Wolf interval

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A wolf interval is an out-of-tune interval in just tempred tuning.

Just tempered tuning uses rational numbers (integer multiplication and division) to compute the frequency of one note from the frequency of another. It has the benefit that notes sound good together as they are harmonics of each other. The problem with just tempered tuning is that no nice integer multiples can split evenly the octave into twelve equal semitones to compute the chromatic scale. The smaller the integer multiplications (and divisions) are, and thus the closer harmonics the notes are, the more unevenly just tempered tuning splits the octave in twelve semitones. In some cases of just tempered tuning some intervals between notes are greatly out of tune. Such intervals are called wolf intervals. An example of a wolf interval is shown in the topic on Pythagorean tempered scale.

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