I am a big fan of music, and music theory has always been my favourite part. I have also learned and even taught many musical instruments, such as accordion and guitar, and have written some tutorials or courses for various purposes. Music theory always lies in the common beginning part before introducing the specific techniques of playing the instruments, unless the course doesn’t want to tell what learners are playing. That’s why I wrote this comprehensive guide to music theory agnostic to instruments, which will save my time to explain music theory on courses over and over again. But more importantly, I hope this guide can share my perspective of understanding music theory with who are interested in the foundation of music.

I try to make this guide as explanatory and Q&A style as possible. I genuinely think there is very less explanation and intuition when it comes to music theory if you are learning music in China. I’ve looked up the music theory part of most popular instruments tutorial or music textbook used in China, and found most of them are just a bunch of jargon definitions and some teaching you how to read sheet music, without telling why. (So I can’t complain many I met who learned an instrument very young cannot play at all without sheet music unless they recited it. Many struggle with music theory a lot. ) But in this guide I try to break this and guarantee every concept explained why it exists or is like that.

It is worth noting that, music theory isn’t any physical law or something. Many rules are created just because it sounds good to human ears thus commonly used in music practice. These kinds of things are very subjective, so there are never right or wrong answers in music theory, and it keeps evolving led by advanced musicians (especially from jazz and experimental music). However, this guide is not going to talk about them but mostly basic things based on the common practice, the solid foundation of most music you’ve heard. I will put less common and theoretical contents in other articles.

Additionally, notation or sheet music are always designed on top of certain music theory concepts. Based on this principle, I always introduce the music theory behind first, then the design logic of the notation. The notation or sheet music parts are wrapped in info boxes, which can make you get a clearer sense of which concepts are introduced by notation (like the denominator of time signature), and which are notation-agnostic music theory (like the numerator of time signature).

So let’s start!

1 Notes

Q: What is a note?

A: In physics, a note is a sound with a specific pitch (frequency, physically speaking) and duration. A series of notes lay out in a specific time order creates a piece of music.

Q: What are the common used pitches in music?

A: As we said, music is a subjective thing, so there are no right or wrong answers, but common practices. The common practices in today and most of the music history can be represented as the Western music system, which divides into 12 notes where correspond to one of the 12 keys on the piano keyboard shown in Figure 1 (other keys on the keyboard are equivalent, i.e. sound similar to these 12 notes. I’ll explain that in “octaves”).

Figure 1: The 12 notes on the piano keyboard.

Q: How were these 12 notes found?

A: For explaining this, I will simplify the history of music theory and put stress on the logic.

Our ancestors found through practices that two strings with a length ratio of 1:2 sound very similar. They sound the same, but just one is higher than the other. They are later called octaves, and considered as equivalent notes.
They then did a lot of experiments on the string length ratio between 1 and 2 and found a way to equally divide the interval between these two notes into 12 which sound right. Note that mathematically, the ratios are not $1 \frac{1}{12}, 1 \frac{2}{12}, \dots, 1 \frac{11}{12}, 2$ , but $2^{\frac{1}{12}}, 2^{\frac{2}{12}}, \dots, 2^{\frac{11}{12}}, 2$ . That’s how the 12 notes were generated, and the method is called the 12 equal temperament.
We’ve only talked about the relative relationship of the 12 notes so far. At this point, we still need to decide what frequency is the starting note i.e. the sound of string ratio 1:1 or 1:2 which generates other 11 notes (or something like how long / tight should the starting strings be) as the standard, i.e. the absolute. This is the job of the tuning in music instruments. It’s hard for ancient people to give a standard with less knowledge of physics and modern technology, but today we generally agree with the international standard that one of the notes of starting strings should be frequency 261.63 Hz (the middle C that we’ll talk about later).

With these 3 steps, the 12 notes we used today are finally decided. Other notes are the 12 notes repeated in octaves.

The 12 notes are equally divided. The interval between two adjacent notes is called a semitone, which is the smallest interval in Western music system.

Q: How many octaves, or, what is the range of frequency) are commonly used in music?

A: Biological facts show that human can hear the frequency from 20 Hz to 20,000 Hz, and can sing the frequency from 80 Hz to 1,100 Hz. Each instruments have their own range of frequency accordion to their physical properties.

The most common used octaves in music are from 27.5 Hz to 4,186 Hz, which is the range of the piano keyboard, a bit wider than human voice. The piano keyboard typically has 88 keys which cover the most common used octaves that sounds normal in music, which is around $88 / 12 \approx 7.33$ octaves.

Q: Why is the piano keyboard designed with black and white keys instead of just 12 white keys?

A: There are certainly ergonomic reasons like making the layout more compact and easy to play, but the most important reason can be abstracted as music theory. Our ancestor later found that there is a series of 7 notes in the 12-note set sound extremely harmonious and natural to human ears, which are the 1st, 3rd, 5th, 6th, 8th, 10th, 12th. These 7 notes are more commonly played, therefore, the piano keyboard is designed to place them more accessible as the white keys, while the remaining 5 notes are placed higher as the black keys.

Now we can tell that the adjacent notes, no matter black or white, are always semitones.

If we only look at the white keys i.e. the 7 commonly played notes, we find the intervals are “2, 2, 1, 2, 2, 2, 1” semitones. That is to say, the interval of 2 semitones is also used a lot, having a name called whole tone.

The 7 notes themselves as a series form a natural major scale. (Former definition of the scale will be introduced in the “Scales” section.)

Q: What are the names of all the notes?

A: The note corresponding to 261.63 Hz is called Middle C in the Western music system. It’s “middle” because it’s in the middle of the piano keyboard, or technically speaking, its frequency lies in the middle octave (4th) of the piano keyboard octave range (7.33 octaves). Its higher and lower octaves are also called C.

The white key notes (if starting from C) can be denoted as letter names C, D, E, F, G, A, B (sometimes another system called solmisation: Do, Re, Mi, Fa, Sol, La, Si). The black key notes between them are denoted with sharps (#) and flats (b) symbols added to the white notes: C#/Db, D#/Eb, F#/Gb, G#/Ab, A#/Bb. Their derivation from white keys also indicates that they are less commonly used.

There are also notations to distinguish notes in different octaves: note name + octave index (in the piano keyboard). For example, C4 is the middle C, C5 is the higher C, and C3 is the lower C.

Q: Why do we start from C, or the frequency of 261.63 Hz (and its multiplication or division by 2)?

A: We can actually start from any frequency. The reason we start from 261.63 Hz (and its multiplication or division by 2) is purely that it was adopted historically and it developed the international standard.

Q: Since this is the standard, why don’t we just call it “A” in an alphabetical order instead of “C”?

A: Historically, the notation “A” was used to represent other “first” or “lowest” concepts. The music theory was not originally like what I’ve talked about. The modern music theory was developed from the historical one, and the results of alignment of modern and historical system make the “C” the most common starting note.

Stave Notations

Stave, or staff, is the notation system that is commonly used to denote music. It has 5 horizontal lines and 4 spaces. The pitch of notes is determined by the position of the note mark on the stave, either in the spaces or on the lines. The higher the note is on the stave, the higher the pitch of the note.

The clef symbol denotes the range of notes that is represented on the stave:

Treble clef (𝄞): middle C lies on first lower ledger line. Used for higher-pitched music
Bass clef (𝄢): middle C lies on the first upper ledger line. Used for lower-pitched music
Less common clefs: alto clef, tenor clef, etc.

The stave notation for notes. Source: Music Mind

Q: How do we measure the interval between two notes other than number of semitones?

A: We can measure the intervals in semitones, but the pure numbers are somehow confusing and not easy to remember. In history, the intervals are turn into terms shown below. These term names are almost derived from the note position in natural major and minor scale. (As octaves are basically equivalent, we only cover intervals less than an octave.)

Semitones	Interval
0	Enharmonic
1
2	Major 2nd (Whole Tone)
3	Minor 3rd
4	Major 3rd
5	Perfect 4th
6	Augmented 4th (Tritone)
7	Perfect 5th
8	Augmented 5th (Minor 6th)
9	Major 6th
10	Minor 7th
11	Major 7th
12	Octave

Each interval creates an unique feeling and has its role in organising notes in music. Please refer to my other post about intervals (not finished) for details.

2 Rhythm

Q: What is rhythm?

A: In the broad sense, rhythm is the pattern of duration of sounds and silences in music.

Q: What are the common tools to represent rhythm?

In the long history of human music practice, beats is the most common tool to represent rhythm. Beats are regular, recurrent pulses that divide music into equal units of time. You can think mathematically that beats are the points on the time axis while notes and silences are line segments.

In this narrow sense, rhythm is a periodic pattern of beats for a piece of music. It is a grid-like container of notes in the timeline.

Note that strong and weak beats are also common practices in music, because human ears can feel boring if all beats are the same (like a monk taps the wooden fish lol), just as if we write a song with all notes are of the same pitch.

Q: How can beat patterns be defined?

A: We assume that beats are (which human can feel comfortable with):

Regular: The time intervals between beats are the same.
Recurrent: The pattern repeats itself in a periodic way.
Have strong and weak beats.

Then it would be much easier to define beat patterns: we can first categorise them by the number of beats in a period, which is called the metre. The number of beats can be any positive integer greater than 1 (as 1 would be again that all beats are the same), like 2 (duple), 3 (triple), 4 (quadruple), etc. Then we can further categorise it by the layout of the strong and weak beats.

Q: Can we list all beat patterns?

A: Mathematically, we can easily list all possible patterns with the above assumptions, but only a subset of them are commonly used in music and make sense to human ears.

For example, the first beat in any meter is usually the strongest beat. The other beats are weaker but don’t have to be the same strength. which means we can have “weaker strong beat” or even more fine-grained strength. But in generally practice, we only use 3 levels – “strong”, “weaker strong” and “weak” beats (I denote them as S, w, W later), because human ears can’t distinguish more than that.

The most common patterns are:

For duple: Sw is the only way for duple meter.
For triple: Sww is common, SWw or SwW sounds weird.
For quadruple: SwWw is common. It can be Swww, but SwWw is more reasonable for a relatively long beat sequence.
For quintuple: SwWww, SwwWw.
For sextuple: SwwWww is common, SwWwWw is often reduced as triple.
…

(Placeholder: I plan to list all of the time signatures in a separate post.)

Q: What are relationship between metres?

A: Metres are somehow equivalent to each other.

When one is a multiple of the other. For example, the SwWw quadruple metre pattern can be reduced to the Sw duple metre pattern by doubling the duration of 1st and 3rd beat. In reverse, the Sw duple metre pattern can be decomposed into the SwWw quadruple or SwwWww sextuple metre pattern. The difference is whether more details on beats are needed for the music.
Some can be additively decomposed into others. For example, the SwWww / SwwWwquadruple metre pattern can be decomposed into the Sw duple metre pattern and the Sww triple metre pattern.

Q: How to measure the speed of music?

A: The speed of music is called tempo, an Italian music term. In ancient and early modern times, people did not have a quantitative way to represent the speed of music, but qualitative words like “allegro” (fast), “adagio” (slow), etc were commonly used.

In modern times, the speed is generally measured in a scientific and quantitative way. It is measured by the beat duration instead of duration of specific notes in the music, because beat is kind of a universal thing that can be applied to any music. Specifically, we usually use the frequency instead of duration: beats per minute (BPM). With the assumption that beats are regular, the BPM is fixed for an amount of time.

Q: How to measure the duration of notes?

A: We can certainly measure the duration of notes in its physical clock time, but that would be very confusing to musicians, not only because it’s a float number but also an absolute value with no reference to the notes in the rest of the music.

Since we now have the uniform grid to accommodate notes, we can measure the duration of notes in the number of beats, like “1 beat”, “2 beats”, or “1/2 beat”, “3/4” beat, etc. It works similarly to the map scale. The notation we are going to introduce (note durations) would make it more clear.

Stave Notations

Stave introduces a marking system to represent the duration of notes. The duration of notes is determined by the shapes of the note marks on the stave. The more filled the note mark is, the longer the duration of the note. Note that they are halving notes symdols, which means the duration of a shorter note is 2 times the duration of the longer note.

Some special symbols as well:

Figure 4: Dotted notes and slur. Source: Wikipedia

Slur: same note pitches connected by a curve line means their durations are added together as a single note.
Dotted notes: 1.5 times the duration of the original note.

Tuplet: Divide the note evenly into several. It usually works when the halving note duration symdols cannot represent. For example, a triplet is 3 notes in the time of 2 notes, a quintuplet is 5 notes in the time of 4 notes, a septuplet is 7 notes in the time of 4 notes, etc.

Since the vertical position of notes on the stave does not determine anything, we must introduce some delimiter to fill the silence gap explicitly, which are rests. Rest notations are similar to note duration notations in terms of rules, but with a different style of shapes.

Barlines are used to divide the periods of rhythm. One bar is one period of the rhythm, i.e. one cycle of the beat pattern.

Until now, we still don’t know how long these note duration or rest notations are. We know the speed of music is measured on beats, so all we need to do is to define the duration of a beat as one of the note or rest durations in the symbols: whole, half, quarter, etc. This is represented by the (denominator of) time signature.

A time signature is a fraction-like symbol $\frac{A}{B}$ :

$A$ is the metre;
$\frac{1}{B}$ note / rest = 1 beat.

From now on, we only use time signature instead of the S,w stuff invented by me.

Q: What is the different between the choice of denominator B in time signature?

A: The choice of denominator B in the time signature doesn’t affect the rhythm of the music at all, but the notation. The more fine-grained the music breaks down on rhythm, the more fine-grained note / rest symbols we need, therefore, the larger B. The setting of B is a trade-off between the complexity of the notation and the readability of the music. We better choose the smallest B that can represent the rhythm of the music.

3 Scales and Melody

Q: What is melody?

Melody is a sequence of notes that humans can clearly perceive as the main theme, distinguishing it from the background elements.

Most of the music we hear features a main melody, which serves as the central component, while other sounds are typically served as accompaniment, but this isn’t always the case. For instance, polyphonic music from the Baroque period contains multiple melodies of equal importance. Some experimental music doesn’t even have a melody at all.

Q: How is a melody formed?

The melody is built on scales. A scale is a sequence of ascending or descending notes that sound good. For example, the 7 notes “C, D, E, F, G, A, B” we discussed in Section 1 form a scale called C natural major scale.

The key differences between scales and other similar concepts, such as chords, are:

Scales are periodic. They can usually be repeated in different octaves. For example, after note B in C natural major scale, it starts again with C in the next octave.
Scales have small intervals between notes, typically ranging from 1 to 3 semitones. For example, the intervals between notes in the natural major scale are “2, 2, 1, 2, 2, 2, 1” semitones.

Melodies can be considered as rearrangement of notes in the scale.

Q: How do we represent scales?

A: Scales are commonly represented in two key components:

The root note (the starting note of the scale)
The sequence of intervals between adjacent notes in the scale

Once these two elements are defined, the entire scale is determined. For example, the C natural major scale has the root note C and the interval sequence 2, 2, 1, 2, 2, 2, 1 (in semitones). The “C” in the name indicates the root note, and “natural major” refers to this specific interval pattern. Starting from C and applying this pattern gives the following notes: D, E, F, G, A, B.

It’s important to note that the root note only determines the pitch of the scale, while the interval pattern actually determines its character. If you keep the interval pattern the same but change the root note (for example, shifting root note from C to G), the resulting scale G natural major has the same structure and feel, but just sounds higher or lower in pitch.

Q: What is the key of a melody, or a song?

A: The key of a melody refers to the scale on which the melody is based. In other words, the key and the scale are essentially the same. For example, in a song written in C major, the melody is primarily built from the seven notes of the C major scale: C-D-E-F-G-A-B.

Often, when someone refers to a key by just a note name—like “C” or “G”—they’re implicitly referring to the major scale rooted at that note. This is because the major scale is the most common and familiar scale in Western music (see below).

Changing the key of a melody is called transposition. This is often used to accommodate a singer’s vocal range if the original key is too high or low. It can also be used to create a different mood or atmosphere in the music.

Q: What is Circle of Fifths?

Key Signature

Q: How many scales are there? How do we categorise them?

Mathematically, it’s possible to list all possible combinations under certain assumptions (similar to the “stars and bars” problem in combinatorics). If you’re interested in the mathematical possibilities, feel free to check out my article about scales (not finished) for more details.

When categorising scales, we focus primarily on their interval patterns. Each pattern automatically has 12 possible transpositions with the 12 root notes.

The period of a scale is usually an octave, which contains 12 notes. We can categorise scales by the number of notes chosen from the 12 notes, such as pentatonic (5-note), heptatonic (7-note). There are more categories in terms of the details of interval patterns, see the complete category list of scales in my article about scales (not finished) for more details.

Q: Which scales are most common and built the foundation of music?

In practice, many theoretically possible scales are rarely used. The most common and foundational scales in Western music are the major and minor scales, which form the basis of most classical, pop, and contemporary music.

Natural major: 2, 2, 1, 2, 2, 2, 1 semitones
Natural minor: 2, 1, 2, 2, 1, 2, 2 semitones
Harmonic minor: 2, 1, 2, 2, 1, 3, 1 semitones
Melodic minor: 2, 1, 2, 2, 2, 2, 1 semitones (ascending), 2, 1, 2, 2, 1, 2, 2 semitones (descending)

Beyond these, other scales are commonly used in specific musical genres or cultural traditions, such as the blues scale in blues and rock, the pentatonic scale in traditional Chinese music, the Phrygian dominant scale in flamenco and Middle Eastern music, etc. Please refer to my article about scales (not finished) for more details.

Q: What are modes?

A: If we take the interval sequence of a scale and start from a different point in that sequence, we get a different interval pattern called a mode of the original scale. For example, the natural major scale has the interval pattern 2, 2, 1, 2, 2, 2, 1, and if we start from the 2nd interval, we get the Dorian scale with the interval pattern 2, 1, 2, 2, 2, 1, 2.

In other words, modes are rotations of the interval pattern of the scale. Therefore, they should be called modes of each other.

The most commonly seen modes are the 7 derived from the natural major (called diatonic modes or church modes):

Ionian (a.k.a. natural major): 2, 2, 1, 2, 2, 2, 1 semitones
Dorian: 2, 1, 2, 2, 2, 1, 2 semitones
Phrygian: 1, 2, 2, 2, 1, 2, 2 semitones
Lydian: 2, 2, 2, 1, 2, 2, 1 semitones
Mixolydian: 2, 2, 1, 2, 2, 1, 2 semitones
Aeolian (a.k.a. natural minor): 2, 1, 2, 2, 1, 2, 2 semitones
Locrian: 1, 2, 2, 1, 2, 2, 2 semitones

If we look closely, we can see that the C natural major scale shares the same notes with D Dorian, E Phrygian, F Lydian, G Mixolydian, A natural minor, B Locrian scales. They are all sequence of C, D, E, F, G, A, B, but starting from different notes. That’s why modes are closely related to each other. We call these scales under the same notes but different starting notes as relative scales.

In fact, even though same notes are shared, the relative scales sound quite different, which also indicates why root notes of scales are also important. If we play the same notes share by relative scales but with a gravity shift on different root notes, we are actually using different scales.

Q: Is there any relationship between the most common, natural major and natural minor scales?

A: As we can tell from the above question, the interval pattern of natural major and natural minor are modes of each other.

If we shift the root note of a natural major scale to the 6th note without change the note we play for the scale, we get the natural minor scale. Therefore, they call each other relative minor and relative major. For example, C natural major and A natural minor are relative scales (not to confuse with the C natural major and C natural minor).

4 Chords and Harmony

Q: How to accompany a melody?

A: Music with only melody itself sounds a bit thin and less textured, and that’s why we usually play or sing a melody with accompaniment. This is what bands and music production are all about.

The accompaniment for a melody consists of many elements:

The rhythm (that we mentioned in Section 2), without note pitches. This is usually done by percussion instruments, like drums.
The harmony, which is the note part with pitches in the accompaniment. This can be done by any instrument with note pitches, like piano, guitar, etc.

Accompaniment often plays a supporting role, but not always. In polyphonic music, for example, multiple melodies are treated with equal importance—one of whichin lower pitch can be considered as accompaniment.

Q: What is harmony built on and how?

A: First of all, harmony usually consists of multiple note pitches, or it’ll sound too boring. To build harmony, we need to know which group of notes sounds good when played together. We call a group of notes sound harmonious, or note combinations, chords. For example, C, E, G sound good when played together, is a chord. G, C, F is another chord, D, F, A, C, E, G, B is also a chord.

The harmony is built on chords to accompany a melody. That is to say, we need different note combinations in the accompaniment when the melody is played at different point. We take the melody “Twinkle, Twinkle, Little Star” in key of C as an example. C, E, G (C major triad) together sounds good with the first “twinkle”, C,F,A (F major triad) sounds good with the second “twinkle”, and we can find what sounds good with the rest of the melody, which is C major triad again, G,B,D (G major triad) and so on. We call the sequence of chords aligned with the melody the chord progression. The chord progression of “Twinkle, Twinkle, Little Star” in key of C is C major triad, F major triad, C major triad …

The harmony part of the music can be built within these group of notes, no matter which way you put them in the timeline. For example, you can simply play the notes one by one, or play them at the same time, etc. The way you organise the notes in the chord is called voicing of the chord. It affects the rhythm pattern (if you imagine your harmony instrument as sort of a percussion instrument) and some nuance feelings, but not the overall function. Because of this, music can be essentially denoted as lead sheet, which is the sheet music with only the melody and aligned chord progression. It represents the essential information of a piece of music about note pitches, regardless of the rhythm and voicing of the chords.

Figure 6: A example lead sheet of “Twinkle, Twinkle, Little Star”. Chords are marked above the melody notes. Source: SheetMusicPlus

Q: How do we represent chords?

A: Chords are commonly represented in two key components, just like scales (chords are anyway sequence of notes if you read them in the pitch order):

The root note (the starting note of the chord)
The sequence of intervals between adjacent notes in the chord (which are sometimes called chord type)

Similarly, once these two elements are defined, the entire chord is determined. For example, the C major triad has the root note C and the interval sequence 4, 3 (in semitones). The “C” in the name indicates the root note, and “major triad” refers to this specific interval pattern. Starting from C and applying this pattern gives the following notes: C, E, G.

It’s important to note that the root note only determines the pitch of the chord, while the interval pattern actually determines its character. If you keep the interval pattern the same but change the root note (for example, shifting root note from C to G), the resulting chord G major triad has the same structure and feel, but just sounds higher or lower in pitch.

Q: How many chords are there? How do we categorise them?

Mathematically, like scales, it’s possible to list all possible combinations under certain assumptions.

When categorising scales, we focus primarily on their interval patterns. Each pattern automatically has 12 possible transpositions with the 12 root notes.

We can roughly categorise chords by the number of notes, such as 3-note chord (triad), 4-note chord. Note that it doesn’t count octaves in the chord as different notes because they are equivalent. There are more categories in terms of the details of interval patterns (i.e. chord types), please refer to my article about chords (not finished) for more details.

Q: Which chords are common used?

In practice, many theoretically possible chords are rarely used. The most common and foundational chords in Western music are triads (3-note chords) and 4-note chords, with intervals around 3-5 semitones between adjacent notes, which form the basis of most classical, pop, and contemporary music.

Major triad: 4, 3 semitones = Root note, Major 3rd, Perfect 5th
Minor triad: 3, 4 semitones = Root note, Minor 3rd, Perfect 5th
Diminished triad: 3, 3 semitones = Root note, Minor 3rd, Diminished 5th
Augmented triad: 4, 4 semitones = Root note, Major 3rd, Augmented 5th
Dominant seventh: 4, 3, 3 semitones = Root note, Major 3rd, Perfect 5th, Minor 7th
Major seventh: 4, 3, 4 semitones = Root note, Major 3rd, Perfect 5th, Major 7th
Minor seventh: 3, 4, 3 semitones = Root note, Minor 3rd, Perfect 5th, Minor 7th
…

For complete list of chord types, please refer to my article about chords (not finished) for more details.

Chord Symbols

With the above representation of chords, we can use chord symbols consisting of the root note and the chord type to denote chords.

The commonly used symbols for the above chords are (we take root note as C for example):

Major triad: C, Cmaj, CΔ
Minor triad: Cm, Cmin, C-
Diminished triad: Cdim, C°
Augmented triad: Caug, C+
Dominant 7th: C7
Major 7th: Cmaj7, CΔ7
Minor 7th: Cm7, C-7
…

For complete list of chord type symbols, please refer to my article about chords (not finished) for more details.

Q: What is the relationship between chords and scales?

Chord notes are typically subset of scale notes. For example, the C major triad (C,E,G) is a subset of the C major scale (C,D,E,F,G,A,B); A minor triad (A,C,E) is a subset of the A natural minor scale (A,B,C,D,E,F,G).

Therefore, when you are playing a melody in a certain scale, you can choose chords that are subsets of that scale to accompany the melody. This creates a harmonious relationship between the melody and the harmony, as they share the same set of notes. Please refer to my article about functional harmony for more details about how exactly notes are chosen to form chords in a scale.

Q: We know that octaves are equivalent, so which octaves should we use in harmony and melody?

A: Theoretically speaking, harmony and melody can be used in any octaves, but in practice, people typically use lower octaves for harmony and higher octaves for melody. The reason is again about what sounds satisfy human ear: the human ear can distinguish higher pitches more easily, so the melody is usually played in higher octaves to make it more prominent and noticeable, and the harmony is played in lower octaves to provide a solid foundation and support for the melody.

That’s why you can see in a band that the melody is usually played by a singer or a high-pitched instrument like a violin, while the harmony is played by a lower-pitched instrument like bass. That’s why you see in a piano, the melody is played by the right hand and the harmony is played by the left hand.

Q: How do we know which chords should be used at different points in the melody?

A: There are nothing right or wrong for this. It all depends on what you think sounds good. However, there are some common practices that can help you find chords that sound good for most of people. That forms the details of functional harmony theory, which is about the roles of different chords in the music. The more you know it, the more confident you have in mind what function a chord has in the music, which helps you to find the right chord suiting what you want to express along with the melody. Please refer to my article about functional harmony for more details.

There is a rule of thumb though, that the melody note often lie in or centered around the group of notes of the chord. It is because melody and chords are all built on scales as we’ve discussed. This is basically how chords synergise with the melody to create a harmonious sound.

By the way, deciding chords is the thing that composer or songwriter often do at the same time with their composing. It’s still part of the music defined by the one who wrote it. You can simply leave it and follow the chords marked in the sheet music (the “official” chord progression).

Q: What kinds of voicing are there to turn chords into harmony part of the music?

A: The most simple voicing is to play the notes in the chord at the same time. This is called block chord.

We can also play the notes in the chord one by one, which is called broken chord (or arpeggio in a classical music context). This gives a more soft and flowing feeling to the music.

The deeper details are concerned with the rhythm pattern of the harmony part. Also in more complex chords, some notes can be omitted to make the harmony part more simple and clear. Other than this, there are tricks linking adjacent chords in the progression, like passing notes. I’m not going into the details here, but you can find more in my other article about chord voicing (not finished).

Q: In reserve, how do we know the chords from sheet music with detailed harmony part, but without chords marked?

A: In the simple case, like the block chords, you can directly tell the notes then the chords. But sometimes it’s rather difficult and ambiguous. In this case, the notes in the melody can sometimes give us a hint, as they are under the rule of thumb above that they often lie in or centered around the group of notes of the chord.

5 Dynamics and Articulations

Q: What is dynamics in music?

A: Dynamics in music refer to the volume or intensity of sound. Music should never be expressed at the same volume throughout, or it will sound very robotic and emotionless. Dynamics can be used to create contrast, build tension, or convey emotion in music.

Q: What are the common terms to represent dynamics?

TBC.

Q: What is articulation in music?

A: Note articulation in music refers to the way notes are played or sung. It includes how notes are started and ended, how they are connected to each other, and how they are emphasized or de-emphasized. Articulation provides subtler details and expression for music.

Articulation is highly dependent on the instrument. For example, a piano player can use the pedal to connect notes (legato), while some percussion instruments can only play detached notes (staccato).

Q: What kinds of articulations are there?

There are articulations that are common across most instruments (we don’t talk about instrument-specific ones like upbow, downbow). We list the common ones here by categories:

Legato: smooth and connected.
Staccato: short and detached.
Accent: emphasizing a note.
Fermata: holding a note longer than its written value.
Marcato: strongly accented.
Tenuto: holding a note for its full value.

Ornamentation:

Grace notes: very short notes played quickly before the main note.
Trills: rapid alternation between two notes.
Mordents: rapid alternation between a note and the note above or below it.

Note Articulation Notations

Articulations are bound with notes, so their symbols are usually placed above or below the note head. Here are the notations: