Yahoo Tuning Groups Ultimate Backup tuning Bach Tuning Website

J. Charles Francis escreveu:
> I am pleased to advise regarding a newly created website on the > Keyboard Tuning of Johann Sebastian Bach. > > The link is:
> > http://bach.tuning.googlepages.com/
> > > Kind regards
> Charles

How would be that in .scl format?

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🔗Brad Lehman <bpl@umich.edu>

> > http://bach.tuning.googlepages.com/
>Thanks Charles! This is the best site on the squiggles I've
>seen.

Among other relevant information omitted, it most clearly has a lack of Johann Caspar Ferdinand Fischer's book _Ariadne musica_ that Bach definitely knew. That book has all manner of interesting spirals and similar drawings: some hand-drawn, some looking as if they were standard stamps by the printer.

A good facsimile edition of the 1715 version is readily available in the "Performer's Facsimiles" series #197; and the only complete CD recording known to me is here:
http://www-personal.umich.edu/~bpl/larips/cd1002.html

Brad Lehman
http://www.larips.com

🔗J. Charles Francis <Francis@datacomm.ch>

|
J. Charles Francis, Suppig Calculus musicus, fifths beat ratios
0, 1, 2. C=273.265 Cornet-Ton
|

0: 1/1 0.000 unison, perfect prime
1: 94.720 cents 94.720
2: 196.860 cents 196.860
3: 297.300 cents 297.300
4: 394.470 cents 394.470
5: 501.210 cents 501.210
6: 592.770 cents 592.770
7: 697.730 cents 697.730
8: 796.680 cents 796.680
9: 895.040 cents 895.040
10: 999.260 cents 999.260
11: 1093.060 cents 1093.060
12: 2/1 1200.000 octave

|
J. Charles Francis, Bach WTC temperament R2-1, fifths beat ratios
0, 1, 2. C=249.072 Cammerton
|
0: 1/1 0.000 unison, perfect prime
1: 95.214 cents 95.214
2: 198.495 cents 198.495
3: 299.124 cents 299.124
4: 395.505 cents 395.505
5: 499.782 cents 499.782
6: 593.259 cents 593.259
7: 699.637 cents 699.637
8: 797.169 cents 797.169
9: 896.314 cents 896.314
10: 999.128 cents 999.128
11: 1093.770 cents 1093.770
12: 2/1 1200.000 octave

francis_r2-1.scl is already in the archive.

Regards
Charles

--- In tuning@yahoogroups.com, Hudson Lacerda <hfmlacerda@...> wrote:
>
> J. Charles Francis escreveu:
> > I am pleased to advise regarding a newly created website on the
> > Keyboard Tuning of Johann Sebastian Bach.
> >
> > The link is:
> >
> > http://bach.tuning.googlepages.com/
> >
> >
> > Kind regards
> > Charles
>
> How would be that in .scl format?
>
>
> --
> '---------------------------------------------------------------
----.
> Hudson Lacerda <http://geocities.yahoo.com.br/hfmlacerda/>
> *Não deixe seu voto sumir! http://www.votoseguro.org/
> *Apóie o Manifesto:
http://www.votoseguro.com/alertaprofessores/
>
> == THE WAR IN IRAQ COSTS ==
> http://nationalpriorities.org/index.php?
option=com_wrapper&Itemid=182
> .---------------------------------------------------------------
----'
> --
>
>
>
> _______________________________________________________
> Abra sua conta no Yahoo! Mail: 1GB de espaço, alertas de e-mail no
celular e anti-spam realmente eficaz.
> http://br.info.mail.yahoo.com/
>

🔗threesixesinarow <CACCOLA@NET1PLUS.COM>

🔗Carl Lumma <clumma@yahoo.com>

🔗J. Charles Francis <Francis@datacomm.ch>

Carl

Apologies if I'm telling you familiar things, but you need to know
that in 1722 chamber music performers including harpsichordists
typically tuned a whole tone lower compared to the church organ. The
lower `Cammerton' pitch standard arose because a more mellow French
string sound (violins etc) became fashionable. The higher 'Cornet-
Ton' pitch standard was the legacy for organs as they were expensive
to adapt.

The "Bach WTC temperament R2-1" is the Bach Wohltemperirte Clavier
diagrammatic tuning at harpsichord pitch ('Cammerton'). It has the
following flat-wise layout in beats (Hz):

1-C-1-F-1-Bb-1-Eb-0-Ab-0-C#-0-F#-2-B-2-E-2-A-2-D-2-G

The "Bach WTC temperament R12-2" is the identical (matching) tuning
at organ pitch ('Cornet-Ton'). It has the following sharp-wise
layout in beats (Hz):

2-F-2-C-2-G-2-D-2-A-2-E-0-B-0-F#-0-C#-1-Ab-1-Eb-1-Bb

Suppig's Labyrinthus musicus diagrammatic tuning has the following
flat-wise layout in beats (Hz):

0-Ab-0-C#-0-F#-1-B-2-E-3-A-2-D-2-G-2-C-2-F-1-Bb-0-Eb

Suppig's Calculus musicus diagrammatic tuning has the following
sharp-wise layout in beats (Hz):

0-Ab-1-Eb-0-Bb-0-F-2-C-2-G-2-D-2-A-2-E-2-B-2-F#-0-C#

You don't need to calculate any of these beat rates as they are
written out by Bach and Suppig. Pitch references (C, Ab) are given
also. All beat relations refer to the one-line octave c'-b' (i.e.
Middle C up to B).

For the Bach case, I did a great deal of calculation to validate the
above, looking at all rotations and reflections of the diagram
this is the origin of cryptic R2-1. Suppig was much easier to
validate as I expected the tuning to land in the one-line octave
like Bach's. If you want the mathematical details, I'm happy to
provide them.

Kind regards
Charles

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> Hi Charles,
>
> Two questions:
>
> 1. What are the "fifths beat ratios"? How does
> one calculate them?
>
> 2. What does it mean, "Bach WTC temperament R2-1"?
> Especially the R2-1 part.
>
> Thanks,
>
> -Carl
>

Bach Tuning Website

🔗J. Charles Francis <Francis@datacomm.ch>

🔗Carl Lumma <clumma@yahoo.com>

🔗Hudson Lacerda <hfmlacerda@yahoo.com.br>

🔗Brad Lehman <bpl@umich.edu>

🔗J. Charles Francis <Francis@datacomm.ch>

🔗threesixesinarow <CACCOLA@NET1PLUS.COM>

🔗Carl Lumma <clumma@yahoo.com>

🔗J. Charles Francis <Francis@datacomm.ch>