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??

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.

Lesson 10: 三連音(Triplets)

In addition to the different note values introduced in Lesson 5 and Lesson 6, there is a special class of notes that occurs frequently in both classical music and contemporary music, called the triplets (三連音). As the name suggests, it is used when you want to divide a duration into 3 equal subdivisions in any simple time signature.

Triplets are used whenever you want to divide any duration into 3 equal parts in a simple time signature, because in any simple time signature, the beats can only be divided into 2, 4,... equal subdivisions (power of 2, basically).

In a simple time signature, usually two quarter notes equal to one half note; and three triplet quarter notes equal to one half note (two normal quarter notes). Similarly, three triplet eighth notes would be equal to one quarter note (i.e. two normal eighth notes). Triplets are usually written with a number '3' above or below the notes. Sometimes, you will see a square bracket or a slur across the triplet, and sometimes only the number is seen. Rests and dotted notes can be used as needed in triplets. This is one of the common ways to write triplets:


Triplets can also be considered the building blocks of compound time signatures, because all beats in compound time signatures are divided into 3 equal subdivisions. E.g. in the common time signature (4/4), if all four beats are written as triplets, it will be equivalent to the compound key signature 12/8. Since all beats in compound time signature are triplets, they will not be labeled as triplets, and therefore, a beat in a compound time signature is a dotted quarter note, instead of a quarter note.

Optional:
There may be circumstances where we want to divide one beat (a dotted note) in a compound time signature into 2 equal subdivisions. To achieve that, a duplet is used. Two duplet eighth notes equal one dotted quarter note (i.e. 3 compound eighth notes). Theoretically, one beat can be divided into n equal subdivisions, by the use of tuplets (the general term for notes like duplets and triplets).

Lesson 9: 拍號 (Time Signatures)

Time signatures typically consist of 2 numbers like in a fraction. It is always written after the key signature at the beginning of a piece, and will not be written again unless the time signature changes halfway in the piece (see Lesson 8). There are 3 types of time signatures: simple, compound, and complex. Each type of time signatures will be disccused below.

The two numbers in a simple time signature tell you the following information:

• Top number: how many beats there are in a bar/measure.
• Bottom number: what the value of one beat is, or the beat value.

E.g. Consider the time signature . The bottom number is 4, which means that each beat is a quarter note; the top number is 2, which means that there are 2 quarter notes in each measure. Similarly, the time signature means that there are 3 beats in each measure, and each beat is an eighth note. An important concept in simple time signature is that each beat can be divided into two subdivisions.



The most commonly used simple time signature is . Because it is so commonly used, it is sometimes written as 'C', which denotes 'the common time'.

In the second type of time signatures: compound time signatures, the numbers are read a little differently.

• Top number: how many subdivisions there are in a bar/measure.
• Bottom number: what the value/duration of one subdivision is.

So what is 'one beat' in a compound time signature? In compound time signatures, each beat is divided into three subdivisions (instead of 2 in simple time signatures). In other words, 'one beat' would be 3 times of a subdivided note in a compound time signature. This also implies that in all compound time signatures, the top number should be divisible by 3 (except for cases like 3/4 or 3/8, because technically it is pointless to have only 1 beat per measure). This is how you can distinguish between simple and compound time signatures.

E.g. The time signature means that each subdivision is an eighth note (bottom number), and there are 6 subdivisions in each measure, meaning there are 6/3 = 2 beats per measure. One beat in this time signature would be a dotted quarter note, because it is 3 times of an eighth note. Similarly, the time signature means there are now 9 subdivisions per measure, which means there are 9/3 = 3 beats per measure. Note that in all compound time signatures, 'a beat' will always be a dotted note.

The third type of time signatures, complex time signatures, are a lot less encountered than simple and compound time signatures. It typically involves a prime number (other than 2 and 3) on the top. E.g. 5/4 or 7/4. In these complex time signatures, a measure can be interpreted differently according to the composer. E.g. for the case of 5/4, the 5 beats can be played as 3+2 or 2+3, and in the case of 7/4, a measure can be divided into 4+3 or 2+3+2, etc.

Things to learn in this lesson:

1. What do the numbers in a time signature stand for?
2. Be able to differentiate between simple, compound, and complex time signatures.
3. What are the differences between simple and compound time signatures?

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 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?

Lesson 6: 音符時值...續集 (Note duration, cont'd)

Having just the whole note, half note, quarter note, eighth note, etc. are not sufficient for expressing more complicated rhythm in most classical or contemporary music. E.g. how do you write 3 beats? There must be a way in music to do that. In fact, there is more than a way!

Dotted Notes

When you add a dot to a note, you add half of its value to the note. E.g. a quarter note is normally 1 beat, so a dotted quarter note would last 1.5 beats. Similarly, a half note is typically 2 beats, adding a dot to it (dotted half note) would make it 2 + 2/2 = 3 beats!

Tie

A tie can occur between two or more notes to add all their values together. E.g. when a quarter note is tied to a half note, then the result would be 2 + 1 = 3 beats. When a quarter note is tied to a sixteenth note, the result would be 1.25 beats. The tie is also used when a note is being stretched across measures.

There are also times in music when nothing is to be played. These periods of silence need to be properly notated as well, thus the need for another class of symbols: rests (休止符).

Just like the notes shown in Lesson 5, there are whole rest, half rest, quarter rest, etc... the duration of which corresponds to their respective notes.

Whole rest

Half rest

Quarter rest

Eighth rest

Sixteenth rest

Rests are also similar to notes in the way that both rests and notes can be dotted. E.g. a dotted quarter rest stands for a rest of 1.5 beats. However, ties cannot be used on rests.

Questions for this lesson:

1. Do you know how to write all the notes/rests presented in this lesson?
2. Can you name all the different notes/rests at sight?
3. Can you calculate the total duration of a string of notes/rests?
   

Lesson 5: 音符時值 (Note duration)

This lesson will teach you about the duration (or length) of different notes. It is really important to know how long each note lasts, because these notes are the building blocks of all songs! If you do not know how long each note last, you will not be able to read the melody in the right rhythm.

Each note that looks different has a different duration in music. The first note presented is called the whole note (全音符):

The whole note usually represents 4 beats. Cases where a whole note does not represent 4 beats will be discussed in later lessons. The whole note is also known as the semibreve.

The second note presented is called the half note (二分音符):

The half note looks like a whole note with a stem attached to its side. Since a half note is literally half of the whole note, it usually represents 2 beats.

As you may guess, the next note that is presented is called the quarter note (四分音符):

The quarter note looks like the half note, but with a solid note head. The quarter note usually represents 1 beat.

If this keeps going. the next note presented would be the eighth note (八分音符):

The eighth note looks like the quarter note with a tail at the end of the stem. It usually represents half a beat.

Is there a sixteenth note (十六分音符)? YES! And it is written by simply adding an additional tail to the eighth note. So, the sixteenth note has two tails at the end of the stem as follows.

As you can see, each time a tail is added to the note, its duration is halved. Therefore, you can create thirty-second note (三十二分音符), sixty-fourth note (六十四分音符), even hundred twenty-eighth note (一百二十八分音符) by adding a tail each time you half a note. However, for the practical purpose of playing the piano for worship purposes, we almost never see anything that is thirty-second note or shorter (thank goodness!).

If all these notes seem overwhelming, just remember that they are basically math equations. In this math system, the whole note is 1, and everything else is a fraction of the whole note. Thus, as long as you can remember the name, you can remember its duration:

whole note = 2 x half (1/2) notes = 4 x quarter (1/4) notes = 8 x eighth (1/8) notes = 16 x sixteenth (1/16) notes... etc.

From now on, you should be able to calculate how many beats are there in the example below:

It is 2 + 1/2 + 1/2 + 1 = 4 beats.

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

1. Do you know how to write all the notes presented in this lesson?
2. Can you name all the different notes at sight?
3. Do you know the relative duration of all the different notes? (e.g. how many half notes equal to a whole note?)
4. Can you calculate the total duration of a string of notes?

Lesson 4: 黑色琴鍵 (Black keys)

From the previous lessons, we see that all the lines and spaces on the staff are represented by a white key on the keyboard. So how are the black keys represented on the grand staff? Before we start to learn about the black keys, we must first learn the concept of whole step and half step.

When playing the C major scale, we learnt that some steps are whole steps and some are half steps. In particular, there is a half step between E and F, and another half step between B and C. Those are the same pairs of notes that do not have a black key between them, so there is only a half step between those pairs. All other pairs of notes that have a black key in between have a whole step between them. This pattern of whole and half steps will hold for ALL major scales.


Now, if we take a half step from C to the right, we will hit the black key that is immediately to its right. We call that black key "C sharp", and it is written as "C#". Similarly, the black key that is immediately to the right side of D is called D-sharp, and it is written as D#. From this, you can deduce that the rest of the black keys are F#, G#, and A# (from left to right). Simply speaking, a sharp will make a note a half-step higher.

There is also another way to write the notation of the black keys. In the last paragraph, we used a sharp to make a note a half-step higher. We can also make a note a half-step lower by adding a flat "b" to it. For example, the black key that is immediately to the left of B, we can call it B-flat, and it is written as Bb in music. Similarly, the rest of the black keys can be written as Ab, Gb, Eb, Db, respectively (from right to left).


Since there are two ways of writing and naming the black keys, naturally, that means each black key on the keyboard can be written in two ways. For example, the black key between C and D is half step higher than C, and is half step lower than D, so it can be written as either C# or Db. In other words, C# = Db. Similarly, D# = Eb, F# = Gb, G# = Ab, A# = Bb. Knowing how to write black keys in different ways is imporatant later on when we learn about keys other than C major. Perhaps this figure below will make memorizing the black keys easier:

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

1. Why are some steps half steps in the C major scale, and why are the rest whole steps?
2. Where are the half steps in the C major scale?
3. What musical symbol should you use to make a note half step higher?
4. What musical symbol should you use to make a note half step lower?
5. Know how to name all the black keys in both ways.

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.