of seven facets within a matrix of twelve equidistant points of a circle, the points of the facets representing the seven scale tones contained within twelve tempered tones.

The Wheel and Stone charts were then published on my "Galaxy" LP jacket to announce and portray the new theory, albeit largely non-verbally, yet fully revealed to anyone who likes to delve into closed systems of knowledge. If you can see a good part of the pattern, you can put together the rest and create a "galaxy".

The Wheel teaches the complete Offset Modal System in geometric, non-verbal fashion. For full comprehension, the Wheel should actually be played by an improvisor on a polyphonic instrument, the unusual network of chords backing the offset modal melody.

The twelve divisions represent the twelve tempered tones or chromatic half steps. You ascend the scale by moving counterclockwise until you arrive at the first division again, an octave higher. In this sense, the page with the Wheel is conceptually a spiral in the depth dimension as you move counterclockwise up the octaves or clockwise back down.

The dots represent the seven tones of various familiar and not so familiar scales. The blue circles around some dots indicate root positions of various exotic major scales, and the corresponding blue lines show major 3rd intervals. The red circles around other dots indicate the roots of exotic minor scales, and the corresponding red lines show minor 3rd intervals. (The Wheel chart construction makes use of the divisions, directions and angles of a horoscope chart, with many interesting correspondences to astrological interpretive techniques.)

The Wheel's first division is in the space just below the left horizontal line (corresponding to the "first house" in astrology and the "rising sign"). I arbitrarily assigned this first division a C note, but it could be any of the twelve chromatic notes.

The inner wheel contains six yellow lines connecting seven yellow dots which represent the familiar seven-tone Greek modes. The yellow lines show perfect 4th intervals. By connecting seven notes that are all 4ths apart, you always get one of the conventional Greek modes.

Starting with the inner Wheel's yellow dot just below the left horizontal line, contained in the first division marked C, and moving counterclockwise up the scale, you have a whole step, whole step, half step, whole step, whole step, whole step, and a half step which returns you to the tonic or root up one octave. This is of course the C major scale, or the Ionian mode in C.


Original art for Triple Wheel chart, shown in black
and white without lines representing intervals.
Following the yellow connecting lines clockwise (downward in pitch) from C, six of the seven C major scale notes all connect in 4ths, until you get to B where the path of 4ths comes to a dead end within this C major scale. Moving in the other direction from C, there is just one yellow line which leads upwards in pitch to F, the note that completes the scale and forms a cul-de-sac at the other end.

From this inner Wheel you can see that the entire seven tone Greek modal network is connected in a series of 4th intervals, as well as being arranged in successive whole steps and half steps (the familiar major and minor 2nds). Thus the familiar Greek modes that still dominate most of today's music can be viewed as melodically colorful scalar intervals or as structural 4th intervals, depending on the composer, the song and the instrument played.

Now offset one of the notes counterclockwise to the next higher division and shift this slightly modified scale over to the middle Wheel. As a somewhat "loaded" metaphor, this looks very much like a valence electron making a "quantum leap" to a higher and less stable energy band.

But which note of the beautifully balanced Greek modal system should be offset? Surprisingly, it is the least obvious note, C itself in this C scale oriented chart, leaving no C scale or C chord to be played. The S-curved arrow on the lower left shows Greek C on the inner Wheel being offset to Db on the middle Wheel.

Now there are five notes in a row separated by whole tones, placed generally in the upper region of the middle Wheel, and centered on A at the top. In fact, the offset mode as seen from A as a root is symmetrical, with major 2nd and 3rd, natural 4th and 5th, and flatted 6th and 7th. I felt an ancient Middle Eastern mood of timelessness when I first improvised in this offset mode, and labelled it "Paradise" on the Wheel.

Exploring the seven notes on the middle Wheel, I discovered the "offset" network of seven exotic modes, each mode generating its own characteristic chord (with various voicings of course). I consider this to be the most musically fruitful element of the whole system. Moving the chordal root a whole step downward from A to G, you have a major scale with raised 4th and flatted 7th, labelled "Natural Overtone". Moving down another whole step to an F root, you have a "Super Major" scale with raised 4th and 5th, and natural 6th and 7th, that is, everything raised but the root.

The middle Wheel's exotic relative minor scales and their derived chords all blend well with the above three offset major scales, especially D minor with a natural 7th, and E minor 7th with a flatted 2nd and natural 6th.

Placed generally in the upper region of the middle Wheel is a sequence of five notes forming most of a whole tone scale. From any possible chord in the offset network you can "escape" into the complete whole tone scale simply by replacing D and E with an Eb, the missing note of the implied six-note whole tone scale. This transition serves as a "catapult" into a more abstract geometry of music and fingers, perhaps conveying a "lost" sensation.

Placed generally in the lower region of the middle Wheel is a sequence of six notes forming most of a diminished eight-tone scale, characterized by alternating whole steps and half steps. Again this provides another musical escape into a more abstract pattern, the full diminished eight-tone scale, simply by replacing A at the top with both an Ab and a Bb.

This "Paradise" is a bit unstable. The partial whole tone sequence (attracting augmented 5th chords) tugs against the partial eight-tone sequence (attracting diminished triads). The apple tastes good but may not digest well!

Both of the above "escape" scales can be accompanied by any of the offset modal chords derived from the middle Wheel, with smooth transitions back and forth between the six, seven and eight-tone scales.

And now another valence electron must make the leap to the next higher division to reach the outer Wheel. Which note shall it be? Here intuition played a role in discovery. Music theory teaches that notes 5ths apart are the most closely related - but why? An explanation: Any pair of low pitched fundamental notes placed 5ths apart will generate compatible overtones with only one upper harmonic clashing.


Transposed Triple Wheel for "Parallel Galaxy" in D.
© Emmett Chapman 2004
G is the note on the Wheel that is up a 5th from the earlier offset C, so I now offset the G to Ab on the outer Wheel as shown by the second S-curved arrow at the upper right of the triple Wheel. A new interval of a minor 3rd (1 1/2 steps from F to Ab) is thus brought into the network - now called the Double Offset Modal System™. From the A root, a Middle Eastern major scale emerges, with flatted 6th and natural 7th (the 1 1/2 step interval). From the E root a 5th away from A, a second Eastern major scale emerges, with flatted 2nd and major 3rd (again the 1 1/2 step interval).

This outer Wheel contains the most colorful and exotic scales of all, and is organized into its own modal network, now with the original Greek modal C and G notes offset to Db and Ab. This pattern further "destabilizes" all the resultant seven-tone scales, creating more space and more clustering. Some very odd scales become integrated to the total system through this outer Wheel, including those with both major and minor 3rds, and a D minor scale with raised 4th and natural 7th (Lydian minor?).

All three networks on the triple Wheel form a coherent superstructure, each network shifting smoothly to the next. Improvising harmonically and melodically on The Stick, I like to make transition over the entire range, from the Greek modes to offset modes to double offset modes, and sometimes into one of the two symmetrical "escape" scales and back again. Such a comprehensive music "theory" of harmony seems to add "will" and direction to my wanderings.

An especially interesting transition zone is between Offset and Double Offset Modes. The middle Wheel with G and the outer Wheel with the offset Ab can be merged together to superimpose an eight-tone scale of unusually colorful chords and modes. Some of the highlights: The A root's scale now has a pair of 7ths both flatted and natural: the Db root's scale now has its missing 5th with half-steps on either side; the D root now has a pair of 4ths both natural and raised, while retaining the 5th, and the G root now has a pair of 2nds (or 9ths) both flatted and natural.

In composing and recording "Parallel Galaxy", I wavered between middle and outer Wheels, at times merging them into a single eight-tone scale containing yet richer versions of the song's chords. Because of how my "Galaxy" song arrangement sat on the fretboard, I transposed the triple Wheel up a 4th, using the root pattern at the top of the Wheel (marked A) as the song's key center, but transposing it to D, the best key for my arrangement of the song. (See my Triple Wheel transposed up a 4th for "Parallel Galaxy" in D.)

My arpeggiated intro and ending pattern of interwoven fingers is based on the offset modal chord progression of D, F#, Bb and back to F# over four bars and repeating. A blue triangle on the middle Wheel delineates this unusual three-chord progression. All three chords are major flatted 13ths with the added colors of three consecutive half steps gained from the superimposed eight-tone scale. The D-13 key center places the three half steps at flatted 7th, natural 7th and tonic (root) degrees of the D scale. The F#-13 chord places them at raised 4th, 5th and flatted 6th (or -13) degrees. And the Bb-13 chord places them at 2nd (or 9th), minor 3rd (or raised 9th) and major 3rd degrees.

After the intro, the Galaxy theme begins with a dominant A7-9+9 chord, as shown on the outer Wheel where the second offset note brings a major 3rd into this A chord. The theme quickly resolves to its key center of D-13 with the "haunting" combination of a natural 7th and flatted 7th.

The "Galaxy" theme's chord progressions move around the Wheel in typical modal fashion from the D major key center. The sub-dominant (IV chord) is a G minor with a major 7th and sometimes a raised 4th, and can resolve to C7+11 (the VII chord) before returning to D (the I chord). Em9b5/13 (a II chord) acts like a m7b5 jazz chord to resolve to the dominant A7 (the V chord). The A dominant 7th chord gets its major 3rd from the outer Wheel. There is also a very similar substitute dominant 7th chord located down a minor 3rd from A with its root at F# and its 5th picked up from the outer Wheel's C#. Both are jazz blues oriented b7-9+9 chords and are interchangeable.


"Strings in Fourths to Infinity"™
fingering chart for the Offset Modal System™.
To make transition to the Double
Offset Modal System, just change
one note at three octave positions
on the chart, moving
to the "X" positions.
© Emmett Chapman, 2004


The Galaxy theme later modulates to other key centers, and with each modulation the Wheel's note pattern would have to be re-lettered to account for the temporary change of key. Still, the triple Wheel itself and its geometry of note relationships always remains the same. In fact, the lettered notes could be dispensed with altogether and the divisions could simply be numbered 1 through 12, creating a more universal Wheel to accommodate all possible transpositions of offset modes within the tempered chromatic scale.

Conceptually, you can multiply the above modes and their derived chords by twelve to account for all possible transpositions of the entire triple Wheel, replacing C in the first division to the left, or A in the tenth division at the top, with any other note of the chromatic scale. Thus the seven offset modes, times twelve transpositions of key center, equals 84 new scales, times three to include the double offset modes and the eight-tone superimposed scales, equals a grand total of 252 exotic scales with which to color your melody lines and harmonic structures.

The fingering of offset scales is not quite as uniform and repeatable as with the Greek modes. You have to memorize a more elaborate finger pattern across a distance of seven strings. The accompanying "Strings in Fourths to Infinity" chart shows how to play the Offset Modes of the middle Wheel. Each fret should be considered an "X" fret, meaning that the scalar fingering pattern will work in any key and register of the fretboard. The lowest pitched fret is at the left. The lowest tuned melody string is across the bottom. There are four symbols for the four fingers as in my "Free Hands" lesson book and Greg Howard's "Stick Book" series with "Staff Tab" - a circle for the first finger, a diamond for the second, a triangle for the third, and a square for the fourth finger. For those Stick players who tap their melody strings using a basic three-fingered technique, just consider every square on this chart to be a triangle, both shapes representing the third finger. Thus your first three fingers play three offset scale notes per string and your right hand spaces the intervals along the frets accordingly.

Though not quite as easy to finger as the Greek modes, there is an incentive - a network of only seven notes to add a "galaxy" of novel chord voicings and melody lines to your music. Each chord or scale taken by itself may not necessarily be new to the repertoire of composers and improvisers, but this system of relating all of them in one combined modal network is as far as I know something new in music theory.


STONE™ chart delineating
the 7-note Offset Modal
System, with a whole tone
sequence toward the top
and a diminished 8-tone
sequence toward the bottom.


My Stone chart offers a simpler presentation of the middle Wheel's offset modes. A7-13 is at the top and takes you counterclockwise through a major scale with flatted 6th and 7th scale degrees - a Mixolydian mode but with a flatted 6th. The pair of minor chords/scales at D and E have been thoroughly explored in many a jazz solo, the D minor scale being Dorian in nature but with a natural 7th, and the E minor scale being Phrygian in nature but with a natural 6th.

In this offset modal network, similar scales and chords come in adjacent pairs, as with the above Dm and Em scales, also the G7 and A7 pair, and the Bm7 and Dbm7 pair, both with raised 4ths. There is also a non-adjacent pair of fascinating b7-9+9 chords with E and Db roots. These four pairs seem to convey a parallel, shifting motion to the offset harmonic structure, reminiscent of Debussy's "wandering" progressions. Standing alone is the F "super major" scale where everything is raised that can be raised, and it works nicely into progressions with G7+11 and A7-13.

The reason why these complex chords and scales don't disintegrate into atonality is that they are all bound together in a meaningful relationship of seven and eight notes. By repetition this offset scale becomes a strong frame of reference as chordal roots move from one scale degree to another, each time casting the system in a "different light".

The Stone chart clearly depicts the shape of each seven-note offset mode. The sequence of whole tones toward the top is marked in blue and the diminished eight-tone sequence toward the bottom is marked in red. There is an element of "good and evil" inherent in this unstable duality of conflicting patterns. The "good" force is of course marked in blue to show 120 and 60 degree relationships of notes in the circle (major 3rds and major 2nds), corresponding to astrology's "harmonious" trine and sextile "aspects" (or angles between planets, sun and moon). The "Darth" force gets the red marking to show 90 degree relationships (minor 3rds), corresponding to the "dissonant" squares of astrology. Flatted 5th relationships of 180 degrees could also be red marked on the Stone and would correspond to the dissonant "oppositions" of astrology.

I get the feeling that somewhere in prehistory this has all been worked out before, somewhere between India or Persia to the east and Arabia or Egypt to the west. I feel I'm on to something magical that permeates my music, something that might offer the "keys" to other ancient sciences and disciplines. Modern composers and improvisors have certainly used their intuition and inspiration to arrive at many of the above scales, but none as far as I know have devised a comprehensive multi-modal system to bring all permutations under creative control. I know the value of this Offset Modal System as relates to my own "Stick" music over the years, and I hope it will also "bear fruit" in the music of other Stick players as well as instrumentalists and composers of all genres (but please no apples).


See also:
Parallel Galaxy
Joe McCollam
November 21, 2004.

Wheel Charts and Offset Modal System
Emmett Chapman
September 10, 2001.

Getting started with the Offset Modal System
Emmett Chapman, Steve Gajdos, Ben Weber
November, 2010.


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