Draft 1 FAQ: Organs with split keys fewer than 19 per octave

Open to discussion - first draft of
------------------------

FAQ TUNING-LIST
Organs with split keys fewer than 19 per octave
by
Ibo Ortgies

------------------------------

From the 15th to the 18th century split keys were added to keyboard
instruments. Split keys offered a rather convenient way to exceed the
limitations of restricted temperaments and tunings in keyboard
instruments, since the essential features of these temperaments were
kept, like for example the pure major thirds of meantone temperament.
Usaully the split keys in the small and one-stroke octave were "broken"
to provide additional keys. Occasionally notes in the two-stroke octave
also were broken, but only eb''/d#'' (more frequent) and g#''/ab'' (less frequent).

Split keys in pythagorean tuning

There are hints provided by Christopher Stembridge and L. F. Tagliavini,
that split keys were already used in organs tuned in pythagorean tuning
in the middle of the 15th century, but at the same time meantone
temperament rose and lead to a greater interest in adding the "tasti
spezzati" or "subsemitonia".
The pythagorean example given by Stembridge and Tagliavini is from an
intarsia showing an extra key between E and F. This may be interpreted as

ex. 1 B - F#- C#- G#
/ \ / \ / \ /
Eb- Bb- F - C - G - D - A - E

or

ex. 2 E - B - F#- C#
/ \ / \ / \ /
Ab- Eb- Bb- F - C - G - D - A

I write the pythagorean tuning with it's "schismatic" major thirds (very
close to pure) as a cut-out of the fifth-third-net of just intonation.
Example Nr. 1 could be written as a straiught chain as well: Cb- Gb-
Db- Ab- Eb- Bb- F - C - G - D - A - E,
but Cb- Gb- Db- Ab- serve as very good major thirds B - F#- C#- G#.
Especially in an organ the "drawing together effect" might render these
pure to the listener.

The split key between E and F would add either the E above C (to ex. 1)

ex. 3 E - B - F#- C#- G#
/ \ / \ / \ / \ /
Eb- Bb- F - C - G - D - A - E

or the pure fifth E to A

ex. 4 E - B - F#- C#
/ \ / \ / \ / \
Ab- Eb- Bb- F - C - G - D - A - E

Meantone extension

In an italian organ around 1500 (four such organs are known before),
tuned in (some) meantone temperament, the first key to be split might be
the a-flat, provided with the g# (as back key) - as can be seen in the
(reconstructed) keyboards of the 2 famous organs in Bologna, Italy, S.
Petronio, the older one from 1475, getting split keys during the rebuilt
by G. B. Facchetti in 1528-1531 and the other organ from 1596 built by
B. Malamini.
Others started with doubling eb/d#.

Later it became usual to split consequently: eb/d#, g#/ab (g# being in
front), bb/a# then c#/db (seldom). There are only two organs known which
had all these 4 split sharps and in both cases all concentrated in one
octave span:
Wolfenb�ttel, Germany, Hauptkirche BMV, 1620-1624 G. Fritzsche, and
Sciacca, Italy, S. Margherita, 1639 G. Sutera and V. Monteleone

Not one known organ with less than 19 notes per octave had *all split
keys (or more) as subsemitones, like the "enharmonic" instruments.

The pattern with eb/d# and g#/ab (14 notes/pitches per octave) seems to
have been frequent. It provides the following possibilities,
symmetrically ordered around the fifth of the 1st mode D-A.

ex. 5 - D#
\ / \
- B - F#- C#- G# -
\ / \ / \ / \ / \
- G - D - A - E -
\ / \ / \ / \ / \
- Eb- Bb- F - C -
\ / \
Ab-

Here the dashes indicate
- meantone fifths
/ pure major thirds
\ minor thirds (as defined by the two previous)
lines with "open end" find their continuation in the next row below
or above

d' was also the middle, symmetrical key on the keyboards with short
octave CDEFGA-c'''.

The keyboard in the bass would look like

D E Bb
C F G A B c

The short octave might have originated from the previous
FGAB-g'',a''-compass by adding the C to the left of the keyboard and the
D and E at the indicated places. Some F-keyboards seem to have been
actually based on D (same pattern, but without the C).

How important the symmetrical aspect might have been regarded is
difficult to say. Amazing is in this respect that the keyboards until
ca. 1700 were rather equipped with extra notes in the bass for F# and
G#, built as split keys (but which are not "subsemitones") as well:

F# G#
D E Bb
C F G A B c

There are a few keyboard designs, deviating from the above sketched
patterns, apparently "omitting" certain keys, like doubling
eb/d# and bb/a#, leaving out the frequent g#/ab), or providing
g#/ab and c#/db , but not eb/d#
whichs possible purpose is explained below.

A Very Short History

It seems to have been Italian organ builders of the mid-15th-C. who were
the first to apply split keys in organ building. Not surprising Italy
was the main center of this development for the first 150 years and
nearly half of the instruments we know of today are to be found in this
country. Until 1600 we leran about 19 organs. From Italy the idea might
have spread to Spain (the picture within Spain still remains somewhat unclear).

In Italy the development seems to faded out after 1660, but shortly
after 1600 however, Germany, which was dominated by musicians under
Italian influence, took a central position. Split keys were promoted by
the leader of the Wolfenb�ttel court chapel, Michael Praetorius, and the
Saxon court organ builder Gottfried Fritzsche. Other promoters were f.
example Henrich Sch�tz (Dresden) and Jacob Praetorius (Hamburg), both
knowing and cooperating with each other and with Fritzsche. Dresden was
the first organ norther of the alps in which split keys were applied
(Schlick 1511 reports a failed attempt at an unknown place by two
unknown builders). The chapel organ was built by G. Fritzsche in
1612-1614 after having planned it together with Sch�tz' predecessor as
chapel master of the electoral court, Hans Leo Hassler. It is hoped by
the way that in the near future this organ will be reconstructed in the
as well reconstructed Dresden castle.

The Manderscheidt-family originally working in and around N�rnberg
(Nuremberg) has to be mentioned too, because they produced several
positives, but also bigger church organs like the recently restored
choir organ in Fribourg, Switzerland, St. Nicolas, built 1654-1657 by
Sebald Manderscheidt.

From these geographical area the idea spread further to surrounding
regions and countries:
- Denmark: only one example known, probably an organ builder
of Saxon origin (the courts of Denmark and saxony
were dynastically linked)
- Sweden: the only country were also local organ builders
took the practice over.
- the Netherlands: the northwest-German organ builder family
van Hagerbeer (1630ies/1640ies)
- Switzerland: Manderscheidt-family (s. above) ca. 1650
- England: 2 organs known, by Bernard Smith (Bernhard Schmidt)
in the 1680ies

In France this tradition did not prevail, there is no safe evidence for
organs with split keys (even not the one example in Paris, St. Nicolas
des Champs, 1632-1636, C. Carlier, is known whether it was realized) and
the Gamba-player Jean-Jaques Rousseau confirmed in 1697 that this
tradition was not to be found in France, contrary to Italy.

At the end of the 17th century there are still large organs built with 3
manuals and pedal in Sweden and Germany, whcih contained 3 split
keys/octave, namely eb/d#, g#/ab and bb/a#, sometimes even going down to
the great octave (Bb/A# occurs), which usually did not happen (Italian
early compasses down to FF, 12-foot, excluded).

With the rise of circulating temperaments the practice disappeared soon
after 1700. The last organ was built by J. and V. F. Bossart in
1716-1721 in Luzern (Switzerland), St. Urban.
About 70 Instruments with 13-16 keys per octave are known today to have
been built during the time sketched above.

The historical informed performance practice movemend lead organ
builders to build organs in meantone tuning again and so the split keys
came back into modern organ building.
With the return of historical oriented organ building and the rise of
historical temperaments and tunings in the practice of instrument
building and performance practice split keys have become a more and more
frequent feature again since the 1970ies, after an interlude of nearly
300 years. Italy, the USA, Sweden and Switzerland might be today the
countries with the highest concentration of existing organs with split
keys, while the development in other traditional organ countries like
the Netherlands or Germany has not yet led to a more frequent re-use
again.

Use

Though split keys could be used in several ways, transposition seems to
be the most important reason for their existence. Transposition to a
variety of intervals was frequent and necessary: The organist had to
provide the proper tones in the liturgy, to play transcriptions
(intabulations) in different applied pitches and to accompany ensembles.

Special designs were developped, for example by apparently "omitting"
certain keys, to enable comfortable transposition by certain intervals
(reflecting probably the relative low or high organ pitch in the
respective region). Designs in other organs lead to the conclusion that
their split keys were used mainly in continuo-playing (Wolfenb�ttel, and
maybe, Sciacca). Another organ (S�nderborg Slotskapel, 1626, rebuilt by
B. (Zencker [?]) and restored recently by Mads Kjersgaard) even has two
manuals, one of them with split keys, that shows some similarity to the
concept of the so-called �transposing" instruments by the German/Flemish
harpsichord builders Ruckers.

----------------------------------
Ibo Ortgies

http://www.hum.gu.se/goart/ortgies/homepage.htm
http://www.hum.gu.se/goart/ortgies/public.html

GOArt (G�teborg Organ Art center) G�teborgs universitet
http://www.hum.gu.se/goart/w-1.htm

--- In tuning@y..., Ibo Ortgies <ibo.ortgies@m...> wrote:

/tuning/topicId_19479.html#19479

Thank you, Mr. Ortgies for your interesting post...

> Split keys in pythagorean tuning
>
> There are hints provided by Christopher Stembridge and L. F.
Tagliavini, that split keys were already used in organs tuned in
pythagorean tuning in the middle of the 15th century, but at the same
time meantone temperament rose and lead to a greater interest in
adding the "tasti spezzati" or "subsemitonia".
> The pythagorean example given by Stembridge and Tagliavini is from
an intarsia showing an extra key between E and F. This may be
interpreted as
>
>
> ex. 1 B - F#- C#- G#
> / \ / \ / \ /
> Eb- Bb- F - C - G - D - A - E
>
> or
>
> ex. 2 E - B - F#- C#
> / \ / \ / \ /
> Ab- Eb- Bb- F - C - G - D - A
>
>
> I write the pythagorean tuning with it's "schismatic" major thirds
(very close to pure) as a cut-out of the fifth-third-net of just
intonation. Example Nr. 1 could be written as a straiught chain as
well: Cb- Gb-Db- Ab- Eb- Bb- F - C - G - D - A - E, but Cb- Gb- Db-
Ab- serve as very good major thirds B - F#- C#- G#. Especially in an
organ the "drawing together effect" might render these pure to the
listener.

I'm sorry to say that I'm not totally "getting" this. Are you saying
that the second chain of fifths above the first starts with an "E"
that is a schisma away from a "normal" Pythagorean "E?"

I guess that must be, since, otherwise the "pure" chain of
Pythagorean fifth would create major thirds that are quite large,
yes?? Quite a bit larger than just.

Is this correct??

Thank you...

________ ______ ______ ___
Joseph Pehrson

Joseph Pehrson:

If you have a string of pythagorean fifths, reduced into a single
octave, going four fifths upward, i.e. C-G-D-A-E will overshoot a 5:4
pure major third by the syntonic comma (81/80, 21.5 cents; this is
the interval that is distributed in MT). If, however, you go _down_ 8
fifths C-F-Bb-Eb-Ab-Db-Gb-Cb-Fb, that diminished fourth will only
differ from a pure 5:4 major third by the interval of the Skhisma
(32805:32768, 1.954 cents). This is, for most (not all) musical
purposes, negligible, and appears to have been widely used as a major
third throughout Islamicate and medieval european music cultures.
However, the convention that Fb:C approximates 5:4 was not accepted
in European common practice music, rather the convention that E:C
approximates 5:4, that is to say, the assumption underlying MT.

Daniel Wolf
Composer, Budapest/Morro Bay
djwolf1@matavnet.hu
http://home.snafu.de/djwolf/

--- In tuning@y..., djwolf1@m... wrote:

/tuning/topicId_19479.html#19483

> Joseph Pehrson:
>
> If you have a string of pythagorean fifths, reduced into a single
> octave, going four fifths upward, i.e. C-G-D-A-E will overshoot a
5:4 pure major third by the syntonic comma (81/80, 21.5 cents; this
is the interval that is distributed in MT). If, however, you go
_down_
8 fifths C-F-Bb-Eb-Ab-Db-Gb-Cb-Fb, that diminished fourth will only
> differ from a pure 5:4 major third by the interval of the Skhisma
> (32805:32768, 1.954 cents). This is, for most (not all) musical
> purposes, negligible, and appears to have been widely used as a
major third throughout Islamicate and medieval european music
cultures. However, the convention that Fb:C approximates 5:4 was not
accepted in European common practice music, rather the convention
that E:C approximates 5:4, that is to say, the assumption underlying
MT.
>
>
> Daniel Wolf
> Composer, Budapest/Morro Bay
> djwolf1@m...
> http://home.snafu.de/djwolf/

Hello Daniel Wolf!

Thank you so VERY much for answering this "riddle..." I guess, then,
I was somewhat right when I asked whether the chain of fifths ABOVE
the initial chain in Mr. Ortgies example started with an "E" that
differed by a skhisma from the "normal" upward chain Pythagorean "E."

Since it wasn't spelled Fb it was confusing to me. Additionally, I
must confess I didn't fully understand the implications of the
"downward" chain...

Most probably many people more familiar with the subject matter had
not trouble understanding what Mr. Ortgies was saying, but the
missing spelling "Fb" really threw it for me....

Thanks again for the help! (I definitely printed this one out...)

______ _____ _____ ___
Joseph Pehrson

Hi Ibo -- not much time, but I just wanted to point out that your
lattices could be a lot clearer if they incorporated a little bit of
redundancy.

For example, the schismic example
>
> ex. 1 B - F#- C#- G#
> / \ / \ / \ /
> Eb- Bb- F - C - G - D - A - E

would be better understood as:

B - F#- C#- G#- Eb- Bb- F - . . .
/ \ / \ / \ /
. . . Eb- Bb- F - C - G - D - A - E

and the meantone example

> ex. 5 - D#
> \ / \
> - B - F#- C#- G# -
> \ / \ / \ / \ / \
> - G - D - A - E -
> \ / \ / \ / \ / \
> - Eb- Bb- F - C -
> \ / \
> Ab-

would be better understood as

. . . G#- D#
/ \ / \
. . . E - B - F#- C#- G#- D#. . .
/ \ / \ / \ / \ / \ /
. . . C - G - D - A - E - B . . .
/ \ / \ / \ / \ / \ /
Ab- Eb- Bb- F - C - G . . .
\ / \ /
Ab- Eb. . .

> lines with "open end" find their continuation in the next row
below
> or above

Good to point that out, but repeating notes in the chart helps one
see exactly how this takes place.

Dear list

reply to mails from
Joseph Pehrson jpehrson@rcn.com
Daniel Wolf djwolf1@matavnet.hu
Paul Erlich PERLICH@ACADIAN-ASSET.COM

Thanks for your first comments - very helpful - I'll work them in

> Date: Tue, 27 Feb 2001 14:32:27 -0000
> From: jpehrson@rcn.com
> Subject: Re: Draft 1 FAQ: Organs with split keys fewer than 19 per octave

> --- In tuning@y..., Ibo Ortgies <ibo.ortgies@m...> wrote:

> /tuning/topicId_19479.html#19479

> > Split keys in pythagorean tuning

...
> > The pythagorean example given by Stembridge and Tagliavini is from
> an intarsia showing an extra key between E and F. This may be
> interpreted as

> > ex. 1 B - F#- C#- G#
> > / \ / \ / \ /
> > Eb- Bb- F - C - G - D - A - E

> > or

> > ex. 2 E - B - F#- C#
> > / \ / \ / \ /
> > Ab- Eb- Bb- F - C - G - D - A

> > I write the pythagorean tuning with it's "schismatic" major thirds
> (very close to pure) as a cut-out of the fifth-third-net of just
> intonation. Example Nr. 1 could be written as a straiught chain as
> well: Cb- Gb-Db- Ab- Eb- Bb- F - C - G - D - A - E, but Cb- Gb- Db-
> Ab- serve as very good major thirds B - F#- C#- G#. Especially in an
> organ the "drawing together effect" might render these pure to the
> listener.

(it's hard to find out in your replies sometimes which are the quotes
and which are your replies - maybe some setting in your mail-program can
solve this?)

> I'm sorry to say that I'm not totally "getting" this. Are you saying
> that the second chain of fifths above the first starts with an "E"
> that is a schisma away from a "normal" Pythagorean "E?"

Thanks, sorry. That needs clarification in my text:

The upper row are major thirds (384,4 cents) which are a schisma (1,9
ct) lower than pure major thirds (386,3 ct).

> I guess that must be, since,

> otherwise the "pure" chain of
> Pythagorean fifth would create major thirds that are quite large,
> yes?? Quite a bit larger than just.

> Is this correct??
>
> Thank you...
>
> ________ ______ ______ ___
> Joseph Pehrson

-------------

> Date: Tue, 27 Feb 2001 15:17:32 -0000
> From: djwolf1@matavnet.hu
> Subject: Re: Draft 1 FAQ: Organs with split keys fewer than 19 per octave

> Joseph Pehrson:

> If you have a string of pythagorean fifths, reduced into a single
> octave, going four fifths upward, i.e. C-G-D-A-E will overshoot a 5:4
> pure major third by the syntonic comma (81/80, 21.5 cents; this is
> the interval that is distributed in MT). If, however, you go _down_ 8
> fifths C-F-Bb-Eb-Ab-Db-Gb-Cb-Fb, that diminished fourth will only
> differ from a pure 5:4 major third by the interval of the Skhisma
> (32805:32768, 1.954 cents). This is, for most (not all) musical
> purposes, negligible,

especially when we think of the possible "pulling effects" between organ
pipes standing rathe close to each other (via air or/and via wind
chest). this might lead to that an interval tuned close to pure will
sound pure. Research on that is ongoing here in the Chalmers Technical
University at the dept. of Technical acoustics (Prof. Mendel Kleiner).
This "pulling" also seems to be relevant in practice, when talking about
the "bad" 1/4-fifths in standard meantone, an impurity which diminuishes
often when chords are heard. Another aspect is that we find pipe flats
where the pipes are ordered in major thirds, which stabilizes the tuning greatly.

> and appears to have been widely used as a major
> third throughout Islamicate and medieval european music cultures.
> However, the convention that Fb:C approximates 5:4 was not accepted
> in European common practice music, rather the convention that E:C
> approximates 5:4, that is to say, the assumption underlying MT.

Maybe in my draft, there should be a link to this explanation on the
pythagorean tuning-FAQ?
Or rather a footnote (which I prefer to the benefit of the reader)

> Daniel Wolf

> Date: Tue, 27 Feb 2001 15:47:11 -0000
> From: jpehrson@rcn.com
> Subject: Re: Draft 1 FAQ: Organs with split keys fewer than 19 per octave

> --- In tuning@y..., djwolf1@m... wrote:

> /tuning/topicId_19479.html#19483

> > Joseph Pehrson:

...
> Hello Daniel Wolf!

> Thank you so VERY much for answering this "riddle..." I guess, then,
> I was somewhat right when I asked whether the chain of fifths ABOVE
> the initial chain in Mr. Ortgies example started with an "E" that
> differed by a skhisma from the "normal" upward chain Pythagorean "E."

> Since it wasn't spelled Fb it was confusing to me. Additionally, I
> must confess I didn't fully understand the implications of the
> "downward" chain...

Maybe Paul Erlich's suggestion of extending my lattices a bit would help?

> Most probably many people more familiar with the subject matter had
> not trouble understanding what Mr. Ortgies was saying, but the
> missing spelling "Fb" really threw it for me....

So I (we all) will struggle, that this can to be understood easilier and better.

Thanks!

> Joseph Pehrson

-----------------------------

> Date: Tue, 27 Feb 2001 19:30:00 -0000
> From: PERLICH@ACADIAN-ASSET.COM
> Subject: Re: Draft 1 FAQ: Organs with split keys fewer than 19 per octave
>
> Hi Ibo -- not much time, but I just wanted to point out that your
> lattices could be a lot clearer if they incorporated a little bit of
> redundancy.
>
> For example, the schismic example

> > ex. 1 B - F#- C#- G#
> > / \ / \ / \ /
> > Eb- Bb- F - C - G - D - A - E

> would be better understood as:

> B - F#- C#- G#-(Eb- Bb- F - C) ...
> / \ / \ / \ /
> ... Eb- Bb- F - C - G - D - A - E

I added the brackets here...

> and the meantone example

...

Paul's suggestion:

ex. 5 ... G#- D#
/ \ / \
... E - B - F#- C#- G#- D#...
/ \ / \ / \ / \ / \ /
... C - G - D - A - E - B ...
/ \ / \ / \ / \ / \ /
Ab- Eb- Bb- F - C - G ...
\ / \ /
Ab- Eb ...

is fine (the dots are more clear when type without spaces)

How about this?
-----------------------

ex. 5 ... G#- D#
\ / \ / \
... E - B - F#- C#- G#- D#...
\ / \ / \ / \ / \ / \ / \
... C - G - D - A - E - B ...
\ / \ / \ / \ / \ / \ / \
Ab- Eb- Bb- F - C - G ...
\ / \ / \
Ab- Eb ...

dashes and slashes indicate
- meantone fifths
/ pure major thirds
\ minor thirds (as defined by the two previous)

dotted lines ... and slashes with "open end" indicate continuation in
the next row below or above.

> Good to point that out, but repeating notes in the chart helps one
> see exactly how this takes place.

kind regards
Ibo Ortgies

----------------------------------
Ibo Ortgies

GOArt (G�teborg Organ Art center) G�teborgs universitet
http://www.hum.gu.se/goart/w-1.htm