Dom François Bedos de Celles

Dom François is mentioned in the Tonalsoft entry for 58-et, apparently
because in his book on the art of organ building, he gives what
Barbour is willing to call a temperament, constructed in 58 equal. In
other words, he gives a 58-et scale. I'd be interested in learning
what the notes of this scale were. There's information on the web
about Dom François, but it concentrates on organ building. Presumably
it uses 10 somewhat sharp fifths, and two very flat ones. Diaschismically?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Dom François is mentioned in the Tonalsoft entry for 58-et, apparently
> because in his book on the art of organ building, he gives what
> Barbour is willing to call a temperament, constructed in 58 equal.

Barbour states that 58-et "is the division that is at the base of Dom
Bedos' temperament, although he chose the pitches for his monochord
somewhat irregulaly from it." Barbour makes two errors here:

1) Bedos did not bother with a monochord.
2) What Bedos describes was not based on an equal division of anything.

Bedos provides a couple of tables that are equivalent to the following:

C -C# : minor half-tone
C#-D : major half-tone
D -Eb : augmented half-tone
Eb-E : minor half-tone
E -F : major half-tone
F -F# : minor half-tone
F#-G : augmented half-tone
G -G# : minor half-tone
G#-A : major half-tone
A -Bb : augmented half-tone
Bb-B : minor half-tone
B -C : major half-tone

He then explains [French accented characters have been ASCII-fied]:

"On peut diviser le demi-ton Mineur en 4 comma, le demi-ton Majeur en
5, & le demi-ton Maxime en 6. On appelle comma la 9e. partie d'un
ton. On distingue le ton en Majeur & en Mineur. Celui-ce est
suppose' compose' de 9 comma, & l'autre de 10."
["A minor half-tone equals four commas; a major half-tone, five; and
an augmented half-tone, six. A comma is the ninth part of a minor
whole step, or the tenth part of a major whole step."](*)

This is where Barbour gets the 58. But this is immediately followed by:

"Ces comma ne sont pas e'gaux entre-eux : il en est de quatre especes,
les Mineurs, les Moyens, les Majeurs & les Maximes. Tout cela est
d'une profonde the'orie, qui n'est ne'cessaire qu'au Mathe'maticien,
mais bien inutile a` notre object; puisqu'il n'est pas question ici de
chercher de nouveaux syste^mes, mais de pratiquer celui qui est
universellement adopte', & en usage parmi tous les Facteurs d'Orgue."
["Commas themselves are not equal: they may be minor, mean, major, and
augmented. This is deep theoretical consideration, necessary to the
mathematician but useless to us, for we are not seeking new
temperaments but learning to use the one universally adopted and
practiced by all organ-builders."]
Bedos has no further comment on the sizes of commas.

Bedos's tuning instructions which follow make it clear that this
universal temperament was something very close to 1/4-syntonic-comma
regular with 3 sharps and 2 flats, with the exceptions (as the above
table implies) that the fifths (aside from the wolf) were not all
supposed to be the same size, and that Bb-D was to be a bit narrow and
to beat slowly ("cette tierce doit-e^tre un peu foible & battre
lentement").

Gordon

(*) English translation by Charles Ferguson, The Sunbury Press,
Raleigh, 1977

--- In tuning@yahoogroups.com, "yah_clav" <clavier@c...> wrote:

> 1) Bedos did not bother with a monochord.
> 2) What Bedos describes was not based on an equal division of anything.

Thanks for you very helpful and informative reply. Monz, it would seem
that Dom François should be removed from the 58-et box on Tonalsoft;
it seems clear he never advocated it, and probably would have been
horrified at the idea.

--- In tuning@yahoogroups.com, "yah_clav" <clavier@c...> wrote:
>
> Bedos provides a couple of tables that are equivalent to the following:
>
> C -C# : minor half-tone
> C#-D : major half-tone
> D -Eb : augmented half-tone
> Eb-E : minor half-tone
> E -F : major half-tone
> F -F# : minor half-tone
> F#-G : augmented half-tone
> G -G# : minor half-tone
> G#-A : major half-tone
> A -Bb : augmented half-tone
> Bb-B : minor half-tone
> B -C : major half-tone
>
> (...)
> "On peut diviser le demi-ton Mineur en 4 comma, le demi-ton Majeur en
> 5, & le demi-ton Maxime en 6. On appelle comma la 9e. partie d'un
> ton. On distingue le ton en Majeur & en Mineur. Celui-ce est
> suppose' compose' de 9 comma, & l'autre de 10."
> ["A minor half-tone equals four commas; a major half-tone, five; and
> an augmented half-tone, six. A comma is the ninth part of a minor
> whole step, or the tenth part of a major whole step."]
>
(...)
>
> "Ces comma ne sont pas e'gaux entre-eux : il en est de quatre especes,
> les Mineurs, les Moyens, les Majeurs & les Maximes. Tout cela est
> d'une profonde the'orie, qui n'est ne'cessaire qu'au Mathe'maticien,
> mais bien inutile a` notre object; puisqu'il n'est pas question ici de
> chercher de nouveaux syste^mes, mais de pratiquer celui qui est
> universellement adopte', & en usage parmi tous les Facteurs d'Orgue."
> ["Commas themselves are not equal: they may be minor, mean, major, and
> augmented. This is deep theoretical consideration, necessary to the
> mathematician but useless to us, for we are not seeking new
> temperaments but learning to use the one universally adopted and
> practiced by all organ-builders."] (...)
>
> Gordon
>

I have to chuckle every time I read this passage, which I had
forgotten about. Bedos leading himself and his readers on a wild goose
chase: first providing some sort of possibly-JI-or-possibly-not
division of the octave into different semitones (but C-D is smaller
than D-E?), then fudging that division with a hint of the 9-comma
theory, finally throwing in the towel completely by admitting he
doesn't know which commas he was talking about in the first place.

(Might the four of them have been the syntonic & Pythagorean commas,
and the lesser and greater dieses, respectively?)

It is a passage just begging to be selectively quoted from, though I
am surprised Barbour made this mistake. Best summarized as 'Bedos was
thoroughly confused about the theoretical basis of his tuning'.

~~~T~~~

Hi Gene and Gordon,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "yah_clav" <clavier@c...> wrote:
>
> > 1) Bedos did not bother with a monochord.
> > 2) What Bedos describes was not based on an equal division
> > of anything.
>
> Thanks for you very helpful and informative reply. Monz,
> it would seem that Dom François should be removed from
> the 58-et box on Tonalsoft; it seems clear he never
> advocated it, and probably would have been horrified
> at the idea.

Thanks for helping me to correct that. Since i don't have
time to hunt down de Celles's work and study it myself
right now, instead of removing him, i put him in parentheses
with a comment about the possibility of error and a link
to Gordon's tuning list post.

http://tonalsoft.com/enc/e/equal-temperament.aspx

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@g...> wrote:

> It is a passage just begging to be selectively quoted from, though I
> am surprised Barbour made this mistake. Best summarized as 'Bedos was
> thoroughly confused about the theoretical basis of his tuning'.

I was surprised that Barbour was willing to call anything which could
be concocted out of 58-et a temperament. And since he knew something I
didn't--that Bedos was not a wild-eyed theoretician, but a thoroughly
practical instrument builder--he really should have known better than
to interpret it in this way.