Wolf interval

In music, a wolf interval is an interval between two notes of a scale which is so far from its ideal ratio that it can not be used. The name comes from the unpleasant sound of such an interval, which seems to "howl".

If the notes are tuned so that some intervals are equal to or very close to their ideal ratios, at least one interval will be far from its ideal ratio and so be a wolf interval.

In modern Western music the notes of the scale notes are tuned as that all tones are equal and all semitones are half a tone. This makes all intervals slightly out of tune, but usable. There are no wolf intervals.

In Pythagorean tuning, the interval G#-Eb is such an interval, known as the wolf fifth. It is only 678.49 cents wide, nearly an eighth of a tone (a quarter of one semitone) flatter than the other fifths of 701.96 cents wide.

Wolf_fifth.ogg (33.1KB) is a sound file demonstrating this out of tune fifth. The first two fifths are perfectly tuned in the ratio 3:2, the third is the G#-Eb wolf fifth. It may be useful to compare this to Et_fifths.ogg (38.2KB), which is the same three fifths tuned in equal temperament, each of them tolerably well in tune.

If the notes G# and Eb need to be sounded together, the position of the wolf fifth can be changed. However, there will always be one wolf fifth in Pythagorean tuning, making it impossible to play in all keys in tune.