# Wolf interval

Under a wolf fifth is defined as a very strong " detuned " fifth, as it occurs in different historical tunings.

## Pythagorean wolf fifth

When using the Pythagorean the notes of the scale (scale) with the help of stacked perfect fifths are defined. Actually should be reached after 12 steps of the root. Actually, however, this tone is to the Pythagorean comma higher than the corresponding octave of the fundamental tone. To all keys to "play" and to be able to close the bottom row to the circle of fifths, the twelfth fifth is adjusted accordingly. The tone sequence then consists of 11 pure and reduced to a Pythagorean comma Quinte, which strongly contradicts the classical notion of euphony. You then said, "The fifth howls like a wolf! "

The Pythagorean wolf fifth is a Pythagorean comma lower than the perfect fifth.

Second statement: Since 11 fifths are larger by 1.955 per cent as the gleichstufige fifth with 700 cents, the 12 fifth is correspondingly smaller: (700 - 11.1, 955 ) = 678.459 cents cents.

Note: In order to better compare intervals in size, they are often on their size with the logarithmic unit cents. It is 1 octave = 1200 cents

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## Meantone wolf fifth

In the mean tone is an even less useful fifth, which is also called wolf fifth. It is, however, not a fifth, but a diminished sixth ( usually Gis - It ). This arises as a rest interval between 11 layered mean- fifths and the seventh octave of the fundamental.

Therefore, the mean- wolf fifth is calculated as the difference between 7 octaves and 11 mean- fifths. It is larger than a perfect fifth.

Second statement: Since 11 fifths to 3,422 per cent (or more precisely 3.42157 cents) are smaller than the gleichstufige fifth with 700 cents, the 12 fifth is correspondingly larger ( 700 11.3, 42157 ) cents ≈ 737.637 cents.

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## Perfect fifth

The perfect fifth, in comparison to the frequency ratio:

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The fifth in Gleichstufiger mood (700 cents) deviates from it only slightly.