Lesson 20: Chords of a Major Key (大調中的和弦) - Part 1

The scale of a major key consists of 7 notes. For example, in the key of C, those 7 notes are: C, D, E, F, G, A, and B. And we have learnt in Lesson 19, a triad is made up of 3 notes are stacked in thirds.

In other words, we can derive 7 distinct triads from a major key scale, with the root of each triad being the different scale degrees. Here is the example in the key of C:

• Starting with 1 (C): C - E - G
• Starting with 2 (D): D- F - A
• Starting with 3 (E): E - G - B
• Starting with 4 (F): F - A - C
• Starting with 5 (G): G - B - D
• Starting with 6 (A): A - C - E
• Starting with 7 (B): B - D - F

By looking at the intervals between the notes in each of these triad, one can easy figure out the quality of the above chords (review Lesson 19 if necessary):

• C - E - G: C Major, or C
• D- F - A: D minor, or Dm
• E - G - B: E minor, or Em
• F - A - C: F Major, or F
• G - B - D: G Major, or G
• A - C - E: A minor, or Am
• B - D - F: B diminished, or Bdim

To summarize, the pattern for the triads in the key of C is as follows:

1M 2m 3m 4M 5M 6m 7dim

In fact, the same pattern applies for all 12 keys!! That means, in the key of D, the triads that can be derived from the key are: D, Em, F#m, G, A, Bm, C#dim. Try to verify that for yourself!

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 18: "Simplified Notation" (簡譜)

Sometimes, the songs that we have to play are only available in what is called the "simplified notation", or 簡譜 in Chinese. Instead of using the staff and notes described in the first few lessons, it uses numbers to represent the melody and rhythm. 簡譜 is something that both musicians and singers in a worship team should learn to be able to read it instantly (except for those who can learn a song much faster by listening), so that the practising process can be streamlined.

Musical Notes & Accidentals

The numbers that you will see in 簡譜 are 1 to 7, each number represents a musical note in the major scale:

• 1 = do
• 2 = re
• 3 = mi
• 4 = fa
• 5 = so
• 6 = la
• 7 = ti

The use of accidentals (sharps, flats, and naturals) in 簡譜 is exactly the same as that in standard notation. If you want to raise a note by a semitone, you write the "#" in front of the note, e.g. #4 means the note "fa" is being raised a semitone.

If a note is in a higher octave, it will have a dot above it. On the other hand, if a note is in a lower octave, it will have a dot below it.

Note Duration & Rests

• Quarter notes (or 1 beat) in simplified notation are represented by an unmodified number.
• Longer notes in whole beats are represented by the addition of hyphens following the number. E.g.
  5 - 6 - means the notes so and la are both 2 beats, and
  7 - - 6 means ti is 3 beats and la is 1 beat.
• Longer notes of other durations can be written as two notes joined together by a tie, just like in standard notation.
• Eighth notes (half beats) are written with one line underneath. E.g.
  1 2 3 2 1 1 : the first two beats consist of eighth notes, and the 3rd and 4th beats are quarter notes.
• Sixteenth notes are written with two lines underneath. Basically, the lines underneath the notes are equivalent to the flags on the 8th and 16th notes in standard notation.
• The concept of dotted notes in standard notation applies in simplified notation as well, except for the half note, since a dotted half note = 3 beats, has to be represented by hyphens in simplified notation.
• Rests are written as "0" in simplified notation. Each unmodified "0" represents a quarter rest. E.g.
  1 0 0 0 means the 2nd, 3rd, and 4th beats have no sound.
  1 - 0 0 means the 3rd and 4th beats have no sound.
  Extended rests must be represented by writing multiple "0"s instead of writing hyphens after the first "0". So, the first example above cannot be written as 1 0 - -
• 8th rests and 16th rests are written as "0" with the corresponding number of lines underneath it.

Key Signature & Time Signature, etc.

• Since there is no staff in simplified notation, the key signature (調號) in standard notation cannot be written out. Therefore, the key of the song is usually declared at the beginning. E.g. "Key: C" means the song is in C major. "D#m" means the song is in D# minor. (The part "Key:" is sometimes omitted)
• The time signature (拍號) of the song typically comes immediately after the key at the beginning of the song, and is written in the form of a fraction. E.g. "4/4" or "3/4".
• Bar lines, double bar line (at the end of a song), and repeat sign are used in the same way as standard notation in simplified notation.

Simplified Notation: Real Life Example

It is the responsibility of the musicians and vocalists in a worship team to learn how to read the simplified notation, because the leaders and vocalists may not all know how to read music (although I still think that everybody in the team should learn how to read music, for their own sake). As a pianist, it is important to be able to play the melody smoothly from any kind of score you are provided, be it in standard notation or simplified notation. In fact, any pianist should slowly become able to play by ear, i.e. be able to play the melody on the piano after hearing it several times.

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 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??