history, Zarlino, 2/7-comma meantone (was: A question...)

hi Graham,

> From: "Graham Breed" <graham@microtonal.co.uk>
> To: <tuning@yahoogroups.com>
> Sent: Monday, March 10, 2003 4:39 AM
> Subject: [tuning] Re: A question and an update on personal tuning
endeavors
>
>
> wallyesterpaulrus wrote:
>
> > zarlino's 2/7-comma proposal was the first ever made with
> > mathematical precision. that's what we were arguing about, and it
> > happened in 1558. by 1571(?), another possibility was in the air --
> > 1/4-comma meantone -- and zarlino changed his preference to this.
> > there were no other alteratives yet defined at this time, except 1/3-
> > comma meantone by salinas. 1/5-comma and 1/6-comma came a bit later.
>
> 1/4-comma meantone must have been in the air at least by 1555, when
> Vicentino wrote his treatise. He describes just thirds, but doesn't
> specify how the fifths be tempered, and uses 31-equal enharmonies that
> wouldn't work so well in 2/7-comma. He says this is the usual way of
> tuning a keyboard. So wouldn't Zarlino have known about it?
>
> <snip>
>
> In this new translation of Zarlino we have
>
> http://sonic-arts.org/monzo/zarlino/1558/cap42-43.txt
>
> the second part, starting "Demonstration from which one can
> understand..." considers some alternative temperament. Can anybody make
> sense of it? He says two intervals are mistuned by half a comma, which
> could be the two whole tones of 1/4-comma meantone. But he also says
> the other intervals should be pure. So is he mishearing a description
> of 1/4-comma meantone, or is this Vicentino's second tuning of the
> archicembalo which requires two manuals to make sense? Or something else?

i was very intrigued by that passage too. it seems to
me that Zarlino is describing a tuning which preserves
all the JI pitches of the diatonic scale except for
the substitution of a "meantone" (it would be that of
1/4-comma) in place of the two JI "tones" of 10:9 and 9:8.

he states clearly that the comma is equally divided in
half, with half added to the one pitch and half taken
away from the other, and that all other intervals remain
the same as JI.

> In 1563, Vicentino moved to Vicenza, which seems to be near Venice.

Vicenza is about 70 km (~45 miles) west of Venice.

> That gave him plenty of time to convince Zarlino of the merits of
> 1/4-comma meantone by 1571.

i like your speculations! :)