Almost all Western Harmony can be experienced as 'modal' -- and also 'symmetric' - at different moments within any tune. When the symmetric tritone interval is intentionally avoided... another form of symmetry takes over - for the moments when each new chord in a progression sounds (or feels) like a new Tonic. These are the moments when the ear lights up with a special color.
What Is Symmetric Modal Fusion:
This study can be thought of as a differentiation (and reintegration) of two opposing (yet complementary) styles (or concepts) of harmonic movement: Diatonic (Modal) Harmony & Symmetric Harmony. Symmetric Modal Fusion is a theoretical observation. The pupose of its design is to provide ideas to train our ears to an enhanced perception (and meaning) of all 12 tones (and all 12 Keys) -- against (or in relation to) one single (central) tone.
All natural harmony is derived from the acoustic overtone series. The Perfect 5th interval is 'dominant' (most audible) in this series of harmonics that propagate (and reflect off the walls of any room) in the most complex ways. As we can see from the figure below - The Perfect 5th interval does not represent the division of the Octave into symmetric parts. What it does represent is the division of the Octave into its 'Golden Section' (Golden Ratio).
Modal Harmony is 'natural harmony' that is derived from Major Scales. It represents all the popular music we know and love in the western world - including: Rock, Blues, Country, and the many forms of Jazz, Pop, Punk, and Metal. The following is an 'idea map' of 'Major Modes' in the motion of the 'Circle Of Fifths.'
Solfege Syllables should be learned and practiced -- to connect the ear to the brain (and the body) in a more meaningful way. Remember --- we learn this stuff to forget this stuff. Each solfege syllable 'means' the same thing in any key.... that's the advantage.
Terminology: We use the word 'Pivot' quite a bit in this study. Here are the distinctions.
While it's true that the Tri-Tone interval divides the Octave into two equal parts - and the Major 3rd divides it into three equal parts - likewise - the Minor 3rd divides it into four equal parts - and the Major 2nd (whole step) divides it into six equal parts... and it's true that these 'root movements' are employed often in symmetric harmony -- the integration of the underpinnings of its ideals (into natural (diatonic) harmony) are mystically arrived at by employing roots that are 'reflective reciprocals' of Perfect Fifths... and reflective intervals in general. Symmetric Harmony puts our ears 'underneath' natural modal harmony by employing its mirror... its 'reflection.' 'Reflective Reciprocals' are employed by asking the question: What fundamental tone would cause a given root to function as the upper tone of a given interval? The tone 'F' (as the fundamental) would cause 'C' (an assumed root) to function as the tone of the Perfect 5th. Now, we see the reciprocal of the 'Golden Ratio.'
We begin an 'idea map' with the contrast between "Natural Reciprocals" (direct inversions) and "Reflective Reciprocal" concepts:
The Reflective Reciprocal of'Mi' is 'Le'
The Reflective Reciprocal of'La' is 'Me'
The Reflective Reciprocal of'Re' is 'Te'
The Reflective Reciprocal of'Ti' is 'Ra'
The Reflective Reciprocal of'So' is 'Fa'
The Reflective Reciprocal of'Fa' is 'So'
The circle of fifths is a mirror in every way.
Digging a little deeper - we find that entire modes may reflect each other -- when a central Tonic is used as a point of reference:
The 2-Way Mirror
Continuing the concept of entire modes reflecting each other - realize that the circle of fifths is a twelve-way mirror. We can illuminate a 2-way mirror using parallel lines. The practice of seeing the relationships between (and within) each half of the circle is excellent exercise for the musician's mind. Observe that the circle is divided in half by the symmetric tri-tone interval. There is only one tri-tone interval for each key... making it unique -- and the ear relies on this uniqueness to calculate its experience. In the following model - each elemental tone inside the circle is thought of as the 'root' of an Ionian mode. The 'circled' tones represent the 'Equivalent Reciprocal' of Dorian. The 'root' of this Dorian Mode (as well as the root of its surrounding modes) is always found one whole-step 'up' from this 'circled' tone. Using the Key (Ionian) of each 'circled' tone as a marker -- we can easily see how the right side of this circle will be 'C' Modes --- and the left side of this circle will be 'F#' Modes (with 'Dorian' in the center).
The 4-Way Mirror... with a Leap in Logic:
Let's take a look at something a bit more 'global.'
In the following model - everything on the right side of the circle is 'aligned' (as we have seen before) --- but an attempt has been made to align the left side with 'C' Modes. This requires a leap in logic that reveals some interesting things about this 'dominant' or 'harmonic' side of the circle. In order to 'align' the left side of the circle with 'C' Modes -- we must assume that each elemental tone inside the circle (on the left side) is flatted --- and then -- we further assume that each flatted tone is the root of a Lydian Mode.
The More Simple Leap... and the turning of the page
The following example makes a leap in logic that is more simple to describe. This circle assumes that 'C' is the Dominant overtone. ('Do' sounds Like 'So'.) Both - the left and right side of this circle will require the practice of healthy assumption(s) for an alignment with logic. The right side assumes that each elemental tone inside the circle is the root of a Lydian Mode ('Fa') --- and the left side assumes each elemental tone inside the circle is the root of a Locrian Mode ('Ti').