),
),
),
).75
The notation, handwriting, and physical structure of the Paduan fragments are themselves important to our understanding of music in Padua in the late fourteenth century. Compositions of this time are found with variants in notation in concordant sources. These variations can tell modern readers what styles and regions were influencing scribes in late fourteenth-century Padua as well as possible sources which copied the fragments or from which the fragments were copied. A study of the transmission of fourteenth century polyphony also requires a study of the physical aspects of the manuscripts. From codicology we can determine the minimum possible lengths of the original manuscripts and discover the layout of missing folios adjacent to those that survive. Paleography enables us to determine what are the characteristics of a specific scribe. Through these traits, we can determine if the scribe was responsible for the copying of any other manuscripts. Giulio Cattin, for example, has been able to show that Rolandus was the scribe of both PadD and I-STr 14.72 By understanding the details of these manuscripts, their contents can be more easily placed in the context of the surrounding musical world.
The notational systems used to transmit the music of PadA, PadB, and PadC vary from piece to piece, from manuscript to manuscript, and from scribe to scribe. Musical notation of late-fourteenth and early-fifteenth century Italy is not characterized by the consistency and universality of interpretation which one would see in music of, say, the eighteenth and nineteenth centuries. Instead, it brings to mind the conflicting notational systems found in experimental music of the twentieth century. The meaning of symbols was modified to fit the needs of the specific composition; and when no existing symbol was suitable, the composer or scribe created new symbols to fill this need. The proper interpretation of a symbol may change from piece to piece or sometimes even within a piece.
Despite this fluidity of meaning of symbols, most compositions can be seen as deriving their notation from one of two notational systems, French or Italian. The differences between the two systems will be outlined below. The majority of pieces in this study do not use "pure" French or Italian notation. Some French elements were nearly always used in compositions primarily in Italian notation, and Italian traits can often be found in compositions grounded in French notational principles.
The existence of different musical systems is primarily shown in the notation of rhythm. Polyphonic music of the fourteenth century used four primary note values, the long or longa, abbreviated ),),),).75
The relationships between the different note values were not fixed. For example, a breve could be divided into two, three, or four semibreves depending on the tempus or divisio of the section, two terms which will be defined shortly. A long could similarly be divided into two or three breves depending on the modus of the section. However, in the repertory of this study, nearly all pieces are written in modus imperfectum, meaning each long is divided into two breves, and the variable relationships will be seen between the other three note values.76
The notation of most piece of fourteenth-century music can be seen to have as its roots one of two types of music notation: French or Italian. Understanding the concepts behind the two notations is necessary for understanding the complexities of the Paduan notational systems of the late fourteenth century. These notational systems took some elements from both the French and Italian systems and invented new elements as well, creating systems unique to each composition.
French notation divides the breve into two or three semibreves, depending on whether the tempus is imperfect or perfect. The semibreves are then divided into either two or three minims depending on whether the prolatio is minor or major. The combination of tempus and prolation produces four possible mensurations: tempus perfectum cum prolatione maiore (9 minims divided up as 3+3+3), tempus perfectum cum prolatione minore (6M: 2+2+2), tempus imprefectum cum prolatione maiore (6M: 3+3), and tempus imperfectum cum prolatione minore (4M: 2+2). These four mensurations can be indicated by symbols 
, 
, 
, 
, respectively. Music of the fourteenth century, however, often omitted these mensuration symbols and relied on groupings of notes within a composition to indicate mensuration. For instance, the pattern: 
at the end of a composition would probably indicate tempus imperfectum cum prolatione maiore, since it appears that the breve () is being divided into two semibreves (), one of which is further subdivided into three minims (). In the Paduan manuscripts in this study, only Sus une fontaine in GB-Ob 229 uses mensuration signs, and there they are used in a slightly different manner as will be seen in the discussion of PadA in chapter 6.
The concepts of "imperfection" and "alteration" are crucial to any study of notation of the late-fourteenth century. In major prolation, a single semibreve is normally equivalent to three minims ( = ). However, a single minim placed in front of a single semibreve can imperfect the semibreve so that the semibreve is equal to two minims and the semibreve and the minim together are the same length as a perfect semibreve ( = 
).
In tempus perfectum, the breve, which normally is equivalent to three semibreves, can likewise be imperfected by a semibreve ( = 
| ). The breve to be imperfected is always the note preceding the shorter note, or imperfectio a parte post, ( = | 
) unless a dot is placed after the first note, in which case the first note receives its full duration and the note following the shorter note is imperfected, or imperfectio a parte ante, (
= | ). The dot, or punctus, has many other uses in the 14th century, as will be shown later. Rests can never be imperfected, though a rest can cause imperfection by substituting for the imperfecting note. These principles are also true with imperfections of the semibreve by the minim.
When two breves or semibreves are adjacent, the rule of similis ante similem perfecta (s.a.s.) comes into play. This rule states that when a note comes before a note of the same value, the preceding note must be perfect.77 For example, would be transcribed as | 
. The dot means the first breve must be perfect (9 eight-notes in this reduction). The following semibreve receives 3 eighth notes and the second breve, because of similis ante similem must be perfect (9 ) necessitating the tie. In order to get realigned with the tempus, it is the following breve which is imperfected by the length of the semibreve. S.a.s governs performance at the semibreve level as well (
). Note that in this example, both the second and the third semibreve must be perfect because of s.a.s. Thus, the lone minim causes an imperfection of a semibreve three notes later.
The complement of imperfection is alteration. While imperfection can be viewed as the shortening of one note so that two notes can fit in the place normally occupied by one, alteration lengthens a note so that two notes can fit in the place normally occupied by three. Like imperfection, alteration only occurs in sections of triple time. So imperfection and alteration of the breve are found only in tempus perfectum (modern day and 
) and imperfection and alteration of the semibreve are found only in prolatio maior ( and ). An altered note doubles in value, so that an altered minim is the same length as a imperfected semibreve (2 ). So in tempus perfectum, the rhythm would cause the second semibreve to be altered and thus be expressed | | . It may appear as if the rhythm could also be expressing two measures of with imperfection of the first breve a parte post (i.e., after the fact) and imperfection of the second breve a parte ante. However, in cases where the breve is followed by two semibreves, alteration takes precedence over imperfection.
In duple time (tempus imperfectum when dealing on the semibreve level, or prolatio minor at the minim level) French notation becomes somewhat simpler, since the lengths of notes are fixed. The same rhythm , which in tempus perfectum required alteration to realize, in tempus imperfectum becomes simply | | in major prolation or 
| | in minor prolation. The dot in duple time is often used as a punctus additionis, which makes the preceding note one and a half times as long. Thus, the punctus additionis functions identically to the dot in modern musical notation ( = ).
Italian notation of the fourteenth century has its roots in the music notation of Petrus de Cruce (fl. late 13th c.) who, according to the theorist Jacobus of Liège in Speculum Musicae "was the first to put four semibreves in a perfect tempus."78 To mark the end of the tempus, Petrus de Cruce placed a dot, or punctus divisionis after the final semibreve. The concept of placing varying numbers of semibreves within a tempus survives in the various divisiones of Italian notation most of which are defined by the number of minims per tempus (recall that a minim is technically a type of semibreve, a semibrevis minima).
The concepts of Italian notation were put forth in Marchetto de Padua’s Pomerium, written c. 1318-19.79 In strict Italian notation (Marchettian notation), the lengths of the breve and the minim are fixed within a divisio. There were six divisiones in practical use which had the following numbers of minims per breve: quaternaria (4), senaria imperfecta (6), senaria perfecta (6), novenaria (9), octonaria (8), and duodenaria (12).80 These divisiones can be divided into two groups on the basis of the number of levels of note values separating the breve from the minima. Quaternaria (.q.), senaria imperfecta (.i. or .s.i.), senaria perfecta (.p. or .s.p.), and novenaria (.n.) each have one level of notes between the breve and the minima. This level, not surprising, consists of the semibreves. In transcriptions, the minima in these divisiones secundae is usually represented by the eighth note. A breve followed by a tempus (or divisio to use the proper Italian term for the space occupied by a breve) filled by minims in each of the divisiones secundae would be noted as below.
Note that these four divisiones are equivalent to the four combinations of tempus and prolation in the French system. The punctus preceding or following a breve is usually omitted, since the breve by definition takes up a whole divisio.81 A semibreve would occupy the length of a quarter note in .q. or .p. or a dotted-quarter note in .i. or .n. In .i. and .n., a semibreve, normally equivalent to 3 minims, can be made equivalent to 2 minims, if followed by a lone minim. This process is identical to imperfection, and will be also be called such in the remainder of this paper. Alteration, however, never appears in the Italian notation system, since the minim is a fixed duration.
In the divisiones tertiae, .o. and .d. there are two levels of semibreves between the breve and the minim. Both are represented by the symbol . Context determines which is used. For example, in .o., where there are eight minims to the divisio, the following example shows the use of both types of semibreve:
(in the divisiones tertiae, the minim is normally transcribed as a sixteenth note). If a measure requires a mixture of the two semibreve types, as in the following .o. example, the final semibreve or semibreves will be lengthened: = | 
| The lengthening of the final notes is called via naturae (the natural way) and has obvious connections to the French conception of alteration.82
Notation types in the Paduan Fragments
By the early fifteenth century many compositions were being written in a style which combined elements from both the French and Italian notational styles. The salient characteristics of this "mixed notation", as Willi Apel called it, cannot be easily stated as they varied from composition to composition. One finds pieces in what is essentially French notation with Italian divisio letters. Also common are compositions which were originally in .o. or .d., and which make the most sense in these divisiones, but which have been rewritten as .q. (with or without letter indications). There are compositions, such as the A piançer l’oche, which are written in Italian .s.i. but use the semibrevis caudata (
) to indicate a perfect semibreve. These compositions use the normal semibreve to indicate imperfect, 2M, semibreves, eliminating the need for imperfection. There are many more examples in the Paduan fragments which do not fit into any of these categories.
Eugene Fellin studied the notation types of non-unica madrigals and cacce and divided the notation into four categories: French, F1 (French modified to the first degree: Italian divisio letters), F2 (French modified to the second degree: Italian divisio letters and puncti divisionis), and Italian.83 Two madrigals did not fit into any of these categories. Fellin’s study was limited by the nature of the repertory studied: madrigals were rarely composed in the last decades of the fourteenth century, when one expects a greater disintegration of Italian notational rules.84 Additionally, since the manuscripts studied, with the exception of the Rossi Codex (I-Rvat 215), were all from the turn of the century, a study of other musical forms such as the ballata would have been a study of music more likely to have been written nearer to the copying of the manuscripts.
More problematic is Fellin’s implication that fourteenth-century music notation can be plotted linearly on a scale from French to Italian. We cannot know where to put a composition that uses imperfection and alternation (French elements) and puncti divisionis without Italian divisiones letters. Placing the notation of Sus unne fontaine on a scale from French to Italian would present particular difficulty since the notation is purely French, but French prolation indications are used in such an unusual manner that classifying the composition as merely French would lose this valuable information, but calling it F1 or F2 would place it with a group of compositions with which it has little in common.
Similarly, there are pieces in Italian notation which are modified from standard Italian notation. Sones ces nachares, mentioned above, is one such example. O cieco mondo (PadC, f. AV) uses notation that is almost purely Italian, except for a few sections in the terzetti where notes are syncopated across the tempus (mm. 37-38, 54-55). While this syncopation might seem a minor detail, the self-contained nature of the breve is one of the most important differences between Italian and French notation.
A further argument against the designation of notational systems such as F1, F2, etc. is that these distinctions create groups which would not have been recognized by the scribes themselves. Although contemporary theorists discussed the differences between Italian and French notation, they did not talk about French notation which had been modified to better fit Italian musical styles. Instead it seems from the evidence in the Paduan fragments and other late trecento Italian sources, that scribes decided what notational system in which to write the composition (either through knowing the piece or through examining other copies of the composition) and then modified the notation to fit the idiosyncrasies of individual pieces. Essentially, a new sub-system of notation was created for each composition.
To a modern reader, the necessity of creating new notational solutions for difficulties in every piece might seem to suggest fourteenth-century notation was in some way immature or broken. This is not the case. The notational systems uses in the late trecento were extremely efficient at transmitting the music which was being written. A 23x31.6 cm folio (9x12.4"), such as f. A of PadB, requires on average four 8.5x11" pages in modern notation to convey the same information. Since the fragments are parchment, saving as much space as possible was probably a high priority.85 The saving of space is also because part notation, rather than score notation, is used (though the equality of voice parts in most fourteenth-century compositions makes this savings not so huge as one might expect).86 The use of textual abbreviations also contributes to the efficiency. However, the notation itself, with its ligatures, closely packed lozenges, and absence of ties, is responsible for much of the savings of space.
The Paduan fragments studied in this thesis are the remnants of three larger manuscripts whose total length cannot be determined. PadA contained at least 70 folios originally. This number is determined by examination of the foliation on the surviving bifolios. Gathering 4 requires two additional bifolios to complete compositions which are incomplete. If these compositions were present, gathering 4 would consist of 10 bifolios, which was as much of a standard for gathering size as existed in fourteenth-century Italy. The next folio must begin a new gathering because it is attached to a folio which could not be part of the previous gathering. Since the final folio of gathering 4 is folio 50V (Pu 1475, f. A), the next gathering must begin on f. 51.88 If the gatherings are of consistent length in this manuscript, the folio connected to f. 51 would be f. 60 and 60V. Folio 60V contains an incomplete composition, Gratiosus’s Alta regina, which also must be continued onto the first folio of another gathering. Again, if the size of the gatherings is standard, the necessity of f. 61 implies folios up to f. 70.
The placement of folio C of Pu 684 as f. 52 is a logical guess but is not the only place the folio could have originally been. Neither f. AV (51V) nor f. C have incomplete compositions on them which would prevent them from being adjacent. In preparing a parchment manuscript a rule known as "Gregory’s Law" states that the hair side of one folio should always be adjacent to the hair side of the next, and vice versa for flesh to flesh in order to have a uniform appearance across an opening.89 This is preserved by having ff. A and C adjacent. Folio CV also requires 3 additional pages to complete Perneth’s Credo, so it could not be f. 45 in gathering 4. Additionally, fragments have tended to have all been taken from the same section of the manuscript, so a placement in the same gathering as f. A and f. B is logical.90
The maximum size of the secular manuscripts PadB and PadC can only be guessed at. PadB’s incomplete compositions Ay si and A piançer l’ochi both imply the existence of at least one additional bifolio surrounding ff. A and B. If Aler m’en veus had a notated second voice (see chapter 4), then at least one other interior folio would be present. Of the parchment manuscripts studied by John Nádas, Pit. and Man/ManP both have flesh side out consistently while I-Fasl 2211 has only one instance of hair out; Sq. uses both hair and flesh out equally.91 There is therefore some reason to speculate that f. A and B represent the second folio from the outside of the gathering in which they originally lay.
PadC tells us even less about its original length. Since f. A and f. B are not part of a single bifolio, we cannot even know for sure if they were originally part of the same gathering. Folio A is self-contained: it does not make any requirements on the contents of folios around it. Folio B requires at one interior and one or two exterior bifolios, the number varying depending on whether the lower voices of Apolinis ecclipsatur were texted or not. For neither PadA nor PadB is there sufficient evidence to substantiate or disprove a theory that these fragments, rather than being parts of larger manuscripts, such as PadA are actually large portions of the type of small "fascicle-manuscripts" which Charles Hamm has asserted constituted the bulk of music distributed by the mid-fifteenth century.92
Identification of scribal hands is important to the study of a manuscript since discernment of sections of copying by different scribes can yield important information about a scribe’s preferences and prejudices. For example, John Nádas points out that some of the variants in notational systems in the pieces studied by Fellin can be attributed to scribal predilection for one or the other notational type, without regard to the composer.93 In I-Fn 26 (Pan.), Nádas notes that there is a perfect correspondence between the notation of Giovanni da Cascia’s madrigals and the scribe who copied them.94 Since scribal initiative has also been discovered in ModA, I-Bc Q 15, and other manuscripts, an identification of scribal characteristics was undertaken for PadB and PadC.95
The details I focused on most carefully were those marks which scribes made often and probably unthinkingly. Nádas asserts that it is in unconscious details, such as clefs and custos rather than ornamental endings with which the scribes distinguish themselves.96 Since it focuses on many details, the bulk of this discussion has been placed with the discussion of the compositions and manuscripts themselves in the following chapters. Because of the brevity of the manuscript fragments, the presence of a single scribe in PadC and particularly because the second scribe of PadB copied only one composition, differences in layers of scribal hands cannot be discerned.
One important detail gained from a study of scribal marks, related to notation, concerns final ligatures. Many pieces and sections of pieces end with a three or more note ligature in one voice. A ligature is a collection of semibreves, breves, and longs connected into a single note to be sung to a single syllable. It appears based on evidence from the Sanctus of f. A in GB-Ob 229 that the scribe intended for the final note of the ligature on the ninth staff to be sung to a different syllable than the rest of the ligature. The ligature appears alone on a new staff just before a vertical line indicating the end of the section to be set to the last two syllables of the word "excelsis". Although text alignment is sometimes quite bad in late fourteenth-century manuscripts, the text would always at least appear on the same line as the music to which it is to be sung. Supporting evidence, though not convincing in itself, can be found in numerous places in the fragments where a long final ligature has text underlying the end, rather than the beginning of the ligature. Additionally, it seems more musical that all voices should begin sounding the final syllable of a piece together, though today’s musical tastes cannot be submitted as evidence for medieval practice.