I’d like to recommend to members two excellent and useful resources about tuning and temperaments. Coincidentally, both by members of our forum.
Carey Beebe’s pages on tuning, and also on temperaments:
[Under Technical Library (no direct links available due to the website design.]
Claudio di Veroli’s excellent and very comprehensive book, now in its fifth and updated edition:
Le 04/01/2023 07:03, Andrew Bernard via The Jackrail écrit :
I’d like to recommend to members two excellent and useful resources
about tuning and temperaments. Coincidentally, both by members of our
forum.
To which I’d add a third one, Paul Poletti’s website:
Just Say Do
Providing historically-accurate resources on tuning and temperament
https://polettipiano.com/wordpress/
I find extremely useful his “color-coded temperament comparison charts”,
which show at once the qualities of the different thirds (and fifths):
Thanks Dennis. Looked at the diagrams by Paul Poletti. Not the way I do things: I prefer the much simpler charts by coordinates instead of colour.
This said, his colour-coded tables are serious and useful work.
Le 04/01/2023 20:15, Claudio Di Veroli via The Jackrail écrit :
Thanks Dennis. Looked at the diagrams by Paul Poletti. Not the way I do things: I prefer the much simpler charts by coordinates instead of colour.
This said, his colour-coded tables are serious and useful work.
Your charts are indeed also very useful, providing they compare the
temperament one wants to compare. Would you have anyway of making such a
chart for the two or three temperaments mentioned in the Goldberg thread
(Barnes, Vallotti, Neidhardt)?
Dennis
Thanks Dennis, I will be glad to do the chart you require as soon as I have some time available, for the benefit of those who do not have my U.T: Book. Will do Barnes, Vallotti and Neidhardt Grosse Stadt, his most popular one (bar Equal which was the one he advocated!!).
Btw., it has been repeated that Vallotti is a temperament published in the 2nd part of the 18th century. Actually it had been endorsed more than a decade earlier by Tartini. How is it possible? The explanation, Vallotti’s temperament was a collaborative work that spanned decades, starting c.1735. It is all explained in my U.T.'s chapter “The Vallotti Saga”, based on detailed research published by Prof. P. Barbieri.
Le 05/01/2023 14:21, Claudio Di Veroli via The Jackrail écrit :
Thanks Dennis, I will be glad to do the chart you require as soon as I have some time available, for the benefit of those who do not have my U.T: Book. Will do Barnes, Vallotti and Neidhardt Grosse Stadt, his most popular one (bar Equal which was the one he advocated!!).
Thanks, but the Neidhardt we’d be interested in is the one I “advocated”
here, Neidhardt 1724 “Dorf”/1732 “Kleine Stadt” . This would show it’s
much better than Vallotti for Bach and the Goldbergs ;-).
OK Will do that instead, although in my book I explain two serious flaws in this temperament.
Remember though that Vallotti can be tuned with the methods in use in Bach’s lifetime: none of these Neidhardt systems using alternations of 1/12 P.c. and 1/6 P.c. can. They require tuning methods that were first described by Kirnberger in the 1770s (if I remember well). This shows that they were not in use back in the Baroque era. When late-Baroque documents say “tuning according to Neidhardt” they refer to Equal Temperament, which he advocated ever since 1706, many years before his famous publications.
Dear Dennis. I could produce a more elegant chart, but this is what I got from my Parametric Spreadsheet (available to readers of my U.T. Book).
As you can see, Neidhardt Small City avoids Vallotti’s 3 Pythagorean Major Thirds, at the cost of having instead 5 almost as bad major thirds. Neidhardt also fails to have all those very good thirds that Vallotti has at G-B, D-F#, A-C# and E-G#.
Neidhardt Small City is actually better only for music that systematically uses tonalities with many accidentals and tends to use flats instead of sharps. This is exactly the opposite of what you need for the Goldbergs, sorry to say.
Le 05/01/2023 21:31, Claudio Di Veroli via The Jackrail écrit :
Remember though that Vallotti can be tuned with the methods in use in Bach’s lifetime: none of these Neidhardt systems using alternations of 1/12 P.c. and 1/6 P.c. can. They require tuning methods that were first described by Kirnberger in the 1770s (if I remember well). This shows that they were not in use back in the Baroque era. When late-Baroque documents say “tuning according to Neidhardt” they refer to Equal Temperament, which he advocated ever since 1706, many years before his famous publications.
But how do you tune CPE’s temperament with “baroque methods”, or some
others? Obviously, many of these descriptions are purely theoretical,
and musicians only came to some kind of approximation. As for Neidhardt,
as Poletti points out, he actually moved AWAY from ET after the years.
In any case, I personally don’t care if Bach or others could or couldn’t
tune Neidhardt. If I think it sounds better than Vallotti - which is
rather obvious -, I’ll simply use a tuner. I don’t think Bach knew about
delrin either. So I’d rather use Neidhardt and bird’s quill than
Vallotti and delrin.
Le 05/01/2023 21:36, Claudio Di Veroli via The Jackrail écrit :
Dear Dennis. I could produce a more elegant chart, but this is what I got from my Parametric Spreadsheet (available to readers of my U.T. Book).
Many thanks for this, Claudio. Much appreciated. The advantages and
disadvantages are clear. As I said, everyone has to decide how big the
thirds can be before they become unbearable. This is a question of
taste, but also depends on the instrument.
Of course! 
