Willi Apel From St. Martial to Notre Dame

From St. Martial to Notre Dame
Author(s): Willi Apel
Source: Journal of the American Musicological Society, Vol. 2, No. 3 (Autumn, 1949), pp.
145-158
Published by: University of California Press on behalf of the American Musicological
Society
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From St. Martial to Notre Dame*
BY WILLI APEL

longed notes, each of which becomes

SOMETIME during the second half
of the 12th century a developa "pedal point" for an extended comment took place that led to one
ofnotes, often 50 to Ioo, in the
plex of
the most fundamental concepts
upperof
part. The melismatic passages
Western music: meter and metrical
(often with ten, twenty, or more
rhythm. The final result stands clearlynotes to a syllable), on the other
before us in the organa tripla andhand, were transformed into tenor

quadrupla of Perotinus, works that passages of a considerably more conwere composed about 200oo. The op-tinuous design and motion, with the
posite end of the line of evolutioncorresponding passage of the duplum
is indicated by the organa dupla of showing only twice to four times as
St. Martial, written in the mid-I2thmany notes as are found in the tenor.
century. All indications support theThese sections, the so-called clautheory that these organa are in freesulae, are the earliest known examples
rhythm, lacking fixed time valuesof polyphonic composition in strict
and rhythmic patterns. Thus withinmodal rhythm. The tenor usually
a relatively short span of time the proceeds in irregular groups (orstyle of rhythm changed into its verydines) of the fifth mode (longae or
opposite, from the free, "Gregorian"duplex longae), while the duplum
rhythm of St. Martial into the rigidmoves in the faster rhythm of the
modal rhythm of Notre Dame.
first mode (alternation of longae and
While the organa of Perotinus rep-breves). Thus Leoninus must be

resent the complete ascendancy ofcredited with the introduction into

modal rhythm, its first appearance ispolyphonic composition of strict
in the works of his predecessor, meter and regular rhythm. The reLeoninus. Leoninus created the stand- maining question is whether, or to
ard form of the Parisian organa, awhat extent, this novel principle is
form based on the distinction bealso embodied in the "pedal point"

tween the syllabic and the melis-sections (usually called organal sec-

matic sections in the Gregorian mel-tions) of his organa. It is this question
odies used in the tenor. The passageswhich forms the topic of the present
in syllabic style (or group style: thatstudy.
is, having one or a few notes to each While the notation of the clausula
syllable) were transformed into tenorsections in Leoninus' organa is clear
sections consisting of single pro-and simple, that of the organal sections presents difficulties that have
*This article is the result of studies made

not been satisfactorily solved. The
in preparation of the fourth, revised edition
notational characters used in these
of The Notation of Polyphonic Music. I am
grateful to the editors of the Journal for giv-sections are essentially the same as
ing me this opportunity to present the topic
are encountered in the clausula sec-

in much greater detail than is possible in the
book. Abbreviations: OHM, Oxford History of
tions

and in modal notation in general, that is, ligatures, conjuncturas,
schaft; CS, Coussemaker, Scriptorum de mu-and single notes. The difference lies
sica medii wvi.
in the highly irregular arrangement
Music; ZMW, Zeitschrift fiir Musikwissen-

schaft; AMW , Archiv fiir Musikwissen-

145

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146 JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY
and combination of these signs, as

Turning now to our main question,
that is, the rhythmic interpretation

mode) encountered in modal nota-

that the following varieties of rhyth-

opposed to the regular grouping of
ligatures (e.g., 3 2 2 2... for the first

tion. Another striking difference is
the fairly extended use of many-note
ligatures and, particularly, conjuncturas, the latter often with as many

as ten notes in descending motion.
In the clausula sections the number

of the organal sections, it appears

mic style must be admitted as possi-

bilities:

A. Free Rhythm. The notes of

the duplum are all essentially isochronous, admitting, of course, a

certain flexibility of tempo and oc-

of notes combined into a single graph casional lengthening of notes, par-

ticularly at the end of a phrase. This
rarely goes beyond four (ligatura
quaternaria). The accompanying re-style is similar to the Solesmes method
of interpreting Gregorian chant, alproduction, showing the organum
duplum Viderunt onmes, illustratesthough the specific principles of this
the chief traits of form, style, andmethod (ictus, etc.) cannot, of
course, be applied, since they have
notation encountered in this period.
no historical foundation.
The short clausula section, "om," appears at the end of the second brace. B. Measured Rhythm. The notes
Organum duplum Viderunt omnes
W1, f. 21 r

Ex. I

itY

IIU'TTF-

"t

I
v

W-

-MIA il"

?-'

-

--l

,

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-

FROM ST. MARTIAL TO NOTRE DAME 147

of the upper part have definite
of 1901, time
pp. i76ff). On the basis of
values, a short (brevis) an
and
extremely
a longjudicious and objective
review
of the remarks found in the
(longa) of double or triple
length,

variousfalling
treatises of the 13th century,
which alternate freely without

Wooldridge,
into regular measures. This
style isalthough briefly admitting the possibility that "in the

similar to the so-called "mensuralist"

interpretation of Gregorian chant
system of Organum purum meas-

ure, as it was understood in the
which has been advocated by P.
Wagner, Dom Jeannin, and others.
thirteenth century, finds no place at
C. Metrical Rhythm. The notes of
all" [p. 185], decides in favor of a
the upper part have definite time
rendition in triple meter, saying that
values, short and long, which are
"it is always perfectly possible to
arranged in regular measures (triple
translate the notes of the upper part
meter).
in measure" and that, on the other

D. Modal Rhythm. The upper

hand, his "attempts to construct from

the given figures, upon a non-mensural basis, phrases containing any
clear musical meaning, have entirely

part is in triple meter, with the notes

falling into the regular pattern of

one of the rhythmic modes.
Judging from the relatively few
transcriptions of organa dupla that
have been published,' the rhythmic

failed" [p. I86]. Accordingly, his

transcriptions are in triple meter,

with a free change of rhythmic patterns, some measures showing tro-

style described under C (above) ap-

pears to be generally accepted as the

basis of transcription for the organal sections of the organa dupla.

A detailed discussion of the whole

chaic rhythm (first mode), others
iambic (second mode). In more recent transcriptions presented by

other scholars this wavering between

problem is found in H. E. Woolthe two rhythmic patterns is gen-

dridge's basic study of early polypherally avoided, and the upper part

ony, in Volume I of The Oxford
appears in what may be considered

a free modification of the first mode,
History of Music (OHM; first edition
Music, no. 29.-Alleluia Pascha nostrum :
1Judea et Jherusalem: OHM, I (Ist ed.), pp.

188ff (facsimile); Riemann, Handbuch der
Musikgeschichte, I, 2, p. 156; Handschin, in
ZMW, X (1927-28), p. I5; Sowa, in Ein ...
Mensuraltraktat (1930), p. xxxviii.-Haec
dies: Adler, Handbuch, I, p. 217 (Ludwig) ;
Besseler, Musik des Mittelalters und der

Ludwig, in ZMW, V (1922-23), p. 448.--

Crucifixus in carne: Handschin, in AMW, VII

(1925), p. 6i.--Propter veritatem: H.

Angles, El codex musical de las Huelgas

(I931), II, no. 47.-Tanquam sponsus: OHM,

I (Ist ed.), p. 195.-Virgo Dei genetrix: ibid.,

Renaissance (I937), pp. 99f (facsimile)p.; 201.-Benedicamus Domino: Davison and
Davison and Apel, Historical Anthology of
Apel, op. cit., no. 28c.
Ex. 2

..,

,,

A J IJ

,, w ..s1 ir,-" " - . m -r,, - . ?3

-4

'01

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148 JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY

involving frequent use of fractio

modi and extensio modi. As an il-

(Simon Tunstede) no doubt suggest

a "free" rhythmic style, but of

course it is difficult for us to delustration we show three transcripexactly the degree of freetions of a passage from Judeatermine
et

dom indicated by them. Moreover
Iherusalem, that is, the closing

we have no way of knowing whether
copula, after the syllable "lem" [Ex.
these descriptions refer to the organa
2].2 Other transcriptions of a recent
dupla of the Leoninus period or perdate (Ludwig, Angles) show the same
haps to others of an earlier period,
general aspect as those by Sowa and
to those of St. Martial or to
Handschin, but only confirm the possibly
imsimilar ones written before Leoninus
pression that, within this general

in Paris, and now lost. In fact, such
framework of rhythm, all questions
assumption would eliminate a difand problems of detail are decidedanon
arising from the fact that
the basis of personal preference ficulty
and
other theorists explain organum duindividual "feeling."
plum (organum purum, organum
The general uncertainty that prevails in this field, and the failurespeciale,
of
organum per se) in terms
of "free modal rhythm"
outstanding scholars to arrive suggestive
at a
than "free rhythm." Thus
uniform solution of the problemrather
on

Johannes de Garlandia (CS, I, p.
the basis of their general premise,
I 14), as well as the Anonymous of
1279 (Sowa, p. 53 and p. 127), draws
vision and new approach to our
a distinction
between modus rectus
question. In the original edition
of
and modus non rectus, ascribing the
The Notation of Polyphonic Music
former to the various types of dis(I942, pp. 266ff) the present writer
(organum triplum, clausulae,
tried to formulate a new theorycantus
remotets, etc.), the latter to organum
garding the problematic "Duplum
per se. We know from the practical
notation," maintaining that its rhyth-

would seem to call for a basic re-

that organum duplum undermic style is that of "free rhythm,"sources
as

went far-reaching changes of style
previously described under A above.
and rhythm during the course of the
I2th century. It is entirely possible
writings of the I3th and I4th centhat some of the writers describe a
turies are quoted in support of this
type of organum different from the
theory. As happens so often in such
one explained by others. If this poscases, the language of these quotasibility is admitted, we can resolve
tions is somewhat ambiguous and to
the seeming contradiction between
a certain extent open to different
statements about notae sine mensura
interpretations.3 Descriptions such

A number of remarks found in the

as "infinita multiplicitate ac miraand others about modus non rectus
by relating the former to organa
quadam flexibilitate" (Anon. de la
written in the style of St. Martial and
Fage), "coherentia vocum immenthe latter to those of the Leoninus
surabilium" (Walter Odington), or
period.
"discurrere per notas sine mensura"
The above-mentioned passage from

2The first line of Ex. 2 is from H. E. Wool-

dridge (OHM, I, p. 189, facsimile); the second line is from J. Handschin ("Die mittel-

Garlandia appears in Wooldridge's

sThe validity of the evidence on which I based
alterlichen Auffiihrungen in Ziirich, Bern und my explanations has been questioned by Man-

Basel," ZMW, X, p. 15); the third line is

from H. Sowa (Ein anonymer glossierter

fred F. Bukofzer and Oliver Strunk. It was
their criticism which induced me to re-

Mensuraltraktat 1279 [1930], p. xxxviii.) examine the entire problem.

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FROM ST. MARTIAL TO NOTRE DAME 149

needsistonot
be said regarding the discantus
study in a free rendition which
[same
as
equipollentia]
in organum.
entirely satisfactory (OHM, I, p.
The longae
and breves in such an or178). Garlandia's term "organum
per
ganum are recognized as follows, that is,
se" very likely means two-voice orthrough consonance (per consonantiam),

ganum (organum duplum)
as opthrough
the form of the notes (per

posed to "organum cum alio,"
that
figuram),
and through the [rule of the]
is, organum duplum with
another
penultimate
(per pemnultimam).

voice part, hence, organumHence
triplum.
the rule: Everything that occurs
We suggest the following translation
anywhere by virtue of consonance, is
called long.
(and interpretation) of the
entire

Another rule: Whatever
passage (CS, I, p. 114: "Organum

has the form

dicitur multipliciter . . ."):of a longa . . .4 is considered long.

Another rule: Whatever occurs before a

long pause,
or before a perfect consoThe term organum is used in various
ways:
nance, is considered
as long.
generaliter [as a general designation
for

polyphonic music] and specialiter [for
The importance of these remarks

organum proper]. Organum generaliter has
lies first of all in the clear distinction

been previously discussed; now we have
that is There
made between two rhythmic
to speak about organum in speciali.

styles either
found in
are two types of organum in speciali,

organum duplum, a

in modus rectus [this term refers
primarily
over,
we learn

that there are longae

modus
rectus
for the discantus secper se [organum duplum] or cum
alio
[ortions
(clausulae), and a modus non
ganum triplum, quadruplum].
Organum
per se is that which is performed
rectus either
for the organal sections. More-

to the clausula sections of organum
duand breves
in this modus non rectus,
plum] or in modus non rectus [this term

and that they are recognized by certain rules involving a consideration
duplum]. By modus rectus we mean that
of consonances, of note forms, and
type of modus which is used for discantus.
of the penultimates. Unfortunately,
The [modus] non rectus is so called in
refers to the organal sections of organum

order to distinguish it from a [modus]these rules are so cryptically ex-

pressed that it is difficult to draw
rectus in which longae and breves are
any definite conclusion from them,
taken strictly according to the principles
of the first mode (sumuntur debito modoexcept a negative one: the transcripprimo, et principaliter). In non rectus, tions discussed and illustrated previ-

however, the longae and breves are [also]
ously (p. I47) are not in agreement
in the first mode, but in a casual manner
with Garlandia's description of mo(ex contingenti). Whatever then is sung
dus non rectus. To be sure, this term
in an irregular rhythm (per non rectam

indicates a free variety of modal
mensuram), as just explained, is called

rhythm, and could therefore be inorganum non rectum [this is identical with

terpreted as indicating the general
"organal sections of organum dilplum"].
style of metrical rhythm (C above)
The equipollentia [that is, relationship of
which forms the basis of these tranthe upper to the lower part in this type
of music] is limited to a single tone
scriptions. However, none of the spe-

[unisono: the sustained note of the tenor],
cific rules given by Garlandia are intill the end of each pzunctus [section based
corporated in these transcriptions.

on one tenor note], where the two parts Somewhat similar are the explana-

meet in a consonance. And this is all that

'Here follows the somewhat obscure passage:
"secundum organa ante pausationem, vel loco
consonantie. . ."

tions and rules given by Franco in

his Ars cantus mensurabilis of ca.

I260 (CS, I, pp. I34b-I35a: "Or-

ganum proprie sumptum ..."):

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I 50 JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY

Organum proprie sumptum [probably
language is perhaps even more cryptiidentical with organum per se] is a song
cal than that of Garlandia, particu-

which is not everywhere measured [this
larly with regard to the "rule of
may refer to the difference between the
the consonance." There is, however,
clausulae and the organal sections, or pos-

a third writer who presents the same
sibly between the upper part and the

subject in explanations as clear and

tenor]. It should be noticed that organutm
detailed as one could wish, namely,
purum exists only above a tenor having a
the famous Anonymous IV of the
single sustained note (sola nota in unisono),
and that whenever the tenor has several

British Museum. As is well known,

this writer was not a professional
notes [written closely] together, discantus
results, as in the following example.5 theorist like Garlandia or Franco,
The longae and breves of this organum
but, in all probability, a young Eng-

lishman
who studied at Paris someare recognized by three rules. The first
is:

whatever is notated as a simple longa
is about 1260 or I27o. His manutime
long, and similarly for breves and semiscript may well represent notes

breves. The second rule is: whatever is

taken during a course given by a

long, must be in consonance (indiget conprofessor
at the Sorbonne (Joh. de
cordantia) with the tenor; if, however,
a
Garlandia?). In fact, the chief value
dissonance appears, the tenor should be
of his "treatise" lies in its much
silent or should adapt itself into a consonance as is shown here [see Ex. greater
3. The spontaneity and diversity of

topics as compared with the treatises

proper which, although more sys-

Ex. 3

...).

- - ,. - , _. ..

dissonance occurs on the note b of the

tematic, frequently limit themselves

to the "rules." We are concerned

here with the last chapter, Capitulum

Septimum, of Anonymous IV, en-

titled "De modis irregularibus." (CS,
I, pp. 361-364). This chapter, as well

upper part. According to Franco the tenor
as part

of the preceding one, has

should either pause at this moment,often
or
been noted for its "mysterious"
move into a consonant note, g].
character and for its "language which
The third rule is: whatever is found im-

is even more disheartening to the stumediately before the rest known as finis
dent in search of proofs of measurepunctorum [that is, the end of a section
based on one tenor note] is long, becausement in the upper part of organum
purum than that of the author of Ars
every penultimate is long. It should also

be noticed that whenever in organumCantus Mensurabilis."' Actually this

purum several notes occur on the same characterization is not entirely corpitch (similiter in unisono evenerint), therect. The second half of the Capifirst only should be clearly sung (percutitulum Sextum, in which we hear
debet), while the others should be held inabout the "diversitatibus" among the
floratura [this indicates a vocal tremolo;"triplis majoribus," that is, the great
see Garlandia's example of florificatio vocis

organa tripla such as Alleluia dies

in CS, I, p. 116, reproduced in OHM, I, p.
sanctificatus, is rather mystifying,

187].

and even more so is the first part of

The fact that two of the most im-

the Capitulum Septimum with its

portant theorists of the I3th century5Here follows a musical example consisting
of a short copula and a clausula in the style

give essentially the same set of rules of Leoninus. See the transcription in OHM, I,
for organum duplum is of no small p. I87.
importance. Unfortunately, Franco's6OHM, I, p. 184.
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FROM ST. MARTIAL TO NOTRE DAME I 5
ceived
description of the notorious modi
ir- to be long through the modus,
whether it is consonant or not.
regulares. This seventh chapter, howFurthermore, in a ligature of two notes
ever, continues after the "dishearten-

(punctus duorum) the first note is long if
ing" description of the irregular
it is in consonance, short if in dissonance.

modes with an extended explanation
[This applies to the notes considered] as
of the consonances in organum pusuch, not as far as [they are subject to the
rum, and how longae and brevesrule
areof] the penultimate just mentioned
recognized in organum purum. The
(in quantum de se et non in quantum
predicta).
language of these explanations is penultima
perFurthermore the last note of two [of a
fectly clear and the principles extwo-note ligature] is long if consonant,
pounded turn out to be of funda-

short if dissonant, at least as such, etc.
mental importance in our problem.
As far as I know, Wooldridge is [same
the exception as before].
Furthermore
only writer to have at least taken

in a ligature of three notes

(punctus trium) the first note is long if in
passing notice of these explanations

consonance, otherwise not; the second is
consonance, otherwise not if con-

(OHM, I, p. I84). Here follows
a
long in

translation of the entire section sidered
(CS, as such (in quantum de se), but
I, p. 362: "Concordantie organi puri
is [always] long if it is a penultimate. Each
..."), with certain passages omitted:
last note of three is long in consonance,

short in dissonance, but long in the above-

The regular consonances of organum
mentioned [case of the] penultimate.
purum are unison, octave, fourth, fifth,
Each note [in a ligature] of four,

minor third (semiditonus) and major third
whether the first, the second, the third, or
(ditonus). [There follows an enumeration
the fourth, is long if it is in consonance,
of the secundariae and tertiae consonances,
short if in dissonance.

that is, the regular consonances plus one
Furthermore two [successive] notes of
the same pitch (in eodem sono), whether

or two octaves].

In organum purum the longae and breves

consonant or not, are performed as a

are recognized in various ways. One oflonga florata.

these is: each initial note (punctus primus), Furthermore currentes with an antecedwhether it is consonant according to theent [note], such as those of eleven notes

above system of consonances, or not, is
in Viderunt, have a certain special manner
either7 a longa parva, or a longa tarda, or
(modum extraneum). [In contrast] to the
a [longa] media; and this in whichever
other [characters] they do not regard
ligature it [the initial note] may occur,whether they are consonant or not;8 and
whether one of two or of three notes, etc.they descend quickly; if the first note is a
There is, however, the following differcurrens [that is, a note in the diamond
ence: if [this note] is consonant [with the
shape of the later semibrevis], then its antetenor], the tenor will sound; if however it
cedent or the second or the third before
is not consonant, the tenor will pause. [is a long].
Similarly each last note [of a section] is In the above-mentioned descent [that
long and consonant.
is, in the example from Viderunt] the
Furthermore each penultimate note beantecedent is not the note before [the
fore a long rest, as [occurs] at the end of
currentes] but the second before, and this
a section [in fine puncti; punctus meansis long; and the first before, although
here a sustained note of the tenor] or of a
ascending, is a currens, because there are
clausula, is long.
actually twelve currentes, not eleven. And
And each penultimate is likewise per-the second note before [the currentes] is
7I read here "aut" for Coussemaker's "ante."

long because it is in the consonance of the

fifth. If it were not in consonance, it
s". . . utrum concordant vel non equaliter

proposse." The meaning of the last two wordswould yet be long, but the tenor would

is not clear to me.

pause, because always the note before, or

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I 5 2 JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY
dis); however, one should not delay too
long before coming to the close.
venience of the descent.
And certain good organistae prefer to
use dissonances rather than consonances in
And this applies essentially to the husuch penultimates, etc., as appears fully
man voice, but is not necessary for instruin the books of organa.
ments. Similar rules apply to currentes
showing ascending and descending mo-Whatever occurs between the abovementioned beginning and the above-mention, or descending and ascending motion,
tioned close is considered as mediation.
with their antecedent or antecedents, etc.
the second or the third before [a group of
currentes] is necessarily long for the con-

Furthermore occasionally there areIn the name and in honor of the Most

Holy Mediator of all, who is the true
many long notes for the sake of variety
Saviour Jesus Christ, Son of the living
(color) or beauty of the melody, whether
and who is the Crown and Glory of
they are consonant or not, as the result God,
of
the performance (quod quidem per all
se the Saints, to which glory may we all
patet in operando).
arrive with the Most Holy.
Furthermore there is a certain duplex
longa florata, and this occurs at the begin-These extended explanations can
ning [of] In nomine sanctissimi alpha, and
be summed up as follows: (i) The
this is called beginning before the beginconsonances are unison, octave,
ning, and is always consonant.
fourth, fifth, major and minor third.

Furthermore there are some who put
(2) Each first note is long. If the first
two or three [notes] in the place of one;
note is dissonant with the tenor, the

and the first of these can be consonant or

tenor pauses (that is, comes in later).
dissonant, and [in the latter case] always
(3) Each final note is long and constarts shortly before the tenor, and the

tenor comes in with the second note if

sonant. (4) Each penultimate note

this is consonant, or with the third, and
before a rest is long, whether consoor not. (5) In ligatures a note is
this third note will be prolonged withnant
a
florification, as previously explained. And
long if it is consonant, short if it is
some [composers] put three or four notes
dissonant (always with the exception
in ligature before the beginning of the
of rule 4). (6) Two successive notes

tenor, and if the last of these is consonant,
the tenor will start with this. If it is dis-

of the same pitch, whether consonant
or dissonant, form a longa florata. (7)

sonant, the beginning will be with the first

Currentes descend quickly, but are

consonant
that
follows.
....
The end note
of In
nomine
sanctissimi
ispreceded by a long note. (8) Perperformed in many ways: some close itformers occasionally deviate from the
rules, by lengthening dissonant notes,
with a single note either at the octave or
or inserting notes (?).
in unison or at the fifth, rarely however
at -the fourth, except in stringed instru- The central rule in this set is rule 5.
ments (in instrumento cordarum), and stillSince

the dupla are always written

more rarely at the major or minor third;
entirely in ligatures, it means that
as men will do according to their pleasure,
each note of the upper part is long if
but the above-described beginning is gen-it forms a consonance with the suserally accepted by all.
tained note of the tenor, otherwise
There are others who place one penultimate before the above-mentioned octave,

whether it be in consonance or in dis-

it is short. This, of course, is exactly

what Garlandia and Franco say, al-

sonance, as long as it is suitable, etc. though in such a brief manner that
There are others who place before one
thiswould probably not dare to use
their remarks as a foundation for a
penultimate one, two, three or more others,

as may be suitable according to one or new
sev- approach to the problem of oreral modes (prout melius competit,9The
vel remaining part of this paragraph is

competunt de uno modo vel pluribusrather
mo-obscure.

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FROM ST. MARTIAL TO NOTRE DAME 153

(dotted
ganum duplum. Together with
the quarter note), while two
dissonant
notes in succession, e.g.
most detailed explanations and
re-

peated statements of Anonymous IV,

g cona b C could be interpreted a
however, they form a highly
vincing body of evidence, leading to
L B/B L, etc. The resulting intera novel interpretation of the organa
pretation
would be essentially in the
dupla, based on the "principle of

same rhythmic style as the transcripconsonance" rather than on the "prin-

tions
ciple of ligatures." In fact, one
and of Ludwig, Handschin, and
others (the metrical rhythm, C, of
the same combination of ligatures
our
tabulation), but would, of course
will have a different rhythmic
patdiffer
tern, depending upon the pitch of from these in many particu
lars. Example 5 shows a transcrip
the tenor notes. Example 4 illustrates
tion of Judea et Jherusalem accord
this important point.

Ex. 4

"

s

It
is
inte
ing to the "rules
of consonance" and
many
ca
in triple meter.
nance
aut
The main advantage of this intermic
form
pretation
is that it eliminates most
the of the
other
arbitrariness that is so disturb-

just
as
m
ing and irritating to the student try(longae,
ing to transcribe an organum duplum
alternate
along the traditional lines. It com-

formati

pletely removes these compositions
triple
me
from the province of
"notational
lar
modal

arises whether in such cases the two

problems," and makes them appear
as examples of an organic musical

basic rhythmic values should bepractice which involved no hairsplit-

modified and adjusted into the frame- ting calculations and which, with a

work of triple meter. Such adjust-little training, could easily be rements are, of course, always possi-

ble. In the case of several consonances
e f e g,

in succession, e.g., each note

would become a longa perfecta

created by a present-day singer.
Nevertheless, the above method of

transcription still includes a certain
amount of "processing," that is, the

adjustment of the groups of longs

Ex. 5

N8

U-

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154 JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY

Example 6 is a rendition of Judea et
and shorts into triple-meter formations. Although these adjustments are
]herusalem in longs and shorts, without metrical adjustments.
relatively easy to make, they often

produce results that are not alto- For

a more extended extended ex-

a Benedicamus Domino from
gether satisfactory. Among these ample
is
the sudden change from trochaic to
W1, pp. 87'/88 may be considered.x0
iambic patterns that results when-The transcription in Example 7

ever there are two dissonant notes

shows the application, not only of

between two consonances; or the
the basic rule 5, but also of the other
frequent occurrence of two, three, rules of Anonymous IV. Thus the
or more "consonant" longae per- first note is long (rule i), but since
fectae, a value that, in all probability, it forms a dissonance with the tenor,
did not appear until a somewhat laterthis enters with the next note, on d'.
Likewise the penultimate of each secperiod.
Moreover, it should be noticed
tion is long, and two successive notes
that the triple-meter adjustment, nat- of the same pitch form a longa florural though it appears to the present- ata, indicated in the transcription by
day musicologist, is in no way cor- a wavy line. The currentes are reroborated or required by the explana-produced as quick sixteenth notes.
Ex. 6

S"MI

40-80WF i4

tions of Anonymous
Each such
IV.
group
In is
fact,
preceded
his
by a
long note, much
which may or
may not be
explanations become
more
in consonance withif,
the tenor.
In the
plausible and convincing
instead
of forcing his longs
latter case
and
the tenor
shorts
pauses, as isinto
sugthe framework of
triple
meter,
we
gested
in our transcriptions
by the
consider them as the two basic elerest. Possibly the tenor also pauses

ments of an essentially different
during the longae floratae which

often fall on dissonant notes. The
rhythmic style, that is, of measured
rhythmic meaning of the conjuncrhythm (B of our tabulation). True
tura ternaria, consisting of a longa
enough, the explanations of Anonymous IV, although compelling as and
re- two currentes, is ambiguous, de-

gards the basic principle of consopending upon whether this sign is
nance, do not contain definite eviinterpreted as the shortest form of
dence as to the basic rhythmic style
the currentes or (as regularly in
of the organa dupla. Nor can a defmodal notation) as the equivalent of

inite conclusion be drawn from Gara ligatura ternaria. Both meanings are
landia's modus non rectus. In view
indicated in the example, the latter in
of this situation it is all the more imsmall notes.

portant to examine the possibility
An interesting problem is posed by
just outlined. Aside from the the
fact
fact that the organal sections of

that it eliminates the last element the
of organa dupla, although generally

arbitrariness, it leads to results that,
written in highly irregular groups of
it seems to me, are most interesting
10See facsimile in The Notation of Polyphonic
Music, p. 255 (4th ed., p. 247).
and worthy of serious consideration.

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FROM ST. MARTIAL TO NOTRE DAME 155

by repeated
ligatures, usually contain short
pas- notes) appear in formations comwhich, from the point of view
sages showing the well-known

binations of the first mode,
3 2 2as well as of melody, show
of rhythm
the familiar
... or 1 2 2 2 .... An example
oc- characteristics

of the first

curs in the second brace of the

mode. Naturally, the modal interpretation of these passages often leads to
Benedicamus Domino, immediately

long values for dissonant notes, in
after the syllable "ne." Obviously

violation of the basic principle of
such passages should be read accordconsonance. However, a reconciliaing to the "principle of ligatures,"
tion of the two principles could be
that is, in a strictly modal pattern,
found
not according to the "principle
of in the statement made by sev-

Ex. 7

I a -

J A . .I..I I .. . . . .10I -W.. ? _

. A_ , 4_ I Id I I i , 1 , -A' 1 1-'. ' ' I . : , ) , .. : I

Temor
pausew?
Tezwr
pause: ?

didi-

.PA
La

I

/00

1

i

.

..

IF. ' -" . . . . ... A]..

consonance," which would result

.

eral theorists that "the tenor pauses,

here in a distortion of what the writ- if a dissonance appears." In fact, if

ing clearly suggests. Possibly Gar-organum duplum were to be ren-

landia was referring to such passagesdered entirely according to the prin(in addition to the clausulae) whenciple of consonance, these statements
he made the distinction between

modus rectus and modus non rectus.

would seem to be pointless, except

for isolated dissonant notes resulting

Modus rectus is also clearly sugfrom the rules 6 and 7 of Anonymous

gested by various ordines on braces
IV. Passages in modus rectus such
3 and 4 of the Benedicamus Domino,
as the above would certainly rep-

in which single notes (necessitated
resent another, and perhaps more
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156 JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY
at the beginning of Viderunt omnes

logical, opportunity for the tenor to

(Ex. 8). The initial passage shows
several groups of three dissonant
notes (e-d-e) between two conso-

pause. In the accompanying tran-

scription these passages are indicated
by an extended horizontal line.
While in these modus rectus pas-

sages modal rhythm appears in opposition to the basic principle of
consonances, the organa dupla also
often include shorter or longer passages in which triple meter appears

nant notes (f). There can be hardly
any doubt that here the consonant

longae are to be lengthened into
longae perfectae. Passages like this

may well be considered as indicating
the transition from measured rhythm

as the result of this principle. A particularly extended example is found

(B) to metrical rhythm (C). A similar problem arises in connection with

Ex. 8

vi?

r

A

h~

Tenor pauts ea.

ol-

^0n
F)o

r.r.

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FROM ST. MARTIAL TO NOTRE DAME 157

at the
of this article,
the passage following thestated
low
g beginning
of
is every reason to believe that
the duplum (Ex. 8, middle there
of brace
the organa of
of St. Martial (as well as
5). Here the strict application

those would
of Compostela) are in free
the principle of consonance
rhythm.
course, it could be arlead to the version given
in Of
our
that we have no definite evitranscription, while modalgued
rhythm

would result if the f' were dence
treated
for thisasassumption, and that
we cannot
decide with absolute cera dissonance, and consequently
rendered as a short note. No doubt the
tainty whether the detailed explanalatter reading would be preferable.tions of Anonymous IV actually reThat the rules of consonance were
fer to the Parisian organa of Leoninus or to the Provengal organa of St.
occasionally modified is expressly
Martial. There are, however, rather
stated by Anonymous IV. Although
compelling reasons for discarding the
he mentions only the possibility of
latter possibility. First it should be
treating dissonant notes as longs, it is
reasonable to assume that consonant
noticed that the organa of St. Martial
in the south of France. It
notes could also occasionally originated
be

treated as shorts "in operando."
is very

doubtful whether, under then

Moreover, the passage in question
prevailing conditions, a Provencal

could also be considered as an ex-

repertory of ca. I 150 was still suf-

ample of modus rectus, since ficiently
the
known in Paris I30 years
writing of ligatures, 5 2 (plic.) later
5 2 to warrant such detailed ex(plic.), is strongly suggestive of planations
the
as Anonymous IV gives.

decisive, however, is the fact
first mode (5=3 2). On the whole More
it
appears that the organum Viderunt
that the organa of St. Martial do not,
as a rule, show the extended puncta
approximates modal rhythm much
more consistently than the Benedica(pedal points) of single sustained
mus Domino. Possibly it represents
notes which form the very foundaa slightly later stage of development.
tion of the principle of consonance."
The introduction of this sustainedAnother interesting detail of this
organum is the extended conjunctura
note style as well as the creation of

in the middle of the second brace.
This is the "currentes cum antece-

the contrasting discantus style for the

clausulae was, no doubt, the work of
the Parisian school, either of Leonidente, ut in Viderunt, undecim punctorum" which Anonymous IV exnus or of his immediate predecessors.
plains in some detail, telling us that
The next step was to find a reconciliation between the sustained-note
actually there are twelve currentes,
not eleven. The quick notes therestyle which inevitably results in nufore include the a' before the demerous dissonant intervals, and the
scending notes, and the preceding prevailing
g'
theory according to which
is long.
two-part composition had to proceed
in consonant intervals. The solution
In conclusion we shall try to outline the development of rhythm durwas the one indicated by Anonymous IV, that is, to make the dissoing the later part of the I2th cennant notes short and the consonant
tury, as it appears to us on the basis

of the above explanations. As we

notes long. Thus it seems that a

fundamental concept of meter, that
repro-

"An organum duplum of St. Martial is
is,
duced in The Notation of Polyphonic Music,
p. 211.

a distinction of long and short

values, appeared in polyphonic music

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I 58 JOURNAL OF THE AMERICAN MUSICOLOGICAL SOCIETY
as the result of an exigency created

by a conflict between traditional

theory and stylistic progress.

The resulting rhythmic style is one

in which longs and shorts alternate
freely, as do the consonant and dis-

sonant notes of the melody. Naturally, there often occur passages
showing a somewhat regular suc-

cession of these values, and these in-

dicate the decisive change from
measured rhythm (B) to metrical

rhythm (C). It is not without interest to notice that this change was al-

most inevitably bound to lead to
triple, not to duple meter. While

organa dupla of Leoninus are in free

modal meter. One reason is, of
course, that our interpretation is

based on evidence found in the theo-

retical sources of the 13th century,
while the customary transcriptions

are without such foundation. In ad-

dition, our theory leads to a much
more organic picture of the evolution of rhythm than results from the

traditional method of interpretation.
This implies a sort of "evolution in
reverse," insofar as the strict modal
rhythm of Perotinus would have de-

veloped out of a preceding stage
characterised by the use of free

formations in triple meter (L B/ L)
require only one dissonance, patterns
in duple meter (L BB/ L) would require two dissonances in succession.

modal rhythm. Such a development,
although not exactly impossible, cer-

nances in the scale, and only two of

sudden appearance of "free modal
meter" in the Parisian organa, nor

Since there are only three disso-

these are contiguous (sixth and

seventh), the mere statistical chance
for such combinations is relatively

small.

The main result of our explana-

tions is a new theory of "the birth
of meter" in polyphonic music.12 It

seems to us that for various reasons

tainly does not follow the natural

lines of evolution. Moreover, no explanation has ever been given for the

would it be easy to find a convincing
explanation for the emergence of this
entirely novel rhythm. We hope that
our explanations of the gradual development of rhythm will be found
more satisfactory from the scientific

as well as from the morphological

this theory is preferable to the curpoint of view.
rent thought according to which the

Boston, Massachusetts

12If we accept the theory of the "mensuralists,"
measured rhythm was used in Gregorian chant,
tion of rhythm. Recent scholars are inclined
at least during its "golden age," up to the
to take a much more cautious view regarding
eleventh or twelfth century. See the survey
the "modal interpretation" of these melodies
in Reese, Music in the Middle Ages (1940),
than was customary ten or twenty years ago.
pp. 143ff. An important recent contribution isSee, e.g., J. Handschin's review of U. Sesini,
W. Lipphardt, "Neue Wege zur Erforschung
Le melodie trobadoriche. . . (1942) in Acta
der linienlosen Neumen," Die Musikforschung, Musicologica, XX (1948), p. 62, and the
I (948), p. 121. Eventually the problem of
present writer's review of H. Angl6s, La
the troubadour and trouv&re melodies will alsomusica de las Cantigas . .. (943) in Specuhave to be included in the study of the evolu- lum, XXII (1947), P. 458.

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