Music Theory/Fundamentals of Common Practice Music

Notation

This section is intended for those without any experience with Western music notation and its associated practices.

Humans with the ability to hear experience sound when delicate structures inside their ears detect waves of pressure traveling through the air (or any other medium to which they are mechanically coupled). When these waves are regular¹ and oscillates at a constant speed, we recognize a tone or note. ² Notes are the basic elements of Western music. They are the most common thing we hear in "songs," in almost every genre, period, or style of music in existence (in western society).

Before we talk about how musicians know what notes to "play," we need to determine one thing. With the exception of the human voice and electronic instruments, how many notes should a piano, for instance, play? How many notes should a violin play? These are important questions to answer because if one instrument can play, say, 15 notes, but another can only play 12, then the notes we hear are going to be different, which means musicians cannot collectively play the same notes of a given song. To find the optimal number, we need to balance "our wants versus our limits." In music, we want as many diverse notes as possible. However, instruments that we cannot make will never allow us to make any "organized sounds." Ergo, we want to follow this formula:

$${\text{limations of our instruments}}\leq {\text{number of notes}}\leq {\text{diversity of notes}}$$

It turns out, unsurprisingly, we found our answer: 12 different tones. However, what does "different" mean in this context?

Pitch

What are "different notes"? To answer that, we need to look back at the definition of "notes". Looking carefully, we find that a note is simply a sound we hear after air molecules are vibrated. The air molecules are vibrated by sound waves. Ergo, we define a tone as a sound wave that oscillates some number of times per second at a constant rate. Let's call the number of oscillations per a given amount of time a frequency. What happens if we increase the frequency of a note? Well, we make it oscillate faster. However, since oscillations determine the note we hear, we, therefore, have a "different note." Eureka, a "different note" simply means a different frequency of a note. In fact, based on the following information, we can create a model:

A frequency determines the "sound" we hear from a "note." To measure a frequency, we use a unit called Hertz (${\text{Hz}}$), which is equal to one oscillation per second. Let's define a "common note" at $440{\text{ Hz}}$.³ Compacting the peaks of the wave, we find that the frequency increases or the number of oscillations per second, ${\text{Hz}}$, increases; we hear this "highness" of the original note of $440{\text{ Hz}}$. Separating the peaks of the wave, the number of oscillations per second, ${\text{Hz}}$, decreases; the resulting sound we hear is of a "lower" note of the original $440{\text{ Hz}}$.

A "low" note or a "high" is the number of Hertz that is either deducted or added onto the original note. The "lowness" or "highness" of a note is the pitch. Although this is not a rigorous definition, according to philosophy, for our purposes this is good enough.

The next time you hear a series of notes, think of all the science at play. When we hear series of higher and lower notes, either singly or in groups, perhaps spaced out at different points in time and of different durations, with the variation in their frequencies, spacing, and lengths patterned in ways that correspond to established rules, we recognize the sound of music.

Writing and Analysis

Written music is presented on one or more staves, which represent a set of notes that may be played in time across one or more instruments. Most contemporary music will consist of a pair of staves, as per this example, showing treble and bass clefs. Staves are divided into regular periods, known as measures or bars. The duration of a measure in a given piece of music is specified with a time signature, which is shown next to the clef. Contemporary music often uses 4/4 and 3/4 time signatures.

This is a pair of empty staves, with treble and bass clefs.

Sometimes, music written for fretted instruments such as guitars will be presented as a tablature rather than a standard musical notation on a staff. A tablature is a more direct way of showing how the instrument should be played, listing finger positions rather than notes. Keyboarded instruments such as the piano offer a simple translation from musical notes to finger positions, while stringed or valved instruments require the player to be able to translate notes into positions along strings, or specific valves that must be opened.

Footnotes

1. Imagine a wave in the ocean but two-dimensional. In that wave, you have an amplitude – the highest displacement of a wave compared to when it is "flat" – and a trough – the lowest displacement of a wave compared to when it is "flat." Say you ask the following question: "How many ripples oscillate in that wave every second?" This question is very often asked that scientists have defined this as a term called frequency, which is again, the number of oscillations that happen in a wave every given amount of time. Ergo, when the waves are oscillating at a frequency that is non-changing, we call that wave regular.
2. The explanation of waves presented here is a little simplified. A sound wave is called a longitudinal wave, which is when the oscillation of a wave is parallel to the direction it is traveling in. All waves must originate from a vibration somewhere, with soundwaves being no exception. The reason we hear sounds at all is due to the vibrations of air molecules. If we did not have air molecules or water molecules in the air, sound cannot be heard. This is the reason why you cannot hear anything in space.
3. We picked the "common note" arbitrarily.