An "unusual" [musical] interval in a given tuning system and style which is felt not to be freely substitutable for an "expected" variety of the same interval.
Sometimes it is asserted that "Wolf" intervals are "unusable" or "unplayable," but this judgment is both contextual and often partial: there are often specific sonorities and usages where these intervals are musically useful even in styles where they are generally considered to be "too out-of-tune" for most purposes.
Wolf intervals are a charactistic feature of most tunings belonging to the meantone family of temperaments; in particular, there is a "wolf 5th" which occurs at the interval which connects the last and first notes in the meantone chain-of-5ths; this is illustrated below.
Meantone tunings most typically have 12 notes, and the most typical set of notes in a meantone chain is:
So the wolf occurs between G#:Eb.
The exact size of the wolf depends on the amount of tempering used to narrow the meantone generator "5th", the size of the wolf widening in direct proportion to the amount of tempering. Here are some examples which are historically and/or theoretically important (along with their ET approximations):
meantone ~cents difference logarithmic ratio tempering ~cents of wolf ~cents of generator wolf - generator wolf:generator ~= EDO - 1/3-comma 757.3513857 694.7862377 62.565148 1.090049492 19-ET - 2/7-comma 746.0861864 695.8103467 50.27583966 1.072255091 50-ET - 5/18-comma 744.2086531 695.9810315 48.2276216 1.069294448 50-ET - 7/26-comma 742.1866943 696.164846 46.02184831 1.066107688 50-ET - 1/4-comma 737.6372869 696.5784285 41.05885841 1.058943626 31-ET - 2/9-comma 731.0659206 697.1758254 33.89009521 1.048610543 105-ET - 3/14-comma 729.1883874 697.3465102 31.84187715 1.045661485 74-ET - 1/5-comma 725.8088276 697.6537429 28.15508465 1.040356817 43-ET - 1/6-comma 717.9231881 698.3706193 19.55256881 1.02799741 55-ET - 1/11-comma 700.0012801 699.9998836 0.001396448 1.000001995 12-ET
Note that the wolf-"5th" disappears in 12-edo tuning, which is essentially the same as 1/11-comma meantone.
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