Harmonic ratio
A simple whole-number ratio between two frequencies, like 2:1 or 3:2.
At a glance
Key signals
0% cross fields · reaches 5 more
- Mathematics
- Physics
- Music
- Explanation
- Examples
- Misconception
- Sourced relations 3
- Attribution
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
A harmonic ratio compares two frequencies.
Mechanism: The ratio is simply one frequency divided by another.
Enables · leads to
Consonancedepends onHarmonic ratioContestedInterpretation
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
dissonance emerges from harmonic ratio.
Mechanism: Dissonance arises when tones stand in complex, non-simple frequency ratios.
- Wikipedia (English & German editions) verifiedmoderate evidence
Just intonationis derived fromHarmonic ratioEstablished
just intonation is derived from harmonic ratio.
Mechanism: Its intervals are taken directly from small whole-number ratios.
- Wikipedia (English & German editions) verifiedmoderate evidence
Musical intervalis derived fromHarmonic ratioEstablished
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.
- Wikipedia (English & German editions) verifiedmoderate evidence
Tuning systemis derived fromHarmonic ratioEstablished
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
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
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.
cross-field
8 within-field, 0 cross-field
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.
What builds on this
1 concept build on this directly, 1 in total, across 3 disciplines.
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.
Through this lens it connects to Frequency, Ratio, Tuning system and Consonance.
Through this lens it connects to Frequency, Tuning system, Consonance and Musical interval.
Where you'll meet it
Journeys that walk you through this idea. You may recognise it from more than one.
Related ideas to explore
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
Concepts
shares a mental model
shares a mental model
shares a mental model
shares a mental model
shares a mental model
shares a mental model
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
- 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.