re: Chaumont

Greetings,

I am looking for information about a temperament by L. Chaumont which he included in his book of organ pieces. Has anyone set this temperament or have a diagram for it in cents?

Many thanks,

John Santoianni

> From: "John Santoianni" <jpsanto@duke.edu>
> To: "Tuning Group" <tuning@yahoogroups.com>
> Sent: Tuesday, September 03, 2002 9:07 AM
> Subject: [tuning] re: Chaumont
>

> Greetings,
>
> I am looking for information about a temperament by L. Chaumont which he
> included in his book of organ pieces. Has anyone set this temperament or
> have a diagram for it in cents?
>
> Many thanks,
>
> John Santoianni

you can use this link to access a webpage which
provides a downloadable Word document in German
which gives information on Chaumont's temperament
(in section 9.4.1.1)

http://makeashorterlink.com/?A25942EA1

(wait a moment for the link to work)

here's my quick-and-dirty translation modified
from that given by babelfish.altavista.com:

---- quote from Klaus Long ----

Lambert Chaumont: "method d`accorder le clavessin" (1695)
Chaumont writes that all 5ths between the pure and the
reduced (= mitteltoenigen) 5th are to be kept at a
moderate tempering and with large 3rds specified more
near be controlled are not. Exceptions in addition are
only the 5ths Bb - F and Eb - Bb, which are to be been
correct too largely or reduced. It is to be always tuned
alternating in 5ths and 8ves.

1. Outgoing from f four 5ths up to A are to be tuned and
be examined then with the F major chord.

2. Now the series of 5ths is continued from A to G#,
whereby each new tone is to be examined as 3rd in a
major-chord.

3. The missing tones Bb and Eb are as 5ths to F and Bb
to join in (see Lindley S.225f).

---- end quote ------

i don't have time now to check the reference to Lindley;
perhaps i can do it tonight or someone else will.
hope that helps.

-monz

Monz,

Many thanks. I appreciate your prompt reply.

John

--On Tuesday, September 03, 2002 12:43 PM -0700 monz <monz@attglobal.net> wrote:

> Lambert Chaumont: "method d`accorder le clavessin" (1695)
> Chaumont writes that all 5ths between the pure and the
> reduced (= mitteltoenigen) 5th are to be kept at a
> moderate tempering and with large 3rds specified more
> near be controlled are not. Exceptions in addition are
> only the 5ths Bb - F and Eb - Bb, which are to be been
> correct too largely or reduced. It is to be always tuned
> alternating in 5ths and 8ves.
>
> 1. Outgoing from f four 5ths up to A are to be tuned and
> be examined then with the F major chord.
>
> 2. Now the series of 5ths is continued from A to G#,
> whereby each new tone is to be examined as 3rd in a
> major-chord.
>
> 3. The missing tones Bb and Eb are as 5ths to F and Bb
> to join in (see Lindley S.225f).
>

John Santoianni
Curator, Organs and Harpsichords
Duke University Chapel
Box 90974
Durham, NC 27708-0974

919.684.2181 voice
919.681.8660 fax
919.451.7031 cell

Here's the scale from the scale database:

Lambert Chaumont organ temperament (1695)
0: 1/1 0.000 unison, perfect prime
1: 76.049 cents 76.049
2: 193.157 cents 193.157
3: 290.909 cents 290.909
4: 5/4 386.314 major third
5: 503.422 cents 503.422
6: 579.471 cents 579.471
7: 696.578 cents 696.578
8: 25/16 772.627 classic augmented fifth
9: 889.735 cents 889.735
10: 997.165 cents 997.165
11: 1082.892 cents 1082.892
12: 2/1 1200.000 octave

translate.google.com wrote:
> Emergence of the tendency level kept at a moderate temperature

Thanks for the laughs Monz.

Manuel

hi John (and also Manuel),

since i see from your signature that you're
associated with the organ described in this
webpage:

http://www.phy.duke.edu/~dtl/36hi_chl.html

i thought some comment on that page's content
would be appropriate:

>> ... Careful examination of [Chaumont's] instructions
>> reveals that they involve tuning a sequence of perfect
>> fifths that, if each fifth were exact, would result in
>> a Pythagorean scale. The text, however, admonishes the
>> reader to narrow each fifth by "tant soit peu"
>> ("ever so little") so that the thirds in major triads
>> specified for tests throughout the sequence are "good".
>> This would appear to be an exact, reproducible prescription
>> for a tuning only if the thirds were made exact, which
>> would make "Lambert Chaumont 1695" precisely the same
>> as the quarter comma meantone tuning published in 1523
>> by Pietro Aron.

that description is good as far as it goes, but it's
misleading. Chaumont's temperament is clearly neither
Pythagorean nor entirely 1/4-comma meantone.

Manuel gives Chaumont's temperament as follows,
according to the file "chaumont.scl" in the
Scala scale archive
<http://www.xs4all.nl/~huygensf/doc/scales.zip> :

cents
C 0.000
C# 76.049
D 193.157
Eb 290.909
E 386.314
F 503.422
F# 579.471
G 696.578
G# 772.627
A 889.735
Bb 997.165
B 1082.892

Manuel, can you please quote the source for these numbers?

the information given by Klaus Long in the link i posted
earlier seems to be somewhat inaccurate, because Peter van Kranenburg's
_Klavierstemmingen_ <http://elektron.et.tudelft.nl/~pvk/stemmingen.pdf>
(in Dutch) gives an illustration of the tuning method in staff-notation
which is lifted directly from Chaumont's treatise.

the left side appears to be cropped from this illustration,
because there is a gap between A:E on the right side of the
first line and the 8ve B:B on the left side of the second line:
the 5th E:B should appear between these. if this is the case,
then i speculate that a 5th Bb:F is also missing from the
very beginning.

Chaumont shows how to tune 5ths and 8ves, checking periodically
with major triads, and van Kranenburg's quoted illustration
begins with F:C. but Chaumont apparently intended the 8ves of Bb
to be the starting point, because he introduces a Bb into the
first major triad checkpoint without showing how to arrive at
a tuning for the Bb. in addition, Long specifies that Chaumont's
tuning was a series of 5ths from Eb to G#, but Chaumont's own
musical illustration uses Ab and not G#, so the nomenclature
of his series actually goes from Ab to C#.

Chaumont marks the 5ths Eb:Bb and Ab:Eb "faible ou forte"
("weak or strong"), which apparently indicates some deviation
from the 1/4-comma meantone which seems to be implied by the
rest of the procedure ... but i'm not sure exactly what he
means by that.

in Manuel's Scala archive tuning, the 5ths in the series
F:C:G:D:A:E:B:F#:C# are all tuned according to 1/4-comma meantone,
~696.578 cents. in addition, the "wolf 5th" C#:Ab is also
tuned to this same interval, which makes it not sound like
a wolf, and indicates that the enharmonic equivalence typical
of a well-temperament is in effect here.

in the Scala tuning, the 5ths in the series Eb:Bb:F are only
a few cents wider than Pythagorean 3:2 ratios, at ~706.257 cents.
the Ab:Eb 5th is the real wolf here, at ~718.282 cents.

the fraction of a syntonic-comma by which these 5ths deviate
from Pythagorean 3:2s is as follows:

(Bb:F) + 1/5
F:C - 1/4
C:G - 1/4
G:D - 1/4
D:A - 1/4
A:E - 1/4
(E:B) - 1/4
B:F# - 1/4
F#:C# - 1/4
Eb:Bb + 1/5
Ab:Eb + ~3/4
(C#:Ab) - 1/4

the reason why the Ab:Eb 5th is only approximately 3/4 of a
comma larger, is because the Ab is tuned with the C# to be
exactly 1/4 of a comma smaller ... and as i state above,
Ab:Eb is the real wolf in this tuning.

it's very odd to me that deviations of -1/4 and +1/5 comma are
mixed together in this tuning, but strange combinations like
this are typical of some well-temperaments.

the major-3rds given in Chaumont's illustration, with the
ones i speculate as missing given in parentheses, are as
follows according to the Scala tuning:

Bb:D 395.992
F:A 386.313
(C:E) 386.314
(G:B) 386.314
D:F# 386.314
A:C# 386.314
Eb:G 405.669
Ab:C 427.373

so according to Scala: F:A, C:E, G:B, D:F#, and A:C# are
all just-intonation 5:4 ratios, which is what they would
also be in 1/4-comma meantone; Bb:D is a bit wider than that,
Eb:G is a few cents narrower than the Pythagorean major-3rd
of ratio 81:64, and Ab:C is the very wide major-3rd which
is almost as large as the 9:7 ratio.

to me, these measurements do not seem to agree with the
tuning Chaumont is demonstrating in his illustration.
feedback is appreciated.

-monz
"all roads lead to n^0"

----- Original Message -----
From: "John Santoianni" <jpsanto@duke.edu>
To: <tuning@yahoogroups.com>
Sent: Tuesday, September 03, 2002 1:52 PM
Subject: Re: [tuning] re: Chaumont

> Monz,
>
> Many thanks. I appreciate your prompt reply.
>
> John
>
> --On Tuesday, September 03, 2002 12:43 PM -0700 monz <monz@attglobal.net>
> wrote:
>
> > Lambert Chaumont: "method d`accorder le clavessin" (1695)
> > Chaumont writes that all 5ths between the pure and the
> > reduced (= mitteltoenigen) 5th are to be kept at a
> > moderate tempering and with large 3rds specified more
> > near be controlled are not. Exceptions in addition are
> > only the 5ths Bb - F and Eb - Bb, which are to be been
> > correct too largely or reduced. It is to be always tuned
> > alternating in 5ths and 8ves.
> >
> > 1. Outgoing from f four 5ths up to A are to be tuned and
> > be examined then with the F major chord.
> >
> > 2. Now the series of 5ths is continued from A to G#,
> > whereby each new tone is to be examined as 3rd in a
> > major-chord.
> >
> > 3. The missing tones Bb and Eb are as 5ths to F and Bb
> > to join in (see Lindley S.225f).
> >
>
>
>
> John Santoianni
> Curator, Organs and Harpsichords
> Duke University Chapel
> Box 90974
> Durham, NC 27708-0974
>
> 919.684.2181 voice
> 919.681.8660 fax
> 919.451.7031 cell

----- Original Message -----
From: <manuel.op.de.coul@eon-benelux.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, September 04, 2002 1:45 AM
Subject: [tuning] Re: Chaumont

> translate.google.com wrote:
> > Emergence of the tendency level kept at a moderate temperature
>
> Thanks for the laughs Monz.

hey, i was in a hurry!

please take a look at the post i just sent, where i
really spent some time examining everything i could
find on Chaumont's tuning.

-monz
"all roads lead to n^0"

> From: "monz" <monz@attglobal.net>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, September 04, 2002 4:05 AM
> Subject: Re: [tuning] re: Chaumont
>
> ...
>
> the information given by Klaus Long in the link i posted
> earlier seems to be somewhat inaccurate, because Peter van Kranenburg's
> _Klavierstemmingen_ <http://elektron.et.tudelft.nl/~pvk/stemmingen.pdf>
> (in Dutch) gives an illustration of the tuning method in staff-notation
> which is lifted directly from Chaumont's treatise.
>
> ...
>
> in Manuel's Scala archive tuning, the 5ths in the series
> F:C:G:D:A:E:B:F#:C# are all tuned according to 1/4-comma meantone,
> ~696.578 cents. in addition, the "wolf 5th" C#:Ab is also
> tuned to this same interval, which makes it not sound like
> a wolf, and indicates that the enharmonic equivalence typical
> of a well-temperament is in effect here.
>
> in the Scala tuning, the 5ths in the series Eb:Bb:F are only
> a few cents wider than Pythagorean 3:2 ratios, at ~706.257 cents.
> the Ab:Eb 5th is the real wolf here, at ~718.282 cents.
>
> the fraction of a syntonic-comma by which these 5ths deviate
> from Pythagorean 3:2s is as follows:
>
> (Bb:F) + 1/5
> F:C - 1/4
> C:G - 1/4
> G:D - 1/4
> D:A - 1/4
> A:E - 1/4
> (E:B) - 1/4
> B:F# - 1/4
> F#:C# - 1/4
> Eb:Bb + 1/5
> Ab:Eb + ~3/4
> (C#:Ab) - 1/4
>
> the reason why the Ab:Eb 5th is only approximately 3/4 of a
> comma larger, is because the Ab is tuned with the C# to be
> exactly 1/4 of a comma smaller ... and as i state above,
> Ab:Eb is the real wolf in this tuning.
>
> it's very odd to me that deviations of -1/4 and +1/5 comma are
> mixed together in this tuning, but strange combinations like
> this are typical of some well-temperaments.

van Kranenburg's paper has a bit more to say about Chaumont:

>> De al genoemde steminstructie van Lambert Chaumont resulteert
>> in een andere variant van de middentoonstemming. Er zijn echter
>> twee manieren om zijn beschrijving uit te leggen. In de eerste
>> versie komt het erop neer dat negen kwinten 1/4 syntonische komma
>> kleiner dan rein zijn (zoals in de zuivere middentoonstemming),
>> en twee kwinten 1/5 syntonische komma te groot, waardoor de
>> wolfskwint kleiner wordt dan in de zuivere middentoonstemming.
>> Bovendien zijn twee van de vier wolfstertsen kleiner geworden,
>> waardoor deze stemming wat milder zal klinken. In de alternatieve
>> interpretatie zijn de negen kwinten 1/5 syntonische komma kleiner
>> dan rein, de twee kwinten (nog steeds) 1/5 syntonische komma groter
>> dan rein, en de wolfskwint dus nog kleiner, zodat de stem-ming
>> in deze interpretatie nog bruikbaarder is dan de eerste variant.

my English translation, only slightly modified from the
fairly good one provided by WorldLingo
<http://www.worldlingo.com/wl/Translate> :

>> Already the called voice instruction of Lambert Chaumont results
>> in another alternative of the meantone tuning. However it is
>> two manners to their description from at to lay (?). In the first
>> version it comes down above that nine 5ths are 1/4 syntonic comma
>> smaller than pure (as in the pure meantone tuning), and two 5ths
>> are 1/5 syntonic comma too large, then thanks to which the wolf fifth
>> becomes smaller, in pure meantone tuning. Moreover two of the four
>> wolf-3rds are smaller, thanks to which this poll what milder will
>> sound. In the alternative interpretation, nine 5ths are 1/5 syntonic
>> comma smaller than pure, two 5ths (still) 1/5 syntonic comma
>> bigger than pure, and the wolf 5th therefore still smaller, so that
>> the poll then in this interpretation is still more useful the first
>> alternative.

my work would have been a little easier if i had done this translation
first, before making my calculations. van Kranenburg's description of
the first alternative is exactly what the Scala tuning shows, as i
described in the quote at the beginning of this post.

-monz
"all roads lead to n^0"

I think it was from an article by Henri Legros in _Visitatio
Organorum_ but I can't check that at the moment.
However in van Kranenburg's article it's given too as one of
two possible interpretations, quoting an article by J. de Bie,
which I haven't read.
The other one is nine 1/5 comma narrow and two 1/5 wide fifths.
Thus in cents:
0: 1/1 0.000 unison, perfect prime
1: 83.576 cents 83.576
2: 195.307 cents 195.307
3: 289.834 cents 289.834
4: 390.615 cents 390.615
5: 502.346 cents 502.346
6: 585.922 cents 585.922
7: 697.654 cents 697.654
8: 781.230 cents 781.230
9: 892.961 cents 892.961
10: 16/9 996.090 Pythagorean minor seventh
11: 15/8 1088.269 classic major seventh
12: 2/1 1200.000 octave

I'll add that one to the archive.

Manuel

I remembered right, it was Henri Legros: "Le tempérament des orgues en
France
aux 17ème et 18ème siècles".
I've scanned the concerning passage:

"Par contre le Belge Lambert Chaumont donne à la fin de son livre d'orgue
(1695), écrit dans le style français, une Méthode d'accorder le clavessin,
exposée de façon un peu trop sommaire, mais qu'on peut comprendre comme
donnant le tempérament mésotonique ou une variante de celui-ci, car les
quintes SIb-FA et MIb-SIb peuvent être accordées `foibles' ou `fortes'. Si
ces deux quintes ont environs de comma majeur de plus que la valeur juste,
au lieu de 1/4 de comma de moins, MIb se trouve baissé de près d'un comma
et l'on a un compromis presque exact entre MIb et RE# ; les tierces SI-RE#
et MIb-SOL ont à peu près la valeur pythagoricienne. La tierce Fa#-LA#
devient aussi utilisable dans des modulations rapides. La quinte du loup
est très atténuée.
Ce tempérament conviendrait assez bien à la musique de plusieurs livres
d'orgue français de la fin du l7ème siècle, comme à celle de Lambert
Chaumont. Mais il est probable que les modifications apportées au
tempérament des orgues en France à cette époque allaient déjà plus loin.
En 1726, Jean-Philippe Rameau décrit un tempérament dans lequel 7 quintes,
au lieu de 11, sont accordées avec un quart de comma majeur de.... "

Manuel

Manuel,

Many thanks,

John

--On Wednesday, September 04, 2002 10:45 AM +0200 manuel.op.de.coul@eon-benelux.com wrote:

> Here's the scale from the scale database:
>
> Lambert Chaumont organ temperament (1695)
> 0: 1/1 0.000 unison, perfect prime
> 1: 76.049 cents 76.049
> 2: 193.157 cents 193.157
> 3: 290.909 cents 290.909
> 4: 5/4 386.314 major third
> 5: 503.422 cents 503.422
> 6: 579.471 cents 579.471
> 7: 696.578 cents 696.578
> 8: 25/16 772.627 classic augmented fifth
> 9: 889.735 cents 889.735
> 10: 997.165 cents 997.165
> 11: 1082.892 cents 1082.892
> 12: 2/1 1200.000 octave
>
> translate.google.com wrote:
>> Emergence of the tendency level kept at a moderate temperature
>
> Thanks for the laughs Monz.
>
> Manuel

John Santoianni
Curator, Organs and Harpsichords
Duke University Chapel
Box 90974
Durham, NC 27708-0974

919.684.2181 voice
919.681.8660 fax
919.451.7031 cell

Monz,

I had mentioned the exact part you quoted to the organ prof and he agreed it was incorrect. Since then I must admit to have forgotten about it but it needs to be addressed at some point.

--On Wednesday, September 04, 2002 4:05 AM -0700 monz <monz@attglobal.net> wrote:

> hi John (and also Manuel),
>
>
> since i see from your signature that you're
> associated with the organ described in this
> webpage:
>
> http://www.phy.duke.edu/~dtl/36hi_chl.html
>
> i thought some comment on that page's content
> would be appropriate:
>
>>> ... Careful examination of [Chaumont's] instructions
>>> reveals that they involve tuning a sequence of perfect
>>> fifths that, if each fifth were exact, would result in
>>> a Pythagorean scale. The text, however, admonishes the
>>> reader to narrow each fifth by "tant soit peu"
>>> ("ever so little") so that the thirds in major triads
>>> specified for tests throughout the sequence are "good".
>>> This would appear to be an exact, reproducible prescription
>>> for a tuning only if the thirds were made exact, which
>>> would make "Lambert Chaumont 1695" precisely the same
>>> as the quarter comma meantone tuning published in 1523
>>> by Pietro Aron.
>
>
> that description is good as far as it goes, but it's
> misleading. Chaumont's temperament is clearly neither
> Pythagorean nor entirely 1/4-comma meantone.
>
> Manuel gives Chaumont's temperament as follows,
> according to the file "chaumont.scl" in the
> Scala scale archive
> <http://www.xs4all.nl/~huygensf/doc/scales.zip> :
>
> cents
> C 0.000
> C# 76.049
> D 193.157
> Eb 290.909
> E 386.314
> F 503.422
> F# 579.471
> G 696.578
> G# 772.627
> A 889.735
> Bb 997.165
> B 1082.892
>
>
> Manuel, can you please quote the source for these numbers?
>
>
> the information given by Klaus Long in the link i posted
> earlier seems to be somewhat inaccurate, because Peter van Kranenburg's
> _Klavierstemmingen_ <http://elektron.et.tudelft.nl/~pvk/stemmingen.pdf>
> (in Dutch) gives an illustration of the tuning method in staff-notation
> which is lifted directly from Chaumont's treatise.
>
> the left side appears to be cropped from this illustration,
> because there is a gap between A:E on the right side of the
> first line and the 8ve B:B on the left side of the second line:
> the 5th E:B should appear between these. if this is the case,
> then i speculate that a 5th Bb:F is also missing from the
> very beginning.
>
> Chaumont shows how to tune 5ths and 8ves, checking periodically
> with major triads, and van Kranenburg's quoted illustration
> begins with F:C. but Chaumont apparently intended the 8ves of Bb
> to be the starting point, because he introduces a Bb into the
> first major triad checkpoint without showing how to arrive at
> a tuning for the Bb. in addition, Long specifies that Chaumont's
> tuning was a series of 5ths from Eb to G#, but Chaumont's own
> musical illustration uses Ab and not G#, so the nomenclature
> of his series actually goes from Ab to C#.
>
> Chaumont marks the 5ths Eb:Bb and Ab:Eb "faible ou forte"
> ("weak or strong"), which apparently indicates some deviation
> from the 1/4-comma meantone which seems to be implied by the
> rest of the procedure ... but i'm not sure exactly what he
> means by that.
>
>
> in Manuel's Scala archive tuning, the 5ths in the series
> F:C:G:D:A:E:B:F#:C# are all tuned according to 1/4-comma meantone,
> ~696.578 cents. in addition, the "wolf 5th" C#:Ab is also
> tuned to this same interval, which makes it not sound like
> a wolf, and indicates that the enharmonic equivalence typical
> of a well-temperament is in effect here.
>
> in the Scala tuning, the 5ths in the series Eb:Bb:F are only
> a few cents wider than Pythagorean 3:2 ratios, at ~706.257 cents.
> the Ab:Eb 5th is the real wolf here, at ~718.282 cents.
>
> the fraction of a syntonic-comma by which these 5ths deviate
> from Pythagorean 3:2s is as follows:
>
> (Bb:F) + 1/5
> F:C - 1/4
> C:G - 1/4
> G:D - 1/4
> D:A - 1/4
> A:E - 1/4
> (E:B) - 1/4
> B:F# - 1/4
> F#:C# - 1/4
> Eb:Bb + 1/5
> Ab:Eb + ~3/4
> (C#:Ab) - 1/4
>
> the reason why the Ab:Eb 5th is only approximately 3/4 of a
> comma larger, is because the Ab is tuned with the C# to be
> exactly 1/4 of a comma smaller ... and as i state above,
> Ab:Eb is the real wolf in this tuning.
>
> it's very odd to me that deviations of -1/4 and +1/5 comma are
> mixed together in this tuning, but strange combinations like
> this are typical of some well-temperaments.
>
>
> the major-3rds given in Chaumont's illustration, with the
> ones i speculate as missing given in parentheses, are as
> follows according to the Scala tuning:
>
> Bb:D 395.992
> F:A 386.313
> (C:E) 386.314
> (G:B) 386.314
> D:F# 386.314
> A:C# 386.314
> Eb:G 405.669
> Ab:C 427.373
>
> so according to Scala: F:A, C:E, G:B, D:F#, and A:C# are
> all just-intonation 5:4 ratios, which is what they would
> also be in 1/4-comma meantone; Bb:D is a bit wider than that,
> Eb:G is a few cents narrower than the Pythagorean major-3rd
> of ratio 81:64, and Ab:C is the very wide major-3rd which
> is almost as large as the 9:7 ratio.
>
> to me, these measurements do not seem to agree with the
> tuning Chaumont is demonstrating in his illustration.
> feedback is appreciated.
>
>
>
> -monz
> "all roads lead to n^0"
>
>
> ----- Original Message -----
> From: "John Santoianni" <jpsanto@duke.edu>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, September 03, 2002 1:52 PM
> Subject: Re: [tuning] re: Chaumont
>
>
>> Monz,
>>
>> Many thanks. I appreciate your prompt reply.
>>
>> John
>>
>> --On Tuesday, September 03, 2002 12:43 PM -0700 monz <monz@attglobal.net>
>> wrote:
>>
>> > Lambert Chaumont: "method d`accorder le clavessin" (1695)
>> > Chaumont writes that all 5ths between the pure and the
>> > reduced (= mitteltoenigen) 5th are to be kept at a
>> > moderate tempering and with large 3rds specified more
>> > near be controlled are not. Exceptions in addition are
>> > only the 5ths Bb - F and Eb - Bb, which are to be been
>> > correct too largely or reduced. It is to be always tuned
>> > alternating in 5ths and 8ves.
>> >
>> > 1. Outgoing from f four 5ths up to A are to be tuned and
>> > be examined then with the F major chord.
>> >
>> > 2. Now the series of 5ths is continued from A to G#,
>> > whereby each new tone is to be examined as 3rd in a
>> > major-chord.
>> >
>> > 3. The missing tones Bb and Eb are as 5ths to F and Bb
>> > to join in (see Lindley S.225f).
>> >
>>
>>
>>
>> John Santoianni
>> Curator, Organs and Harpsichords
>> Duke University Chapel
>> Box 90974
>> Durham, NC 27708-0974
>>
>> 919.684.2181 voice
>> 919.681.8660 fax
>> 919.451.7031 cell
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> Yahoo! Groups Sponsor
> ADVERTISEMENT
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery on hold
> for the tuning group. tuning-digest@yahoogroups.com - change your
> subscription to daily digest mode. tuning-normal@yahoogroups.com -
> change your subscription to individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
> Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.

John Santoianni
Curator, Organs and Harpsichords
Duke University Chapel
Box 90974
Durham, NC 27708-0974

919.684.2181 voice
919.681.8660 fax
919.451.7031 cell