• Exposed: The Intervallic Relationship Between Third Intervals And Other Intervals

    in Experienced players,Piano,Theory

    You arrived on this page because you want to learn about the relationship between third intervals and other intervals.

    Attention: If you’re a beginner and not sure of what intervals are, don’t worry, we’re covering all that in this lesson.

    All I need is for you to give me the next ten minutes to break down the secret relationship that third intervals have with other intervals like fifths, sixths and sevenths.

    A Quick Review On Intervals

    Intervals according to Jermaine Griggs, “…are the building blocks of chords.” These building blocks (intervals) are a product of the relationship between any two notes, in terms of the distance (in pitch) between them.

    The following notes…

    E-A:

    B-D#:

    F#-B:

    D-B:

    …can all be considered as intervals, and this is not just because of the distance in pitch between the notes, but the relationship between them.

    “Check Out The Scale Relationship Between These Intervals…”

    The interval E-A:

    …encompasses the first four tones of the E major scale:

    …which are E, F, G, and A:

    …consequently, it’s called a fourth interval.

    The interval B-D#:

    …encompasses the first three tones of the B major scale:

    …which are B, C#, and D#:

    …consequently, it’s called a third interval.

    The interval F#-B:

    …encompasses the first four tones of the F# major scale:

    …which are F#, G#, A#, and B:

    …consequently, it’s called a fourth interval.

    The interval D-B:

    …encompasses the first six tones of the D major scale:

    …which are D, E, F#, G, A and B:

    …consequently, it’s called a sixth interval.

    The Classification Of Intervals According To Quality

    Intervals can be classified according to these five qualities:

    • Perfect
    • Major
    • Minor
    • Augmented
    • Diminished

    Perfect intervals are the most stable set of intervals, while major and minor intervals are considered to be consonant with the two key types – major and minor.

    Augmented and diminished intervals sound unpleasant and harsh, consequently, they are rarely used. Take the augmented fourth interval (aka – “tritone”) as an example.

    A Short Note On Third Intervals

    Third intervals are basically intervals that encompass three degrees of any give scale, or three letter names.

    Using the C major scale:

    …or any other scale you are familiar with, you can form third intervals by stacking two notes that are three letter names apart from each other.

    Calculating three letter names from C:

    …entails C, D, and E:

    …therefore, C to E:

    …is a third interval.

    In the same vein, calculating three letter names from F:

    …entails F, G, and A:

    …consequently, F to A:

    …is a third interval.

    There are four known qualities of third intervals…

    • The major third
    • The minor third
    • The augmented third
    • The diminished third

    Although third intervals are usually considered important because they are used in the formation of tertian chords, there are also a variety of reasons why they are considered to be important and you’ll be finding out in the next segment.

    The Relationship Between Third Intervals And Other Intervals

    Third intervals are related to other intervals like the fifth, sixth, and seventh intervals. Without further ado, let’s explore the relationship between third intervals and these other intervals.

    The Relationship Between Third And Fifth Intervals (Triad Formation)

    A triad is a collection of three related notes [agreeable or not], played or heard together.

    A triad can be formed by stacking three notes of a given scale that are apart from each other by a third interval. Using the C major scale:

    …a triad can be formed from C:

    …by stacking third intervals. A third interval from C:

    …E:

    ….and another third interval from C-E:

    …is G:

    Altogether, we’ve stacked three notes together – C, E, and G:

    …to form the C major triad.

    Although the C major triad is built off third intervals, it consists of the first, third, and fifth tones of the C major scale:

    …which are C, E, and G:

    …respectively. Consequently, triads are said to be a product of the relationship between third and fifth intervals.

    “Pay Attention To This…”

    Starting from any given note, you can form a triad using the relationship of third and fifth intervals.

    From C:

    …adding a note that is a minor third above (which is Eb):

    …and another note that is a perfect fifth above C (which is G):

    …produces the C minor triad:

    From D:

    …adding a note that is a major third above (which is F#):

    …and another note that is an augmented fifth above C (which is A#):

    …produces the D augmented triad:

    Using different qualities of third and fifth intervals will produce different chords too. Check out how four known triad qualities can be formed using third and fifth intervals…

    • Major third + perfect fifth = major triad
    • Major third + augmented fifth = augmented triad
    • Minor third + perfect fifth = minor triad
    • Minor third + diminished fifth = diminished triad

    In a nutshell, the relationship between third and fifth intervals can be seen in the formation of triads.

    Relationship Between Third And Sixth Intervals (Inversion)

    The relationship between third and sixth intervals is a very important one because it is based on the inversion of intervals.

    Third intervals are invertible because they can add up with another interval to form an octave. The size (aka – “width”) of intervals that can add up to third intervals to form an octave are sixth intervals.

    A major third (C-E):

    …and a minor sixth (E-C):

    …intervals add up together (C-E and E-C):

    …to form an octave (C-C):

    You’re probably asking “how do I know the interval to add up to a given third interval to form an octave?”

    Well, inverting any given third interval produces the interval that can be added up to it, to form an octave. Given D-F (a minor third interval):

    …inverting it produces F-D:

    …which can add up to D-F (D-F and F-D):

    …to form an octave (D-D):

    It is no coincidence that F-D (the inversion of D-F):

    …is a sixth interval. Third and sixth interval are related by inversion because they add up to form an octave, and the inversion of a third interval produces a sixth interval and vice-versa.

    Suggested Reading: Harmonization Of The Major Scale Using Third And Sixth Intervals.

    Relationship Between Third And Seventh Intervals (Skeleton Voicing)

    In the study of chords, although all tones are important, however, the third and seventh tones are considered to be the most important tones. Heck, music scholars believe the third and seventh tones to be the skeleton in the “chordboard”!.

    Due to the fact that the third and seventh tones of the C major seventh chord:

    …are E and B:

    …the C major seventh chord can be played as E-B:

    …over C on the bass:

    Although the fifth tone of the C major seventh chord (which is G):

    …is omitted, the skeleton voicing of the C major seventh chord:

    …doesn’t really sound any much different from the regular C major seventh chord:

    Seventh chords of different qualities can be formed using different third and seventh intervals. Check out how three commonly used seventh chord qualities can be formed using third and seventh intervals…

    • Major third + major seventh = major seventh chord
    • Minor third + minor seventh = minor seventh chord
    • Major third + minor seventh = dominant seventh chord

    In a regular 2-5-1 chord progression in the key of C…

    Chord 2 (which is the Dmin7 chord) can be formed by the relationship between a minor third (D-F):

    …and a minor seventh (D-C) interval:

    Check it out:

    Chord 5 (which is the Gdom7 chord) can be formed by the relationship between a major third (G-B):

    …and a minor seventh (G-F) interval:

    Check it out:

    Chord 1 (which is the Cmaj7 chord) can be formed by the relationship between a major third (C-E):

    …and a major seventh (C-B) interval:

    Check it out:

    Final Words

    Getting to this segment lets me know how serious you are in learning about third intervals and the relationship they have with other intervals.

    In a subsequent lesson, we’ll be expounding on each of these relationship…

    • Third and fifth intervals
    • Third and sixth intervals
    • Third and seventh intervals

    Thank you for your time and see you then!

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    Chuku Onyemachi

    Head of Education at HearandPlay Music Group
    Onyemachi "Onye" Chuku is a Nigerian musicologist, pianist, and author. Inspired by his role model (Jermaine Griggs) who has become his mentor, what he started off as teaching musicians in his Aba-Nigeria neighborhood in April 2005 eventually morphed into an international career that has helped hundreds of thousands of musicians all around the world. Onye lives in Dubai and is currently the Head of Education at HearandPlay Music Group and the music consultant of the Gospel Music Training Center, all in California, USA.

    Related posts:

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    2. Another Perspective To The “Part-Over-Root” Voicing Of Major Ninth Chords
    3. An In-Depth Breakdown Of The Classic 1-4 Walk-Up Chord Progression
    4. How To Approach An Unfamiliar Hymn In 4 Steps
    5. You Can Hardly Play Three Hymns Without The Chromatic Supertonic Chord
    6. Chord Quiz: “What Do You See?” (Part 1)
    7. A Lesson On The Scale Degree Seventh Chords Of The Melodic Minor Scale


    Related posts:

    1. The Diminished Matrix: Who Else Wants To Connect The 2-5-1 Chord Progression?
    2. Another Perspective To The “Part-Over-Root” Voicing Of Major Ninth Chords
    3. An In-Depth Breakdown Of The Classic 1-4 Walk-Up Chord Progression
    4. How To Approach An Unfamiliar Hymn In 4 Steps
    5. You Can Hardly Play Three Hymns Without The Chromatic Supertonic Chord
    6. Chord Quiz: “What Do You See?” (Part 1)
    7. A Lesson On The Scale Degree Seventh Chords Of The Melodic Minor Scale




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