Wolf interval
particularly dissonant musical interval spanning seven semitones present in most meantone tuning systems
A wolf interval is audibly out of tune within a particular musical tuning system. A common example is the abnormally small fifth that results from the Pythagorean comma.
Definition
Particularly out of tune intervals produce an unpleasant effect that remind listeners of a wolf's howl. Wolf fifths are produced by a specific tuning system, widely used in the sixteenth and seventeenth centuries: the quarter-comma meantone temperament. More broadly, it is also used to refer to similar intervals (of close, but variable magnitudes) produced by other tuning systems, including Pythagorean and most meantone temperaments. Wolf fifths were sometimes labeled imperfect or Procrustean.
When the twelve notes within the octave of a chromatic scale are tuned using the quarter-comma meantone systems of temperament, one of the twelve intervals apparently spanning seven semitones is actually a diminished sixth, which turns out to be much wider than the in-tune genuine fifths,
In mean-tone systems, this interval is usually from C♯ to A♭ or from G♯ to E♭ but can be moved in either direction to favor certain groups of keys.
The eleven perfect fifths sound almost perfectly consonant. Conversely, the diminished sixth used as a substitute is severely dissonant: It sounds like the howl of a wolf, because of a phenomenon called beating. Since the diminished sixth is nominally enharmonically equivalent to a perfect fifth, but in meantone temperament, enharmonic notes are only nearby (within about 1/4 sharp or 1/4 flat); the discordance of substituted interval is called the "wolf fifth".
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This entry incorporates text from “Wolf interval” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.