PART II: Acoustic Axes of Modulation
3.1 Equal-Tempered Tonality as a Culturally Internalized Predictive Grid
To discuss microtonality with precision, the baseline against which deviation becomes perceptually meaningful must first be established.
Within contemporary Western musical culture, the twelve-tone equal-tempered (12-TET) system functions as the dominant predictive grid. From early exposure, listeners internalize intervallic relationships structured around the division of the octave into twelve equal semitones. Harmonic progression, tonal resolution, consonance expectations, and melodic contour are shaped within this framework.
This internalization is rarely explicit and does not require formal training. Repeated exposure alone is sufficient for probabilistic encoding (Huron, 2006). Predictive processing accounts of the auditory system describe expectation as the product of a hierarchical generative model that is continuously updated by incoming sensory evidence, with each level of the hierarchy weighting incoming prediction error according to its estimated precision, or reliability (Friston, 2010; Feldman & Friston, 2010; Hohwy, 2013). In equal-tempered tonal music, the auditory system stabilizes high-precision priors around a small set of recurring regularities: specific interval sizes, stable tonal centers, hierarchical harmonic relationships, and resolution tendencies such as the dominant to tonic cadence. This is the mechanism formalized by Vuust, Heggli, Friston, and Kringelbach (2022) in their predictive-coding-of-music (PCM) model, and by Koelsch, Vuust, and Friston (2019) in their account of how tonal music generates precise, high-confidence expectations that can then be violated for expressive effect.
Over time, these patterns become embodied as high-precision predictive priors. They shape not only aesthetic preference but perceptual anticipation itself.
This baseline is culturally specific, neither biologically universal nor historically inevitable, and the present model treats it as such. Equal temperament is acknowledged as the dominant predictive conditioning of the cultural environment from which this model emerges, a declaration that prevents unintended universalization and positions microtonality correctly: not as an abstract mathematical deviation, but as a modulation relative to an interiorized predictive grid.
3.2 Microtonal Traditions Beyond the Western Frame
Microtonal systems are not experimental anomalies. Most of the world’s musical traditions employ intervallic structures that diverge from equal-tempered division: Arabic maqam systems, Indian raga traditions, Persian dastgah, and a wide range of Southeast Asian tuning systems operate with intonational distinctions that differ substantially from Western equal temperament, and listeners within those traditions develop predictive models aligned with those structures accordingly.
This point has recently been made forcefully within the predictive-coding-of-music literature itself. In a formal correspondence to Vuust et al. (2022) published in Nature Reviews Neuroscience, Savage and Fujii (2022) argue that a genuinely explanatory predictive coding of music must be built as a cross-cultural framework from the outset, since core constituents of the PCM model, including chord-based harmony, are historically and culturally specific rather than universal features of music. This is a substantive theoretical constraint, not a caveat: any model of tonal or microtonal expectation that treats one tuning system as the neutral default risks mistaking cultural conditioning for perceptual law.
From a predictive perspective, no tuning system is inherently destabilizing. Destabilization occurs relative to internalized expectation. The present work therefore does not propose microtonality as intrinsically disruptive or transformative; it proposes that when intervallic relationships deviate from a listener’s culturally internalized predictive grid, anticipatory precision is modulated, and this modulation is what the Perceptual Attenuation Field (PAF) engages.
The PAF is not tied to a specific interval system. It does not depend on quarter-tones, just intonation ratios, or any particular tuning framework. It concerns the modulation of predictive precision relative to whatever tonal structure has been internalized by the listener. Microtonality, in this study, refers broadly to structured deviation from the dominant intervallic expectations of a given cultural context.
Direct behavioral evidence that listeners can rapidly build new predictive models for a genuinely non-12TET system exists, and it strengthens this claim considerably. Loui, Wessel, and Hudson Kam (2010) exposed listeners with no prior training to melodies composed in the Bohlen-Pierce scale, a musical system built on a 3:1 frequency ratio rather than the 2:1 octave that underlies virtually all Western and most non-Western tunings. After only 25 to 30 minutes of passive exposure, listeners showed measurable recognition, generalization, and sensitivity to the statistical regularities of the new scale, along with increased preference for melodies that conformed to it. This is evidence of true microtonal statistical learning, not a proxy drawn from atonality, and it directly supports the claim that predictive models of tonal structure are acquired rather than fixed, and can be rebuilt for an unfamiliar interval system within a single listening session.
3.3 Microtonality as Structured Ambiguity
Within equal-tempered tonal music, resolution tendencies are strongly encoded: harmonic progressions imply direction, cadences imply closure, and intervals imply stability or tension according to culturally stabilized hierarchies.
When intervallic relationships are altered, through detuning, non-equal divisions, or continuous pitch gliding, resolution becomes less predictable, and the auditory system encounters increased uncertainty regarding tonal center, intervallic stability, or harmonic destination. Working with atonal melodies built from Schoenberg’s twelve-tone rows, Mencke, Quiroga-Martinez, Omigie, Michalareas, Schwarzacher, Haumann, Vuust, and Brattico (2021) reported a relevant pattern across two separate samples: in a MEG sample of 20 non-musicians, the mismatch negativity response to pitch, timbre, intensity, and location deviants did not differ significantly between tonal and atonal melodies, while in a separate behavioral sample of 39 non-musicians, accuracy and confidence in detecting pitch deviants were significantly lower in the atonal condition. This pattern, an unchanged low-level prediction-error signal alongside reduced conscious accuracy and confidence, is consistent with the interpretation that heightened tonal uncertainty selectively reduces the precision weighting assigned to higher-level, cognitively accessible expectations without eliminating prediction itself; the study itself does not use the term precision weighting, and the interpretation offered here is this paper’s, not the original authors’.
More direct evidence for precision modulation under musical uncertainty comes from Quiroga-Martinez, Hansen, Højlund, Pearce, Brattico, and Vuust (2019), who manipulated the entropy of melodic sequences directly and found that the amplitude of the MMNm to pitch and slide deviants was reduced in high-entropy compared to low-entropy melodic contexts, with no corresponding reduction for intensity or timbre deviants. Because MMNm amplitude is a standard neural index of prediction-error weighting, this result is a more direct demonstration, within the tonal domain rather than the atonal one, that increasing structural uncertainty measurably reduces the precision assigned to pitch-related predictions specifically.
It is important to state the scope of this evidence accurately. Mencke et al. (2021) worked with atonal, not microtonal, material; the two are not equivalent manipulations. Atonality removes tonal hierarchy through pitch-class organization, whereas microtonality alters the intervallic content within or beyond that hierarchy. What the two share, and what makes the finding structurally relevant to PAF, is that both are ways of increasing tonal uncertainty relative to a listener’s internalized 12-TET model. The Mencke et al. findings therefore function as a structurally analogous empirical precedent for the frequency axis of PAF, that is, evidence that tonal-uncertainty manipulations measurably redistribute predictive precision in exactly the direction this model proposes, rather than as a direct test of microtonal detuning itself.
Microtonality does not produce chaos. It can be structured, coherent, and internally consistent; the ambiguity introduced is patterned, not random. This patterned ambiguity reduces the dominance of specific resolution trajectories: without a strongly implied tonal endpoint, expectation remains active but less anchored. In predictive terms, the system continues to generate forecasts, but the probability distribution broadens, and anticipation operates within a wider field of plausible continuations rather than converging on a single stable tonal attractor. This widening directly informs predictive density: where highly codified tonal structures compress expectation toward narrow outcomes, microtonal modulation diffuses that compression. The result is redistribution, not absence, of prediction.
3.4 Suspension of Tonal Resolution and Temporal Continuity
Tonal systems structure time through goal-directed movement: harmonic tension builds and resolves, cadential closure marks structural boundaries, and listeners anticipate these boundaries even without formal training.
Microtonal practice, particularly when detached from conventional harmonic progression, suspends this goal-directed structure. Without clear dominant to tonic relationships or standardized resolution patterns, time is organized less teleologically. This shift from directional progression toward sustained presence does not imply the absence of organization; rather, frequency relationships become less about moving toward closure and more about sustaining field continuity.
Sustained tonal ambiguity of this kind is not simply tolerated by listeners; there is at least a theoretical case, developed with supporting corpus analysis, that it can be a source of aesthetic engagement. Mencke, Omigie, Wald-Fuhrmann, and Brattico (2019), in a Hypothesis and Theory article rather than a controlled experiment, proposed that uncertainty in atonal music can generate pleasure precisely because it invites active, exploratory prediction rather than passive confirmation of a known model, supporting the proposal with a music-theoretical and music-information-retrieval analysis of a 100-segment corpus showing that atonal and tonal classical music differ quantitatively in key and pulse clarity. Mencke, Omigie, Quiroga-Martinez, and Brattico (2022) subsequently framed atonal listening as a model system for studying exploratory perceptual behavior under sustained uncertainty, again as a theoretical and prospective contribution rather than as a report of a listener behavior experiment. Taken together, these two papers make a reasoned theoretical case, not yet a directly documented empirical finding, that a listener oriented toward maintaining coherence within an evolving frequency field, instead of anticipating discrete harmonic events, is a plausible and actively argued mode of music perception.
3.5 Predictive Density in the Frequency Domain
Predictive density, as used throughout this study, refers to how concentrated or diffuse a listener’s precision-weighted expectations are across the space of plausible continuations at a given moment: high predictive density means precision is concentrated on a small number of expected outcomes, low predictive density means it is spread across many. In the frequency domain, this can now be specified concretely. In highly codified tonal environments, predictive density concentrates around resolution nodes: anticipation compresses toward expected harmonic endpoints. Microtonal modulation redistributes that density across a broader spectrum of intervallic possibilities; prediction remains active but less tightly constrained.
This redistribution is best understood through the precision-weighting mechanism at the center of contemporary predictive processing accounts of perception (Feldman & Friston, 2010; Lao-Rodríguez, Cacciato-Salcedo, & Malmierca, 2026), and it is precision weighting, specifically, that Quiroga-Martinez et al. (2019, described in Section 3.3) manipulated directly: increasing melodic entropy reduced the MMNm response to pitch deviants without affecting timbre or intensity deviants, showing that precision reduction under uncertainty is feature-specific rather than a general dampening of auditory processing. Precision weighting determines how much influence a given prediction error is allowed to exert on belief updating: high-precision errors drive strong updates, while low-precision errors are down-weighted in favor of existing priors. When tonal structure is highly codified, the auditory system can assign high precision to a narrow set of harmonic expectations. When that structure is loosened through microtonal deviation, precision is necessarily redistributed across a wider set of plausible outcomes. From an experiential standpoint, this redistribution corresponds to reduced urgency of harmonic resolution, increased tolerance for ambiguity, and stabilization within non-finalized tonal space.
The PAF does not require microtonality to generate instability; it requires modulation of precision relative to expectation. In some contexts, subtle detuning suffices; in others, more pronounced deviation is required. The determining factor is not the interval itself but its relationship to the listener’s prior model.
3.6 PAF and Intervallic Neutrality
The Perceptual Attenuation Field is not dependent on a specific tuning system. It does not require quarter-tone scales, just intonation, spectral tuning, or non-Western modal frameworks as intrinsic components. It requires only that frequency relationships participate in modulating predictive precision relative to an interiorized tonal structure.
For a listener conditioned within Western equal temperament, microtonal deviation expands predictive variance. For a listener conditioned within another tonal system, different forms of deviation play the same structural role, a point that follows directly from the cross-cultural constraint on predictive coding of music articulated by Savage and Fujii (2022). PAF is structurally relational, not intervallically prescriptive; its coherence lies in the modulation of expectation rather than adherence to specific pitch ratios.
3.7 Empirical Anchors and Their Limits
It is worth stating plainly what the frequency axis of PAF can and cannot claim at this stage. The precision-weighting framework (Friston, 2010; Feldman & Friston, 2010), the predictive-coding-of-music model (Koelsch et al., 2019; Vuust et al., 2022), its cross-cultural correction (Savage & Fujii, 2022), the direct precision-reduction findings of Quiroga-Martinez et al. (2019), and the atonal-uncertainty literature of Mencke and colleagues (2019, 2021, 2022, of which only the 2021 study is a controlled experiment; the 2019 and 2022 contributions are theoretical) together establish, with peer-reviewed support of varying empirical weight, that (a) tonal expectation is precision weighted, (b) increased tonal uncertainty measurably redistributes that precision from confident, veridical prediction toward broader, exploratory prediction, and (c) this redistribution is theoretically argued, and in part empirically shown, to be compatible with sustained aesthetic engagement rather than mere confusion. What has not been tested directly is the specific claim that structured microtonal detuning, as used in long-term immersive sound practice, produces the same redistribution to the same degree as atonality; the Bohlen-Pierce learning results of Loui et al. (2010) show that new microtonal systems can be learned quickly, but not that PAF-style detuning within a familiar system produces the same precision redistribution as full atonality. That is the open empirical question this section leaves for future collaboration.
3.8 Transition to Temporal and Spatial Axes
Frequency modulation alone does not constitute the Perceptual Attenuation Field; it represents one axis of a broader acoustic architecture. In isolation, microtonality alters predictive anchoring but does not by itself reorganize perceptual continuity.
It is through the integration of frequency modulation (microtonal ambiguity), temporal extension (delay and its related techniques, including modulation, pitch-shifting, and granular processing), and spatial diffusion (reverberant immersion) that the theoretical possibility of a coherent field emerges.
The following section examines the temporal axis: how delay structures modify the perception of gesture, causality, and anticipation. Only after each axis has been analyzed independently does the formal definition of the Perceptual Attenuation Field become structurally complete.