A Prism

Spectral components within white light...

A resonator is a device or system that naturally oscillates at some frequencies with greater amplitude than at others. Resonators are used to either generate specific frequencies or to select specific frequencies from a signal. “Select” in this context means that the resonator will attenuate all other frequencies except the so-called “resonant frequencies”. Thus a resonator is a type specialized filter; it passes the resonant frequencies and cuts all other frequencies. If a resonator is excited by some form of broad-band, spectrally-dense input signal such as a burst of white noise, or an impulse click, or the transients of a physical strike or pluck, or the noisy breath of a woodwind player, or the consonants of a vocalist, the resonator will quickly attenuate all non-resonant frequencies while allowing the resonant frequencies to sustain, or ring, or oscillate significantly longer than the non-resonant frequencies.

Consider the analogy of the prism. A prism is a triangular piece of glass that can be used to separate white light into its constituent spectral colors (i.e. the colors of the rainbow). The white light that enters the prism is equivalent to a broadband audio signal. “White” in the context of white light, as well as white noise, refers to the fact that the light or the noise signal has equal amplitude at all frequencies within the spectrum. The prism breaks apart the white light in a way that clearly demonstrates the presence of the various spectral components (i.e. colors). If the prism were able to selectively attenuate or cut some of these colors while at the same time passing or augmenting others, then the prism would be functioning like a resonator in many ways. This would be an even more accurate metaphor if the prism continued to output -- i.e. ring or oscillate at -- the selected colors for some time after the white light input was stopped. In other words, if we could build a prism that passed only red and yellow while cutting all other colors and it made red and yellow ring or sustain for some period of time after we turned off the input, this would be very similar to the behavior of a resonator. Kaleidoscope functions much like a selective time-varying prism by reacting to the musical input in very specific ways: drastically augmenting certain frequencies and drastically attenuating others.

Musical INSTRUMENTS

Kaleidoscope uses the same principal that all physical musical instruments use to create and modify sound: resonance...

In the real physical world, all musical instruments use acoustic resonators that filter sound waves at specific frequencies. Resonators are a fundamental building block of the mathematics and physics of physical sound generation and filtering. Every musical instrument has resonators! Some generate the sound directly, such as the Strings in Stringed instruments, the head of a drum, the wooden bars in a xylophone, and the pipes in an organ. Some modify the sound by enhancing particular frequencies, such as a piano soundboard or the sound box of a guitar or violin. Organ pipes, the bodies of woodwinds, and the sound boxes of Stringed instruments are also examples of resonators. There is in fact an entire branch of musical instrument synthesis research and development called Physical Modeling that deals specifically with these topics and related ideas. Even real-world acoustic spaces such as anything from a small closet, telephone booth, or automobile, to large spaces such as concert halls and cathedrals can also be considered a type of resonator called an Acoustic Cavity Resonator. Kaleidoscope offers two primary types of resonators: Strings and Springs.

Strings

String Theory...

The Strings found on all Stringed musical instruments are simple resonators. Stringed instruments work by applying some excitation force in the form of a hammer strike, or a plectrum pluck, or the rubbing action of a bow to the String. This sets the String into motion and it begins to oscillate. In the spectral sense, the excitation action supplies a form of broadband noise. The String resonator takes this input energy and refocuses it into a select set of resonant frequencies determined primarily by the String's length, mass, and tension. Many types of resonators in the real world actually resonate at more than one frequency, and in the case of Strings these frequencies follow the harmonic series. Thus if the String oscillates at a fundamental frequency of 100Hz, it will also simultaneously oscillate at integer multiples of this frequency (i.e. 200, 300, 400, 500...). String resonators contain harmonics in the frequency domain and can be modeled as simple feedback delays in the the time domain.

String resonators can also be used for delay, reverb, and granular type effects when the resonator frequency is so low that it its delay period length moves out of the audio frequency range!

Springs

Spring into action...

Spring resonators are the simplest variety of resonators. Springs oscillate at only one single frequency: the fundamental frequency. Spring resonators do not contain harmonics. A “Mass On A Spring” model and a Pendulum are two examples of such systems. This type of system is called a Simple Harmonic Oscillator in physics, and its behavior is called Simple Harmonic Motion. Shown below are the impulse response and spectrum of a Spring model without damping. It is identical to a sine wave.

Due to their single resonant frequency, sinusoidal nature, Springs are ideally suited to create any arbitrary spectrum by summing a large number of them together and precisely tuning each individually to any desirable tuning. Fourier and Modal Analysis methods can effectively be used to accurately model the resonant behavior of much more complex objects and match their spectrums. This can be thought of as a form of additive synthesis. An additive synthesizer with enough resolution in both time and frequency can effectively perfectly synthesize any sound.

To repeat: Spring resonators do not contain harmonics. A single Spring resonates only at fundamental frequency. At high enough feedback, Springs effectively produce sine waves. At low feedback they produce narrow band filter effects. Multiple Springs can be used as a form of additive synthesis.

Damping

Resonators in the real world do not continue to oscillate forever; they lose energy over time. This is called Damping in physics and is caused by things such as friction. In Kaleidoscope we refer to this as Feedback. This type of action creates exponential decay in the amplitude of the oscillation of the resonator. Shown below are examples of the behavior for damped Strings and Springs. Springs produce exponentially decaying sine waves. Strings produce an exponentially decaying series of delays.

In String Resonators individual harmonics do not necessarily have the same amount of feedback. In fact, in almost all real physical systems, including a plucked String as well as a concert hall, high harmonics generally have much lower feedback than the fundamental frequency. There is a Frequency Dependent Damping effect that generally happens in real-world systems, and this is referred to as Damping in Kaleidoscope.

High feedback produces more resonance and longer decay times. Spectral peaks at the resonant frequencies become taller and narrower, and stop band areas are more and more attenuated as feedback increases. Low feedback settings act more like band-pass filters and are not strongly resonant. Frequency dependent Damping achieves variable feedback amounts at different frequencies, and generally this is used to make high frequencies decay faster than low frequencies, as is commonplace in nature.

Adjusting Feedback and Damping can morph Kaleidoscope's behavior between that of a filter and that of an oscillator!

Driving

Resonators are specialized filters; they produce no sound of their own. Therefore to achieve an audible output, a resonator must be given some form of input energy. In the physical world, this input typically comes in the form of some form of impulsive energy input such as hammer strike of a plectrum pluck or some form of bowing action. In physical modeling synthesis the input is generally an impulse or a short burst of noise. In Kaleidoscope we take this concept much further and allow the user to feed any variety of audio signal into Kaleidoscope’s massively parallel resonator bank. The incoming audio signal becomes the driving force supplied to the resonators. The output of this system is an incredibly complex, yet strangely familiar, combination of the characteristics of the input signal, the resonator settings, and the action of the Image Maps, which we will discuss in the next section.

Feeding Kaleidoscope percussion loops for example is quite similar to the excitation forces that rhythmic hammer strikes supply to the resonators in instruments such as piano, xylophone, lute and other similar instruments. Feeding Kaleidoscope some variety of slowly enveloped noise would simulate the action found in bowed String instruments. Feeding it material that is already strongly tonal with long periods of static sustained notes will produce less predictable results where the result will depend heavily upon the spectral overlap of the input signal, the current tuning used in Kaleidoscope, and its feedback setting. In such cases, low feedback settings can be used in Kaleidoscope to achieve incredible dynamic filter effects. Feeding Kaleidoscope signals that are a mixture of transients and more sustained tones, such as a vocal signal, which is a mix of sustained vowels and transient consonants can achieve otherworldly results.

The real magic of Kaleidoscope, however, is found in the fact that we are not dealing with a single String or Spring resonator. We are dealing with up to 512 of them, which can each be independently tuned, independently modulated on input and output, and independently spatialized. This is similar to using your voice or drum loop to conduct a symphony played on a 512-String guitar, where each of the Strings is also independently moving around in space according to your specific choreography!