The Impact of Nonlinear Distortion on the Perceived Brightness and Roughness of Electric Guitar Chords

All rights remain with the authors under the Creative Commons Attribution 4.0 International License (CC BY 4.0). Proc. of the 17th Int. Symposium on Computer Music Multidisciplinary Research, London, United Kingdom, 2025 The Impact of Nonlinear Distortion on the Perceived Brightness and Roughness of Electric Guitar Chords Richard Berrebi1*, Agathe Mangialomini1,2*, Etienne Thoret3+[0000-0002-8214-6278] and Richard Kronland Martinet1+[0000-0002-7325-4920] 1 Aix-Marseille University, CNRS, Perception Representation Image Sound Music (PRISM) UMR7061 2 University of Tours, CNRS, Centre d’études supérieures de la Renaissance (CESR) UMR7323 3 Aix-Marseille University, CNRS, Institut de Neurosciences de la Timone (INT) UMR7289 [email protected] [email protected] *The two authors contributed equally to this work +Senior co-authorship Abstract. When it comes to qualify the nature of audio effects, such as nonlinear distortion, it is not uncommon to observe artists or audio engineers using semantic descriptors such as “warmth”, “smooth”, “rough” or “bright”, to give a specific indication on the timbre itself, altered by those effects. One of the many ways of modifying sound is the nonlinear distortion synthesis technique, also called waveshaping. While a lot of different hardware implementations of distortion effects have their own specificities, each is designed to generate new partials thanks to a nonlinear function. On the other side, it is unclear to which distortion parameter(s) "roughness" and "brightness" refer to, and we don't know yet if those characteristics have a close relation to nonlinear distortion. In this study, we investigate the effect of the nonlinear distortion induced by a guitar pedal, the Boss DS-1, on the perceived brightness and roughness. First, an acoustic analysis reveals how the various controls of the guitar pedal affect the brightness and the roughness of a guitar chord. Then, a listening test confirmed that perceived evolutions of brightness and roughness are coherent with their related presets related to them. Keywords: Brightness, Roughness, Waveshaping, Nonlinear Distortion, Timbre, Guitar. 1 Introduction Nonlinear distortion is used in many modern genres such as Jazz, or Rock music, and is mostly coupled with an electric guitar. Many rock subgenres, such as metal [10] or punk [20], often use this effect with a specific chord selection, such as major chords Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 59 R. Berrebi and al. (like the largely used “power chord”). These artistic choices in the music production of this “extreme music” could induce strong feelings in the listener, like, for instance if somebody wants to enhance his mood or to match his anger [29]. However, we may ask whether these emotions are driven by consistent patterns that connect listener affect to sound production. We consider the specific case of the use of distorted guitar. For audio effects such as nonlinear distortion, it is common to describe the resulting timbre by using adjectives or qualifiers. A large lexicon of semantic descriptors has been established, including adjectives such as “crunchy”, “bright” or “full” [25]. Each of them has a relationship with specific settings. For instance, “fizzy” and “bright” are related to “increased treble” settings. As a first glance, it is noticeable that nonlinear distortion strengthens the higher overtones of a guitar: in consequence, the beating partials increase the auditory dissonance, which lead to increase the sensation of roughness [10], and, on the other hand, the high frequencies of the guitar’s timbre are more charged, which could be assimilated as “bright” [4]. Regarding nonlinear distortion, as Hartman [8] says, one can talk about it when new partials are added to the output signal spectrum (while, in the temporal domain, for a periodic signal, its original period is preserved, and only the amplitude is clipped). This technique is particularly useful for altering the timbre of musical instruments [14]. As Roads [27] summarizes, to create nonlinear distortion, we have to pass the input signal into a “shaping function”, whose x-axis is the level of the input signal, and the y-axis is the level of the output signal. According to the shape of the nonlinear function, if the input amplitude value is superior to the output amplitude value, the waveform is clipped, distortion appears and adds new partials (called “modulation products”, according to Roads) into the spectrum. Most common shaping functions [14, 27] behave linearly for input level values around 0, while partials are generated as the input level increases. Some examples of these functions are hyperbolic tangent, sinusoid or exponential. Each has its own features and will generate partials in a different way. One of the consequences of the introduction of those partials, is the appearance of strong energy in the high frequencies of the spectrum [10]. It is often difficult to characterize the signal of timbre instruments processed by nonlinear distortion, due to its non-reversible and unpredictable behavior [24]. This is why it is interesting to analyze this phenomenon from a perceptual perspective. Timbre descriptors, also called “features”, have been developed [19, 22, 23] to quantify the spectro-temporal characteristics of musical timbres. Some of them could give us indications on the brightness of a timbre. Brightness is often defined as “the amount of high-frequency content perceived in the spectrum of a sound”. It is strongly correlated with the acoustic feature of spectral centroid [7, 18], which indicates the barycenter of the spectrum (with equivalent energies at the right and at the left of this barycenter). Spectral centroid is expressed as [22]: ∑"($)&($) !"# $%& ∑&($) !"# $%& (1) With x(n) the weighted frequency value (bin number), and f(n) the center frequency of that bin. It’s not uncommon to use nonlinear effects to control the brightness of the Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 60 The impact of nonlinear distortion on the perception of electric guitar chords timbre timbre [4, 38], sometimes coupled with spectral equalization [31] (it could be an explanation for the semantic association between “bright” and “increased treble”, as mentioned earlier). Brightness is not the only acoustic feature that we can highlight as a result from nonlinear synthesis techniques: inharmonicity [17] and increased auditory roughness [5] could also be noticed. Roughness was first mentioned by Helmholtz [9], by considering the effect produced by closely spaced high-frequency partials in the spectrum. Indeed, roughness sensation depends on the interval between two beating tones. According to Lichte [16], in musical timbres and complex tones, roughness is present when consecutive partials are above the sixth and is a function of the location of such partials. From a perceptual point of view, roughness is often associated to “sensory dissonance” [28], and is emphasized when two sinusoids lie within the same critical band [6, 37] (the way that our ear perceives the spectral content, and could be modelled by a filter-bank, like the well-known Bark scale [36] or Mel scale [32]). It is sometimes associated to a rubbing sensation and physical friction [34]. On the spectrum, the closer two frequencies are, the slower the beating, and the timbre will be perceived as “smooth”. On the other hand, when two frequencies diverge into separate critical bands, roughness sensation will attenuate and two separate pitches will begin to be distinguishable [34]. Zwicker and Fastl proposed a model to compute perceived roughness [37] with, for unit reference, one 1 kHz sinusoid of 60 dB 100% modulated by a frequency of 70 Hz in amplitude, to define one Asper. This model is based on the observance of roughness in a frequency band between 70 Hz and 300 Hz, with the modulation frequency ("'()) multiplied by the modulation depth (ΔL): * = "'() ∫Δ-*(.)/. +,-./01 &(2) Considering the literature, there is a lack of studies linking nonlinear distortion and auditory roughness, even if Lichte briefly mentions it [16]. For brightness, some authors studied nonlinear distortion to manipulate the perceived brightness in the musical timbre [1]. Some of them studied precisely the effect of distorted guitar on brightness and sharpness [33], but did not linger on roughness. In its “Metal Music Studies”, Jan-Peter Herbst [11] studied some acoustic features (including brightness and roughness) of the distorted guitar [10], by taking into account the “pleasantness” of the chord. However, those studies don’t delimit how the controls of a distortion guitar pedal affect those two acoustic features. This is what this study is all about: how the controls of an existing model of nonlinear distortion affect the perceived brightness and roughness of the timbre of a guitar chord, and how to determine a relationship between them? To set a realistic musical context, we took one of the most used distortion pedals by rock guitarists: the Boss DS-1. This pedal is analogic, and as we will see later, we must have a full ability to control the parameters. An accurate way to reproduce this effect into a digital environment is the “white-box approach” (for analog reproductions in digital), to get a realistic emulation of this distortion pedal [35]. This modelling approach is based on the knowledge of the circuits and the components of the Boss DS1, which are opened to the public [39], allowing the development of a controllable implementation, very close to the reality of an analogue Boss DS-1 [2]. This effect has Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 61 R. Berrebi and al. three important controls: the “distortion” control, which is a pre-gain (corresponding to the Gain+filter block in figure 1) before the passage of the signal through the nonlinear function (an approximation of the hyperbolic tangent [2], corresponding to the Saturing nonlin block in figure 1), the “tone” control, that splits nonlinearly the signal in two bands (bass and the treble, corresponding to the Tone filter block in figure 1) and carries out the balance between them, and then the “level” control, that acts like a volume control, to readjust the possible volume loss. Fig. 1. Block diagram of distortion pedal [35] In the following, two acoustic spaces for both brightness and roughness will be defined, in which their evolution will be analyzed according to the Boss DS-1 controls. Next, a perceptual experiment that confirms the previous results found will be detailed and will conclude on how these controls affect brightness and roughness. Throughout this study, brightness and roughness will be considered separately and a relation between those two characteristics of the timbre will not be established. 2 Acoustic Analysis 2.1 Design and procedure For the acoustic analysis, we decided to use through the well-known analysis by synthesis methodology established by Risset and Wessel [26]. We considered a guitar chord and applied various quantified Boss DS-1 presets to it. Those sounds are called “measurements” in this study. This set of sounds were used to build up an acoustic space for both brightness and roughness, using spectral centroid and the roughness model mentioned previously. Measurements consisted of 2420 recordings of only one one-shot guitar chord cut from the first few seconds of the file “directinput_Set1_maj.wav” [21], which is an A# major (A#-D-F). The guitar used for this chord was the Ibanez PF300, recorded directly from the input (not from an amplifier, to avoid any additive nonlinear distortion) using the Audient iD14 audio interface. To make those 2420 measurements from this guitar chord, we took a MATLAB implementation of the Boss DS-1 [2], and we quantified each parameter (“distortion”, “tone” and “level”) with a step of 0.1. The parameters “distortion” and “tone” have a range of values between 0 and 1, and the “level” parameter has a range of values between 0 and 2. After quantization, we obtained a total amount of 2420 combinations, or “presets” of the Boss DS-1 implementation, by excluding all the cases where the “level” parameter is equal to 0 (the level parameter is acting as the output volume control, so if its value is set to 0, no signal will be emitted). We applied those presets on this chord to get 2420 Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 62 The impact of nonlinear distortion on the perception of electric guitar chords timbre different sounds. The total duration of each measurement is 3 882 ms. The loudness of these measurements was calculated using the Loudness K-weighted Full Scale (LKFS, ITU-R BS.1770) and equalized in LKFS value of -18. 2.2 Timbre descriptors Method. For brightness modeling, the spectral centroid of the Timbre Toolbox [23] was used. The latter is computed for each 25 ms time frame, using the ERB-spaced gammatone filter bank decomposition of the signal to obtain a representation close to perceptual reality. As a time-varying descriptor, spectral centroid (in Hz) was summarized through the statistics of the median, as a measure of central tendency. For roughness modeling, the model of Zwicker & Fastl [37] was used through the acousticRoughness MATLAB function, based on ISO 532-1 [12]. Just like brightness, the roughness model is a time-varying model (in Aspers), so it was summarized through the statistics of the median. All these values were represented in two acoustic measurement spaces, to get an overview of the variation in brightness and roughness as a function of the parameters of the Boss DS-1 in the Figures 2 and 3. Brightness analysis. For brightness, the “tone” parameter of the Boss DS-1 is playing a crucial role and is responsible of the shifting of the spectrum barycenter. At each “tone” value (figure 2), the spectral centroid is moving one step further. The “distortion” parameter plays a supporting role in the increasing of the brightness, especially when it reaches extreme values from 0.6-0.7 to 1 (figure 2). This effect is mostly visible at high “tone” values (the movement becomes steeper and steeper as the “tone” increases). This is probably because, as a crossover filter (balancing bass and trebles), the “tone” keeps more and more high frequencies for values above 0.5. The “level” control (not visible in figure 2, for the sake of clarity and readability) doesn’t play a specific role in the behavior of the brightness, which shows that its sole purpose is to adjust the output volume. To summarize, brightness increases with the “distortion” amount, in line with the “tone” setting, as it was previously mentioned in introduction [4]. Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 63 R. Berrebi and al. Fig. 2. Evolution of brightness (median spectral centroid, in Hz) as a function of the Boss DS-1 parameters: distortion (x-axis) and tone (in different colors for each curve), and level fixed at 1. Roughness analysis. For roughness, the analyses are less straightforward. For midrange “tone” settings (figure 3), e.g., 0.3, 0.4, 0.5 and 0.6, the shape of the plot is the same (the maximum of roughness is reached for low “distortion” values), while the “level” doesn’t play a crucial role. Also, for very small and very high “tone” values, e.g., as 0 to 0.2, and 0.7 to 0.9 (0.2 and 0.9 in figure 3), the shapes of the plots have some similarities between them: there is a consequent gap between small and very large (after 0.5) “distortion” values. For these values, the “level” control seems to contribute to the generation of roughness: for instance, for “tone” values like 0 and 0.1, the gap is quickly reached for high values of “level”. This gap tends to increase with the “tone” setting (as we see a “peak” of roughness at the end of each plot gradually shrinking). As the auditory roughness was described in the introduction, for extremely low or extremely high “tone” values, and at high levels of distortion, it is logical that roughness increases: the number of new beating tones (distortion products) increases, while a very small portion of the spectrum (in the bass or the treble range) is retained by the extreme filtering, which reduces the total bandwidth of the output signal. All these factors increase the “chances” of observing and perceiving roughness. Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 64 The impact of nonlinear distortion on the perception of electric guitar chords timbre Fig. 3. Evolution of roughness (median roughness, in Aspers) in function of the parameters of the Boss DS-1 implementation: distortion (x-axis), level (y-axis) and tone fixed at 0.2, 0.5, 0.6 and 0.9. 3 Experiment 3.1 Method Participants. 12 listeners were recruited with an average age of 27.92 years (M=26; SD=8.68 y.o,) and a range of 29 years. They were native French speakers or spoke French fluently and did not present any hearing impairment. 3 of them are guitarists with an average age of 24 years (M=26; SD=3.46 y.o,) and a range of 6 years. 6 of them listen to rock music with an average age of 28.67 years (M=26.5; SD=6.56 y.o,) and a range of 19 years. Design. Listeners were tested individually in a soundproof booth. Stimuli were presented on Sennheiser HD 800 S headphones using an Apple MacBook Pro 2024 and an audio interface Focusrite Scarlett 2i2 (with a fixed volume). The graphical user interface was developed using MATLAB 2024. Procedure. We divided the experiment in two parts (of 10 stimuli for each), to evaluate separately the brightness and the roughness characteristics of the timbre. In each part, the participants evaluated the perceived brightness and perceived roughness difference Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 65 R. Berrebi and al. for each stimuli pair. A numeric scale from 0 to 10 was used: 0 for “completely identical”, and 10 for “completely different”. Each part of the experiment had a total of 45 pairs to evaluate. Each block proceeded in three phases: the first one was a familiarization phase, where the participants listened to each stimulus (in a random order for every participant). The second phase was the training phase: the participants evaluated two test pairs to familiarize themselves with the interface. The third phase was the pairwise evaluation, where the participants evaluated the 45 pairs of stimuli on the scale from 0 to 10. Between each block, the participants were entitled to a break. At the end of the experiment, the participants completed a questionnaire to provide their age, their sex, their strong hand, indicating if their profession is related to sound and acoustics, if they play a musical instrument and what genres of music they listen to. Stimuli. We selected 10 stimuli for the perceptual evaluation of brightness and 10 other different stimuli for the perceptual evaluation of roughness from the 2420 sounds previously made in section 2.1. For the selection of each stimuli group, we carefully chosen the preset values associated with the sound, for maximum variance. Also, to avoid introducing bias, we ensured that for theses pre-settings, the growth of brightness and the growth of roughness were not correlated. Indeed, for the brightness presets, brightness grows at each stimulus index, but not the roughness associated with these same presets, and vice versa. A click at the end of the stimuli was audible, so we made a volume fade out with a decreasing exponential of 120 milliseconds to remove it. 3.2 Data analysis Inter-listeners agreement. Before running the analysis, we checked the reliability of participants answers by computing the inter-rater reliability and by computing intraclass correlation coefficients. For brightness, an inter-rater correlation coefficient of 0.685 was obtained, using Pearson correlation with /"1 = 143, which is a fairly high value for behavioral ratings. We computed intraclass correlation using ICC(3,1), ICC(2,1) (4 = 31.14, 6 = 7.11 ∗10"##2) and ICC(k,1) coefficients: we got 0.6916, 0.6689 and 0.9569, which was enough to consider the sample as coherent, generalizable, and reliable. For roughness, we got an inter-rater correlation coefficient of 0.53, using Pearson correlation with /"1 = 143, which is good too for behavioral ratings. We computed intraclass correlation using ICC(3,1), ICC(2,1) (4 = 14.51, 6 = 1.55 ∗ 10"34) and ICC(k,1) coefficients: we got 0.5205, 0.4695 and 0.9068, which give us less variability between the stimuli, and some disagreements. Multidimensional scaling. The two blocks (brightness and roughness) were analyzed using nonmetric MDS [13, 30] through the evaluation phase of each participant (a symmetric 10x10 dissimilarity matrix for the 10 stimuli, with 45 evaluations). For its capability to evaluate an entire sample of participants, INDSCAL [3, 15] was used to model the nonmetric MDS. INDSCAL has no specificities but has weights on each dimension for each listener, and allows for differences among individual listeners or latent classes Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 66 The impact of nonlinear distortion on the perception of electric guitar chords timbre of listeners, respectively [19]. For both brightness and roughness block, INDSCAL was computed on 2 dimensions. Fig. 4. INDSCAL group stimulus space for both perceptive evaluation (with in blue the stimulus number and in red the values of the controls: “d” for “distortion”, “t” for “tone” and “l” for “level”). To validate the coherence between the acoustic analysis in section 2.1 and the perceptual experiment, a correlation was computed between the distances of the measurements of our stimuli (10 stimuli of brightness and 10 stimuli of roughness) and with the Euclidean distances computed in the INDSCAL of each block. For brightness, a great correlation (;1= 0.739, p < 5 ∗ 10"5, /" =43, CI95% [0.534, 0.871]) was found for the entire sample. If the rock music listeners are isolated from the sample, the distances correlate better (; = 0.815, p = 0, /" = 8, CI95% [0.641, 0.914]). If the same is done by isolating the guitarists from the sample, distances correlate still (; = 0.672, p < 1.015 ∗10"3, /" = 8, CI95% [0.416, 0.837]). For roughness, perceptual evaluation correlated with measurements too (; = 0.5378, p < 0.0005, /" =43, CI95% [0.303, 0.718]). If the rock music listeners are isolated from the sample, the distances correlate a bit more (; = 0.467, p < 1.4 ∗ 10"6, /" = 8, CI95% [0.199, 0.666]). If the same is done by isolating the guitarists from the sample, distances correlate again (; = 0.442, p < 2.6 ∗ 10"6, /" = 8, CI95% [0.158, 0.661]). All correlations were computed using Spearman correlations, and 95% confidence intervals were computed by bootstrapping the correlations, using 2000 bootstrap samples. The stress obtained for the INDSCAL of brightness has a value of 0.176, and for the INDSCAL of roughness, 0.209. (the entire sample). At the end of our analysis, for each block (brightness and roughness), a space in two dimensions was established, matching one or two controls of the Boss DS-1: For brightness, dimension 1 fits with “tone” control (; = 0.762, p < 0.011, /" = 8, CI95% [-0.213, 0.968]), while dimension 2 fits with “distortion” control (; = -0.796, p < 0.006, /" = 8, CI95% [-0.973, 0.138]). For roughness, dimension 1 fits with “distortion” control (; = 0.975, p < 1.55 ∗ 10"3, /" = 8, CI95% [0.901, 1]). For brightness, those correlations confirmed our hypothesis where we stated that “tone” and “distortion” controls were responsible for shifting the spectral centroid to Proc. of the 17th International Symposium on CMMR, London, UK, Nov. 3-7, 2025 67