Technical Library TEMPERAMENTS III: Grammateus Entire Contents Copyright ©2005 CBH

By splitting the wolf into two or more parts, we can reduce its severity.

Henricus Grammateus proposed just such a temperament in 1518, with all the fifths perfect except those from B♭ to F, and B to F♯. The trick is in determining just how much half a comma is, but it is quite possible to tune it using an “equal-beating” method. Here is how:

1. Tune a chain of six perfect fifths on the sharp side from C, around through to B.

2. Tune your f a perfect fifth below middle c': This completes the naturals.

3. Temporarily tune your f♯' a perfect fifth above b, and then tune down the octave from both these notes to f♯ and B. (We are working in the octave below middle c', because you will find it easier to hear the beats.) We must now flatten the f♯ so that the fifth it makes with B is narrow by exactly half a comma. Lower your f♯ until it beats at the same speed with b above it, as d below it. Check your “half-wolf” (werewolf?) fifth B–f♯—is it ok?

4. Continue tuning absolutely perfect fifths from F♯ to A♯. If you’ve been particularly successful, your b–f♯' fifth will beat ever so slightly faster than a♯–f, because it is just a semitone higher.

The thirds are usable, especially when you get into the sharp keys, and the two baby wolves not impossible. Many players use this temperament for the Fitzwilliam Virginal Book.

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