Appendix

Note:
A non-proportional font like "Courier" is necessary to view the diagrams and examples undistorted!

Introduction
From the 15th to the 18th century keys were added to keyboard
instruments as 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.
Split keys were inserted in those places where there are usually upper
keys between diatonic notes can be found.
Usually the split keys between c and c'' were "broken" to provide
additional keys. 
Occasionally notes outside this range also were broken, in the treble
only eb''/d#'' (more frequent) and g#''/ab'' (less frequent) and in the
bass G#/Ab and Bb/A# occur, but very seldom (s. chapter "A Very Short History").
Split keys for any f#/gb, in whatsoever octave, are until now not known.
Split Key Design
A keyboard may look like this from above:
ordinary keyboard keyboard where eb 
without split key is "split"
back back
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | d# |
| | | | | | |_____| | ___
| | | | | | | | |
| | | | | | | | |
| | eb | | | | eb | | |
| |_______| | | |_______| | _|_
| | | | | |
| | | | | |
| | | | | |
| d | e | | d | e |
|_______|_______| |_______|_______|
front front
In a few preserved keyboards in organ positives by the Manderscheidt
family (s. in chapter "A Very Short History") the front part of the
*lower upper key (eb) might be ca. 2 cm long (+/-2-3 mm)
- the distance being indicated by the vertical line to the right in the drawing.
Viewed from the front a section will look like
_____
/ \
| d# |
_______ _|_____|
/ \ / : \
| eb | | : eb |
___|_______|___ ____|_______|____
| :_ _|_ _: | | :_:_|_ _: |
| | | | | |
| d | e | | d | e |
|_______|_______| |________|________|
And in 3-D:
a keyboard seen from the right
/ /
/ /
/ /
/ / /
/ d# / / / 
/____/ / / 
/ | | / / / /
/ / /| | / / / /
/ / / / |____| / / / /
/ / / / /| / / / /
/ / c# / / eb / |/ / / f# /
/ /_____ / /_____ / / / /_____ /
| | | | / / | | /
| | / | | / / | | /
|_____|/ |_____|/ / |_____|/
/ / / /
/ / / /
c / d / e / f / g
___/__________/__________/__________/__________
| | | |
| | | |
| | | |
___|__________|__________|__________|____
Designs for g#/ab etc. would be similar. 
Added Keys or Split Keys in Pythagorean Tuning
The pythagorean chain of perfect pure fifths 
Gb- Db- Ab- Eb- Bb- F - C - G - D - A - E - B
provides us with the four notes Gb- Db- Ab- Eb, which work as major
thirds (F#- C#- G#- D#) to some of the main keys of the modal system.
These major thirds are so close to pure, that they result practically in
a cut-out of Just Intonation where the diatonic notes (or better, the
notes from the old hexachord-system - therefore including both B and Bb)
get major thirds which are only the small amount of 1,9 cents, the so
called schisma (s. below), lower than pure. 
The scheme
ex. 1 Gb- Db- Ab- Eb- ... 
/ \ / \ / \/
...Bb- F - C - G - D - A - E - B
is therefore practically the same as:
ex. 2 F#- C#- G#- D#- ... 
/ \ / \ / \/
...Bb- F - C - G - D - A - E - B
as which it might have originated once - adding pure major thirds to the
most used diatonic notes.
The chain of pure perfect fifths from 
Cb- Gb- Db- Ab- Eb- Bb- F - C - G - D - A - E
results like the previous ex. 1 in practice in:
ex. 3 B - F#- C#- G#-(Eb- Bb- F - C)
/ \ / \ / \ /
... Eb- Bb- F - C - G - D - A - E
Note: the brackets indicating that the repeated notes are just
continuing the chain of fifths.
All slashes and lines indicate here and the following
diagrams *pure intervals!)
A similar chain of pure perfect fifths 
Fb- Cb- Gb- Db- Ab- Eb- Bb- F - C - G - D - A 
will be practically
ex. 4 E - B - F#- C#-(Ab- Eb- Bb- F) ...
/ \ / \ / \ /
... Ab- Eb- Bb- F - C - G - D - A
The upper rows, for example B - F#- C#- G# in ex. 3. turn out to be
major thirds, which are only a very small amount, the so-called schisma,
lower than pure (s. below for an explanation).
E - B in ex. 1 and A - E in ex. 2. can not be pure fifths:
The fifth E - B in ex. 3, is in fact not a perfect (impure) fifth, but
a pythagorean diminuished sixth E - Cb, and is a syntonic comma below
the pure fifth, because this E is higher than the pure major third to C. 
In the following ex. 5 the pure E (pure major third to C) indicated by a '
E in this example is generated by four pure perfect fifths - it is
audible higher than pure.
ex. 5 E'
/
C - G - D - A - E
The difference between those two E-s is called the syntonic comma (s. Appendix)
Another way to show what happens is to combine the chain of fifths and
the pure major third
ex. 6 E'
/
Fb- Cb- Gb- Db- Ab- Eb- Bb- F - C - G - D - A - E
Fb is only slightly below the E' which serves as pure major third to C.
For practical reasons we can say that Fb = E'
I call those intervalls, actually pythagorean diminuished fourths
(C-Fb in our previous example), which are practically pure major thirds
(very close to C-E') "schismatic thirds"
Especially in an organ the "pulling-effect" ("drawing together") might
render these "schismatic thirds" pure to the listener. And it is not
unlikely, that pythagorean tuning might have been derived not from the
chain of fifths, but from the diatonic notes, which got pure major
thirds added ...
Because of this difference another E , pure to C, might have been
inserted on a keyboard of a pythagorean tuned organ.
There are hints provided by Christopher Stembridge and L. F. Tagliavini,
that extra keys were actually 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. 
In ex. 3 there is only the E, therefore an E' might have been inserted
as extra key.
In ex. 4 there is the E' already there (in the upper row), and E might
have been added to the lower row to make the pure chord e-g#-b available.
The split key between E and F would add either the E above C (to ex. 3)
ex. 7 E - B - F#- C#- G#
/ \ / \ / \ / \ /
Eb- Bb- F - C - G - D - A - E
or the pure fifth E to A (ex. 4)
ex. 8 E - B - F#- C#
/ \ / \ / \ / \
Ab- Eb- Bb- F - C - G - D - A - E
It might be that there have been other keys added in other instruments,
depending on the resp. chain of fifths and the total number of keys. But
this remains speculative until we'll know of documents...
Meantone Extension
In an italian organ around 1500 (4 examples known before 1500), tuned in
a 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:
Wolfenbüttel, 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 (the "enharmonic"
instruments) had *all five split keys (or more) as subsemitones.
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 ~~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 here
~~ meantone fifths
/ pure major thirds
\ minor thirds (as defined by the two previous)
"wavy" lines (~~) and slashes with resp. "open end" indicate
continuation in the next row below or above. Which is nothing else than
Ab~~Eb~~Bb~~F~~~C~~~G~~~D~~~A~~~E~~~B~~~F#~~C#~~G#~~D#
a chain of meantone-tuned perfect fifths, not indicating the third-relations.
Adding split keys widens the possible range from the "usual" meantone
major thirds (8), minor thirds (9) and triads (8 minor and 8 major):
1 2 3 4 5 6 7 8 (9)
C~~~G~~~D~~~A~~~E~~~B~~~F#~~C#~~G#
\ / \ / \ / \ / \ / \ / \ / \ / \ 
Eb~~Bb~~F~~~C~~~G~~~D~~~A~~~E~~~B
1 2 3 4 5 6 7 8 
(with added d# and ab) to: 
1 2 3 4 5 6 7 8 9 10 (11)
F~~~C~~~G~~~D~~~A~~~E~~~B~~~F#~~C#~~G#~~D#
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ 
Ab~~Eb~~Bb~~F~~~C~~~G~~~D~~~A~~~E~~~B~~~F#
1 2 3 4 5 6 7 8 9 10 
plus db and a#:
1 2 3 4 5 6 7 8 9 10 11 12 (13)
Bb- F - C - G - D - A - E - B - F#- C#- G#- D#- A#
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
Db- Ab- Eb- Bb- F - C - G - D - A - E - B - F#- C#
1 2 3 4 5 6 7 8 9 10 11 12 
shown in the following "lattice"...
ex. 6 ~~G#~~D#~~A#
\ / \ / \ / \
~~E~~~B~~~F#~~C#~~G#~~D#~~
\ / \ / \ / \ / \ / \ / \
~~C~~~G~~~D~~~A~~~E~~~B~~
\ / \ / \ / \ / \ / \ / \
~~Ab~~Eb~~Bb~~F~~~C~~~G~~
\ / \ / \ / \
Db~~Ab~~Eb~~
Short Octave and Split Keys
d' was also the middle, symmetrical key on the keyboards with short
octave CDEFGA-c'''.
The keyboard with a short octave 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. F-keyboards could 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 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.
Terminology
The "lattice" diagrams above are used as a "informal" way to show the
symmetry of meantone and the central key d, resp. the fifth D - A is
also the fundament of the most "popular" pythagorean tuning "Gb"-H ... 
Interesting that the organ builders kept until the 20th century the
nomenclature of the pythagorean tuning, saying "d#" even when a "real"
eb is tuned. This also was the standard in the so-called "new German
organ-tablature" in the 17th century. This was a notation in which notes
were expressed by letters and extra signs for rhythms (s. J. G. Walthers
"Musicalisches Lexicon", table XXI) also stayed with this standard.
A c-minor-triad would be notated in a keyboard tablature or tablature
score of the 17th century "c ds g", an Eb-major-triad "d# g b" 
("b" indicating here b-flat in the German way - remember B-A-C-H...). 
The added split keys keys were marked in the Fritzsche- and
Manderscheidt-tradition with an "#" on the pipes (and in contracts):
name sounding
note
ds eb
ds# d#
--------------------
gs g#
gs# ab
This can be found for example in the specification-draft from 1612 by
Hans Leo Hassler for the future organ in the castle chapel of the
electoral court in Dresden, completed by Gottfried Fritzsche probably
end of 1612. A facsimile of this important document is easily
accessible in Gress 1993 (p. 76-77, transcription p. 102-103).
A report from Breslau/Wroclaw, that the organ in Stiftskirche St.
Vincenz, built in the 1660ies by J.C.B. Waldhauser mentions "dis" (eb)
and "dass" (d#).
Michael Praetorius ("De organographia", 1619) wrote however (only here?)
"es" and "ds", "gs" and "as".
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 Wolfenbüttel court chapel, Michael Praetorius, and the
Saxon court organ builder Gottfried Fritzsche. Other promoters were f.
example Henrich Schütz (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 finished by G. Fritzsche in 1612
after having planned it together with Schütz' 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 Nürnberg
(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 where 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, as far as we know today. There
is no safe evidence for any organ with split keys and the Gamba-player
Jean-Jaques Rousseau confirmed in 1697 that this tradition was not to be
found in France, contrary to Italy. Even the only example in Paris, St.
Nicolas des Champs, 1632-1636, C. Carlier, is not known whether it was
at all realized or only a contract or draft, not carried out later.
At the end of the 17th century there are still large organs built with 3
manuals and pedal in Sweden and Germany, which contained 3 split
keys/octave, namely eb/d#, g#/ab and bb/a#, sometimes even going down
below c: Bb/A# occurs in a few cases. Split keys below c were otherwise
only to be found in some Italian early compasses, but those where
keyboards extended down to FF - 12-foot-organs thus.
With the rise of circulating temperaments the practice disappeared in
organ building soon after 1700. The last organ was built by J. and V. F.
Bossart in 1716-1721 in Luzern (Switzerland), St. Urban.
The history of piano's with less than 19 keys/octave is not well known.
Broadwood is reported to have built a piano in 1766 which had all upper
keys split.
About 70 organs with 13-16 keys per octave are known today to have been
built during the time sketched above. This is however very likely only
the "tip of the iceberg" and a closer look to literare and archives
might reveal many more examples.
The historical informed performance practice movement 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
Split keys could be used in several ways and circumstances: Continuo
practice, intonation aid, "fancy pieces", etc. 
Transposition could well 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 developed, which made only sense in transposition,
for example by apparently "omitting" certain keys, to enable comfortable
transposition by certain intervals. This might for example reflect the
relative low or high organ pitch in the respective region. 
Another organ (Sønderborg 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.
Designs in other organs lead to the conclusion that their split keys
were used mainly in continuo-playing (Wolfenbüttel, and
maybe, Sciacca).
Selected literature:
Burgemeister, Ludwig. Der Orgelbau in Schlesien. Straßburg, 1925.
Reprint, edited by, Hermann J. Busch, D. Großmann and R. Walter,
Frankfurt, 1973.
Gress, Frank-Harald. "Die Gottfried-Fritzsche-Orgel der Dresdner
Schloßkapelle: Untersuchungen zur Rekonstruktion ihres Klangbildes." 
Acta organologica [Germany] 23 (1992): 67-112.
Lindley, Mark. "Stimmung und Temperatur." 
In Hören, Messen und Rechnen in der frühen Neuzeit = Geschichte der
Musiktheorie, Vol.6, edited by Frieder Zaminer, 109-331. Darmstadt:
Wissenschaftliche Buchgesellschaft, 1987.
Ortgies, Ibo. "Subsemitoetsen bij historische orgels tussen 1468 en 1721
[Split keys on historical organs between 1468 and 1721]."
Het Orgel [Netherlands] 96, no. 6 (2000): 20-26.
This article appeared slightly earlier in German and Swedish (the Dutch
version is however the most recent):
———. "Subsemitonien in historischen Orgeln. Ein Überblick über die Entwicklung
zwischen 1468 und 1721." 
Concerto [Germany] 17, no. 156 (2000): 22-25.
———. "Subsemitoner i historiska orglar. En överblick över utvecklingen mellan
1468 och 1721."
Tidig Musik [Sweden], no. 2 (2000): 26-31.
Praetorius, Michael. Syntagmatis Musici Tomus Secundus. De
Organographia. 
Wolfenbüttel, 1619. 
Reprint, ed. by Wilibald Gurlitt, in: Documenta musicologica. 1. Reihe:
Facsimiles XIV. Kassel, Bärenreiter: 1958, 1980.
Ratte, Franz Josef. Die Temperatur der Clavierinstrumente.
Quellenstudien zu den theoretischen Grundlagen und praktischen
Anwendungen von der Antike bis ins 17. Jahrhundert. 
Edited by Winfried Schlepphorst. Vol. 16, Veröffentlichungen der
Orgelwissenschaftlichen Forschungsstelle im Musikwissenschaftlichen
Seminar der Westfälischen Wilhelms-Universität. Kassel: Bärenreiter, 1991.
Seydoux, François. "Die abenteuerliche Odyssee eines bedeutsamen
Instruments oder Das Freiburger Pedalpositiv von Sebald Manderscheidt
aus dem Jahre 1667." 
In Musicus Perfectus. Studio in onore di Luigi Ferdinando Tagliavini
"prattico & specolativo" nella ricorrenza del LXV° compleanno, edited by
Pio Pellizzari, 49-106. Bologna: Pàtron editore, 1995.
Seydoux, François. "L'Orgue de Chœer de la Cathédrale de St-Nicolas,
Fribourg." 
In Cathédrale St-Nicolas Fribourg. Inauguration de 'lorgue de chœur
restauré (Sebald Manderscheidt, 1657), edited by Seydoux, François,
Wolfgang Rehn, Patrice Favre, and Luigi Ferdinando Tagliavini. Fribourg
[Switzerland], 1998: 14-34.
Seydoux, François. "L'Orgue de Chœer de la Cathédrale de St-Nicolas,
Fribourg." 
La Tribune de l'Orgue 51, no. 1 (1999): 4-12.
Stembridge, Christopher. "The Cimbalo Cromatico and other Italian
Keyboard Instruments with Nineteen or More Divisions to the Octave." 
Performance Practice Review 6 (1993): 33-59.
Stembridge, Christopher. "Italian organ music to Frescobaldi." 
In The Cambridge Companion to the Organ, edited by Nicholas J. 
Thistlethwaite and Geoffrey Webber, 148-163. Cambridge, 1998.
Stembridge, Christopher, and Denzil Wraight. "Italian Split-keyed
Instruments with Fewer than Nineteen divisions to the Octave."
Performance Practice Review 7 (1994): 150-181.
Tagliavini, Luigi Ferdinando. Considerazioni sugli ambiti delle tastiere
degi organi italiani. [Thoughts on the keyboard ranges of Italian
organs]. 
Edited by Friedemann Hellwig, Studia organologica: Festschrift für John
Henry van der Meer zu seinem fünfundsechzigsten Geburtstag. Tutzing:
Schneider, 1987.
Tagliavini, Luigi Ferdinando. "Notes on Tuning Methods in
Fifteenth-Century Italy."
In Charles Brenton Fisk. Organ Builder. Volume One. (Essays in his
Honor), edited by Fenner Douglass and others, 191-199. Easthampton
(Mass.), 1986.
Walther, Johann Gottfried. Musicalisches Lexikon oder Musicalische Bibliothec.
Leipzig, 1732. Reprint, Kassel, Bärenreiter: 1953.
Acknowledgements:
This FAQ was created with the support of members of the Tuning-list and
others, especially:
I'd like to thank for valuable hints help:
Graham Breed, Dale C. Carr, Paul Erlich, Massimilano Guido, John A. de
Laubenfels, Joseph Pehrson, Margo Schulter.
Further acknowledgements are listed in my above mentioned article.
Appendix
Pythagorean Comma./.Syntonic Comma = The Schisma 
The schisma is the difference between the 
pythagorean comma (12 pure perfect fifths - 7 octaves) and the 
syntonic comma (4 pure perfect fifths - 1 pure major third - 2 octaves)
The schisma is then 
(12 pure perfect fifths - 7 octaves) 
- ( 4 pure perfect fifths - 2 octaves - 1 pure major third)
Now forget the octaves, because they are just here to keep us in an
"audible range" and we can use the fourths as complementary intervals of course.
Resolving the brackets and without the octaves it is
12 pure perfect fifths 
- 4 pure perfect fifths 
+ 1 pure major third
--------------------------------------------------------
= 8 pure perfect fifths + 1 pure major third
8 pure perfect fifths + 1 pure major third
is represented by the chain
E'
/
Fb- Cb- Gb- Db- Ab- Eb- Bb- F - C
The difference between the Fb and the E' is the schisma (the E' being
this small amount of 1,955 cents higher than Fb).