## 3 The Q1 Synth System
* Amplitude (_amp_): defines the loudness of the sound. * Reverberation (_reverb_): defines the amount of reverberation to add to the sound. * Modulation index (_mod index_): defines the number of components in the sound spectrum. The higher this index, the higher the number of components. * Harmonicity ratio (_harmonicity_): working alongside _mod index_, this parameter defines the richness of the sound. The higher this ratio, the richer the sound. * LFO frequency (_[fo freq_): the low-frequency oscillator (LFO) creates a vibrato or tremolo effect. The higher the frequency, the faster the vibrato. * LFO depth (_[fo depth_): defines the intensity of the vibrato. In a nutshell, the system uses the angles (\(\theta\), \(\varphi\), and \(\lambda\)) of the Bloch sphere to interpolate parameter values for the FM algorithm. First, the user defines which synthesis parameters each angle will control. For instance, by default the system associates the following parameters:  
* \(\theta\) inclination = {_freq_, _amp_, _reverb_},
* \(\varphi\) azimuth = {_mod index_, _harmonicity_},
* \(\lambda\) phase = {_[[fo freq_, _fo depth_]. In 'Advanced' mode view, the system shows sliders on either side of the Bloch sphere. They are used to specify the range of values for each parameter (Figure 6). Each sphere axis is assigned a pair of slider banks, enabling the values at each extreme to be interpolated as the sphere is rotated. For example, when the state vector is pointing north, (\(|0\rangle\) position), the frequency, amplitude, and reverb parameter values will correspond to the sliders on the left side of the screen. When the state vector is pointing south (\(|1\rangle\) position), these parameters correspond to the sliders on the right. When the sphere is between these poles we hear an interpolation between each slider pair, corresponding to the angle of inclination. It is possible to save presets. Similarly, pairs of slider banks are assigned to the azimuth (interpolating between the \(|+\rangle\) and \(|-\rangle\) directions), and the sphere's phase. By re-orienting the sphere around these planes, the user interpolates between the slider settings at each extreme. All interpolations are linear. For example, if a pair of controls is set to 0% on the left and 100% on the right, when the sphere is rotated to the middle, the parameter value will be equal to 50%. Figure 5: A simple FM synthesis scheme with two oscillators: a modulator and a carrier. Whereas \(d\) defines the amplitude and \(f_{m}\) the frequency of the modulator, respectively, \(a_{c}\) defines the amplitude of the carrier. The sinusoidal output from the modulator is added to the frequency of the carrier (\(f_{c}\)). We note that in quantum computing, a measurement causes the state vector to 'collapse' instantly to either \(|0\rangle\) or \(|1\rangle\)[16]. However, we took the liberty to convey this concept artistically: we added a virtual time delay to sonify the 'collapse'. Thus, after a measurement, Q1 Synth makes an animated trajectory of the red dot towards the corresponding pole. In doing so, the synthesiser performs a complex, multidimensional modulation, interpolating between all parameters simultaneously until the red dot reaches its final destination, at which point the sound fades out.