Vicentino (Was: RMS tuning on Xenwiki

On 3 August 2010 21:42, genewardsmith <genewardsmith@sbcglobal.net> wrote:

> I think you need more than that to pin a 5-limit version of mohajira on him.

I found something in the archives from the first time this came up,
when I remembered more about it. Yahoo's search server's playing up
so I'll copy it here

On reviewing this, I think I should draw a distinction between the
enharmonic system and the tuning of the archicembalo. The former has a
minor diesis equal to half a chromatic semitone, and a major diesis equal
to a chromatic semitone less a minor diesis. In the latter, the minor
diesis is equal to the difference between a diatonic and chromatic
semitone, and the major diesis is equal to the chromatic semitone.
Vicentino starts off noting this difference, but doesn't always make it
strict in the notation. The reference to neutral thirds being consonant
is in the book on the archicembalo. The books on the diatonic, chromatic
and enharmonic genera only recognize strict 5-limit vertical harmony.

Also, although he does mention somewhere that the whole tone divides into
five roughly equal parts, in the examples of the enharmonic genus he only
divides it into four. So the system, but not always the notation, is
fully consistent with a quartertone scale. Hence 24&31. In Book I of
Music Practice, he's strict about this in the divisions of the whole tone
and examples of the different dieses, but not when he introduces some of
the derived intervals. It's here he says that the enharmonic dieses are
"identical" to the extended meantone intervals on the archicembalo, and
the one can stand in for the other for the sake of "compositional
convenience". In Book III of Music Practice, he spells one of the
enharmonic tetrachords such that the notation won't work in 24-equal, so
must be ignoring the distinctions he made in Book I.

Graham