1 Theory – Additional Information


1D Triads

Below is a list of all types of triads in three categories : common, uncommon and rare. All chords are presented as a numeric pattern.

Common triads

ChordIn CN. pattern

Uncommon triads

ChordIn CN. pattern

Rare triads

ChordIn CN. pattern
X Quartal Up(No symbol) C-F-Bb1-4-b7
X Quartal Down(No symbol / C9omit3) C-G-D1-5-9

Note: Rare chords are rarely used by themselves but are used as rootless voicings quite often. We cover voicings in Chapter 2.

1F Chord Inversions

Understanding inversions regarding intervals

Playing any two notes that are not the same will create an interval. An inversion is simply putting one of the interval notes “over” the other one and playing it an octave higher/lower. The “old” interval and the “new” interval should both add up to 12 semitones. For example C and Eb form a minor third. A minor third contains 3 semitones (not counting the root). If we invert it so that the C goes an octave higher then the new interval is 12-3=9 semitones (not counting the root) away from Eb. Likewise if we drop the Eb an octave lower it is still 9 semitones away from C. When we do another inversion in the same direction we get back to the “original” inversion since 12-9=3 semitones, only this time an octave higher or lower depending on our direction on inverting. 

Now that we got the “boring” basics out of the way we can get into some practical information. Inversions are not restricted to two notes. In fact inversions are most commonly used with three note triads. The same rules apply as above. Triads are the chords that are generally used regarding inversions. The second inversion is specifically common in playing two hand chords/voicings  (bass note + triad usually in 2nd inversion) and chord voicings called “upper structure voicings” (3-7 + triad usually in 2nd inversion). We cover those in depth in Chapter 2 that covers chords and voicings. 

Four note inversions are also used, although less commonly. Their root position and 2nd inversions are mostly used as a specific chord voicing that has many different possible names: “rooltess/Bill Evans/Box/AB” voicings. We cover those as well in depth in Chapter 2. 

Chords containing five or more notes can in theory be inverted as well but for practical reasons we will not include them in these lesson series. These type of “wide” inversions are used mainly for composing and arranging when dealing with multiple instruments each containing different registers. Some more advanced chords do touch on the subject briefly. 

1G Extensions and Alterations

Background information on extensions

We can approach extensions by viewing them from two different perspectives. Firstly let us break down how four note chords form harmony. The first note (1 = Root) determines the root of the chord. The third note (3) determines if the chord is a major or minor. The fifth note (5) determines if the chord is a “normal”, diminished or an augmented chord. And finally the seventh note (7) determines if the chord is a major seven, minor seven, dominant seven or a diminished seven chord. These notes are all that is needed to determine the harmony of any chord. A scale (most scales) has seven notes and these four (1-3-5-7) are only part of it. So what is happening to the rest of the scale notes?

Now we get to the other perspective which is looking at a numeric pattern for a scale again. But this time it will cover two octaves instead of one meaning that 1 becomes 8 after the 7 and so forth (look at the illustration below). Here is the full numeric pattern for any scale covering two octaves : 1-2-3-4-5-6-7-8-9-10-11-12-13-14-1. The notes 8-10-12-14 are the same notes as the chord tones that determine harmony (1-3-5-7), just an octave higher. Let us highlight all of them 1-2-3-4-5-6-78–9-10-11-12-13-14-1. These tones will not change during this lesson so we can keep them “frozen” for now. This lesson concentrates on the notes that are not highlighted (2,4,6,9,11,13) since they do not alter the underlining harmony but “extend” or “complement” it only. These are the chord extensions.

Chord tones and extensions over two octaves. Example in C.

In the illustration above you can see the general idea behind extensions (also called tensions or tension notes). They “fill in” the chord tones with the notes of the rest of the (major) scale. Since extensions are usually played on top of the foundation which is the chord tones (1-3-5-7) their respected numbers are over 7. If the notes are played in one octave together with the chord tones then the numbers are under 7. The picture shows clearly the relationship between scales and chords. Scales are build in seconds (vertically – 1,2,3,4,5,6,7,8) and chords are build in thirds (horizontally – 1-3-5-7-9-11-13).

When to use 2,4,6 and when to use 9,11,13 extensions?

In a nutshell if the chord has a 7 in it we use 9,11 and 13 as extensions and if not then we use the notes 2,4,6. It is debatable if 2,4 and 6 are considered extensions or just chord notes. But 9,11 and 13 are always considered extensions. For example C6 will not have a 7 while C13 will have a 7 (b7). 

Naming chords with extensions

The name of a chord is always the highest number it contains. For example a minor seven chord with a nine in it is in fact a minor nine chord (Cm9). Other examples are Cm11, C13. 13 chords that are not dominant are usually written as 6/9. 

Note: Often composers and arrangers will use “shortcode” for writing chords and just give the minimum information needed for the harmony. So most chords will be written using the 1-3-5-7 pattern even though they might contain extensions. The exception is when the melody note is very evident it represents the “change” to the harmony. For example a Cmaj7#11 chord would strongly imply that the #4 (=#11) is an important melody note. This is good to know when choosing target notes for improvisation as we will see in Chapter 3 that covers soloing and improvisation.

Naming chords with alterations

For alterations they are usually added after the “basic” four note chord. For example C7b9 and Cmaj7#11. If there are several alteration they are all named in increasing order. For example C7#9b13. If the chord contains all alteration a more commonly used chord versions is C7alt. 

The #11 extension in major chords

If we go “by the book” theory-wise a full extended (chord featuring all extension) C major chord would look like this : 1-3-5-7-9-11-13. There is a very strong dissonance between the 3rd and 4th (11th) note because there only a semitone away and both have a “dominating” nature. They cannot exist in a musical sense at the same time (the same is true with b7 and 7 chord tones). There is a consensus among musicians and composers that this kind of interval clash is not musically pleasing. That is why in a major chord (or any chord containing a major 3rd) that has a 4 or 11 in it the 4 or 11 is raised by a semitone to a #4 or #11. Thus a full extended C major chord looks like this: 1-3-5-7-9-#11-13. In contrast there is no problem with C minor extended chord (1-b3-5-b7-9-11-13) since the interval between the b3rd and 4th (11th) is two semitones instead of one. 

Extensions and Alterations Table

Chord Type Common chords In C Base chord Common extensions / alterations
Major Cmaj9/#11/13
Minor Cm9/11/13 1-b3-5-b7
Dominant C9/11/13 
Half-Diminished Cø9
Diminished Cdim9/11 1-b3-b5-bb7
MajorMinor CmMaj9
1-b3-5-7 (C-Eb-G-B) 9

(c) Sibil Yanev 2019