# Root movement



## millionrainbows (Jun 23, 2012)

There are only 6 possible intervals of root movement (as in tonal functon/stations).

This way of looking at root movement makes more sense if you look at the chromatic scale as circular, and notes as identities, without regard to intervallic distance. 
On a circle, all intervals can be easily seen as invertible. This reveals the fact that triad construction and root progression are both contingent upon _identity_, i.e. note names, as in a 'station' on the circle, rather than a _quantity_ or static intervallic _distance_ from a given note. Thus tonality, as we know it, is dependent on direction around an hierarchical circle, with note-names as identities, more so than static "distances" or quantities from a given note. This is because of the harmonics of a note, going in a "direction" of importance from a fundamental to its harmonics.
If tonality is seen as "gravity", then this way of separating _pitch identity_ from _interval distance_ may become more valuable when looking at a floating, global, gravity-based view of tonality as a localized "sphere of influence" (as in Bartok).

Schoenberg speaks in his text "Structural Functions of Harmony" of traditional root progression, and he classifies the root progressions into three categories:

*1. Strong, or Ascending: (a) A fourth up, identical with a fifth down; (b) A third down
2. Descending: (a) A fourth down, identical with a fifth up; (b) A third up
3. Superstrong: (a) One step up; (b) One step down.*

That makes 5 ways to move a root, if we remember that a steps (seconds) and thirds can be minor or major. That is, (2) thirds + Fourth/fifth + (2) steps (minor or major second), with the tritone as "odd man out" or 6.

FURTHER THOUGHTS: To remember these root progressions & their relative strengths, it will help to think of them simultaneously as being steps from one root note to another, traveling forward through time horizontally, and also as harmonic intervals, sounding simultaneously at once, vertically:

*1. Strong, or Ascending: (a) A fourth up, identical with a fifth down; *

...this is because when we hear fourths as a simultaneous sounding of two notes, *we always hear fourths with the top note as root;* in root function terms, we have moved *UP TO* this note (higher in pitch, within the upper octave above the root); this makes it *'strong' *or *'ascending'* *TO* the root on top.

A fifth down (lower in pitch below the root, in the octave below the root) is the inversion; when we hear both notes at once, *we always hear fifths with the bottom note as root,* as we do with all fifths. Every head-banger knows this. Spread out horizontally, a fifth down means the second (bottom) note is root.

*(b) A third down:* we hear the second note as root, or resting point. Makes sense. Listen to Cream play "Spoonful."

*2. Descending: (a) A fourth down, identical with a fifth up;** we hear the top of the fourth as root, still,* but we have moved away from it to a _weaker_ note; thus, it is _"descending."_ *If we hear a fifth, again, the bottom note is root;* but we have moved a fifth up to the weaker note; thus, it is _"descending,"_ or getting weaker. By 'weak' or 'strong' we mean simply *reinforcing* a root or key center, or '*weakening'* the root or key, and moving away from it, to perhaps another key.

*(b) A third up.* We hear the bottom note as root, but we jumped up, away from it. It's getting weaker.

*3. Superstrong: (a) One step up; (b) One step down.* We hear the second note as a new root. I need to think about this one some more.

So my point is this: we need to ponder the differences, similarities, and correspondences between horizontal thinking, which progresses on a time-line (which is what root movement is concerned with), and vertical thinking, which happens all-at-once, and lets the ear decide what emerges from aggregates of vertical notes.


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