PART III: Formalization of the Perceptual Attenuation Field<\/p>\n
The previous sections examined frequency, time, and space as distinct axes of perceptual modulation. Each revealed a structural possibility: tonal anchoring softens, temporal linearity loosens, spatial localization diffuses.<\/p>\n
None of these axes alone constitutes the Perceptual Attenuation Field. Treated independently, microtonality remains an intervallic phenomenon, delay a temporal technique, reverberation an acoustic effect. The PAF does not emerge from isolated manipulation; it emerges from integration. The relevant question is not how each axis redistributes prediction within its own domain, but how their convergence reorganizes perceptual continuity as a whole: what happens when segmentation across all three domains decreases simultaneously.<\/p>\n
Perception is structured through segmentation: events are distinguished from background, moments are separated from one another, sources are localized within spatial coordinates. Section 2.3 already established the relevant account of why this matters here: Zacks, Speer, Swallow, Braver, and Reynolds (2007) treat an event boundary as the signature of a local prediction error, so that segmentation and prediction are two descriptions of the same underlying process rather than separate topics. Segmentation is not a flaw, since it is necessary for orientation, action, and environmental navigation, but it can also generate perceptual competition, since discrete events demand attention, sharp boundaries reinforce distinction, and localized sources anchor orientation.<\/p>\n
When frequency, time, and space converge toward continuity rather than fragmentation, the perceptual landscape shifts. Continuity does not mean uniformity; it means reduction of abrupt discontinuities. Within immersive microtonal environments shaped by temporal extension and spatial diffusion, segmentation softens across multiple dimensions at once: harmonic resolution no longer sharply demarcates tonal boundaries, temporal edges blur through overlapping delay structures, and spatial localization diffuses into environmental depth. When these softenings coincide, the perceptual field reorganizes from discrete-event dominance toward continuous-field coherence.<\/p>\n
The term attenuation requires precise clarification, because it is doing real theoretical work rather than serving as a loose metaphor, and because a single word is being asked to cover two changes in precision weighting that point in opposite directions. Both need to be named separately before the term can be used honestly.<\/p>\n
At the level of individual events, within each of the three axes described in Sections 3 through 5, attenuation names a reduction of precision under increased uncertainty. Microtonal ambiguity, overlapping delay, and diffuse reverberation each widen the range of plausible outcomes the auditory system must entertain, and the precision assigned to any single, sharply anchored prediction falls as a result; this is the sense documented directly by Quiroga-Martinez et al. (2019) and, with the caveats stated in Section 3.3, by Mencke et al. (2021). Here, low precision, not high precision, is what attenuates the dominance of a discrete event: the event stops commanding confident, narrow prediction because the model of it has become less certain.<\/p>\n
At the level of the field as a whole, a different and effectively opposite change is doing the work. A texture with stable, learnable statistical regularities, of the kind McDermott and Simoncelli (2011) describe, is not unpredictable; it is highly predictable at the level of its summary statistics, even though no individual grain or moment within it is predictable on its own. Once the auditory system has inferred those regularities, the field as a whole is precisely and confidently predicted, and further input consistent with it generates little prediction error. This is the sense in which the field-level claim is genuinely analogous to sensory attenuation as documented by Kiepe, Kraus, and Hesselmann (2021): in the classical self-generated-sound case, an accurate, high-precision forward model predicts the sensory consequences of one’s own action and that high-precision prediction suppresses the resulting error; in the field-level case proposed here, an accurate, high-precision statistical model of the ongoing texture would, by the same logic, suppress the error generated by input that continues to match it. High precision, not low precision, is what attenuates in this second sense.<\/p>\n
These two mechanisms are not the same, and treating them as a single, undifferentiated use of the word attenuation would misrepresent both the frequency-axis evidence and the sensory-attenuation literature. The event-level sense (Sections 3 to 5) is attenuation through increased uncertainty and reduced precision. The field-level sense, which is the one genuinely analogous to sensory attenuation, is attenuation through increased predictability and increased precision at a different, more global grain. PAF’s claim is that structured immersive listening can produce both in the same session, moving from event-level uncertainty toward field-level statistical predictability as the listener’s model of the whole configuration stabilizes; that two-stage claim, not a single undifferentiated mechanism, is what the rest of this section formalizes. It is also worth stating plainly that sensory attenuation itself is a less settled phenomenon than a first citation of it suggests: subsequent work, including from one of the same research groups, has shown conditions under which self-initiated stimuli are processed with enhanced rather than suppressed sensitivity, and isolating sensory attenuation cleanly from other predictive mechanisms remains an open methodological problem in that literature. The field-level analogy drawn here inherits that same uncertainty and should be read as a plausible extension of a genuine but still-debated effect, not as an extension of settled ground.<\/p>\n
Attenuation, in the sense used throughout the rest of this study unless otherwise specified, refers to the resulting reduction in the dominance of sharply bounded perceptual events within the overall experiential field, whichever of the two mechanisms above is doing the work at a given moment. In highly segmented environments, perceptual attention oscillates between discrete anchors; in a continuity-oriented environment, these anchors lose exclusivity. The field becomes primary; the event becomes secondary.<\/p>\n
When segmentation decreases across multiple axes simultaneously, continuity becomes the organizing principle. Continuity here is not temporal duration alone; it is multi-dimensional coherence: tonal continuity without forced resolution, temporal continuity without rigid linear progression, spatial continuity without strict localization boundaries.<\/p>\n
In such a configuration, perception operates less through tracking discrete events and more through maintaining global coherence. The listener is not deprived of structure. On the contrary, structure becomes pervasive and environmental rather than episodic. This shift does not imply loss of discrimination; it implies a reweighting of perceptual emphasis. Discrete events remain possible; they are simply embedded within a dominant field.<\/p>\n
A field, in this context, is an immersive perceptual configuration in which boundaries are softened, continuity is sustained, and discrete segmentation does not dominate attention. The field is not empty; it is internally dynamic, and microtonal variation, temporal layering, and spatial depth continue to operate within it. What changes is their relation to perceptual anchoring: the field becomes the primary experiential reference, and instead of moving from event to event, perception stabilizes within an evolving continuum. This stabilization is not forced; it emerges from structural coherence across frequency, time, and space.<\/p>\n
The Perceptual Attenuation Field (PAF) is defined as:<\/p>\n
A structurally integrated acoustic configuration in which frequency modulation, temporal extension, and spatial diffusion converge to reorganize perceptual continuity by attenuating the dominance of discrete segmentation, in the two senses distinguished in Section 6.3, while preserving the field’s own internal statistical structure.<\/p>\n
Each component of this definition is deliberate. \u201cStructurally integrated\u201d emphasizes convergence across axes rather than isolated technique. \u201cAcoustic configuration\u201d keeps the definition within the domain of sound design rather than clinical or interventionist language. \u201cReorganize perceptual continuity\u201d states the central mechanism at the experiential level. \u201cAttenuating the dominance of discrete segmentation\u201d specifies the two-mechanism sense of attenuation established in 6.3. The earlier phrase \u201cwithout reducing internal complexity\u201d has been replaced above because it was not precise enough to defend: dense reverberation and high-density granular processing measurably reduce the depth of temporal modulation available in a signal, so a literal reading of unreduced complexity would be false on acoustic grounds. What the model actually claims is narrower and defensible: the field retains statistical structure, learnable regularities at the level of its own summary statistics, rather than collapsing into unstructured noise, even as fine-grained, event-level detail is necessarily reduced by the same processes that build the field.<\/p>\n
This definition is only partly documented, and the honest place to say so is here, in the definition itself, rather than only in Section 7. Each axis individually rests on a documented empirical basis in adjacent literatures: precision-weighted prediction in general (Feldman & Friston, 2010; Parr, Pezzulo, & Friston, 2022), tonal-uncertainty redistribution for the frequency axis (Quiroga-Martinez et al., 2019; Mencke et al., 2021), source-environment separation and its limits for the spatial axis (Ivanov et al., 2022; Traer & McDermott, 2016), and the two-mechanism account of attenuation itself (Kiepe et al., 2021, for the field-level sense). What is not documented, by any of these sources individually or together, is the integration claim that actually defines PAF: that combining the three axes produces an effect different in kind, not just in degree, from what each axis produces alone. That claim is this model’s central untested hypothesis, not a conclusion the cited literature supports, and Section 7.4 states what testing it directly would require.<\/p>\n
The PAF does not depend on specific intervals, specific delay times, or specific reverberation technologies. It depends on relational modulation relative to a listener’s internalized predictive structure. Where segmentation is culturally reinforced through strong tonal hierarchy, rigid rhythmic teleology, and precise spatial localization, PAF-like configurations emerge through the integrated softening of these anchors. Where different predictive priors exist, as the cross-cultural correction to predictive-coding-of-music models makes explicit (Savage & Fujii, 2022), the relational threshold is expected to shift accordingly, though this specific cross-cultural prediction has not itself been tested.<\/p>\n
This relational framing must not be read as a claim that any outcome, in any direction, would be consistent with PAF; a model compatible with every possible result explains none of them, and stating the model’s actual falsification condition belongs here, not only in Section 7. The claim that integration matters, stated in Section 6.6, makes a specific directional prediction available: in a factorial design that independently manipulates the frequency, time, and space axes (present or absent, in a 2 by 2 by 2 arrangement) and measures a proxy for segmentation attenuation, such as event-boundary detection accuracy or MMN amplitude to a deviant embedded in the configuration, PAF predicts a superadditive interaction between the three axes, a combined effect larger than the sum of the three individual-axis effects. If the three axes instead produce only additive, independent effects with no interaction, the specific claim that they integrate into a field is falsified, even though each axis’s individual effect might still hold on its own. This is the model’s actual falsification condition, and it is deliberately stated here as a testable prediction rather than as a general appeal to falsifiability.<\/p>\n
PAF therefore remains structurally relational rather than technically prescriptive. Its coherence lies not in interval mathematics or signal processing, but in the organization of experiential continuity.<\/p>\n
If perceptual continuity becomes dominant over segmentation, three structural implications follow directly from the mechanisms already established in this section: event urgency decreases, as fewer high-precision endpoints compete for perceptual resources; narrative linearity softens, as segmentation-dependent structure is redistributed across the field; and environmental immersion intensifies, as the system’s precision weighting shifts toward global, field-level regularities.<\/p>\n
These are theoretical extrapolations from an interpretive framework built on converging, peer-reviewed evidence, not empirical claims about PAF as tested in its integrated form. The following section addresses the theoretical boundaries and conceptual risks of this model directly, which is necessary to prevent overextension and to preserve epistemic integrity as the model is applied phenomenologically.<\/p>\n","protected":false},"menu_order":6,"template":"","class_list":["post-59","paf_section","type-paf_section","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.lovefrequencies.org\/microtonalia.live\/wp-json\/wp\/v2\/paf_section\/59","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.lovefrequencies.org\/microtonalia.live\/wp-json\/wp\/v2\/paf_section"}],"about":[{"href":"https:\/\/www.lovefrequencies.org\/microtonalia.live\/wp-json\/wp\/v2\/types\/paf_section"}],"wp:attachment":[{"href":"https:\/\/www.lovefrequencies.org\/microtonalia.live\/wp-json\/wp\/v2\/media?parent=59"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}