Andrew Horner

Machine Tongues XVI: Genetic Algorithms and Their Application to FM Matching Synthesis

Historically, frequency modulation (FM) synthesis has required trial and error to create emulations of natural sounds. This article presents a genetic-algorithmbased technique which determines optimized parameters for reconstruction through FM synthesis of a sound having harmonic partials. We obtain the best results by using invariant modulation indices and a multiple carrier formant FM synthesis model. We present our results along with extensions and generalizations of the technique.

Detection of random alterations to time-varying musical instrument spectra.

The time-varying spectra of eight musical instrument sounds were randomly altered by a time-invariant process to determine how detection of spectral alteration varies with degree of alteration, instrument, musical experience, and spectral variation. Sounds were resynthesized with centroids equalized to the original sounds, with frequencies harmonically flattened, and with average spectral error levels of 8%, 16%, 24%, 32%, and 48%. Listeners were asked to discriminate the randomly altered sounds from reference sounds resynthesized from the original data. For all eight instruments, discrimination was very good for the 32% and 48% error levels, moderate for the 16% and 24% error levels, and poor for the 8% error levels. When the error levels were 16%, 24%, and 32%, the scores of musically experienced listeners were found to be significantly better than the scores of listeners with no musical experience. Also, in this same error level range, discrimination was significantly affected by the instrument tested. For error levels of 16% and 24%, discrimination scores were significantly, but negatively correlated with measures of spectral incoherence and normalized centroid deviation on unaltered instrument spectra, suggesting that the presence of dynamic spectral variations tends to increase the difficulty of detecting spectral alterations. Correlation between discrimination and a measure of spectral irregularity was comparatively low.

Nested modulator and feedback FM matching of instrument tones

Most previous work with nested and feedback frequency modulation (FM) has matched harmonic musical instrument tones with only a single carrier. This paper introduces a genetic algorithm technique for optimizing parameters for several carriers. We give results using the method to match a trumpet, tenor voice and Chinese pipa. The results show that feedback FM often gives the best matches when we compare the techniques against the same number of table lookups, indicating that feedback FM is a good choice for software synthesis. Double- or triple-nested modulator FM gives the best results for the same number of carriers, making them the best choices if nested FM hardware is available.

A highly sensitive graphene woven fabric strain sensor for wearable wireless musical instruments

Highly flexible and sensitive strain sensors are essential components of wearable electronic devices. Herein, we present a novel graphene woven fabric (GWF)/polydimethylsiloxane (PDMS) composite as a highly flexible, sensitive strain sensor capable of detecting feeble human motions with an extremely high piezoresistive gauge factor of 223 at a strain of 3% and excellent durability. A wireless wearable musical instrument prototype made of the composite sensor demonstrates conversion of human motions to music of different instruments and sounds.

A genetic algorithm-based method for synthesis of low peak amplitude signals

The maximum amplitude of a waveform corresponding to a particular harmonic spectrum depends on the phases of its harmonic components. A waveform with a low peak‐to‐rms ratio is desirable in situations requiring a maximum signal‐to‐noise ratio. This paper introduces a genetic algorithm‐based method for selecting the phases that produces better results than previously described methods. Results for four different amplitude spectra are given. For the case of a flat spectrum with up to 40 harmonics, the genetic algorithm finds peak factors (peak/√2 rms) ranging from 0.98 to 1.24.

Toward orthogonal non-individualised head-related transfer functions for forward and backward directional sound: cluster analysis and an experimental study

Individualised head-related transfer functions (HRTFs) have been shown to accurately simulate forward and backward directional sounds. This study explores directional simulation for non-individualised HRTFs by determining orthogonal HRTFs for listeners to choose between. Using spectral features previously shown to aid forward–backward differentiation, 196 non-individualised HRTFs were clustered into six orthogonal groups and the centre HRTF of each group was selected as representative. An experiment with 15 listeners was conducted to evaluate the benefits of choosing between six centre-front and six centre-back directional sounds rather than the single front/back sounds produced by MIT-KEMAR HRTFs. Sound localisation error was significantly reduced by 22% and 65% of listeners reduced their front–back confusion rates. The significant reduction was maintained when the number of HRTFs was reduced from six to five. This represents a preliminary success in bridging the gap between individual and non-individual HRTFs for applications such as spatial surround sound systems. Statement of Relevance:Due to different pinna shapes, directional sound stimuli generated by non-individualised HRTFs suffer from serious front–back confusion. The reported work demonstrates a way to reduce front–back confusion for centre-back sounds generated from non-individualised HRTFs.

Double-modulator FM matching of instrument tones

This article introduces a technique for optimizing double-modulator frequency modulation (FM) parameters to match an arbitrary harmonic instrument tone. The method uses a genetic algorithm to optimize the parameters, and it works for a group of double-modulated carriers. Previous work in double-FM matching has only matched a single carrier, restricting these techniques to matching sounds with static spectra. We give results using the method to match the dynamic spectra of the trumpet, Chinese erhu, and pipa. Finally, we compare the double-FM matching results with those found by formant-FM and wavetable matching, giving guidelines for when to use double-FM matching instead of other synthesis techniques.

Auto-Programmable FM and Wavetable Synthesizers

Replicating musical instruments is a classic problem of computer music. Historically, FM and wavetable synthesis have required trial-and-error optimization of the parameters. Recent work has used evolutionary computation to evolve parameters for synthesizing sounds. Genetic algorithms are particularly efficient and effective at auto-programming FM and wavetable synthesizers to replicate given sounds. This paper surveys FM and wavetable matching techniques with an emphasis on evolutionary methods.

Spectral modelling and timbre hybridisation programs for computer music

Software packages developed for visualising time-varying timbres, finding parameter settings for modelling acoustic instrument tones, and for synthesising timbres are described. The sndan package, written in C for Unix machines, provides spectrum analysis, pitch tracking, spectrum display, parameter modification, and additive synthesis. Other programs that estimate the best possible parameters for recreating acoustic sounds using techniques such as multiple FM and wavetable synthesis and extended nonlinear/filter synthesis are outlined. Hybrid instruments created by fashioning sounds out of the recombined spectral characteristics of two or more very different tones are also presented.

Low peak amplitudes for wavetable synthesis

The peak amplitude of a waveform for a particular spectrum depends on the phases of its harmonic components. Previous work on peak amplitude reduction has only considered individual spectra. This paper compares various phase selection methods, and shows that genetic algorithm optimization gives results 10%-25% lower than the other methods.