• Beyond Distance: The Second Dimension of Intervals

    in Piano,Theory

    intervals

    The relationship between notes produces melody and harmony.

    The relationship between notes that are played or heard separately is known as melody while the relationship between notes that are heard together is called harmony.

    Except rhythmic ideas, virtually everything in music that has anything to do with “pitch” falls under melody and harmony. I can rephrase this by saying that licks, runs, chords, and chord progressions, etc., are all products of the relationship between notes.

    An interval is vital in the understanding of melody and harmony because it is the relationship between “two” notes – the distance between them.

    While it requires much more than two notes to play the shortest lick or run, the knowledge of the intervallic relationship between two notes will help you figure out the outcome of the relationship between three, four, five notes, etc.

    In this post, we’re going beyond the regular understanding and use of intervals as simple tools to depict the distance between notes. We’ll be exposing the second dimension of intervals in music.

    Two Dimensions of Intervals

    There are two dimensions to intervals: quantity and quality.

    Quantity refers to the number of letter names these two notes encompass.

    Quality refers to the harmonic property of these two notes.

    First Dimension – Quantity

    This is the dimension that describes the distance between notes using ordinal numbers.

    Ordinal numbers include 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, etc. Here’s how ordinal numbers are used:

    The interval C-D:

    …encompasses two letter names, C and D:

    …therefore, it is described as a second (2nd).

    The interval D-G:

    …encompasses four letter names, D, E, F and G:

    …therefore, it is described as a fourth (4th).

    Important…

    In situations where you want to determine the interval between letter names that have sharp and flat symbols (aka – “pitch modifiers”), you’ll have to initially disregard the sharp and flat symbols.

    For example, the interval C-F#:

    …should initially be considered as C-F:

    This will show us its true size.

    The interval C-F:

    …encompasses four letter names, C, D, E, and F:

    …therefore, it is described as a fourth (4th).

    Therefore, C-F# is a fourth.

    If you’re given C-Gb to determine its size, the same thing applies…

    The interval C-Gb:

    …should be initially considered as C-G:

    This will show us its true size.

    The interval C-G:

    …encompasses five letter names, C, D, E, F, and G:

    …therefore, it is described as a fifth (5th).

    “Can I Shock You?”

    The number of letters an interval encompasses determines its size, NOT the way it looks on the piano.

    Consider the last two intervals we explored: C-F# and C-Gb.

    C-F#:

    C-Gb:

    It’s amazing to know that both intervals can be played using the same finger keys on the piano. Heck, they even sound the same. But, because of the difference in spelling, their sizes are different.

    C-Gb is a fifth while C-F# is a fourth.

    There are several examples like that on the piano. C-D# and C-Eb are another example.

    C-D#:

    C-Eb:

    They look alike and don’t sound any different from each other. But, because of the difference in spelling, they vary in size. Check them out below.

    The interval C-D#:

    …according to what we covered earlier should be considered as C-D:

    …if we must determine its exact size.

    The interval C-D:

    …encompasses two letter names, C and D:

    …therefore, it is described as a second (2nd).

    Therefore, C-D# is a second.

    On the other hand, the interval C-Eb:

    …should be considered as C-E:

    …if its exact size is to be determined.

    The interval C-E:

    …encompasses three letter names, C, D, and E:

    …therefore, it is described as a third (3rd).

    Make this a rule if you can…

    You should never say the size of an interval unless it is spelled. This is because the size of an interval cannot be determined unless it is spelled.

    With your knowledge of the first dimension of intervals, you can actually determine the distance between notes on the piano.

    C-D#:

    …is a second.

    C-A:

    …is a sixth.

    But beyond the description of distance, there’s another dimension to intervals that I want to show you – quality.

    Second Dimension – Quality

    This is the dimension to intervals that goes beyond the description of distance.

    In this dimension, intervals are described according to their relationship to a given major scale using adjectives like perfect, major, minor, augmented, and diminished.

    Beyond what intervals represented in the first dimension – size and compass – the second dimension takes it an extra mile by creating a relationship between two notes based on a given major scale.

    Also, it’s worthy to note that the adjectives like perfect, major, minor, augmented and diminished have their respective meanings in chord formation (aka – “harmonic implication”).

    These meanings tend to describe the outcome of the interval when heard, in terms of pleasantness (aka – “consonance”) and unpleasantness (aka – “dissonance”).

    The harmonic implication of an interval is described using adjectives. Below are the meaning of the adjectives we covered earlier…

    Perfect Intervals

    Perfect intervals are universally consonant. What this means is that they are the most stable intervals. Whenever they are used in chord formation, they sound pleasant. One of the most important perfect intervals in chord formation is the perfect fifth interval. All tertian chords that are built off the interval of the perfect fifth are considered to be stable.

    Major Intervals

    Major intervals are built off the 2nd, 3rd, 6th, and 7th tones of the major scale. They are not as stable as perfect ones (heck, the 2nd and 7th are even considered to be dissonant). One of the most important major intervals in chord formation is the major third interval. All tertian chords that are built off the interval of the major third are considered to be major chords.

    Minor Intervals

    Minor intervals are smaller than major ones by a half step. Lowering a major interval by a half step would produce a minor interval. One of the most important minor intervals in chord formation is the minor third interval. All tertian chords that are built off the interval of the minor third are considered to be minor chords.

    Augmented Intervals

    To augment is to make larger. Augmented intervals are larger than perfect and major intervals by a half step. All augmented intervals sound unpleasant (dissonant).

    Diminished Intervals

    To diminish is to make smaller. Diminished intervals are smaller than perfect and minor intervals by a half step. All diminished intervals sound unpleasant too. One of the most important diminished intervals in chord formation is the diminished fifth interval. All tertian chords that are built off the interval of the diminished fifth are considered to be unstable.

    Final Words

    Intervals in music are really worth more than the tools we describe distances with. The perfect fifth in the key of C major:

    …means much more than a distance or compass of five notes:

    The term perfect represents stability.

    You must also note that there are other fifths too, the augmented and diminished fifth.

    You’ll be able to relate to chords more when you have knowledge of the second dimension of intervals.

    In our 16-week chord revival program where we’re exploring various chord classes, we usually begin each post by breaking each chord into intervals.

    By determining the intervals a chord is made up of (aka – “intervallic components”), we can know whether it’s major or minor, stable or unstable.

    I hope your knowledge of the second dimension of intervals will contribute as much as it can to your understanding of chords.

    Bye for now.

    Take care.

    The following two tabs change content below.
    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 the head of education, music consultant, and chief content creator with HearandPlay Music Group sharing my wealth of knowledge with hundreds of thousands of musicians across the world.

    Attention: To learn more about this, I recommend our 500+ page course: The "Official Guide To Piano Playing." Click here for more information.




    4steps600x400jpg

    gospelnewbanner3jpg

    { 0 comments… add one now }

    Leave a Comment

    Previous post:

    Next post: