A - The nucleus

1. The most typical and best-known Tetrad is the DOMINANT Seventh,
- the chord of V, in this case, G⁷,
     producing a flattening progression ("downward")
- with a FRAME composed of two members of the Series of Fifths,
     G (the COMMON TONE ) and D (the PROPER TONE)
     - the Primary Notes;
- with a Major Third, B (the MEDIAN), and a Seventh, F (the MOTRIX),
     - the Secondary Notes.

-Resolution of the Secondary Notes of the DOMINANT chord of G⁷ :
- The Seventh (MOTRIX F), pushed by the COMMON TONE G (which remains in place),
     resolves down to the Third (MEDIAN E) of the TONIC Chord of C (I).
- The Third (MEDIAN B) resolves in the opposite direction,
     up to the PROPER TONE C of the TONIC chord.
- The Fifth, PROPER TONE D, is free to resolve to either Primary Note,
     but usually resolves to the PROPER TONE C of the TONIC Chord.
          The TONIC chord, being in a position of rest, on the Beat,
               is preferably presented without a MOTRIX.
- The "Fundamental Bass", G-C, consists of the root of each chord.
- We will have 5 voices in all these examples: the 4 chordal tones and the Fundamental Bass.

These 5 voices are often used for rudimentary accompaniments
but, for more elegant writing, 4 voices are judiciously chosen among them.

2. What happens to the TONIC Chord of I when it resolves to the DOMINANT?
- in this case the chord of C⁶, producing a sharpening progression
     (it has a sixth as MOTRIX A, because it resolves "upward" a fifth)
- with a FRAME composed of G (the COMMON TONE) and C (the PROPER TONE)
     - the Primary Notes;
- with a Major Third, E (the MEDIAN), and a Sixth, A (the MOTRIX)
     - the Secondary Notes.

-Resolution of the Secondary Notes of the TONIC Chord of C⁶ :
- The Sixth (MOTRIX A), pushed by the COMMON TONE G (which remains in place)
     resolves up to the Third (MEDIAN B) of the DOMINANT Chord of G.
- The Third (MEDIAN E), resolves in the opposite direction,
     down to the PROPER TONE D of the DOMINANT Chord.
- The Root, PROPER TONE C, is free to resolve to either Primary Note,
     but usually resolves to the PROPER TONE D of the DOMINANT Chord.
The Dominant chord, being in a position of rest, on the Beat,
     is presented without a MOTRIX.
- the "Fundamental Bass", C-G, consists of the root of each chord.
Notice the inverse symmetry with the G⁷-C, DOMINANT-TONIC, progression.

Swings
This alternating between the two same chords is what we call a "Swing".
     This Swing has the note G as COMMON TONE.

Terminology of the IV chord
For reasons which will become increasingly clear as we progress, the use of the term "Sub-Dominant" to denote the chord of IV, which is situated (on the degree of the scale) just below the DOMINANT Chord, would be misleading and imprecise. We prefer to see it in the Window, on the other side of the TONIC chord and to call it the "COUNTER-DOMINANT" ("COUNTER" for short) and hope that you will eventually find that this change was worth while.

3. The COUNTER-DOMINANT Chord (IV) also resolves to the TONIC Chord (I).
- in this case the chord of F⁶, producing a sharpening progression
     (it also has a sixth as MOTRIX D, because it resolves "upward" a fifth)
- with a FRAME composed of C (the COMMON TONE) and F (the PROPER TONE)
     - the Primary Notes
- with a Major Third, A (the MEDIAN), and a sixth, D (the MOTRIX)
     - the Secondary Notes.

-Resolution of the Secondary Notes of the COUNTER Chord of F⁶ :
- The Sixth (MOTRIX D), pushed by the COMMON TONE C (which remains in place),
     resolves up to the Third (MEDIAN E) of the TONIC Chord of C.
- The Third (MEDIAN A) resolves in the opposite direction,
     down to the PROPER TONE G of the TONIC chord.
- The Root, PROPER TONE F, is free to resolve to either Primary Note,
     but usually resolves to the PROPER TONE G of the TONIC Chord.
The TONIC Chord, being in a position of rest, on the Beat,
     is presented without a MOTRIX.
- the "Fundamental Bass", F-C, consists of the root of each chord.
This progression is identical to the TONIC-DOMINANT progression.

4. Now, what happens to the TONIC Chord (I) when it resolves to the COUNTER?
- in this case the chord of C⁺⁷, producing a flattening progression
     (it has a seventh as MOTRIX B, because it resolves "downward" a fifth)
- with a FRAME composed of C (the COMMON TONE) and G (the PROPER TONE)
     - the Primary Notes
- with a Major Third, E (the MEDIAN), and a Major Seventh, B (the MOTRIX)
     - the Secondary Notes.

-Resolution of the Secondary Notes of the TONIC Chord of C⁺⁷ :
- The Seventh (MOTRIX B), pushed by the COMMON TONE C (which remains in place),
     resolves down to the Third (MEDIAN A) of the COUNTER Chord of F.
- the Third (MEDIAN E) resolves in the opposite direction,
     up to the PROPER TONE F of the COUNTER Chord.
- The Fifth, PROPER TONE G, is free to resolve to either Primary Note,
     but usually resolves to the PROPER TONE F of the COUNTER Chord.
The COUNTER Chord, being in a position of rest, on the Beat,
     is presented without a MOTRIX.
- the "Fundamental Bass", C-F, consists of the root of each chord.
This progression is very similar to the DOMINANT-TONIC progression.

Another "Swing", this one with COMMON TONE C

Beware of triads!
In each Tetrad, two Triads are "hidden"
     - the real Triad, in which the MOTRIX is missing,
          but the FRAME remains, (the last chord in all the preceding examples) and
     - a deceptive Triad, in which the COMMON TONE is missing,
          and in which the two secondary notes could easily be mistaken for a FRAME.
In the G⁷ Tetrad, we have
     - the real Triad of V (G, B, D)
     - the deceptive Triad of VII (B, D, F).
In the C⁶ Tetrad, we have
     - the real Triad of I (C, E, G)
     - the deceptive Triad of VI (A, C, E).
In the F⁶ Tetrad, we have
     - the real Triad of IV (F, A, C)
     - the deceptive Triad of II (D, F. A).
In the C⁺⁷ Tetrad, we have
     - the real Triad of I (C, E, G)
     - the deceptive Triad of III (E, G, B)

It is interesting to note that we have here every diatonic triad available
within the nucleus of the major mode.
The three major triads are, evidently, all real triads,
but the three minor triads, as well as the diminished triad (with 2 minor thirds) are deceptive.
These deceptive triads are incomplete major tetrads (without the COMMON TONE),
and should never be confused with the real minor triads of the Tail in the top of the Window.

B - The tail

Progressions are all flattening ("downward") , from Em⁷, the chord of III,

"down" to Am⁷, the chord of VI

"down" to Dm⁷, the chord of II,
"down" to the DOMINANT Chord, G⁷ (V), which in turn resolves
"down" to the TONIC Chord, C ( I ).

Notice how the COMMON TONE
becomes the PROPER TONE of the next chord - (E- E, A- A ...)

The ANTECEDENTS
These are the ANTECEDENTS to the DOMINANT and we give them the following names
- "III", Em⁷ - the ANTE-3;
- "VI", Am⁷ - the ANTE-2;
- "II", Dm⁷ - the ANTE-1.

The Circle
Were we to continue indefinitely in the same direction, we would come back to our original chord and have produced what we call a "circle" (in this case a flattening circle).

-In this example,
     we start on the TONIC Chord C⁺⁷,
     then progress "down" to the COUNTER Chord, F⁺⁷,
     then progress "down" to the ANTE-4 Chord, the "BUCKLE*" chord, Bm^7-5,
     then progress "down" to the ANTE-3 Chord, Em⁷,
     then progress "down" to the ANTE-2 Chord, Am⁷,
     then progress "down" to the ANTE-1 Chord, Dm⁷,
     then progress "down" to the DOMINANT Chord, G⁷,
     then finally progress "down" to the TONIC Chord of rest, C, without MOTRIX.

* This "BUCKLE" chord acts as a link between one extremity of the window and the other.
It has the sharpest note (B) as its root and the flattest (F) as its fifth.
One should not be surprised of its unusual shape (a "hunch-back" FRAME) and instability.
It is almost impossible to treat it as a chord of rest.

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Those browsing might wish to see -
2. The Diatonic Minor Mode
3. The Chromatic Major Mode
4. The Chromatic Minor Mode