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.