## 1 Introduction  
Audio synthesis has an extensive history that can be traced back to long before the first computer sounds were generated by [PERSON] in 1957 [1] (p. 273). In 1897, [PERSON] patented the Telharmonium, an electromechanical instrument. It used multiple rotating notched wheels that periodically close an electrical contact with metal brushes. The signals from these mechanical oscillators were added to imitate familiar orchestral instruments [1] (pp. 8-12). The principle of creating a complex sound by adding simple signals later became known as additive sound synthesis. Another way to arrive at interesting sounds is subtractive sound synthesis. Here, one starts with a harmonically rich signal and filters it to remove harmonic content and to change the timbre. The Trautonium [1] (pp. 32-34), invented by [PERSON] in the late 1920s, is an early instrument that combines subtractive synthesis with an innovative interface. [PERSON] and his pupil [PERSON] have written music for the Trautonium that is still performed today. Today, a variety of sound synthesis methods are used in many music genres: from experimental electronic music over jazz to rock and pop. A large variety of methods have been invented over the years. Some of the most commonly used sound synthesis methods are described below:  
* In sampling synthesis [2], entire notes of an acoustic instrument are recorded and stored in memory. The samples usually vary in musical parameters, such as pitch, dynamics and articulation. The samples are often transposed and looped during synthesis. * In wavetable synthesis [3], only a single period of a sound is stored in a cyclic buffer. Different pitches are then created by reading out the buffer with different increments. By mixing between multiple phase-locked wavetables over time, a more lively sound can be generated. * In frequency modulation (FM) synthesis [4], the frequency of a carrier signal is modulated by another oscillator. If the modulation frequency is in the audible range and if the frequency deviation (i.e., the amount by which the carrier frequency changes) is sufficiently large, then a sound with a complex spectrum emerges. FM synthesis was popularized by the Yamaha DX family of synthesizers in the 1980s [1] (p. 333-334). * In waveshaping synthesis [5], a signal from an oscillator is passed through a nonlinear shaping function. This distorts the original signal and can create a complex spectrum. * In physical modeling [6], the source of a sound is described with a physical model of equations. Physical modeling can be used to imitate acoustic instruments by simulating relevant aspects of their composition and functionality. * Granular synthesis [1] (pp. 335-338) is based on short audio \"grains\" of up to 50 ms. These grains are superimposed and form a structure with a high density of acoustic events. Because the number of parameters is excessive if each grain is controlled individually, more abstract parameters, such as overall density, are used. Recently, several approaches have been proposed that use neural networks for musical sound synthesis. Autoencoder-based systems reconstruct the spectrogram and let the user modify the low-dimensional latent representation of the sound in order to control the timbre [7]. NSynth [8] synthesizes musical notes on the basis of a WaveNet-based autoencoder architecture, which allows the user to morph sounds. Other approaches use Generative Adversarial Networks (GAN) [9], Recurrent Neural Networks (RNN) and Conceptors [10]. Gaussian Processes (GP) are used in machine learning for classification and regression. They have applications in various fields. We make use of GPs as a method for sampling continuous functions randomly. The sampled functions are then used in wavetable or waveshaping synthesis. Sampling multiple times from the same GP generates wavetables or shaping functions that sound perceptually similar. However, they are not identical.