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Research draft

interval

vr.tr.interval · XCT.TME

Let an agent handle musical intervals by name, size in semitones and cents, frequency ratio and tuning system.

Thing Registry Cross-cutting context

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

frequency ratio

relates to - pitch

frequency

is part of - musical structures

scale and chord

is confused with - a different sense

time interval

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

consonanceSupermajor intervalharmonic intervalPythagorean intervalIncomposite intervaleleventhtwelfththirteenthfourteenthfifteenthninthpure intervaloctavemicrotoneoctave designationtritoneneutral intervaltenthneutral seventhaugmented octavediminished octavepseudo-octaveLimma

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.

  1. What is the interval name? definition
  2. Is an enharmonic spelling intended? boundary

Direction and type

Melodic or harmonic.

Type

Melodic or harmonic.

  1. Is it melodic or harmonic, ascending or descending? definition
  2. Is it simple or compound? definition
Size Semitones, cents, ratio.

Size depends on tuning.

Measure

Cents and semitones.

Size

Size values.

  1. How large is it in semitones and cents? measurement
  2. In which tuning system? definition

Ratio

Frequency ratio.

Ratio

Frequency ratio.

  1. What frequency ratio does it correspond to? measurement
  2. 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.

  1. Is it consonant or dissonant in this style? definition
  2. How is it resolved? definition

Context

Scale and chord.

Context

Role in context.

  1. What role does it play in this chord or scale? definition
  2. 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.

  1. Which tuning system is used? definition
  2. What reference pitch? measurement

Practice

Tuning by ear or device.

Tuning practice

How it is tuned.

  1. How can this interval be tuned accurately? action
  2. 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?