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??

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. 

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.