The Power Of Limits

     While the concepts of 'Symmetric Modal Fusion' involve the entire circle. The study of 'Modal Jam Theory' focuses on 'half' the circle (the other half being seen/heard as a 'reflection'). These articles (The Power Of Limits) are an attempt to reveal why:

     This first example shows where we draw this dividing line -- as we can see... our half (of study) is taken out of the middle by including the Dominant ('G') and its Tri-tone Substitute ('Db'):

     
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​          The Eternal Flat (b)

​     The most obvious reason we draw this line can be seen in the next example. If we continue around the circle (more than half way), the 'root' in the center (our symmetric root) drops by one half-step -- and this is where the symmetry (of each mode in relation to a central root) ends. This is an incomplete model - but with a little study we can see where it goes. This model has five 'rings' with all twelve 'elements' branching out like 'spokes' of a wheel. The completed model would have eight 'rings' - with the last ring being identical to the first ring. Then - it would repeat infinitely.     
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​     We can make a "whole" lot of interesting (and colorful) harmony using only the 'C' Modes shown in the first ring of this (infinite) model. As for the 'small part' of the circle (the remaining five tones) - we will explore these tones as reflections... as mirrors within the circle. This is the 'Power Of Limits.' 
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            Practically Speaking:

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     The following model represents a more practical understanding -- and reveals the impact of the tri-tone interval as a 'dominating' factor of tonal harmony: 

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