• The Diminished Matrix: Who Else Wants To Connect The 2-5-1 Chord Progression?

    in Chords & Progressions,Experienced players,Piano,Theory

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    We’ll be looking at the diminished matrix in today’s lesson.

    The term diminished matrix sounds quite big right? However, at the end of this post, you’ll be able to make the 2-5-1 chord progression sound more interesting by connecting it in other related keys using this matrix.

    Let’s get started!

    Quick Review Of The 2-5-1 Chord Progression

    The movement of chords from one degree of the scale to another creates a chord progression. The C natural major scale [just like every other scale] has eight degrees…

    C:

    …the first degree.

    D:

    …the second degree.

    E:

    …the third degree.

    F:

    …the fourth degree.

    G:

    …the fifth degree.

    A:

    …the sixth degree.

    B:

    …the seventh degree.

    C:

    …the eighth degree.

    The 2-5-1 chord progression is the root movement of chords from the second degree of the scale to fifth degree of the scale and then to the first degree of the scale.

    In the key of C major:

    …a 2-5-1 chord progression moves from chord 2:

    …the D minor seventh chord, to chord 5:

    …the G dominant seventh chord, then to its final harmonic destination – chord 1:

    …the C major seventh chord.

    “We Can Make It Spicier Using Ninth Chords”

    Chord 2:

    …the D minor ninth chord, to chord 5:

    …the G dominant ninth chord, then chord 1:

    …the C major ninth chord.

    Now that we’ve reviewed the 2-5-1 chord progression, let’s put it aside for a while and talk about the diminished matrix.

    The Diminished Seventh Outline

    Due to time constraint, we’ll not go into all the necessary details on the diminished seventh chord. However, here’s what you need to know about the diminished seventh chord as it relates this lesson:

    The diminished seventh chord can be formed by dividing the octave into four equal parts.

    The octave (which is a series of eight notes) if divided into four equal parts creates a diminished outline. Although the octave is a series of eight notes, there are 12 semitones within its compass.

    Using the C to C octave:

    …as an example, we have C to C:

    …an eight-tone series. However, within that same C to C:

    …compass, are also twelve tones:

    Notwithstanding that the octave is an eight tone series, it contains as much as twelve equal parts. If you divide these twelve tones [that fall within the compass of an octave] into four equal parts, you’ll have a distance of three half steps (aka – “the sesquitone“.)

    Attention: If you do the math, 12 semitones divided by 4 is equals to 3 semitones. The diminished outline is based on the number “three”, which is derived from the division of the octave into four equal parts. Also note that a distance of three half steps is known as the sesquitone.

    To outline a diminished seventh chord in the key of C, we’ll have to divide its octave into four equal parts, with each part consisting of a sesquitone.

    Let’s do it step-by-step

    A sesquitone from C:

    …is Eb:

    A sesquitone from Eb:

    …is Gb:

    A sesquitone from Gb:

    …is A:

    A sesquitone from A:

    …is C:

    If you put everything together, you have C:

    …to Eb:

    …to Gb:

    …to A:

    …which outlines a diminished seventh chord:

    Submission: I know that the appropriate spelling of the C diminished seventh chord is C-Eb-Gb-Bbb. However, permit me to use simpler enharmonic alternatives like in the case of the C diminished seventh chord where I substituted Bbb with A.

    Check out the outline of the diminished seventh chord in all twelve keys…

    C diminished outline:

    C# diminished outline:

    D diminished outline:

    D# diminished outline:

    E diminished outline:

    F diminished outline:

    F# diminished outline:

    G diminished outline:

    G# diminished outline:

    A diminished outline:

    A# diminished outline:

    B diminished outline:

    Let’s get into the diminished matrix

    The Diminished Matrix

    The diminished matrix is a witty harmonic framework that every serious pianist should learn. This framework is formed by the outline of the diminished seventh chord. In the key of C:

    …where the diminished outline:

    …consists of the C, Eb, Gb, and A notes, our duty is to connect the 2-5-1 chord progression in those keys. Connecting the following 2-5-1 chord progressions:

    A 2-5-1 chord progression in the key of C

    A 2-5-1 chord progression in the key of Eb

    A 2-5-1 chord progression in the key of Gb

    A 2-5-1 chord progression in the key of A

    ….produces the diminished matrix.

    The Diminished Matrix In The Key Of C

    Let’s get started with the diminished matrix in the key of C by learning the 2-5-1 chord progressions in the keys of C, Eb, Gb, and A using ninth chords.

    A 2-5-1 Chord Progression In The Key Of C

    Chord 2:

    …the D minor ninth chord, to chord 5:

    …the G dominant ninth chord, then chord 1:

    …the C major ninth chord.

    A 2-5-1 Chord Progression In The Key Of Eb

    Chord 2:

    …the F minor ninth chord, to chord 5:

    …the Bb dominant ninth chord, then chord 1:

    …the Eb major ninth chord.

    A 2-5-1 Chord Progression In The Key Of Gb

    Chord 2:

    …the Ab minor ninth chord, to chord 5:

    …the Db dominant ninth chord, then chord 1:

    …the Gb major ninth chord.

    A 2-5-1 Chord Progression In The Key Of A

    Chord 2:

    …the B minor ninth chord, to chord 5:

    …the E dominant ninth chord, then chord 1:

    …the A major ninth chord.

    Now that we’ve covered how to play the 2-5-1 chord progression in diminished matrix, let’s talk about how we can connect them.

    Connecting The 2-5-1 Chord Progression Using The Diminished Matrix

    The 2-5-1 chord progressions we just played in several keys in the diminished matrix can be connected using chord (aka – “pivot chord“) that would help us move smoothly from one key to the other.

    This connection makes it look like we’re literally modulating and that of course, is what we’re doing.

    In the series of 2-5-1 chord progressions we’re playing, after playing it in the key of C major, our destination key is the key of Eb major. At this point, what matters here is how to connect chord 1:

    …in the key of C major to chord 2:

    …in the key of Eb major. This is where we need the pivot chord to connect us from the original key (which is the key of C major) to the destination key (the key of Eb major.)

    The pivot chord that connects these keys is the altered dominant chord and here’s how it works…

    After playing the C major ninth chord:

    …which is chord 1 of the original key (C major), play the C altered dominant chord:

    …as a pivot chord to connect you to the F minor ninth chord:

    Attention: The pivot chord is to be played in between chord 1 of the original key and chord 2 of the destination key.

    In a nutshell, after a 2-5-1 chord progression in the original key, play the pivot chord over the same bass note of chord 1 to prepare you for chord 2 in the destination key.

    Take note of the following…

    After a 2-5-1 chord progression in the key of Eb, the Eb altered dominant chord prepares you for another 2-5-1 chord progression in the destination key (Gb major.)

    After a 2-5-1 chord progression in the key of Gb, the Gb altered dominant chord prepares you for another 2-5-1 chord progression in the destination key (A major.)

    After a 2-5-1 chord progression in the key of A, the A altered dominant chord prepares you for another 2-5-1 chord progression in the destination key (C major.)

    Suggested Reading: Altered Dominant Voicings.

    Final Words

    The 2-5-1 chord progression if connected in a diminished matrix sounds very effective in jazz, gospel, and R & B styles.

    Due to the fact that most of the time, songs end with the 2-5-1 chord progression, instead of playing the regular 2-5-1 chord progression and ending the song, you can get adventurous by connecting other 2-5-1 chord progressions in related keys using the diminished matrix.

    Although this takes you entirely out of the key, but believe it or not it sounds good and most importantly, you need to note that after taking you out of the key, it brings you back again. This happens because the end of the matrix is the octave.

    Thank you for your time!

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    Hello, I'm Chuku Onyemachi (aka - "Dr. Pokey") - a musicologist, pianist, author, clinician and Nigerian. Inspired by my role model Jermaine Griggs, I started teaching musicians in my neighborhood in April 2005. Today, I'm privileged to work as a music consultant and content creator with HearandPlay Music Group sharing my wealth of knowledge with thousands of musicians across the world.

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    { 4 comments… read them below or add one }

    1 zino

    good

    Reply

    2 feyi

    G dominant seventh chord in the diagrams above got me confused in the sense that. G minor seventh chord should be “G-B-D-F”. Lets assume we using the polychords way where G will be pressed with left hand and “B-D-F” right hand, it would have been understandable. now am seeing another formation entirely, i don’t understand, please explain.

    Reply

    3 Don

    Actually, Feyi, you have to flat the third in order for it to be a minor seventh chord. So, a G minor seventh chord would be G-Bb-D-F. The G dominant seventh chord is G-B-D-F.

    Reply

    4 Daniel

    Great!

    Reply

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