Definition of stretch chords
We call “stretch chords” triads whose FRAME has been stretched at one end
     by the use of a Non-chordal Tone -
          (a) a p+7 at one end, below the root, or
          (b) a s6 (or s-6, whichever is diatonic) at the other end, above the fifth.

We will not use color in the musical examples (or in the text)
     because these stretch procedures apply to triads which might take either direction
          (with a substituted seventh or sixth).

Producing the stretch chords

- We have here, in the usual Key of C major -
     (a) the TONIC triad, C, where we could double either the root or the fifth,
     (b) the triad with a push+7 (an Em sound), where we must double the fifth,
     (c) the triad with a sus6 (an Am sound), where we must double the root.

Not deceptive triads
These stretch chords should not be confused with deceptive triads
     which are the result of Incompleteness.
- On the stretch chord Cp+7, the note B is a Non-chordal Tone replacing the root C,
     and not the descending MOTRIX of the chord C+7, resolving to the MEDIAN A.
- On the stretch chord Cs6, the note A is a Non-chordal Tone replacing the fifth G,
     and not the ascending MOTRIX of the chord C6, resolving to the MEDIAN B.

- We have here -
     (a) the DOMINANT triad, G, where we could double either the root or the fifth,
     (b) the triad with a push+7 (a Bm sound), where we must double the fifth,
     (c) the triad with a sus6 (an Em sound), where we must double the root.

Note the Em sound in both the TONIC and DOMINANT stretch chords.

-We have here -
     (a) the COUNTER triad, F, where we could double either the root or the fifth,
     (b) the triad with a push+7 (an Am sound), where we must double the fifth,
     (c) the triad with a sus6 (a Dm sound), where we must double the root.

Notice the Am sound in both the TONIC and COUNTER stretch chords.

-We have here -
     (a) the ANTE-1 triad, Dm, where we could double either the root or the fifth,
     (b) the triad with a push+7 (an F+5 sound), where we must double the fifth,
     (c) the triad with a sus-6 (a Bb sound), where we must double the root.

-We have here -
     (a) the ANTE-2 triad, Am, where we could double either the root or the fifth,
     (b) the triad with a push+7 (a C+5 sound), where we must double the fifth,
     (c) the triad with a sus-6 (an F sound), where we must double the root.

-We have here -
     (a) the ANTE-3 triad, Em, where we could double either the root or the fifth,
     (b) the triad with a push+7 (a G+5 sound), where we must double the fifth,
     (c) the triad with a sus-6 (a C sound), where we must double the root.

-We have here -
     (a) the Buckle Chord, Bm-5, where we could double either the root or the fifth,
     (b) the triad with a push+7 (a Bb sound), where we must double the fifth,
     (c) the triad with a sus-6 (a G sound), where we must double the root.

Notice the Bb sound in both the ANTE-1 and Buckle stretch chords.

The two Stretch Chord sounds on the same Chord Function
Let’s start with the DOMINANT chord and resolve it to the TONIC.
Since the sus6 can act as a permanent Non-chordal Tone more easily than the push+7,
     we will place it at the end and start with the push+7 sound.

-We have chosen a cadential disposition
     with the Orbit 1-1 line in the Soprano and with the Fundamental Bass.
First, the movements between the 2 stretch chords -
     - the push+7, F#, in the Tenor, resolves to G, the root; and
     - the sus6 is added in the Soprano where the fifth D was.
     - Then, we must replace the doubling of the fifth by the doubling of the root
          which could have been accomplished by just sending one of the Ds to G.
          However it is often more elegant (keeping everyone busy), to
               - send the fifth D which does not pick up the sus6, in the Alto, to the MEDIAN B, and
               - send the MEDIAN B, in the Bass, to the root G.
Second, resolve the DOMINANT to the TONIC
     - resolve Orbit 1 - Orbit 1, D to C, in the Soprano,
     - resolve Orbit 3 0(3) - Orbit 2, G to E, in the Tenor,
     - resolve the Fundamental Bass, G to C, in the Bass, and
     - quite exceptionally, send the MEDIAN B, to the root G, in the Alto.
          Much, much more will be said of this later.

The complete circle

-We can apply the same procedures to each chord of the circle
     and get this constantly descending result.
There is a 3-part canon in the upper voices,
     and the Bass repeats the same MEDIAN to root displacement all the way through.

In chromatic minor

-A new, more somber color, appropriate to a sad, painful experience.

You might enjoy hearing this with the violin ascending obligato, which is placed at the end of a piece called “The Last Five”.

How “The Last Five” was written
1. The end was written first - the piano part, then the violin obligato.
2. The final DOMINANT/TONIC cadence of the piano (G/Cm) was then transposed to
     (a) TONIC/COUNTER (Cm/Fm) and (b) ANTE-1/DOMINANT (Dm-5/G), and
     followed by the half-circle (Ab/Dm-5/G/Cm) for the opening statement,
     with the vioiln obligato preceding the piano as a pick-up.
3. Then, the piano part, solo, was placed before this, with a short intro.
4. The rest was development and arranging,
     but the stretch sounds were maintained throughout the whole piece.