Lesson 19: Chords(和弦) and Triads(三和音)

In music theory, a chord(和弦) is a general term that is defined as a set of two or more notes that sound simultaneously. The chords that we commonly see in worship songs can be further categorized into triads (三和音) and seventh chords (七和弦). Occasionally, we also come across chords that do not belong to either of the aforementioned categories. We will focus on the triads in this lesson, and learn about seventh chords in the next.

As the name suggests, a triad is a chord that consists of 3 notes. Also, they are stacked in thirds (i.e. the interval between the first and second note, and the interval between the second and third note are both 3rds, either major or minor). When stacked in 3rds, the 3 notes in a triad are called (from bottom to top):

• the root [R],
• the third [3], which can be at an interval of major or minor 3rd above the root
• and the fifth [5], which can be at an interval of diminished, perfect, or augmented above the root. (this will be illustrated shortly)

Since there are two possibilities for the interval between the root and the third (major or minor 3rd) and there are two possibilites for the interval between the third and the fifth (major or minor 3rd), by permutation, we can deduce that there can be 4 possibilities for triads. We call these the quality of the triads. Here are the 4 different qualities: major, minor, diminished, and augmented.

Major triad: R-3-5.

• It consists of a Major 3rd from R to 3 and a minor 3rd from 3 to 5.
• This is also commonly known as the "major chord".
• It is usually written with just the capital letter of the root, e.g. C, F.
• Example: C-E-G

Minor triad: R-b3-5.

• It consists of a minor 3rd from R to b3 and a Major 3rd from b3 to 5.
• This is also commonly known as the "minor chord".
• It is usually written with the capital letter of the root followed by an "m" or "-", e.g. Cm, F-. It is also sometimes written with the small letter of the root, e.g. c, f (less commonly seen in worship music).
• Example: C-bE-G

Diminished triad: R-b3-b5.

• It consists of a minor 3rd from R to b3 and another minor 3rd from b3 to b5.
• The diminished triad contains and diminished 5th above the root.
• It is usually written with the capital letter of the root followed by "dim" or "º", e.g. Cdim, Fº.
• Example: C-bE-bG

Augmented triad: R-3-#5.

• It consists of a Major 3rd from R to 3 and another Major 3rd from 3 to #5.
• The augmented triad contains and augmented 5th above the root.
• It is usually written with the capital letter of the root followed by "aug" or "+", e.g. Caug, F+.
• Example: C-E-#G

Each of the above triads have a distinct mood to it, regardless of what the root note is. Try playing the above examples on the piano to hear the difference. Once you are familiar with the examples, try to play these triads with different root notes.

Lesson 14: Names of Diatonic Notes

Before, learning any chords, it is important to know the difference between a diatonic note and a chromatic note.

A diatonic note is defined as a note that is in the major scale of the specified key. E.g. E is a diatonic note in the key of C (C-D-E-F-G-A-B), and Bb is a diatonic note in the key of F (F-G-A-Bb-C-D-E), etc. Any note that are not diatonic are considered chromatic. E.g. all the black keys are considered chromatic in the key of C, since the scale of C major consists of white keys only.

There are 7 notes (do-re-mi-fa-so-la-ti) in a diatonic scale; each of them has its function and characteristic, and therefore, have its own "technical names":
- First note (do): Tonic
- Second note (re): Supertonic
- Third note (mi): Mediant
- Fourth note (fa): Subdominant
- Fifth note (so): Dominant
- Sixth note (la): Submediant
- Seventh note (ti): Leading tone

It is important to know how to relate the names of all the diatonic notes to the intervals between them. E.g. the interval between the tonic and dominant is Perfect 5th, and the interval between the tonic and the leading tone is Major 7th. Can you figure out the intervals between the mediant and the submediant? And the interval between supertonic and leading tone? You can use the piano keyboard to help you figure out the intervals of all the possible combinations in the key of C (the simplest key). But ultimately, your goal is to be able to figure out all these intervals in all keys in a flash.

If you need a way to help you remember those names, try this:

- Think of tonic as the center,
- Supertonic is the note above tonic, and leading tone is the note leading to the tonic.
- The dominant is the 5th note above the tonic, and the subdominant is the 5th note below the tonic (i.e. the 4th note).
- The mediant is the middle point between the tonic and the dominant, and the submediant is the middle point between the subdominant and the tonic.

Does everything make more sense now??

Lesson 12: 音程 (Intervals), Part 2

This lesson will cover more advanced topics in "intervals".

Enharmonic (異符同音) intervals

It is important to note that the interval number is determined by how the two notes are spelled. E.g. the interval between D and F# is major 3rd, but the interval between D and Gb is diminished 4th. Even though F# and Gb are the same note on the keyboard, because they are spelt differently, they need to be written differently (F is a 3rd and G is a 4th in D major). This applies not only to the upper note, but to the root as well. E.g. the interval between F# and C is diminished 5th, but the interval between Gb and C is augmented 4th.

Inversion of intervals

To invert an interval, simply raise the lower note by one octave. That will bring it above the upper note, and making the upper note the root note. After the notes are inverted, the interval between the new root note and upper note can be determined the way described before.

There is also a shortcut to determine the inverted interval. The interval number of the inverted interval is always equal to 9 minus the original interval number. What about the quality of interval? Here is the rule for inverting intervals (try to verify it yourself!):

Major becomes minor, and vice versa
Augmented becomes diminished, and vice versa
Perfect stays perfect

E.g. the interval from C to A is major 6th, so the interval number of the inverted interval (from A to C) is 9 – 6 = 3. And using the rule above, the inverted interval should be a minor interval. Therefore, the interval from A to C should be minor 3rd.

Compound interval

Up to this point, we have only considered intervals that are not more than an octave. In reality, intervals can go beyond an octave. To determine any interval that is greater than an octave, simply follow the following steps:

1. raise the root note by one octave (or lower the upper note by one octave), so that the notes are now less than an octave apart
2. determine the interval between the notes as described previously
3. add 7 to the interval number to get the actual interval

E.g. to determine the interval between C and high E, we first determine the interval from C to E, which is major 3rd. So, the actual interval is major 10th after we add 7 to the interval number.

Lesson 11: 音程 (Intervals), Part 1

The term "intervals" (音程) refers to the distance between two notes. It can also be considered as the difference in pitches (or frequency) between two notes. The concept of intervals is very important, because they are the building blocks of chords.

There are two types of intervals in music: melodic interval and harmonic interval. Melodic interval is the interval between two notes when they are played one after another. Harmonic interval is the interval between two notes when they are played simultaneously (e.g. in a chord). In both cases, the lower-pitched note is called the “root”, and the interval is always defined as the interval from the root to the upper note.

Melodic interval:

Harmonic Interval:

Calculating intervals

To determine the interval between two notes, you always start from the root and count the number of steps to the upper note. Consider the root as the “doh” of the scale, and determine which note in the scale the upper note is. E.g. to determine the interval between F and A, we start with F as the “doh” of the scale (i.e. F major), then A is “mi” (the 3rd note) in F major.

The interval number is the number of degree of the upper note in the key of the root. So, in the previous example, A is a 3rd above F, or you can say that F and A are a 3rd apart. (doh = unison, re = 2nd, mi = 3rd, fa = 4th, so = 5th, la = 6th, ti = 7th, doh’ = 8th/octave)

But the interval number alone is not sufficient to describe an interval. We need to specify the quality (型態) of interval between F and A (quality of interval). If the upper note is actually IN the major scale of the key of the root, then the interval is either perfect (純音程) (unison, 4th, 5th, octave) or major (大音程) (2nd, 3rd, 6th, 7th). Let’s look at the example again. Since A is in the scale of F major, and it is the 3rd note of the scale, so the interval from F to A is major 3rd.

For a note that is NOT in the major scale of the key of the root, you can determine the quality of interval by counting how many semitone (or half step) it is above or below the note that is in the scale. Here are the qualities of interval that are not major nor perfect:
- augmented (增音程): one semitone larger than a major/perfect interval
- minor (小音程): one semitone smaller than a major interval
- diminished (減音程): two semitones smaller than a major interval, or one semitone smaller than a perfect/minor interval.

Can you tell the intervals between the following pairs of notes? (leave your answers in the comments)
- F and Ab
- F and A#
- F and Abb

In summary, just remember that unison, fourth, fifth, and octave can be (from low to high pitch) diminished, perfect, augmented; whereas second, third, sixth, and seventh can be diminished, minor, major, augmented.