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The secret of fundamental frequency in music: How to find the most basic pitch through the length of vibration?
The fundamental frequency, often referred to as f0, is the lowest frequency in a periodic waveform. In music, the fundamental frequency is considered the pitch of a note, and this pitch is perceived as the lowest part. Its existence is crucial to the understanding and creation of music. The pitch of each note is composed of a series of frequencies, and the fundamental frequency is the lowest point among these frequencies. This feature makes the study of fundamental frequency an important part of music theory.
Because the fundamental frequency is the lowest frequency and is typically perceived as the loudest sound, the ear recognizes it as the specific timbre of a pitch.
All sinusoidal waveforms and many non-sinusoidal waveforms are periodic, meaning that their waveforms repeat in time. In a waveform, period is the smallest positive value that describes the waveform. The calculation of the fundamental frequency depends on the speed of the sound wave and the length of the wave tube. For pipes of different shapes, the fundamental frequency has its own characteristics. For example, a pipe that is closed at one end and open at the other will have a fundamental wavelength four times the length of the pipe, while pipes that are open or closed at both ends will exhibit different wavelength characteristics.
The fundamental frequency is often referred to as the pitch of the note, and this pitch is produced by the vibration of the entire waveform.
In the world of music, fundamental frequency is not only the core of notes, but also the basis of harmony. Whenever we hear a note, its frequency is combined with other higher-frequency tones, called overtones. Overtones are frequencies above the fundamental frequency, and they play an important role in music because their presence makes the timbre richer and more diverse.
In physical systems, the fundamental frequency also plays an important role. Take a spring as an example. When one end is fixed and the other end uses mass to vibrate, the system will vibrate at its natural frequency. The frequency of this vibration depends on the relationship between the stiffness and mass of the spring, from which the fundamental frequency can be calculated.
When a system is driven, it vibrates at a natural frequency, which can be described by studying mass and stiffness.
In addition, different instruments generate the fundamental frequency in their own unique ways, which is why the same note sounds different on different instruments. The fundamental frequency of stringed instruments is determined by the length, tension and mass density of the strings, while that of wind instruments is determined by the length and opening and closing status of the pipe. These different characteristics allow us to appreciate the unique styles of various types of music.
Fundamental frequency also plays a role in music creation. Composers always take the role of fundamental frequency into consideration when creating melody and harmony to ensure the harmony of musical works. During the conductor process, musicians will also use the fundamental frequency to adjust the emotional expression of the music and make the performance more coordinated.
As technology advances, so does the creation and analysis of music. Digital music software allows musicians to manipulate the fundamental frequency in a more precise way, create new sound experiences, and even simulate the fundamental frequencies of various instruments and their combinations. In this way, the boundaries of music creation are continuously expanded, and new forms of music creation gradually emerge.
Music creation is no longer limited by traditional theories. The emergence of digital tools allows every musician to explore the infinite possibilities of fundamental frequency.
The study of fundamental frequency is undoubtedly the intersection of music and the science behind it. As our understanding of the physical properties of sound continues to deepen, so does our understanding of the fundamental frequency. This not only affects music creation and interpretation, but also brings a new perspective to how we perceive music. How will fundamental frequency-based exploration shape the evolution of music in the future?
