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In graph Frontier

Harmonic ratio

A simple whole-number ratio between two frequencies, like 2:1 or 3:2.

At a glance

Type
Mental models 1
Role in the graph
Cross-disciplinary bridge
reaches 5 discipline lenses

Key signals

Cross-disciplinary reach
Disciplines
3
  • Mathematics
  • Physics
  • Music
Evidence & development

Dependencies

What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.

Foundations · builds on

Harmonic ratiois derived fromFrequencyEstablished

Open Frequency →

A harmonic ratio compares two frequencies.

Mechanism: The ratio is simply one frequency divided by another.

Enables · leads to

Consonancedepends onHarmonic ratioContestedInterpretation

Open Consonance →

Consonance is linked to simple harmonic ratios.

Mechanism: Simple ratios make the two waves line up often, which many listeners hear as stable — though what sounds 'pleasant' is also cultural.

Confidence: The physics link is real, but consonance judgements also depend strongly on culture and exposure.

Dissonanceemerges fromHarmonic ratioEstablished

Open Dissonance →

dissonance emerges from harmonic ratio.

Mechanism: Dissonance arises when tones stand in complex, non-simple frequency ratios.

Sources:
Just intonationis derived fromHarmonic ratioEstablished

Open Just intonation →

just intonation is derived from harmonic ratio.

Mechanism: Its intervals are taken directly from small whole-number ratios.

Sources:
Musical intervalis derived fromHarmonic ratioEstablished

Open Musical interval →

musical interval is derived from harmonic ratio.

Mechanism: An interval is heard as the frequency ratio between two tones, e.g. 3:2 for a perfect fifth.

Sources:
Tuning systemis derived fromHarmonic ratioEstablished

Open Tuning system →

Tuning systems are built from harmonic ratios.

Mechanism: A tuning system decides which ratios to keep exact and which to approximate.

System context

Harmonic ratiois aRatioEstablished

Open Ratio →

A harmonic ratio is a simple whole-number ratio.

Mechanism: Notes an octave apart vibrate in a 2:1 ratio and a fifth in 3:2; the pleasing intervals of music are ratios of frequencies — mathematics you can hear.

Octaveis aHarmonic ratioEstablished

Open Octave →

An octave is a 2:1 harmonic ratio.

Mechanism: The higher note vibrates exactly twice as fast as the lower one.

Structural role & consequence

Interpreted from the current atlas graph — what the connections mean, not just how many there are.

  • Currently dark in the atlas: no verified source · no key date stored · 8 of 8 of its relations lack claim-level evidence.

    atlas representation · Describes the current Thinking OS representation, not the state of the world.

  • Builds on 1 foundation (requires / depends-on / derived-from / emerges-from).

    structural · Structural graph analysis — not a claim of importance, causation or history.

  • Structural neighbourhood: 8 → 32 → 90 concepts reachable within 3 hops.

    structural · Structural reach — being reachable is not the same as being understood.

  • All 8 of its relationships stay within its own discipline — a field-specific concept in the current atlas.

    structural · Structural graph analysis — not a claim of importance, causation or history.

0%

cross-field
8 within-field, 0 cross-field

0 of 8 relations carry evidence · concept unsourced

Strengths & constraints

Constraints

  • Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
  • No dated history stored — the atlas records no key date for this concept. atlas representation

Conditions

  • Its dependency reading rests on 1 foundation relation. structural
  • Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural

Dependency radial

What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.

FrequencyConsonanceDissonanceJust intonationMusical intervalTuning systemHarmonic ratio◀ builds onenables ▶

What builds on this

1 concept build on this directly, 1 in total, across 3 disciplines.

Cognitive ScienceMathematicsMusic

Structural downstream reach along dependency edges — not a claim of historical necessity.

Seen through each discipline

How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.

Where you'll meet it

Journeys that walk you through this idea. You may recognise it from more than one.

Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.

This idea also appears in…

The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”

Networks49 disciplines · 38 concepts
Environmental Science
Discrete Mathematics
Educational Science
Network Science
Urban Planning
Agriculture
Anthropology
Biophysics
Business
Design
Earth & Space Sciences
Electrical Engineering
Environmental Engineering
Epidemiology
Evolutionary Biology
Forestry
Geography
Linear Algebra
Linguistics
Literature
Logistics
Management
Organic Chemistry
Philosophy
Political Economy
Political Science
Polymer Chemistry
Statistical Physics
Supply Chain Management
Sustainability Science
Systems Biology
Veterinary Medicine
See the pattern →

Concepts

  • Supply chainEconomicsManagementEngineering

    shares a mental model

  • AnalogyCognitive ScienceLinguisticsPhilosophy

    shares a mental model

  • DiffusionChemistrySociologyStatistical Physics

    shares a mental model

  • NetworkNetwork ScienceSociologyDiscrete Mathematics

    shares a mental model

  • PatternCognitive ScienceBiologyDesign

    shares a mental model

  • Food webEcologyBiologySystems Biology

    shares a mental model

Explained by stage
lower secondary

When two notes' frequencies form a simple ratio (like 2:1), their waves line up often. Music theory is full of these ratios — they are mathematics you can hear.

Mental models at work here

The scientific picture
  • Connects 8 other ideas across 3 disciplines.
  • A cross-disciplinary bridge — its connections reach into 5 other fields.
  • Most of its connections are of the “Dependency” kind.
  • It exercises 1 reusable thinking pattern.
  • It features in 1 learning journey.

Derived from the graph’s real structure — observations, not a score.

Sources

No primary source is attached to this concept yet. In a real deployment this would be required before publication.