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 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 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 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.

Lesson 8: 如何讀譜 (Reading piano scores)

The few most important things that you will need to pay attention to when playing songs/pieces are those illustrated in the following diagram:

• Clefs: Most worship songs that you will encounter will have treble clef on top and bass clef at the bottom. However, in classical music, it is not uncommon to have either all treble clefs or all bass clefs for both hands, so it is always good to check.
• Key signature: This tells you what key the song is in. The key signature is shown on all the staffs throughout the piece. The key of a song can change in the middle of it, so it is important to pay attention to such changes.
• Time signature: This tells you how many beats are there in each measure (or bar). However, this is completely unrelated to the tempo (speed) of the piece. A more extensive explanation on how to read time signature will be covered in later lessons.
• Bar lines: A bar line is drawn to separate measures. E.g. each bar has 4 beats in a given song, then a bar line will be drawn every 4 beats.

In addition to the components mentioned above, there are also other components that define the song/piece. For example,

• the tempo of the piece is typically written at the beginning of a piece, above the 1st line.
• the dynamics (relative loudness) of the piece can be written anywhere in the piece and changes as the piece goes.
• there are also a wide variation of words used in music to mark the mood in the piece.

Lesson 3: 譜號(The clefs)

In lesson 2, we learnt that the grand staff consists of the combination of treble clef and bass clef. They are the most common clefs used or seen in music. Whenever we want to write notes that are outside the 5 lines of the treble or bass clef, we have to add extra ledger lines to "contain" the notes. The further away the note is to the 5 lines, the more ledger lines you will need to write. (Note: Ledger lines are called "leger lines" in U.S.)

The treble clef is also known as the "G clef" because when you write it, it starts at the line where G above the Middle C is.

Similarly, the bass clef is also known as the "F clef", because it starts at the line where F below the Middle C is.

Optional: Although the playing the piano only requires you to know these two clefs, it is important to know that there exists other clefs that are commonly used in other instruments as well.

For example, the clef shown below is known as the "alto clef" (中音譜號). The line where the center of the alto clef lies on is where Middle C is. It is used most commonly for instruments where their range of sounds are near the Middle C, such as the viola (中提琴).

The clef shown below is the "neutral clef", and it is is only used in instruments without any specific pitch, such as some of the percussion instruments.

Lesson 2: 五線譜(The Grand Staff)

The grand staff is the most widely used system of musical notation. Generally, knowing how to read music on the grand staff is regarded as "knowing how to read music" in the lay man's term. The "grand staff" consists of two staffs stacked together as follows:

There are two clefs in the grand staff. The one on the top is called the treble clef (高音譜號); the one at the bottom is called the bass clef (低音譜號). There are 5 lines in each staff. Notes can be written on the lines or between the lines (in the spaces). Notes written on the lines are called line notes; and the notes written in the spaces are called space notes.

The grand staff also provides a "visualization" of the music in a sense, because notes that are higher up in the staff will have a higher pitch (with a few exceptions). The figure below shows that the Middle C on the piano is also in the middle of the grand staff.

This image is obtained from this website.

It is extremely important to memorize what notes each line and space refers to, because that will allow you to read music scores more quickly. You should be familiar with the notes that you can look at the note and know which letter it refers to immediately. Similarly, you should know the notes well enough that you can write down every note on the grand staff immediately when you are asked to do so. It should not be very difficult if you have memorized the letters in Lesson 1, because it is just cycles of C, D, E, F, G, A, B. And remembering where the Middle C is located on the grand staff helps you to count your steps up or down the staff to see where the notes belong to.

Questions that you should be able to answer at the end of this lesson:

• What are the clefs mentioned above? What are the differences between them?
• What are line notes and space notes? (Try to write examples of them)
• Be able to name notes that are written on the grand staff without thinking (for too long).
• Be able to write any note on the grand staff without thinking (for too long).