Pythagorean tuning
E375058
Pythagorean tuning is a musical tuning system based on pure perfect fifths derived from simple whole-number ratios, historically linked to the mathematical and philosophical ideas of the Pythagoreans.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Pythagorean tuning canonical | 3 |
| Pythagorean intervals | 1 |
| Pythagorean intonation | 1 |
| Pythagorean scale | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3642133 — 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: Pythagorean tuning Context triple: [Pythagoreanism, associatedWith, Pythagorean tuning]
-
A.
Equal temperament
Equal temperament is a musical tuning system that divides the octave into equal steps, allowing instruments like the piano to play in all keys with consistent intonation.
-
B.
Harmonics
Harmonics is an influential ancient treatise by Claudius Ptolemy that explores the mathematical and philosophical foundations of musical theory.
-
C.
Byzantine neumatic notation
Byzantine neumatic notation is a medieval musical notation system used to record the melodies and modal nuances of Byzantine liturgical chant.
-
D.
Die Lehre von den Tonempfindungen
Die Lehre von den Tonempfindungen is Hermann von Helmholtz’s foundational 19th-century treatise on the physiological and psychological basis of musical tone and acoustics.
-
E.
Phrygian
Phrygian was an ancient Indo-European language once spoken in central Anatolia, known primarily from inscriptions and associated with the Phrygian kingdom.
- 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: Pythagorean tuning Target entity description: Pythagorean tuning is a musical tuning system based on pure perfect fifths derived from simple whole-number ratios, historically linked to the mathematical and philosophical ideas of the Pythagoreans.
-
A.
Equal temperament
Equal temperament is a musical tuning system that divides the octave into equal steps, allowing instruments like the piano to play in all keys with consistent intonation.
-
B.
Harmonics
Harmonics is an influential ancient treatise by Claudius Ptolemy that explores the mathematical and philosophical foundations of musical theory.
-
C.
Byzantine neumatic notation
Byzantine neumatic notation is a medieval musical notation system used to record the melodies and modal nuances of Byzantine liturgical chant.
-
D.
Die Lehre von den Tonempfindungen
Die Lehre von den Tonempfindungen is Hermann von Helmholtz’s foundational 19th-century treatise on the physiological and psychological basis of musical tone and acoustics.
-
E.
Phrygian
Phrygian was an ancient Indo-European language once spoken in central Anatolia, known primarily from inscriptions and associated with the Phrygian kingdom.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
just intonation-based tuning
ⓘ
musical tuning system ⓘ |
| appliesTo |
chromatic scale
ⓘ
diatonic scale ⓘ |
| basedOn | pure perfect fifths ⓘ |
| constructsScaleBy | cycle of fifths ⓘ |
| contrastedWith |
5-limit just intonation
ⓘ
equal temperament ⓘ meantone temperament ⓘ |
| deemphasizesConsonanceOf |
major third
ⓘ
minor third ⓘ |
| developedIn |
Greek Antiquity
ⓘ
surface form:
ancient Greece
|
| dominantInPeriod |
Middle Ages
ⓘ
Early Renaissance ⓘ
surface form:
early Renaissance
|
| emphasizesConsonanceOf |
perfect fifth
ⓘ
perfect fourth ⓘ |
| hasAlternativeName |
3-limit tuning
ⓘ
Pythagorean tuning ⓘ
surface form:
Pythagorean intonation
|
| hasCharacteristicInterval |
Pythagorean comma
ⓘ
Pythagorean major third ⓘ Pythagorean minor third ⓘ apotome ⓘ limma ⓘ |
| hasMathematicalBasis | whole-number ratios ⓘ |
| hasPhilosophicalBasis | harmony of the spheres ⓘ |
| hasPrimeLimit | 3-limit ⓘ |
| hasProblem | Pythagorean comma accumulation ⓘ |
| historicallyLinkedTo |
Pythagoras
ⓘ
Pythagoreanism ⓘ |
| influenced |
Boethian music theory
ⓘ
medieval music theory ⓘ |
| relatedConcept |
Pythagorean tuning
self-linksurface differs
ⓘ
surface form:
Pythagorean intervals
Pythagorean tuning self-linksurface differs ⓘ
surface form:
Pythagorean scale
|
| resultsIn |
narrow minor thirds
ⓘ
wide major thirds ⓘ wolf fifth ⓘ |
| usedFor |
Burgundian School of music
ⓘ
surface form:
Renaissance music
medieval European music ⓘ |
| usedIn |
Gregorian chant intonation (historically)
ⓘ
early polyphonic music ⓘ |
| usesIntervalRatio |
2187:2048
ⓘ
256:243 ⓘ 2:1 ⓘ 3:2 ⓘ 4:3 ⓘ 9:8 ⓘ |
| usesPrimeFactors |
2
ⓘ
3 ⓘ |
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: Pythagorean tuning Description of subject: Pythagorean tuning is a musical tuning system based on pure perfect fifths derived from simple whole-number ratios, historically linked to the mathematical and philosophical ideas of the Pythagoreans.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Pythagorean intervals
this entity surface form:
Pythagorean scale
this entity surface form:
Pythagorean intonation