interval
Let an agent handle musical intervals by name, size in semitones and cents, frequency ratio and tuning system.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent handle musical intervals by name, size in semitones and cents, frequency ratio and tuning system.
In music, the difference in pitch between two notes, named by the number of scale steps (second, third, fifth) and quality (major, minor, perfect), and expressed as a frequency ratio.
What it is for: Describing melody and harmony, tuning instruments and analysing music.
It can be name and identify it by ear or score; compute its size in semitones and cents; tune it, in a tuning system; use it, in composition and analysis.
Distinguishing features
Pitch difference between two notes
Named by number and quality
Size depends on tuning system
Harmonic (simultaneous) or melodic (successive)
What it looks like
Two notes on a staff at a distance, or two sounds heard together or in sequence.
Physical character
octave ratio: 2:1 frequency ratio - 1200 cents
equal-tempered semitone: 100 cents
How it is recognised
Distance between noteheads on a staff
Names such as perfect fifth, major third
Ratios such as 3:2 for a just fifth
Related models
is measured as - physical basis
relates to - pitch
is part of - musical structures
is confused with - a different sense
In practice
Families and kinds
perfect, major, minor, augmented, diminished intervals
consonant and dissonant intervals
just and Pythagorean intervals
compound intervals such as the eleventh
microtonal intervals
Standards and regulation
ISO 16 standard tuning A = 440 Hz
Failure modes and hazards
Mixing tuning systems when computing sizes
Enharmonic confusion (augmented fourth vs diminished fifth)
Also called
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.interval-communication
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Naming Number and quality.
Names encode function in tonal music.
Name
Interval name.
Name
Name of the interval.
- What is the interval name? definition
- Is an enharmonic spelling intended? boundary
Direction and type
Melodic or harmonic.
Type
Melodic or harmonic.
- Is it melodic or harmonic, ascending or descending? definition
- Is it simple or compound? definition
Size Semitones, cents, ratio.
Size depends on tuning.
Measure
Cents and semitones.
Size
Size values.
- How large is it in semitones and cents? measurement
- In which tuning system? definition
Ratio
Frequency ratio.
Ratio
Frequency ratio.
- What frequency ratio does it correspond to? measurement
- How far is equal temperament from just intonation here? measurement
Function Role in music.
Intervals build harmony and melody.
Consonance
Consonant or dissonant.
Consonance
Consonance status.
- Is it consonant or dissonant in this style? definition
- How is it resolved? definition
Context
Scale and chord.
Context
Role in context.
- What role does it play in this chord or scale? definition
- Which tradition defines that role? provenance
Tuning Getting it in tune.
Tuning decides how intervals sound.
System
Equal, just, other.
Tuning system
The tuning system.
- Which tuning system is used? definition
- What reference pitch? measurement
Practice
Tuning by ear or device.
Tuning practice
How it is tuned.
- How can this interval be tuned accurately? action
- What beat rate indicates tuning? measurement
What the second pass must settle
- Should each interval be a separate entry?
- How should tuning systems be linked?
- How should non-Western interval systems be represented?