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 17: Tempo (速度)

Tempo is an Italian word for "speed". It is typically specified at the beginning of a piece. The tempo of a piece defines its mood and difficulty to play. It is very common in classical music to have changes of tempo or mood (or both) in the middle of the piece, although this is less common contemporary worship music. In contemporary worship music, the tempo changes usually take place when we want to flow to the next song flawlessly.

Tempo is either given in words or in beats per minute (BPM). All classical music described their tempos in words, because the metronome (拍子機) was not invented back then. Although the modern prints of most classical music would include the mathematical tempo (BPM) as well, for convenience. Here are some examples of tempo markings:

• Largo: very slow (最缓板)
• Allegro: fast and bright (快板)
• "♪ = 120": 120 eighth notes per minute

As a member in a worship team (whether you are singing or playing an instrument), it is very important to learn how to keep a steady tempo, because the congregation will have a hard time following an unsteady tempo. The person playing the instruments may not notice that he/she is playing at an unsteady tempo, especially if he/she is playing something that unfamiliar, because he/she is focused on trying to figure out what to play next, and not keeping count of the beats.

The key to learn how to keep a steady tempo is: practise, practise, PRACTISE! Your ultimate goal is to be able to keep a steady tempo inside you. Here are some suggestions:

• Know the songs well: listen to it over and over again, and try to count the beats while listening. It is even better if you can figure out its time signature and count accordingly. (In my opinion, “knowing a song well” means you are able to sing that song with accurate rhythm and melody when you are not listening to it.)
• Practise with a metronome: start from a slow tempo first and slowly increase it to the level you want. You must play the song WITH RHYTHM even at the slowest tempo, NEVER play the easier part faster and the harder part slower, because that will only make it harder for you to learn the rhythm in the whole song. (You should keep doing this until you can start to keep a steady tempo on your own.)
• Play along with the CD/MP3: to practice songs for which you have the CDs or MP3s, you can play the song on your CD player or computer, and then try to play the chords on your instrument simultaneously, matching the chords in the song itself. One good thing about playing along is that the CD or MP3 will not stop for your mistakes, so you are forced to keep moving on. This is the best way to learn how to respond to your own mistakes without lagging a beat in real time. However, it is not very helpful to do this exercise when you are not familiar with the song yet.

At the end of the lesson, I want to stress the distinction between tempo and time duration of notes (see Lesson 5 and Lesson 6). The tempo of a song and the length of a note are two completely different concepts, and should not be regarded as the same concept at any time.

Lesson 16: Minors(小調) - Part 2: Minor Scales (小調音階)

Just like all major keys, each minor key has its own scales. The difference is that there are different modes of minor scales: natural, harmonic, and melodic minor scales. Each of these modes will be explained below using C major/A minor as illustration.

Natural Minor (自然小調)

The natural minor scale is exactly the same as its relative major scale, but with a different starting point. (Hint: you will need to know all the relative keys in Lesson 15 first!) It starts at the 6th note (submediant) of the relative major scale instead. Recall the C major scale: C-D-E-F-G-A-B-C. Since A minor natural scale is just C major scale but starting at A instead, the A minor natural scale would be: A-B-C-D-E-F-G-A. Comparing it with the A major scale (A-B-C#-D-E-F#-G#-A), the A minor natural scale has lowered 3rd, 6th, and 7th degrees.

Harmonic Minor (和聲小調)

The harmonic minor scale is a natural minor scale with a raised 7th degree. Thus, the A minor harmonic scale would be: A-B-C-D-E-F-G#-A. Another point to note about the harmonic minor is that this is the only scale in which there is an interval that is more than a whole step; the interval between the 6th degree (F) and 7th degree (G#) is an augmented 2nd.

Melodic Minor (旋律小調)

The melodic minor scale is probably the most complicated mode of minor scales, because its ascending pattern is different from its descending pattern (in both natural and harmonic minor scales, the ascending and descending patterns are the same). The descending pattern of the melodic minor is the same as the natural minor. However, the ascending pattern of the melodic minor contains raised 6th and 7th degrees. Thus, the A minor melodic scale would look like this: A-B-C-D-E-F#-G#-A-G-F-E-D-C-B-A.

Each of the above mode of minor scale has its own characteristic in sound. Ideally, a pianist should be able to distinguish between these three different modes by ear. Try playing each of the above minor scales on the keyboard to hear how differently they sound, and contrast it with the major scale.

Assignments

1. Determine the intervals between all the adjacent notes for all three modes of minor scales.


2. The derivation of A minor scales (natural, harmonic, and melodic) is illustrated above. Can you write out all 3 types of minor scales for the other 11 keys? (Note: it is much easier to determine the key signatures of each minor key first)

Lesson 15: Minor(小調) - Part 1: Relative Minor(相對小調) and Parallel Minor(平行小調)

Relative Minor (相對小調)
Each major key has a unique relative minor. This relative minor has the following properties:

• it has the same key signature as the major,
• the tonic (1st note) of the relative minor is always the submediant (6th note) of the major key.
• the tonic of the relative major is always a minor 3rd above the tonic of the minor (that is the interval from la to do).

E.g. In C major, the submediant is A, so the relative minor of C major is A minor. Since the key signature of C major does not contain any sharps or flats, the key signature of A minor also does not contain any sharps or flats. The key signatures of all the minor keys can be figured out in the same way.

E.g. In E major, the submediant is C#, so the relative minor of E major is C# minor. You may wonder what C# minor is, because we have never seen C# major. The fact is, C# is the enharmonic equivalent of Db (i.e. same note but written differently), so C# minor is actually "equivalent" to Db minor, but due to certain constraints to be explained later, it has to be written as C# minor, and cannot be written as Db minor.

In general, minors sound "sadder" than majors. Composers sometimes take advantage of this property of relative minors to change the mood of a song without changing the key signature.

Parallel Minor (平行小調)

The parallel minor of a major key is simply the minor that has the same tonic (i.e. start on the same note). E.g. the parallel minor of C major is C minor.

Obviously, parallel keys do not have identical key signatures. One can figure out the key signatures of the minor keys by going back to the relative major: counting a minor 3rd from the tonic of the minor key to figure out the tonic of its relative major, then figuring out the key signature of that major key. There is also a "shortcut" to figure out the key signature of any minor key.

To determine the key signature of a parallel minor, add 3 flats to the key signature of that major. Eamples:

• C major has no sharp/flat. So the key signature of C minor has 3 flats.
• F major has 1 flat (Bb). So the key signature of F minor has 4 flats.
• F# major has 6 sharps. Since flats cancels out sharps, the key signature of F# minor has 3 sharps.

Conversly, we can determine the key signature of a parallel major, by adding 3 sharps to the key signature of that minor.

Back to the example in the previous section about C# minor. If we used the shortcut above to determine the key signature of the parallel minor of Db major, what will we get? Db major has 5 flats, adding 3 flats to it will mean that Db minor has 8 flats, which would not make sense, because 1) there are only 7 notes in the whole keyboard (C,D,E,F,G,A,B), and 2) the maximum number of sharp/flat that can be in a key signature is 6 (in the case of F# or Gb major).

Therefore, we can only use sharps in the key signature of Db minor, which would make it C# minor instead of Db minor. But how many sharps? Now, we know that a key signature with 6 flats is equivalent to a key signature with 6 sharps, and remember from the Circle of Fifths that 7 flats = 5 sharps (and vice versa). By extending this pattern, we can deduce that 8 flats would be the same as 4 sharps. So, the key signature of C# minor has 4 sharps.

Lesson 13: 如何數拍子

Most songs have a time signature 拍號. Its time signature will be one of those that are introduced a few lessons ago, e.g. 4/4, 3/4, 6/8, etc. Each of these time signature has its own characteristics in sound, which is indicated by its strong beat 重拍. By listening to the downbeat of a song, one can distinguish the time signature of the song. As a musician, it is extremely important to be able to "hear" the time signature of a song, especially when you are to play a song without a score. Also, a musician must be able to count the beats of a song correctly so that he/she can play it in the way it is supposed to sound.

Here is how each time signature should sound like:

1. 4/4:   ONE     two     THREE     four
2. 3/4 or 3/8:   ONE     two     three
3. 2/4 or 2/2:   ONE     two
4. 6/8 or 6/4:   [ONE     two     three]     [TWO     two     three] 
5. 9/8 or 9/4:   [ONE     two     three]     [TWO     two     three]     [THREE     two     three]

The bolded ONE is always a strong beat 重拍, no matter what time signature the song is. In the 4/4 time signature, THREE is considered a semi-strong beat 半重拍, so it is not as strong as the first beat, but still stronger than 2nd and 4th beat.  In compound time signature, you should be able to hear the 1-2-3 in each beat. Sometimes, songs in compound time can sound like this: one-one-two, one-one-two (where one is long and two is short). This is called the swing pattern, which is commonly heard in Jazz. A song that has this pattern is most likely in compound time, but you would still have to figure out whether it is 6/8, 9/8, or 12/8 by listening to the strong beat.