Let’s summarize from the last few posts:
Interval – the distance from the root note to the note being named.
a) Unison – the same note, same pitch. Perfect, augmented (½ step up), diminished ( ½ step down)
b) Second – 1 step above the root is major, ½ step is minor.
c) Third – Major or minor.
d) Fourth –Perfect, augmented or diminished.
e) Fifth – Perfect, augmented or diminished.
f) Sixth – Major or minor.
g) Seventh – A major seventh is ½ step below the octave, a minor is a full step below the octave.
h) Octave – Perfect, diminished or augmented.
i) Ninth – Major or minor.
j) Eleventh– Major or minor
k) Thirteenth – Major or minor.
There could be others but these are the most common.
Most ordinary chords are built on combinations of thirds. A triad is 3 notes consisting a root and 2 thirds above it like C E G is a C major triad. A 7th chord is built by adding another third on the triad, 9th is another, etc.
We’ve been through some of the simple chord substitutions like the iim7 for IV7 because of their relative similarity. One of the next most common is the iiim7 for the IM7, once again due to the similarity. For example, the notes in the CM7 chord are C, E, G, B. The notes in the corresponding iiim7, Em7, are E, G, B, D. The Em7 is like CM9 without the C root. Less common but very effective is the b2 or tri-tone substitution. This is a dominant 7th built on the b2 of its tonal center. In C, where the root is CM7 (possibly with some higher intervals added), the b2 would be a Db7. This is obviously not part of the the scale itself. The b2 is commonly preceded by a iim7. In C major, it would Dm7, Db7 and then CM7, or iim7, bII7, IM7.
I’ve seen a lot of discussion recently on the pros and cons of calling the tri-tone substitution a bII7 instead. Much of it depends on whether the tonal center is changing. In a typical I IV V based progression, the tonal center does shift (and that point is debatable also) on the 5th measure. After 2 measures, it shifts back to the main tonal center. The shift the V7 at the end is for creating tension which relaxes when the tune repeats measure 1.
The above example is also based on a I IV V progression but uses a IM7 as a tonic instead of the blues normal dominant 7th. The second measure uses a iim7 instead a IVM7 – in this case, Dm7. The Eb7 in measure 4 is used to shift the tonal center to Dm. Measure 6 contains a Db7 to lead the tonal center back to C. Measure 9 uses the 3rd inversion (F as the lowest note) to lead to the dominant 7th which a b2 substitution.
Here’s a practice video of the same exercise
The pdf of the exercise can be download here.