Sine wave
サイン波

When a house becomes quiet at night, the low hum of a refrigerator or the vibration of a distant train can suddenly become clear. The thin ring of a lightly struck glass and a voice from a phone speaker both reach the ear by moving the air in a room. We usually hear them not as waveforms, but as the presence of an object, its distance, and the size of a space. A sine wave removes as much of that material character as possible and leaves the motion of sound like a single line.

An ideal sine wave has only one frequency and is the simplest basic waveform. Frequency is the number of vibrations in one second and is heard mainly as pitch. It is not accurate, however, to describe the sine wave as the smallest particle of sound. Air pressure changes continuously through time, and the ear receives the whole movement. Fourier analysis separates a complex sound into sinusoidal components in a way that is somewhat like separating white light into colors. It does not break sound into physical grains; it provides a clearer view of what the sound contains.

Combining only two simple tones already produces an unexpected movement. When sine waves at 440 Hz and 441 Hz are played together, the pitches are nearly the same, yet the level seems to swell and shrink about once each second. This beating occurs because the waves alternately reinforce and cancel each other. A sine wave with little motion of its own begins to carry rhythm through a very small frequency difference. This opens a larger question: perhaps pitch, timbre, rhythm, and space are different views of the same phenomenon heard from different distances.

A piano, guitar, and human voice can play the same note and still be easy to distinguish because each sound contains many components beyond the reference pitch. Harmonics near integer multiples of the fundamental, partials shifted by material and construction, and brief components that appear only at the attack rise and decay at different rates. Timbre is shaped not only by a list of frequencies, but by the way those components enter and leave through time.

Additive synthesis builds this layered condition in the opposite direction. Instead of beginning with a rich sound and removing parts, it prepares several sine waves and assigns each one a pitch, level, starting time, and decay. In cooking terms, it is closer to adding ingredients one by one than to diluting a finished flavor. The principle is easy to understand, but every added component creates more decisions. The central design problem is therefore how to make many small sounds behave as one playable timbre.

The Max Patch in the reference links is a small listening instrument that switches the same pitch among sine, sawtooth, triangle, and square waves. The differences can also be imagined without using software: a thin sound without corners, a bright and rough sound, a soft sound with a little contour, and a hollow sound with a firm edge. Each basic waveform gives the same pitch a different surface.

An ideal sine wave contains one frequency component and appears as a single line in a spectrum display. The absence of upper components makes it smooth, but it also exposes small differences in level, stereo position, and distance from a speaker. A low sine tone can press against the body on a large sound system, while a small speaker may be unable to reproduce the fundamental and make the tone almost disappear.

A sawtooth wave contains both even and odd harmonics at two, three, four, and further multiples of the fundamental. In the ideal waveform, higher harmonics gradually become weaker, but the decline is slow enough to leave many upper components. The result is a bright, sharp contour. This is why synthesizers often begin with a sawtooth wave when creating brass like tones, thick string textures, and sounds that will be shaped by a filter.

A triangle wave contains mainly odd harmonics, and its upper harmonics become weak much more quickly. In formula form, the amplitude of the nth harmonic is approximately one divided by n squared. The formula is less important than the shape it describes: the higher components become thin very quickly. A triangle wave therefore has more contour than a sine wave without becoming as bright as a sawtooth wave, making it useful for soft basses and gentle lead tones.

A square wave with a fifty percent duty cycle also contains mainly odd harmonics, but its upper components remain stronger than those of a triangle wave. This creates a hollow, tube like quality and the clear outline associated with older game machines. Moving a filter can turn it into a heavy bass, while short notes can make it behave like electronic percussion. A basic waveform is not a finished timbre; it is material for deciding what will later be added or removed.

In The SINE WAVE ORCHESTRA stay, presented at YCAM in 2017, each visitor selects the frequency of a small device and attaches it to spiral copper wire installed in the space. Each device produces one sine tone. The exhibition begins with few sounds, then every placement adds another pitch and creates different patterns of beating and resonance around the room. A choice made by someone without specialist performance training becomes part of the work immediately.

The simplicity of the sine wave functions here as an entrance to participation. A visitor does not need to master a complex instrument; selecting a frequency and a position is enough to change the space. Even as more tones accumulate, they do not become one uniform mass. Differences in pitch, placement, and duration remain audible as a history of the exhibition. If additive synthesis combines partials into one timbre, this work can be understood as a composition that combines the decisions of many people into one sound field.

In test pattern [100m version], numerical data is converted into rapidly changing black and white images and precise sound. A projection surface one hundred meters long and a powerful sound system turn information that normally remains inside a screen into an environment that can be entered on foot. Sine tones and short pulses do not remain in the background; together with flickering light, they reach the body directly. A reduced set of materials does not make the work quiet. Enlarged to this scale, the limited materials place the entire space under tension.

A small frequency difference or a short repetition may seem modest in a tabletop experiment. Given large loudspeakers, a wide floor, and long duration, however, the eyes and ears respond to speed and intensity before interpreting meaning. The work shows that a simple signal does not necessarily produce a simple experience. Reducing the number of elements can instead enlarge each difference until it becomes impossible to overlook.

The pipe organ, used for centuries before electronic instruments, cannot be identified as the direct ancestor of additive synthesis. It is nevertheless a useful comparison for understanding how several sounds can form one timbre. When an organist selects stops, ranks of pipes with different sizes and materials sound together. Even when one key is pressed, several pitches and resonances overlap inside the reverberation of the building.

Modern digital additive synthesis can arrange not only harmonics at integer multiples, but also slightly shifted frequencies and irregularly spaced partials. This makes metallic sounds and unstable spectra possible. Yet controlling hundreds or thousands of sine waves one by one is impractical. Instruments such as Razor and Odessa group those components into larger shapes that can be moved as brightness, distribution, spectral peaks, or comb like spacing.

Odessa can generate up to 2560 sinusoidal partials. With a low fundamental, partials above the hundredth can still remain within the range of human hearing, so the number of components affects density. A larger number does not automatically make a better sound. Unless many components can move as one coherent form, the user is faced not with a timbre, but with an endless list of settings.

The Verbos Harmonic Oscillator takes the opposite approach by placing the first eight harmonics under individual sliders. The Kawai K5000 S offered much more detailed additive design, but that freedom also required the management of many parameters. Directly touching a small number of components and moving a large number through broader shapes provide different kinds of value. The first makes one harmonic easy to follow by ear, while the second allows the entire timbre to be transformed at once.

Make Noise Spectraphon analyzes the frequency structure of an incoming sound and uses those characteristics to create new material. Here sine components are not only ingredients prepared in advance. They become tools for reading the interior of a sound that already exists. A moment of a voice or instrument can be captured, extended, and moved to another pitch, bringing hidden structures to the foreground. Additive synthesis is therefore both a method of creating sound from the beginning and a method of listening again to sounds that are already present.

The Max Patch and Ableton M4L device in the reference links provide six sine waves with controls for frequency, level, and left to right position. What happens here is not limited to music production. Place two tones close together and they create beating; separate them and they are heard as a chord; distribute them across left and right and the sound seems to widen in space. The same materials receive different names, rhythm, harmony, timbre, or space, according to the relationships between them.

Moving one sine wave by only a few hertz can create a slow pulse across the whole sound. Reducing one upper component can soften a sharp tone. Changing stereo position can alter distance without adding reverberation. The simpler the structure, the more clearly the result reveals which differences were noticed and which were preserved. This is less a question of technical equipment than a judgement about how several things should relate to one another.

Returning to the refrigerator heard in the quiet room, its hum is also not a single line. The motor, the vibration of the cabinet, and the resonance of the floor and walls form a small ensemble. Seen closely, their relationship becomes the design of timbre. Heard from farther away as a movement through time, it becomes composition. The sine wave is not material reserved for specialists in electronic music. It is the most concise entrance to understanding that everyday sounds arise from relationships among many movements.