Subminor and supermajor¶
Microtonal interval categories lying respectively between diminished and minor and between major and augmented intervals under a stated tuning system.
Core Idea¶
The labels often refer to specific just-intonation ratios but can be used more broadly; interval number, direction, tuning, cents and enharmonic spelling determine the identity. Frequency ratios or pitch distances place an interval between adjacent conventional quality classes, while inversion exchanges corresponding subminor and supermajor forms. 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.
The load-bearing residual is not the broad topic of music theory. It is the domain-specific identity determined by the tuning and reference pitch, interval number and direction, frequency ratio or cents, diminished, minor, major and augmented boundaries, naming convention and inversion relation are explicit.
Scope of Application¶
Subminor and supermajor belongs to music theory and is useful where the analyst can specify the typed music theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the tuning and reference pitch, interval number and direction, frequency ratio or cents, diminished, minor, major and augmented boundaries, naming convention and inversion relation are explicit. The scope is broad within that domain but bounded by the need for the tuning and reference pitch, interval number and direction, frequency ratio or cents, diminished, minor, major and augmented boundaries, naming convention and inversion relation 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 reference pitch, interval number and direction, frequency ratio or cents, diminished, minor, major and augmented boundaries, naming convention and inversion relation 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 Subminor and supermajor 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 Subminor and supermajor. Subminor and supermajor 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 theory 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 reference pitch, interval number and direction, frequency ratio or cents, diminished, minor, major and augmented boundaries, naming convention and inversion relation are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of music theory because they reuse the typed music theory carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Frequency ratios or pitch distances place an interval between adjacent conventional quality classes, while inversion exchanges corresponding subminor and supermajor forms., and type the carrier, state every parameter and convention in the definition, test that the tuning and reference pitch, interval number and direction, frequency ratio or cents, diminished, minor, major and augmented boundaries, naming convention and inversion relation are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Subminor and supermajor Domain-specific
Parents (1) — more general patterns this builds on
-
Subminor and supermajor is a kind of Classification Prime
The proposed strict upward parent is
prime:classification.
Hierarchy path (1) — routes to 1 parentless root
- Subminor and supermajor → Classification
Neighborhood in Abstraction Space¶
Subminor and supermajor sits in a crowded region of the domain-specific corpus (3rd 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
- Pitch class — 0.95
- Cell (music) — 0.94
- Chord progression — 0.94
- Bridge chord — 0.94
- Rule of the octave — 0.93
Computed from structural-signature embeddings · 2026-09-08