Preface

Most of us born in this era had been exposed to music at a very young age. As for myself, it was in junior school when I first tried to learn to appreciate music. My parents played piano scores by Richard Clayderman, a well-known French pianist who has composed and played many popular works. In 2025, Mr Clayderman played in the new year party at the city concert hall in Wuhan, and it has been such a pity that I wasn't able to join it and listen to him playing in person.

As I'm growing older, the number of music pieces that I have listened to is also increasing. I was a bit conservative about music before I entered college, and was only interested in pure music, especially piano scores. I was once disgusted about all the music that is loud and disturbing, with only one exception: pieces by Michael Jackson, who was considered by me a role model in pop music. It was when I entered college that I almost fully embraced European and American pop, and later Japanese pop, and some representative Chinese pop music in the 90s and early 2000s. I still listen to symphonies and pure piano scores, but it's not as often as before. Nowadays, I listen to all sorts of music, and the fear about failing to learn even the most basic knowledge about music throughout my entire life gets stronger as I complete my career as an engineering bachelor student. This encourages me to get exposed to music theory, at least I have to do it before I go to work, whereas I'm completely a layman. Nevertheless, thanks to those established musicians who are enthusiastic about teaching the public about music, and the modern information technology, even a layman such as myself can learn something about music now.

I have chosen music theory in a western view as a fair start point, which is for my information also the most popular choice to professional people. It is systematic, thoroughly researched, and most important of all, offers many options for us to learn, regardless of whether we want to do it professionally, or simply get exposed to the basics.

Before I formally learnt anything about music, a well-established intuition about music is that music consists of "sounds with levels". By saying "levels", I'm actually referring to the feature that sounds can be somehow comparable to each other, in most cases. In a scientific viewpoint, it is essentially the frequency of sounds that gives them this property, and even though conventional instruments never produce pure sounds - sounds with only a single fixed frequency, we can still compare them subjectively by their frequencies by extracting a sound that's the most average, most representative and centered one. This feature, using academic words, is referred to as tonality: a feature that some sounds have a higher frequency, while others have a lower frequency. Using these different tones as basic building blocks, western people have constructed a magnificent framework of what's called tonal music, where we call each individual sound a pitch. Pitches represent an average or subjective level of how high or low the sounds are. Each of pitches is generally a mixture of many truly pure tones of single frequencies. By adjusting the portion of consisting pure tones, we generate pitches of different flavors: some are like pitches generated by a piano, and some are by a violin, etc. These flavors are called timbre or tone color by professionals, and it is this timbre that allows us distinguish between instruments even when pitches of (in average) the same frequency are being played.

Music Staves

Music Pitches

Tonality, or the feature that pitches are comparable, and can be distinguished by frequencies, offers a chance for people to take them down. I learnt in primary school about the basics of numbered notation of pitches, where a piece of music can be denoted by a series of numbers such as 3, 3, 3, 3, 3, 3, 3, 3, 5, 1, 2, 3 (Jingle Bells). This is a direct and numeric way to show the discrepancy of pitches, and can be helpful in many practical occasions. However, a more traditional way of noting these pitches is by writing them as a staff, which consists of several horizontal lines. Scores use these lines and the space between them to note pitches. A pitch that is marked on a line or in a space that's visually higher than another pitch, is also higher than that pitch. The number of horizontal lines can change according to both historical and practical reasons: for example, while most staves have 5 horizontal lines (as shown below), which allow them to denote 5 + 4 = 9 pitches, while many bass players use staves with 4 horizontal lines because a standard 4-string bass has 4 strings. Lute players in the Renaissance also used 4-line staves. Staves with even fewer lines can be used in chants as well.

In the above figure, we have four pitch notes marked by 𝅘𝅥. The second pitch is higher than the first, the third is higher than the second, while the fourth note is the same as the first one. When we are looking at the pitches, we should pay attention to the round part which we call the notehead. A notehead is the center of weight of that note, and is responsible for indicating the pitch it's related to. If the notehead of a note A is higher than that of another note B, then A is higher than B. Except the notehead, the vertical, slim line attached to the notehead is called a stem, it does not affect pitch, but represents the duration of that pitch (which we will discuss later). It is possible that we have small tails (flag) connected to these stems (like in 𝅘𝅥𝅮), they act as a supplementary evidence of how long the pitch lasts, just like their stems.

As we have mentioned, staves usually contain five horizontal lines, between each two of the lines there are four spaces. From the bottom to the top, we call each of the staff lines the first, the second, ..., and the fifth staff line. Similarly, the spaces are called from the bottom to the top the first, the second, the third and the fourth staff space. In the figure above, the notes are located respectively at the first line, the first space, the second line, and the first line.

Clefs

Suppose we have two staves, and there's one pitch at the lowest line of both of them, how can we compare these two pitches? Clearly we can't say that they are equal, since they are on different staves. One can presume that the first line of the first staff is exactly the fifth line of the second staff, or the contrary. This problem reminds us to define a "reference" that represents a relatively fixed pitch. No matter what staves are involved, the line or space that the reference point is located at should always represent the same pitch. This reference is known as a clef. Let take a look at the following figure:

In the figure above, the clef is shown by the symbol 𝄞, which is known as the G clef. The line that G clef 𝄞 is tangled at represents the pitch denoted by letter G (which is shown as symbol 𝅝 in this figure), which is also known as the treble clef. Similarly, we have the C clef 𝄡 (the tenor clef) and the F clef 𝄢 (the bass clef). The line where the vertical center of a C clef 𝄡 is located at represents a pitch denoted by letter C, while the line where the center of the colon ":" of an F clef 𝄢 is located represents a pitch denoted by F. Conventionally, the G clef 𝄞 is placed on the second line, while the F clef 𝄢 is on the fourth line. The position of C clefs 𝄡 could be placed at any line.

Some scores have two or even more parallel staves. These scores are called grand staves. Each of the staff in grand staves has its own clefs. By specifying a clef, we can derive what pitches are represented by the notes.

References

Yang et al., this is an example reference.