Wolf interval

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A wolf interval or wolf is an interval that does not come across as just. Specifically, a wolf fifth in a 12-tone chromatic scale is the breaking point in the circle of fifths where it is technically a diminished sixth. By extension, the wolf interval has the following senses:

  1. An interval which is technically not what it appears to be on the keyboard. In meantone[12], there are four such major thirds – unless we expect septimal intepretations – in addition to the wolf fifth. This is an artifact in keyboard design and can be solved by adopting an isomorphic keyboard layout.
  2. An interval which impresses the listener as discordance, and/or sounds like an out-of-tune other interval, due to its sheer complexity and/or lack of proper harmonic context. For example, 40/27 is a wolf fifth that occurs in 5-limit just scales like zarlino. This is more often known as the impure or imperfect fifth. Historically, it gave rise to the use of meantone, which moderates its effect by distributing the syntonic comma among four fifths.