Vicentino's second tuning

The Scala archive doesn't have Vicentino's second tuning, at least as
that is described on the Tonalsoft webpage, so I'm posting it below.
It consists of a chain of 1/4-comma meantone fifths from Gb to B#,
where there is another note 1/4 comma above all the notes from Gb to A#.

The Scala archives do have a 217-edo version. 217 maps 5 to 504 steps,
and hence has a version of 5^(1/4) at 126 steps; however 217 is 7*31,
and this 1/4-comma fifth is actually a 31-et fifth. Much closer to
Vicentino's specifications would be to use 441-et, which maps 5 to
1024 steps, and hence has a version of 5^(1/4) at 256 steps. I also
give a 441-edo version of Vicentino below.

Also in the Scala archives is vicentino1, which claims it is the usual
archecembalo tuning. It is 31-et, plus five notes up by a major third.
Did Vicentino ever explicitly close the circle of fifths like this?
I'm planning to write a 31-et article for Wikipedia, and would very
much like to know.

Also, did someone not recently mention an early composer in this list
who used diesis inflections in his music? Searching hasn't turned it up.

! vicentino36.scl
Vicentino's second tuning of 1555
36
!
5.376572
76.048999
81.425572
117.107858
122.484430
193.156857
198.533429
269.205856
274.582429
310.264715
315.641287
386.313714
391.690286
462.362713
503.421572
508.798144
579.470571
584.847143
620.529429
625.906002
696.578428
701.955001
772.627428
778.004000
813.686286
819.062859
889.735285
895.111858
965.784285
971.160857
1006.843143
1012.219715
1082.892142
1088.268715
1158.941142
1200.000000

! vicentino2q441.scl
Vicentino's second tuning in 441-edo
36
!
5.442177
76.190476
81.632653
117.006803
122.448980
193.197279
198.639456
269.387755
274.829932
310.204082
315.646259
386.394558
391.836735
462.585034
503.401361
508.843537
579.591837
585.034014
620.408163
625.850340
696.598639
702.040816
772.789116
778.231293
813.605442
819.047619
889.795918
895.238095
965.986395
971.428571
1006.802721
1012.244898
1082.993197
1088.435374
1159.183673
1200.000000

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> The Scala archive doesn't have Vicentino's second tuning, at least
as
> that is described on the Tonalsoft webpage,

http://sonic-arts.org/monzo/vicentino/vicentino.htm

> so I'm posting it below.
> It consists of a chain of 1/4-comma meantone fifths from Gb to B#,
> where there is another note 1/4 comma above all the notes from Gb
to A#.
>
> The Scala archives do have a 217-edo version. 217 maps 5 to 504
steps,
> and hence has a version of 5^(1/4) at 126 steps; however 217 is
7*31,
> and this 1/4-comma fifth is actually a 31-et fifth. Much closer to
> Vicentino's specifications would be to use 441-et,

How about 205? This does much better than 217 but reduces the
cardinality of the ET, instead of more than doubling it.

> which maps 5 to
> 1024 steps, and hence has a version of 5^(1/4) at 256 steps. I also
> give a 441-edo version of Vicentino below.
>
> Also in the Scala archives is vicentino1, which claims it is the
usual
> archecembalo tuning. It is 31-et, plus five notes up by a major
third.
> Did Vicentino ever explicitly close the circle of fifths like this?

Vicentino's first tuning was a (1/4-comma) meantone chain of 31
notes, plus 5 notes at a pure fifth above 5 of the central notes in
the set of 31. It would be most odd to supply five additional *major
thirds* when the major thirds are already pure (or close enough, if
31-equal is used for the meantone chain).

> I'm planning to write a 31-et article for Wikipedia, and would very
> much like to know.
>
> Also, did someone not recently mention an early composer in this
list
> who used diesis inflections in his music? Searching hasn't turned
it up.

Vicentino did that.