Notation Manual

by Ross W. Duffin
based on the Notation Manual in

Guillaume Dufay - Chansons

Forty-five settings in original notation from Oxford, Bodleian Library MS Canonici 213
Edited by Ross W. Duffin, Ogni Sorte Editions, © 1983.
This version (© 2000) uses the font Squarcialupi

Contents
Clefs & Signatures (B ? & b) 2

Notes & Rests (œ x e q h w W m –´ ≈Œ Ó∑„ l) 3

Other Symbols (% ; U r) 4

Ligatures (tyH:) 5

Mensuration (c o ç ø) 6

Diminution (C O Ç Ø) 7

Proportion (o2 C£) 8

Augmentation (ç) 9

Imperfection (w h q) 10

Alteration (o w h h w) 11

Dots (o w h . h w) 12

Coloration (h. h. s s s) 13
NOTATION MANUAL
Clefs & Signatures DUFFIN

Clefs are signs showing the pitch of the notes on the staff. They
? 
are usually based on C (B) or F ( , ), although the G clef (&)
begins to appear more frequently in the later 15th century. Within a
piece, clefs may change at the beginning of a new line of music or
even within a line if the range of the part suddenly shifts.

Placements of middle C:
B B
≠≠≠
B ≠≠≠
B ≠≠≠
B ≠≠≠ ≠≠≠
Typical placements of the F below middle C:
? ?
≠≠≠
? ≠≠≠ ≠≠≠
Typical placement of the G above middle C:

≠≠≠
&
Flat signatures, as in the example below, apply to the notes on
which they sit, not to those an octave above or below. They may
change in the middle of a piece.
b
?
≠≠≠
b
NOTATION MANUAL
Notes & Rests DUFFIN

m maxima ll or ≠≠
≠≠ lll
W longa „ or ≠≠
≠≠ l
w brevis ∑
≠≠
h semibrevis Ó
≠≠
q minima Œ
≠≠
e or E semiminima ´
≠≠
x fusa ≈
≠≠
–
œ semifusa ≠≠
N.B. Englished names are often used (e.g., long, breve, minim).
The long occasionally appears at the end of a piece or section and
seems to function there simply as a long note of indefinite value
(like a modern fermata). The two smallest values (both notes and
rests) are rare in the 15th century. Rests can occur on any line.
NOTATION MANUAL
Other Symbols DUFFIN

Custos
"guardian" (from the same root as our
English word "custodian"): appears at ;
≠≠
the end of a line and indicates the first
pitch of the next.

Sign of Congruence
indicates where the parts "come together"
%
at the ends of sections, and sometimes
where fuga parts enter and end.
≠≠
Corona
functions like a modern fermata at
U
section endings. Otherwise, it is
taken to indicate homophony.
≠≠
Repeat Sign
indicates that the music r
≠≠ (Repeat once)
of the preceding section
is to be performed once
for each line between
the dots.
®
≠≠ (Repeat twice)

R
≠≠ (Repeat 3 times)

NOTATION MANUAL
Ligatures DUFFIN

Ligatures are two or more notes written in a kind of notational

shorthand. They are also thought to indicate syllable divisions in
texted parts. Note that the oblique shape represents only the two
notes at its extremities.

Rules for Ligature Interpretation

1. An upward stem on the left of a ligature t or z = h h

makes the first two notes semibreves u =hhw
W
2. A downward stem on the left of a ligature « =wW
'
makes the first note a breve

3. A downward stem anywhere after the

beginning of the ligature makes the
v =Ww
preceding note a long

4. All middle notes are breves if there are u u =hhw w w w

wW
no interior stems (see No. 3)

5. An oblique note:
in initial position without a stem is a long
u =Ww
in final position is a breve

6. A square initial note is:

wu =www
a breve if the next note ascends
wu =Www
a long if it descends H=ww
7. A square final note is:
N.B. '=WW w
t =hhw
a breve if approached from below
a long if approached from above
« =wW
'
NOTATION MANUAL
Mensuration DUFFIN

Just as a whole rest in modern notation can have different durations de-
pending on the time signature, so many of the notes and rests of this earlier
notation can have different durations depending on the mensuration. There
are no barlines to mark each measure nor to distinguish one mensuration
from another, but the rhythmic organization is there just the same.
In order to find this organization in situations where no mensuration sign
is given, two questions must be answered: 1. Does the breve contain two
semibreves or three? 2. Does the semibreve contain two minims or three?
The first question refers to what is known as the tempus, i.e., the breve-
semibreve relationship. If the breve contains 3 semibreves, the tempus is
said to be perfect and it is indicated by a mensuration sign in the form of a
perfect (complete) circle: o. If the breve contains only 2 semibreves, the
tempus is said to be imperfect, and it is indicated by a mensuration sign in
the form of an imperfect (incomplete) circle: c.
The second question refers to what is known as prolatio (or prolation),
i.e., the semibreve-minim relationship. If the semibreve contains 3 minims,
the prolation is said to be perfect or major, and it is indicated by a dot in the
middle of the mensuration sign: ø or ç. If the semibreve contains only 2
minims, the prolation is said to be imperfect or minor, and it is indicated by
the absence of a dot in the middle of the mensuration sign: o or c.
Thus, for example, o indicates a mensuration of perfect tempus and im-
perfect prolation (tempus perfectum, prolatio minor), and ç indicates a men-
suration of imperfect tempus and perfect prolation (tempus imperfectum,
prolatio maior). The chart below illustrates tempus and prolation for each of
the four basic mensurations. It should be noted that minims are equivalent
in all of these mensurations, i.e., a minim in one mensuration has the same
duration as a minim in any other, as long as one of the mensurations is not
diminished or augmented.

Tempus Prolation
c w = h h imperfect h = q q imperfect
ç w = h h imperfect h = q q q perfect
o w = h h h perfect h = q q imperfect
ø w = h h h perfect h = q q q perfect
NOTATION MANUAL
Diminution DUFFIN

The term diminution refers to the halving or otherwise shortening

of the values of the notes, and it is indicated either by a line drawn
O
through the mensuration sign ( ) or by a cipher (e.g., o2 , for
which, see Proportion).
Theorists of the period and modern writers both disagree over
whether the line through the mensuration sign called for a speeding
up of the notes to twice their normal speed or to some lesser
amount. This is primarily a performance practice concern (in
consecutive usage) rather than a notational one, however, since
almost all simultaneous instances of diminution with integer valor
(undiminished) mensurations in the early 15th century call for a
doubling of the speed, as follows:
Diminution Chart
c w =h h = q q \q q
C W =w w = h h |h h = qq\qq|qq\qq
o w = h h h = q q \q q \q q
O W = w w = h h h |h h h = qq\qq\qq|qq\qq\qq
ç w = h h = q q q \q q q
Ç W = w w = h h |h h = qqq\qqq|qqq\qqq
ø w = h h h = q q q \q q q \q q q
Ø W = w w = h h h |h h h = qqq\qqq\qqq|qqq\qqq\qqq
NOTATION MANUAL
Proportion DUFFIN

Proportion refers to the use of numerical signs to indicate a

change in the speed of the notes from integer valor. The most
2
common of these is , as in o2 c2
or
!
, both of which call for
2
a doubling of the speed of the notes. That is, represents
(proportio dupla). (In all cases, the upper value replaces the lower
2
value from the preceding section.) Since o would then seem to
O
cause the notes to move at the same speed as , a comparison of
the contrasting organizations of the two is shown here:
o w = h h h = q q \q q \q q
o2 W = w w w = h h |h h |h h =qq\qq|qq\qq|qq\qq
O W = w w = h h h |h h h =qq\qq\qq|qq\qq\qq
As can be seen, o2 causes three imperfect semibreves of o to
be replaced by three imperfect breves of o2, whereas O causes a
perfect breve of o to be replaced by two perfect breves of O.
Most proportions are straightforward (even complex ones like ª
3£
are at least specific) but is sometimes confusing since it is used
¡ 3
by itself to represent both and . In general, in the early 15th
£
century means (sesquialtera) and in the later 15th century it tends
¡
to mean (proportio tripla). Eventually, however, C3
(meaning
C£ ) emerges as the standard triple mensuration.
d
One other special proportion case is the sign which is
¢
equivalent to the numerical proportion at the semibreve level in o
O ç
and , and on the minim level in :
o w =h h h = q q \q q \q q = d w w =h h |h h =q q \q q |q q \q q
ç w =h h = q q q \q q q = d w w =h h |h h =q q \q q |q q \q q
NOTATION MANUAL
Augmentation DUFFIN

Augmentation may be indicated by a numerical proportion sign

¤
such as , where the lower value is greater than the upper (in
this example, two notes replace three of the same value from the
previous section), thus slowing the speed of the notes. This is
normally reserved for cancellation of previous proportions, however.
A more typical use of augmentation occurs after around 1480,
where the signs ø and especially ç are used simultaneously with
other mensurations to indicate a slowing of the notes to the next
level, as follows:

o w = h h h = q q \q q \q q
ø ç h=q q q=e e e e e e
This kind of augmentation is typically used for cantus firmus
statements in masses and motets.
NOTATION MANUAL
Imperfection DUFFIN

In mensurations where notes are grouped in threes, i.e., those in

which either tempus or prolation or both are perfect, imperfection
or alteration may apply. Imperfection usually means making a note
that is potentially worth three of the next lower value worth only two.

Rules for Imperfection

1. A note is perfect before another note or rest of the same
kind.

2. A note is perfect if followed by two or three (or multiples of

three) of the next lower value. Thus, for example,
o w h h w or o w h h h w makes the first w perfect.
3. A note is imperfected if followed or preceded by one or by

more than three of the next lower value. Thus, ç h q w,

ç q h w, or ç h q q q q w makes the h imperfect.
4. Where imperfection by both a following note and a
preceding note is possible, the former takes precedence.
Thus, for example, owhwW w
makes the first imperfect.

5. Rests cannot be imperfected, but they can cause

imperfection of a note.

In addition, notes can sometimes be imperfected by values

w
smaller than the next lower one, most frequently as a by a q in ç
and ø, or a W by a h in O, sometimes imperfecting a note on more
than one level: ø h w q = h. h. h q (in 2:1 reduction).
)
NOTATION MANUAL
Alteration DUFFIN

In mensurations where notes are grouped in threes, i.e., those in

which either tempus or prolation or both are perfect, imperfection
or alteration may apply. Alteration means doubling the value of a
certain note in order to complete the triple grouping (perfection) of
the mensuration.

Rules for Alteration

1. When two semibreves ( hh z
or ) are placed between
two breves (or perfections) in perfect tempus, the
value of the second semibreve is doubled:
hh = the time of h hh
=

h hh
)

2. When two minims are placed between two semibreves

(or perfections) in perfect prolation, the value of the
second minim is doubled:
qq = the time of q qq
=

q qq
)
NOTATION MANUAL
Dots DUFFIN

The familar dot of addition (that which adds one-half again to the
value of the note it follows) occurs frequently. However, another
type of dot occurs, too: one that is identical in appearance to the
dot of addition but different in function.
This so-called dot of division is used to separate perfections.
Functioning therefore almost like a modern barline, it helps to
make clear where imperfection and alteration should apply in
mensurations that have some triple organization. (It is often a
sign of impending alteration.) Thus, the dot of division does not
necessarily change the duration of the note preceding it. It is
usually distinguished by its placement between notes of equal value
(sometimes between the stems of minims) or on either side of rests.
An example of its use and effect is seen here:

o w h . h h w
imperfected dot of division altered

ç h q . q q h
This kind of dot can also be used to create artificial alteration
or imperfection. In so doing, it creates displacement from the
prevailing mensuration and is known as a punctus syncopationis,
as in this example:

ø ç h . q . q h q q which, in 2:1 reduction = h . q q h q q

NOTATION MANUAL
Coloration DUFFIN

Coloration is indicated by the blackening of the notes (originally

the reddening or voiding of black notation) and is usually taken to
mean that each note loses one third of its value (but see below).
Notes in coloration are always imperfect; rests within a passage in
coloration are affected like notes of the same value. The normal
notes of white mensural notation with their corresponding black-
ened forms are: m W w h q e E or
µ ¬ ∫ s e q (rare)
The minim in coloration (e) is identical to one of the forms of
the normal semiminim and this creates some potential confusion.
The intended form is often clear from the context ( eee indicating
coloration or ee indicating semiminims).
There are really two kinds of coloration. Triplet coloration
occurs when two normally imperfect notes are replaced by three
blackened notes, as cww=∫∫∫ chh=sss , , or
cqq=eee . Hemiola coloration occurs when two normally
perfect notes are replaced by three blackened (imperfect) notes, as
ow.w.=∫∫∫ çh.h.=sss o w.=hhh
or . In , and
∫=ss h=s q=e
, so, ironically, and . By the same token,
q=e ç in . Thus, the smaller notes do not lose one third of their
value but, rather, produce a hemiola-like change of accent.
Two other types of coloration are the so-called half coloration,
as in ¸ Y or , where only the note that belongs to the colored part
of the ligature is affected, and the so-called minor color, where
s e = q .  e in the later 15century. This term seems to have been
th

made up by the scholar Willi Apel, though the interpretation is valid.