Perceptual Atomic Noise

PERCEPTUAL ATOMIC NOISE Kristoffer Jensen University of Aalborg Esbjerg Niels Bohrsvej 6, DK-6700 Esbjerg [email protected] ABSTRACT signal point-of-view that creates sound with a uniform distribution and spectrum, or the physical point-of-view A noise synthesis method with no external connotation that creates a noise similar to existing sounds. Instead, is proposed. By creating atoms with random width, an attempt is made at rendering the atoms perceptually onset-time and frequency, most external connotations white, by distributing them according to the perceptual are avoided. The further addition of a frequency frequency axis using a probability function obtained distribution corresponding to the perceptual Bark from the bark scale, and with a magnitude frequency, and a spectrum corresponding to the equal- corresponding to the equal-loudness contour, by loudness contour for a given phon level further removes filtering the atoms using a warped filter corresponding the synthesis from the common signal point-of-view. to the equal-loudness contour for a given phon level. The perceptual frequency distribution is obtained by This gives a perceptual white resulting spectrum with a creating a probability density function from the Bark perceptually uniform frequency distribution. scale, and the equal-loudness contour (ELC) spectrum is created by filtering the atoms with a filter obtained in 2. NOISE the warped frequency domain by fitting the filter to a simple ELC model. An additional voiced quality Noise has been an important component since the parameter allows to vary the harmonicity. The resulting beginning of music, and recently noise music has sound is susceptible to be used in everything from loud evolved as an independent music style, sometimes noise music, contemporary compositions, to meditation avoiding the toned components altogether. The music. distinction between noise and tone has been clear for a long time. Helmholtz [5] and Schaeffer [6] opposed 1. INTRODUCTION harmonic sounds to unvoiced sounds. The mpeg 7 audio description [7] distinguishes between harmonic and The unvoiced sounds are used in many musical percussive, coherent and non-coherent, and sustained situations, from the abundance of cymbals and hihats in and non-sustained sounds. rhythmic music to the musique concrète of Schaeffer, Zwicker [8] found that band-pass filtered noise with the stochastic (random) processes of Xenakis, the large bandwidth has low relative pleasantness, as granular music of modern computer music or noise compared to sinusoids and band-pass filtered noise with music. low bandwidth. Three noise prototypes are identified here; random Noise as a component of music is found in its purest values (dice noise), random events (Geiger noise), and form in some percussion instruments, and in particular random frequencies (cymbal noise). The atomic noise in the unvoiced consonants of the human voice. The has previously been shown [1] to produce almost all futurist proposed, seemingly without success [9], a pure noise types, while permitting to vary the degree of series of instruments; the intonarumori that produced Geiger-, or cymbal-ness, thus easily creating a large rumbles, whispers, creaks, and other noises. Schaeffer variety of sounds with little natural connotation. This is went on to collaborate with Pierre Henry on musique done by adding atoms with random amplitude, width, concrète, in which recorded sounds, many of them frequency and onset time. unvoiced, were used in the compositions. Stockhausen Other noise synthesis methods include the formant- and others used electronic generators, sinusoids and wave-function (FOF) with random onset time [2], used white noise in their early works. Another composer, to resynthesize naturally occurring musical noises. The Xenakis, used stochastic processes in both compositions shaken instruments have a random event distribution but also in the creation of new sounds. The distinction that can be modelled through the stochastic event between composition and sound events have been modelling [3], while most other musical instruments blurred even more in the granular synthesis [10], a need random irregularities on the frequencies and method in which long music pieces can be obtained by amplitudes to produce an interesting sound [4]. random summation of time or frequency shifted short The atomic noise was created to produce sounds (10-50 msec) grains, often extracted from a short which demanded no control over the spectral or the sampled waveform using a random selection and temporal envelope. Contrary to the granular synthesis or manipulation process. the musique concrète, or the different noise synthesis The use of noise has been further enlarged by two models, there is no ‘original’ timbre that is retained in recent trends. In the noise music, adapts such as the resulting music. Merzbow or Caspar Brötzmann, use noise played In this work a further attempt is made to remove the extremely loud in a generally rather static way. ‘Noise ‘external’ influence of the music, by abandoning the 2 music becomes ambience not as you learn how to listen, ⎛ t−t0 ⎞ t − t −⎜ ⎟ or when you accept its refusal to settle, but when you atom(t) = a cos(2πf 0 )e ⎝ σ ⎠ . (1) are no longer in a position to accept or deny’ [11]. This sr stands in full opposition functionally with the use of noise to create ‘relaxation and calm, promoting sleep, The amplitude a is a random variable with a Gaussian and blocking annoying noises’ [12]. By mixing and distribution and the frequency f is random values with editing the perceptual atomic noises together, looping uniform distribution, t0 is the onset time and σ is the them, and ending up with an entire piece of music, it standard deviation (width) of the Gaussian. sr is the becomes obvious that the perceptual atomic noises can sample rate. The atomic noise is created by inserting also make up complex contemporary music. one new atom at time t0, if the random value drawn is greater than the probability threshold p. 3. ATOMIC NOISE As σ is approaching zero, the corresponding signal gets small duration and large bandwidth, thus The atomic noise [1] is a method used to easily create approaching the Geiger noise. As σ increases, the any kind of sounds between three kinds of prototypic sinusoids get more duration and less bandwidth, and the noises, without any attempt to model spectral or signal approaches the cymbal noise. Examples of the temporal envelope behaviour. These three prototypic atom noise as a function of σ and p are shown in figure noises are the dice, cymbal and Geiger noises. The 1. atomic noise is created by adding atoms with random Increasing width of atoms 15000 amplitude, frequency, duration and onset time. The ) z H ( 10000 different prototypic noises are created by setting the y enc distribution parameters appropriately. In addition, the 5000 equ r atomic noise harmonicity is varied by different f 0 procedures; either the time or frequency distribution is 0 1 2 3 4 5 time (sec) made periodic, or a short created noise (frozen noise) is Increasing probability of atoms repeated. 15000 ) z H ( 10000 3.1. Noise prototypes y enc 5000 equ r The random values (dice) method of creating unvoiced f sounds is the most common method today. By using a 0 0 1 2 3 4 5 new, uncorrelated, value at each time sample, an time (sec) unvoiced, uncoloured sound is obtained. The distribution of the random values has not been found to Figure 1. Spectrum of atomic noise with increasing σ be very important, perceptually. (top) and p (bottom). The summation of a large number of sinusoids with random frequencies evenly distributed on the 3.3. Tone from noise frequencies also renders an unvoiced sound, if the Since the Geiger noise becomes harmonic when the number of sinusoids is high enough. As the sound probability of pulses increases at periodic times, and resembles that of a cymbal for a relative low number of similarly, the cymbal noise becomes harmonic when the sinusoids, this noise generation method is called cymbal probability of sinusoids increases at periodic noise. frequencies, a periodic distribution for the stochastic Pulses randomly distributed in time are heard as a signals is proposed [1]. The periodic distribution is ticking noise, reminiscent of a Geiger counter, when the based on a triangular window, raised to the wth power, number of pulses is low. Pierce [13] differentiates w between slow random pulses, which are heard as x p(x) = Λ x − 0 0 ≤ x ≤ x (2) separate pulses, whereas at a few hundred pulses per 2 0 second, not all pulses are detected individually. Above a few hundred pulses per second, a smooth noise is heard, Λ is a normalization necessary to obtain a power with no individual pulses perceivable. density function and w is the harmonicity coefficient. A 3.2. Atom noise synthesis harmonicity value of zero produces unvoiced sounds, while a higher value produces a more toned sound. The If the notion of random value, time and frequency is eq. (2) is repeated for the duration of the noise, or up to retained, much of the noise types can be obtained [1] by the Nyquist frequency, in case of time and frequency adding together a large number of sinusoids with periodic distribution, respectively. Another method for random amplitude and frequency, multiplied by a creating tone from noise is by using frozen noise (short Gaussian shape with random standard deviation at noise segment), and repeat it. Warren [14] used frozen random starting times, noise to show the perception of infrapitch (very low frequency pitch) and found whooshing, motor boating, and noisy pitch sound, with additional rattles, clangs and other metallic types of sounds dependent on the the perception and possibly the attention to each repetition rate. component is weighted equally. 4. PERCEPTUAL ATOMS 4.2.

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