In the modern age of electronic composition, it is essential to understand the nature of music and the fundamental principles of digital audio processing, whether you are learning audio processing, music composition, mixing, vocaloid and other synthesized vocal engines. Similarly, the use of high-level programming languages still requires an understanding of compiling principles and memory allocation.
For example, have you ever thought about these questions：
-What exactly are sample rate and sample depth? What do they do?
-How can I use EQ to help reverse engineer music?
-Why do the MIDI notes I write in the piano window get stuck and don’t sound?
-Why does DAW often buzz a note tail after finishing exporting audio?
-Is there a difference in quality between WAV, FLAC and MP3, and what is the difference?
This section will explain what sound is, some of the underlying logic of music theory, and how to compose and mix music on a computer.
The nature of sound
Sound is a mechanical wave, which is the vibration of an object. Sound traveling in the are is a longitudinal wave, in which the change in density of gas molecules in the air, i.e. the change in air pressure, is perceived by the human ear and understood as sound.
Different instruments produce sound in different ways. Percussion instruments such as drums transmit vibrations from a solid to the air, while wind instruments such as flutes rely on the vibrations of the air column itself to produce sound.
If we were to visualize the change in density/position of a gas molecule, it would look something like this.
A fundamental tone is a sine wave of corresponding frequency. The higher the frequency, the higher the pitch and the shorter the wavelength. Generally, 440Hz is used as the standard tone A.
Harmonicity and Equal Temperaments
An interesting phenomenon is that for two tones, the simpler their frequency ratios are, the more harmonious and stable they sound. For example, 440Hz and 880Hz together are harmonic (1:2), but 440Hz and 450Hz are not so harmonic (44:45).
In addition to concordance, there is also interference between the sounds, resulting in the Beat frequency phenomenon of changing intensity, which is subjectively perceived as a rapid jittering of the sound volume. The frequency of the jitter is directly related to the frequency ratio of the tone. This characteristic is generally used in piano tuning, but it also occurs in the synthesizer section later on. The causes of beat frequency are shown in the figure.
Frequency ratios and harmonicity are the foundation of temperaments and harmonology. Different intervals have different harmonicities depending on their frequency ratios: perfect fifths are harmonic, and tritones are tense. Multiple intervals placed together form chords with different sound effect, thus building the whole music theory.
In the history, people have invented many different temperaments. In general, tones with frequency ratios that are multiples of each other have the same name, e.g., 440 Hz for A, 880 Hz for A in the higher octave. In ancient times, it was commonly used to obtain the scale by multiplying the length of the string or wind instrument by two-thirds. This practice actually multiplies the frequency by a factor of 1.5 (than rising or falling to the same octave) to obtain the perfect fifth.
The resulting scale, with simple integer ratios between intervals such as fifths and thirds, is called pure temperament. However, when the pure temperament is multiplied by a factor of 1.5 and returns to the base note after a cycle of fifths, it produces a certain amount of error from the original frequency of the base note. Equal temperaments solved this problem: the frequencies within an octave were divided in
This way the scale is perfectly level with respect to the key and is closer to the frequencies of the fifths.
The resulting scale, with simple integer ratios between intervals such as fifths and thirds, is called pure temperament. However, when the pure temperament is multiplied by a factor of 1.5 and returns to the base note after a cycle of fifths, it produces a certain amount of error from the original frequency of the base note. People use equal temperament to solve this problem: the frequencies within an octave were divided using a ratio of $2^\frac {n}{12}$.
This way the scale is perfectly level with respect to the key and is closer to the frequencies of the fifths.
Harmonics and overtones
On a real instrument, the string/air column can vibrate at two, three, four, etc. times its fundamental frequency, in addition to its fundamental frequency. These higher frequency vibrations are called Harmonics, or Overtones. Load a vst piano in the DAW, press a key, and observe the resulting frequency:
The instrument produced many overtones in the multiplications of the base frequency. such as 880Hz. 1.3Khz and 1.8KHz. Mathematically speaking these are the different terms of the Fourier series. We will talk about that later.
These harmonics are the overtones of the base note. The overtones of different instruments are identical in frequency but vary in intensity, and therefore their timbre is different.