Musical tuning

Musical tuning is the choice and arrangement of pitches used to tune instruments or define a musical system. It determines how intervals and keys relate, and whether instruments can play together across different tonal centers.

Equal temperament: A tuning system that divides an octave into equal logarithmic pitch steps. Its equal semitones make transposition practical while leaving most intervals slightly impure.
Musical interval: The perceived distance between two musical pitches. A tuning system specifies the sizes of intervals between its pitches.
Pythagoras: An ancient Greek philosopher traditionally associated with discoveries about numerical ratios in musical consonance. Pythagorean tuning takes its name from the tradition linking musical intervals to simple ratios.
Piano tuning: The adjustment of a piano's strings to establish pitch relationships across its keyboard. Piano tuning uses stretched octaves to accommodate the instrument's inharmonic strings.
Twelve-tone equal temperament: The system that divides an octave into twelve equal semitones. It is the dominant fixed-pitch tuning in much modern Western music.
Just intonation: A tuning system built from simple whole-number frequency ratios. It produces pure intervals in selected tonal contexts, unlike fixed equal temperament.
Frequency ratio: The quotient of two frequencies, often used to express the physical size of a musical interval. Simple ratios can produce consonant intervals in just intonation.
Aristoxenus: A fourth-century BCE Greek music theorist who analyzed musical intervals through hearing and melodic context. His approach contrasts with tuning theories that derive pitch chiefly from numerical ratios.
Guitar tuning: The assignment of pitches to a guitar's open strings. String layout and fretting create practical compromises between open-string harmony and intonation.
Arabic maqam: A modal system organizing melodic practice in Arabic music through characteristic scales, motifs, and pathways. Maqam practice can use flexible intonation and pitch distinctions not captured by a single fixed tuning.

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