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 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??

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 7: 調號 (Key Signatures)

In Lesson 4, we learnt that the black keys can be represented on the staff using sharps (#) or flats (b). And the reason for having sharps and flats is that white keys alone cannot be used to represent all the scales in different keys.

So, how many different keys are there in total? By looking at the keyboard again, we see that there are 7 white keys and 5 black keys in each octave. Therefore, there are 7+5=12 different keys in total. Each of these keys are named by the note it starts with. E.g. the key that starts with C is called C Major.

Each major (大調) key has a unique key signature (調號), with a unique number of sharps or flat. By "unique", it means that e.g. A major's key signature has 3 sharps, so whenever you see 3 sharps, it must be A major and nothing else. This will be slightly different when we learn about the minors (小調), but let's not worry about them yet.

In order to tell how many sharps/flats each of the 12 keys have, we have to construct their scales.

• Starting with C major (C大調), which has no sharp nor flat. To construct the next scale, we go to the 5th note in the scale of C major: G.
• The key that starts with G is G major (G大調), and you will find that it will have one sharp (F#) if you construct its scale using the pattern shown in Lesson 4.
• To construct the next scale, we, again, go to the 5th note of the scale of G major: D.
• Repeat this process and you will find that all 12 keys will be constructed. (It is easier to do this exercise at a keyboard/piano.) Some of them will have sharps in their key signatures, and some will have flats.

The process of constructing scales can be summarized by the Circle of Fifths (調的五度循環):

The logic behind the Circle of fifths is that when you go clockwise, the next key is always a perfect 5th from the current key. This is the more technical way of saying that the next key always starts on the 5th note of the current key. Note that the keys on the right of the Circle of fifths are the keys with sharps in their key signatures, and the ones on the left are those with flats in their key signatures. As you may notice that F# (or Gb) major is at the bottom of the circle, because its key signature can be either 6 sharps or 6 flats. This is the theory behind differnt keys, but the most important thing is to remember ALL the key signatures, which are summarized below:

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

1. Can you name the associated major key by looking at the key signatures?
2. Can you write the key signatures for any given majore key?
3. Can you remember how many sharps or flats each of the major key has?