Mersenne’s laws of vibrating strings
E609411
Mersenne’s laws of vibrating strings are early 17th-century mathematical relations that quantify how a string’s frequency depends on its length, tension, and mass per unit length, forming a foundation of musical acoustics and wave theory.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Mersenne’s laws of vibrating strings canonical | 1 |
| Mersenne’s laws relating frequency, length, and tension of a string | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6642033 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Mersenne’s laws of vibrating strings Context triple: [Marin Mersenne, knownFor, Mersenne’s laws of vibrating strings]
-
A.
The Theory of Sound
The Theory of Sound is Lord Rayleigh’s landmark two-volume treatise that systematically established the mathematical and experimental foundations of acoustics.
-
B.
The Dynamical Theory of Sound
The Dynamical Theory of Sound is a foundational treatise by mathematician and physicist Horace Lamb that rigorously develops the mathematical principles underlying acoustics and wave propagation.
-
C.
The Science of Musical Sound
The Science of Musical Sound is a book by engineer and acoustics researcher John R. Pierce that explains the physical and perceptual principles underlying how music and sound are produced, transmitted, and heard.
-
D.
The Physics of Music
The Physics of Music is a foundational text that explains how physical principles such as vibration, resonance, and wave behavior give rise to musical sounds and acoustical phenomena.
-
E.
Pythagorean harmony of the spheres
The Pythagorean harmony of the spheres is an ancient philosophical and cosmological concept proposing that the movements of celestial bodies produce a hidden, mathematically ordered music reflecting the harmony of the universe.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Mersenne’s laws of vibrating strings Target entity description: Mersenne’s laws of vibrating strings are early 17th-century mathematical relations that quantify how a string’s frequency depends on its length, tension, and mass per unit length, forming a foundation of musical acoustics and wave theory.
-
A.
The Theory of Sound
The Theory of Sound is Lord Rayleigh’s landmark two-volume treatise that systematically established the mathematical and experimental foundations of acoustics.
-
B.
The Dynamical Theory of Sound
The Dynamical Theory of Sound is a foundational treatise by mathematician and physicist Horace Lamb that rigorously develops the mathematical principles underlying acoustics and wave propagation.
-
C.
The Science of Musical Sound
The Science of Musical Sound is a book by engineer and acoustics researcher John R. Pierce that explains the physical and perceptual principles underlying how music and sound are produced, transmitted, and heard.
-
D.
The Physics of Music
The Physics of Music is a foundational text that explains how physical principles such as vibration, resonance, and wave behavior give rise to musical sounds and acoustical phenomena.
-
E.
Pythagorean harmony of the spheres
The Pythagorean harmony of the spheres is an ancient philosophical and cosmological concept proposing that the movements of celestial bodies produce a hidden, mathematically ordered music reflecting the harmony of the universe.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
acoustics law
ⓘ
physical law ⓘ wave theory principle ⓘ |
| appliesTo | ideal stretched string ⓘ |
| appliesToInstrument |
guitar
ⓘ
harp ⓘ piano ⓘ violin ⓘ |
| assumes |
constant tension
ⓘ
perfect flexibility of the string ⓘ small amplitude vibrations ⓘ uniform linear mass density ⓘ |
| category |
classical mechanics
ⓘ
theoretical acoustics ⓘ |
| combinedFormula | f = (1 / 2L) · √(T / μ) ⓘ |
| describedIn | Harmonie universelle NERFINISHED ⓘ |
| field |
mechanics
ⓘ
musical acoustics ⓘ physics ⓘ vibrations ⓘ |
| formulatedInCentury | 17th century ⓘ |
| formulatedInDecade | 1630s ⓘ |
| foundationFor | theory of musical pitch for string instruments ⓘ |
| historicalSignificance |
early quantitative link between music and mathematics
ⓘ
precursor to modern string vibration theory ⓘ |
| implies | wave speed on a string equals √(T / μ) ⓘ |
| influenced |
development of wave equation
ⓘ
later work in mathematical physics of vibrations ⓘ |
| involvesQuantity |
fundamental frequency
ⓘ
harmonics ⓘ wave speed on a string ⓘ |
| mathematicalForm |
f ∝ 1 / L
ⓘ
f ∝ 1 / √μ ⓘ f ∝ √T ⓘ |
| namedAfter | Marin Mersenne NERFINISHED ⓘ |
| publicationYear | 1636 ⓘ |
| relatesQuantity |
frequency of vibration
ⓘ
mass per unit length ⓘ string length ⓘ string tension ⓘ |
| states |
frequency is inversely proportional to string length
ⓘ
frequency is inversely proportional to the square root of mass per unit length ⓘ frequency is proportional to the square root of tension ⓘ |
| usedIn |
design of stringed musical instruments
ⓘ
tuning of stringed instruments ⓘ |
| validUnderCondition |
fixed boundary conditions at both ends
ⓘ
linear elastic behavior of the string ⓘ negligible stiffness of the string ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Mersenne’s laws of vibrating strings Description of subject: Mersenne’s laws of vibrating strings are early 17th-century mathematical relations that quantify how a string’s frequency depends on its length, tension, and mass per unit length, forming a foundation of musical acoustics and wave theory.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Mersenne’s laws relating frequency, length, and tension of a string