Lipps–Meyer law¶

A historical music-perception hypothesis that a melodic interval sounds more final when its terminal tone occupies a power-of-two relation in the interval’s frequency ratio.

Version: v1 · 2026-09-08 · History
Domain-specific #: 5361
Origin domain: music psychology
Subdomain: music psychology

Core Idea¶

The proposed law links octave-equivalence arithmetic to closure judgments, but terminology, tuning, direction, context and empirical support must be stated because later evidence and theories of tonal expectation are broader. Listeners internalize octave-related tonal hierarchies, and an interval ending on the ratio’s power-of-two component is predicted to produce stronger perceptual closure. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application¶

Lipps–Meyer law belongs to music psychology and is useful where the analyst can specify the typed music psychology carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the tuning and frequency ratio, interval direction, terminal tone and power-of-two criterion, melodic context, listener population, finality measure, control intervals and empirical support are explicit. The scope is broad within that domain but bounded by the need for the tuning and frequency ratio, interval direction, terminal tone and power-of-two criterion, melodic context, listener population, finality measure, control intervals and empirical support are explicit. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity¶

The abstraction clarifies a crowded vocabulary by making the tuning and frequency ratio, interval direction, terminal tone and power-of-two criterion, melodic context, listener population, finality measure, control intervals and empirical support are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Lipps–Meyer law can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity¶

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Lipps–Meyer law. Lipps–Meyer law compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning¶

Identify the carrier. State what the elements, states, objects, or observations are: the typed music psychology carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the tuning and frequency ratio, interval direction, terminal tone and power-of-two criterion, melodic context, listener population, finality measure, control intervals and empirical support are explicit independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of music psychology because they reuse the typed music psychology carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Listeners internalize octave-related tonal hierarchies, and an interval ending on the ratio’s power-of-two component is predicted to produce stronger perceptual closure., and type the carrier, state every parameter and convention in the definition, test that the tuning and frequency ratio, interval direction, terminal tone and power-of-two criterion, melodic context, listener population, finality measure, control intervals and empirical support are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Lipps–Meyer law Domain-specific

Parents (1) — more general patterns this builds on

Lipps–Meyer law is a kind of Tension And Release Prime

The proposed strict upward parent is prime:tension_and_release.

Hierarchy path (1) — routes to 1 parentless root

Lipps–Meyer law → Tension And Release

Neighborhood in Abstraction Space¶

Lipps–Meyer law sits in a crowded region of the domain-specific corpus (23^rd percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Harmony, Tuning & Musical Form (24 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08