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The early use of the sign (stroke).

The sign [half note] has been much discussed as an indicator of proportion or mensuration. This article will reopen the investigation of its pedigree and significance.(1) Only one actual use of C may date from earlier than 1420. It occurs in the unique pair of pieces, one circular and one in the shape of a heart, attributed to Baude Cordier and copied at an uncertain date in the first quarter of the 15th century as an addendum to the Chantilly manuscript (see ex.13 for the circle canon).(2) Both pieces equate the semibreve of [half note] with the minim of a signature without stroke in another simultaneously sounding part. A natural inference is that if [half note] means 2:1 when it can be verified in simultaneous use, it ought also to mean 2:1 in the many cases of sectional, successive use that cannot be checked against a different simultaneous signature. Accordingly, most editors have further reduced the note values of [half note] sections, or added an instruction to sing their music at double speed.

But not all music responds well to this formula. The 2:1 interpretation is most seriously challenged by sacred pieces with [half note] signatures that enter the manuscripts around 1430. Dufay, Binchois, Lymburgia, Grossin, Lantins and others of that generation use [half note] for entire sections of compositions where a 2:1 relationship between signatures with and without strokes requires identical or similar music to be rendered at different tempos.

One category of pieces affected is that of `ut supra' Kyrie and Agnus settings where music to be repeated appears with alternating [whole note] and [half note] signatures. Ex. 1 shows the Kyrie by Grossin as transcribed by Reaney,(3) with the second of each identical group of three marked to be performed twice as fast under [half note] as [whole note], with values halved.

[Example 1 OMITTED]

A second type (mostly Glorias and Credos) alternates sections with different vocal scoring. Ex. 2 shows part of a Binchois Gloria as transcribed by van den Borren.(4) Duets and trios alternate, with [whole note] and [half note] signatures; this time the note values of passages in [half note] are further halved from those of [whole note].

[Example 2 OMITTED]

For the Cordier songs, and for all cases of simultaneous use of [half note] and [whole note], a 2:1 relationship is inescapable. There is strong, even unassailable, but much later theoretical support for it, especially from theorists in the German tradition.(5) However, some scholars have been understandably reluctant to apply this proportion to cases (such as those just illustrated) where the musical relationship between consecutive sections discourages even a small increase in speed, and where the only justification for suggesting such an increase is the assumption that this is what [half note] means. There is support for readings of [half note] that require a less sharply accelerating proportion, either with a reduction by one-third (3:2) or some other proportion, or as an inexact tempo mark.(6) Others have drawn from Tinctoris a licence merely to sing slightly faster.(7) That is the nearest we have come to being let off the hook, and performers of pieces like exx.1 and 2 will have greeted that concession with relief.

So what does C mean? Faster in a 2:1 proportion? Faster by a third? Faster tempo by a slight or unspecified amount? Theoretical support has been adduced for all of these. The one consensus is that [half note] is an indication to speed up. However, I think we are still not completely out of trouble. The premise that identical music within the same composition, in the case of threefold Kyries, or similar music in the case of alternating sections, has to be performed at different tempos, one faster, even a little faster than the other, does not sit happily alongside aesthetic gleanings from this repertory; indeed, apart from the special cases of isorhythmic acceleration and rare mensuration canons, we are entirely dependent on this interpretation of [half note] for the belief that such accelerations were ever applied to more straightforward music.
Table 1 Manuscripts cited

Short name      Full reference

Aosta           Aosta, Biblioteca del Seminario, MS. 15

Bodley 652      Oxford, Bodleian Library, Ms. Bodley 652

Bologna Q15     Bologna, Civico Museo Bibliografico
                Musicale, Q15

Cambrai 6, 11   Cambrai, Bibliotheque municipale, Mss.
                6, 11

Chantilly       Chantilly, Musee Conde, 564 (olim 1047)

Fountains       London, British Library, Add. Ms. 40,011B

Hatton 81       Oxford, Bodleian Library, Ms. Hatton 81

Modena A        Modena, Biblioteca Estense, [Alpha].5.24

Old Hall        London, British Library, Add. Ms. 57,950

Oxford 213      Oxford, Bodleian Library, Ms. Canon.
                misc. 213

Oxford 229      Oxford, Bodleian Library, Ms. Canon.
                Pat.lat.229 (part of fragmentary Padua A)

Trent 87-92     Trent, Castello del Buonconsiglio,
                Monumenti e Collezioni Provinciali
                (formerly the Museo Provinciale d'Arte),
                Mss. 1,374-9 (formerly Mss. 87-92)

Yoxford         Ipswich, Suffolk Record Office,
                HA30:50/22/13/15




All the theoretical evidence for any meaning of dates from the 1470s or later, and Tinctoris figures centrally in explanations of [half note]. But unless it is demonstrably still relevant, the tradition he represents has no special authority for music more than 40 years older,music that may even antedate his own approved period. To be sure, our desire for clear statements leads us to milk the theorists for all they can yield. But however valid the late theorists may be for late practice, we are faced earlier in the century with plural and changing traditions to whose early stages Tinctoris may not be a qualified witness, whether he is thought to be prescribing performance a little or a lot faster, in a precise or imprecise proportion. Let us set these later theorists aside and approach earlier usage of [half note] without the prejudice of hindsight.

Around 1400 mensuration signs of any kind were still quite new, and they remain rare at the beginning of a piece. There are no initial signatures in the Fauvel manuscript, the Machaut manuscripts, or even the later Ivrea manuscript. It was and is possible to diagnose the prevailing mensuration, and even changes of mensuration, from context and without signs, for example in Machaut's Rondeau 10, Rose lis, where the alternation of mensural changes is unsignalled except by changes in note groupings and rest patterns.(8) Among a great variety of proportional signs and colorations used around and after 1400, very few notational usages could have been viewed as standard representations of particular temporal relationships; conversely, very few temporal relationships enjoyed monopoly of a single sign. Versions of the same piece in different manuscripts could fluctuate widely. In Ciconia's Sus une fontayne, for example, the signatures in the Modena A manuscript are closer to the usage that became standard, but there is no reason to doubt that the signatures in its other source, eccentric in terms of later practice, were the ones Ciconia used, compiled as this manuscript was in Padua, under his nose, and during his lifetime. See table 2.(9)
Table 2 Mensuration signs in Ciconia, Sus une fontayne

Modena A     Oxford 229 (Padua A)
f.28         f.38v (56v)

  O                 O

  C                 C

 ??                ??

 ?? (= 4:3)         3




Strokes through signatures of any kind are conspicuously absent from early 15th-century manuscripts. Use of [half note] to indicate a 2:1 proportion is confined to the Cordier pieces and had no currency before the 1420s, at the earliest, nor is it used previously, with this or any other meaning. Although [half note] indeed always means 2:1 in simultaneous use in later manuscripts, whether for short proportional passages, tenor repetitions, or whole pieces, the 2:1 proportion was not normally notated with a stroke early in the 15th century. Many ways of indicating proportions were explored in manuscripts such as Chantilly, Modena A and Old Hall, by means of colorations, numerals, inverted signs, stems and flags, but not strokes. Even if a few more scattered examples should come to light, they can hardly change the force of the argument that its early use is not well documented. A 2:1 relationship is often not indicated at all but could easily be inferred by performers accustomed to lower redundancy of information than we now expect from our notation.

To repeat, apart from the Cordier pieces, I have found no use of strokes through signatures until the 1420s. After that, [half note] appears in simultaneous proportional usage only, I think, in the early 1430s, in late additions to Bologna Q15 in works mostly by Dufay, including isorhythmic motets, and in Oxford 213 in further songs by Cordier and others. It was only one of several ways by which these composers indicated duple proportion.

Strokes through other signatures are similarly scarce. They raise different issues, especially with respect to the early use of ?? in relation to [whole note]. I shall not deal with them here, but only with [half note], and then only in the context of successive sections. It is because perfect time was the predominant mensuration around 1430 that the stroke was applied in the first instance to [whole note]. I exclude cases where 2:1 is confirmed by simultaneous use with another signature, and I exclude isorhythmic motets, where proportions between sections may be determined by other means. All the cases considered here change to [half note] for a section in all voice parts at the same time, whether or not that section is self-contained.

Still troubled by the problem pieces introduced above, I set out to explore how [half note] had come to be understood in a proportional or accelerating sense and whether all reasonable alternatives had been exhausted. What else could it mean, instead or as well? Arguments that multiple meanings would have been confusing need not detain us. More than one meaning for [half note] is now assumed by several scholars: 2:1 for simultaneous use, and simply `faster' for successive use. Even in straightforward pieces, singers were accustomed to construing from the context whether a coloured minim in the same piece and under the same signature meant a semiminim, or was part of an imperfection group, or was subject to triplet sesquialtera coloration. Many pieces where a semibreve in one voice part is equated with a minim in another are unsigned.(10) After all, the signum congruentiae can be used as a fermata, a co-ordination mark, a canonic instruction, a song form marker, or the entry of another voice: such multiplicity of use does not trouble us. Multiple meanings can be demonstrated copiously; indeed, it is now admitted by most scholars that, while [half note] must mean 2:1 or semibreve: minim in simultaneous use, it cannot always require such a dramatic acceleration in successive sectional use. Once it is accepted that [half note] may not mean the same thing in all contexts, might it not mean yet other things than those hitherto proposed?

Thus, a musician in 1420 had exposure to no theorists who mentioned [half note] and to little or no use of [half note] in musical manuscripts. He would have expected on most occasions to figure out the mensuration without help from a sign. He would have seen a wide and inconsistently used range of signs and colorations in the first quarter of the 15th century, showing little standard practice, apart from the four primary mensuration signs. If indeed he happened to know the Cordier pieces (assuming they already existed), he would have seen the proportional use of [half note] as just one of many ways of representing duple proportion. It would not yet have been clear which of those many usages would become strong or standard. No one yet knew that [half note] would come to take on a standard meaning as a proportional sign. Around 1400 the same effects are still signalled in widely differing ways, and the same signs are used with widely differing meanings, including non-mensural meanings.

Ex. 3 shows some uses of strokes to indicate tenor repeats. These are precise according to the number of statements, and in the last case they even show diminution graphically.(11) Ex. 4 shows small circles to indicate sectional repeats in the lower voices of a rondellus, in the 14th-century English manuscript Hatton 81. Apart from the Cordier pieces, the only uses of [half note] in musical manuscripts before 1420 have no mensural significance. Ex. 5 shows [half note] used as a signe de renvoi: in ex. 5a in conjunction with a corrected line to reinforce the point of repetition; in ex. 5b to show the insertion point of similarly marked omitted material in the margin.(12) Similar signs are also common in much later musical manuscripts, as is the tendency to place a stroke through clefs and dal segno signs. Cappelli gives several meanings for [half note], including a common abbreviation for obiit, and as a way of distinguishing 0 (zero) from [whole note] (the letter), as in some current usage.(13) These extra-musical uses, whether or not in musical manuscripts, further establish a range of meanings for C. The angle of the stroke seems not to be significant. It can be vertical, horizontal or oblique in conjunction with any of its meanings. Our musician of 1420 was at least as likely to have encountered strokes, [whole note], and [half note] as general-purpose signs as to associate them solely with a fixed proportional meaning.

[Examples 3 to 5a OMITTED]

There is one use of [half note], and one only, in the first layer of Bologna Q15, compiled in the early 1420s. The Gloria by Guillaume Legrant is a wholly unusual piece,(14) and I believe it may be the earliest piece to use [half note] with any meaning after the two Cordier songs, and the first use for any purpose in a sacred genre. The sections alternate duets in c with three-part sections in 0. This Gloria is laid out on the page like a four-part piece (ex.6), though no more than three parts sing at a time. This is not readily apparent from the unlabelled voice parts of Reaney's transcription (ex.7). The cantus sings throughout. It is joined by the second part (ex.6, top right) in duets only, and by the tenor and contratenor (ex.6, bottom left and right) in trios only. Because cantus II and contratenor alternate, cantus II sings only in c sections and the contratenor only in [half note] sections. There is therefore no need for signature alternation by sections in these parts. Similarly, the unus/chorus indications for these parts are not repeated. But neither are those indications repeated in the cantus, where the alternation is as clearly intended, and the sections are signed alternately with C and [half note]. In other words, the [half note] signs coincide with changes of scoring, perhaps duplicating and making superfluous the continued repetition of unus and chorus. They mark the sections where the cantus is joined by tenor and contratenor (chorus) instead of by the second cantus for duets (unus).

[Examples 6 & 7 OMITTED]

As there was no precedent at this time for strokes through signatures to signify a special successive mensural usage, and as the stroke seems here to be fulfilling another function as a scoring co-ordinator, it may be that nothing more than an alternation of imperfect and perfect time (C and O) was intended by the signs. The [whole note] mensuration signs were provided with strokes simply to provide a route-map through an unusually scored piece. A later simplification of the Legrant Gloria in Trent 92 interleaves the alternating cantus 11 and contratenor so that it looks like Reaney's three-part piece, albeit with contrasted ranges for the conflated second cantus and contratenor parts. All three parts then have the alternate sections signed c and Phi respectively. As co-ordinators these would now be redundant unless, as the ranges suggest, this part was still intended to alternate between a high second cantus and the lower contratenor. Reaney's transcription further halves the note values of the [half note] sections, providing a striking contrast of tempo between sections and for similar cadence formulae. We might expect in such alternations that nimble duos would move faster, the trios more sedately. But in other pieces with similar alternative by contrast, it is indeed the duos that are signed with [half note] and the trios that appear to move slower.15 There is no detectable convention of relative speeds for alternating duos and trios, i.e. for which is faster. Earlier pieces (from the Ciconia generation) alternate duos and trios without mensural change, and provide no precedent for a tradition whereby tempo change would be expected at such alternations. Sometimes in the next generation it seems to be one, sometimes the other, that has the stroke; such contradictory tempo structures, often set in stone by a policy of note reduction, must raise suspicions about a mensural interpretation.

One of several ways [half note] works seems indeed to be as a vocal scoring marker; it coincides with, duplicates or replaces other indications (including signa, unus/ chorus markings, voice labels and rests). It is not a specific prescription for either a duet or a trio; rather, the stroke through the signature functions as a toggle switch (or what is also known in computer terminology as a flag), in other words, it has a switch function in turning a feature on or off, but there is no significance to whether the switch is up or down, to whether the signature does or does not have a stroke. This solves the problem that [half note] consistently represents neither duets nor trios.(16) [half note] is a composite sign, a view encouraged by the absence of a simple term for it.(17) The circle, as always, signifies tempus perfectum; the stroke is a co-ordination mark, a segno. At the mensural level, the alternation of C and [half note], and hence, as we shall see, of [whole note] and [half note], should be treated as if the circles were uncut.(18)

After the Legrant Gloria, the next appearances of [half note] are not until the second layer of Bologna Q15, around 1430, and in younger manuscripts with which it shares concordances. Some of these [half note] are in simultaneous contexts requiring 2:1 proportion, including isorhythmic motets by Dufay. Others are in successive sectional contexts, and it is these latter cases I consider here.

A paired Gloria and Credo by Binchois alternate sections in two and three parts.(19) As in the Legrant Gloria [whole note] marks the duets and [half note] the tuttis; the duet comes first. In other pieces it is the other way round; the tutti starts.(20) A cut signature almost never opens these alternating pieces, but serves as a toggle at the first change of scoring. The choice of signature usually depends on whether the duet or the trio starts the piece. This Gloria and Credo each consist of a series of duets in [half note] time that continue into a three-part section marked , but without a barline at the change and without coming to rest. All the three-part sections cadence with a long and a double bar. These sections are designated as unus/ chorus respectively in the Gloria in Bologna Q15, indications which may be redundant once the toggle significance of the [half note] implemented, whether in a modern score or a contemporary arrangement.

There are three sources of the Credo. Ex. 8 shows the Trent 92 version. Interesting features include signes de renvoi on the lower two staves, identifying a route for the performer, and [half note] signs for sections a 3. At `Et in unum' the [half note] is duplicated (the second sign should probably have been erased once it had been superseded by the more precisely placed first one), and at `Et incarnatus' there is a signum over the breve (on which the parts cadence) and [half note] before the following semibreve that imperfects it, i.e. not where the measure would change at the beginning of a perfection, but (if, as here, different) where the scoring changes for the new phrase.(21) At `Genitum non factum' there is no [half note] but only a signum, as in Cambrai 11. At the same points, the Cambrai 11 copy of this Credo (ex.9) has no [half note] but instead only signa congruentiae, which coincide with entries of the third voice after rests and thus appear to be co-ordination points. In neither source do the signs appear with barlines or section dividers, but they always coincide with switches of vocal scoring. The music does not halt at these points, making it quite hard to change tempo, but if the signs simply acknowledge scoring changes (and hence become redundant when the music is scored), no tempo change is needed. Are we really to believe that these two evidently synonymous notations signal different ways of performance, or rather that the same thing is being notated using different general-purpose signs?

[Examples 8 & 9 OMITTED]

In the matching Gloria, [half note] is used in all sources and there are no signa congruentiae. If the two signs have different meanings, the Cambrai manuscript in which both Gloria and Credo appear would then mismatch the members of the pair in the very respect on which their pairing most strongly depends--signature alternation. At any rate, some movements in some sources of this paired Gloria and Credo have only signa, some only [half note] some a mixture, some both. These permutations support synonymous use of signa congruentiae and [half note] with some notational redundancy.

The complex scoring and layout of the Legrant 1 Gloria finds a parallel in another Binchois Gloria-Credo pair.(22) The cantus and the third part (called `concord' in the edition) never rest. The three-part texture alternates contratenor and tenor (instead of cantus II and contratenor, as in the Legrant). There are a few short four-part sections.

Manuscripts are not entirely consistent as to whether or not they restate signatures at successive sections; to absolve [half note] from always signifying mensural change in relation to [whole note] inevitably increases the number of restatements that are mensurally redundant. The line through a circle that is already doing duty as a mensuration sign serves as a toggle which sometimes seems to mean `Yes, I know it is redundant to repeat the circle, but I am doing so in order to make the distinction of applying a stroke.' Put another way: a mensuration sign may be repeated in order to accommodate a stroke. It is often assumed that the annotated antecedent of a notated signature ``as different. This is usually but not necessarily so. To recognize [whole note] and [half note] as mensurally the same does increase the number of mensurally redundant signature restatements, but many such repetitions have another purpose. Some changes of scoring coincide with a shift from imperfect to perfect time (as at `Genitum non factum'), as we have seen. All changes of scoring in this Credo are marked either by a change of mensuration or, if there is no change of mensuration, by [half note].[half note] here always coincides with- and I would suggest, signals--a change of scoring, and never follows uncut [whole note] [whole note]unless there is such a change (`Et incarnatus').(23)

We saw that the Legrant Gloria underwent some complex reshuffling in order to simplify the scoring changes that had driven the earlier rotator to indicate them experimentally with [half note]. A similar rearrangement was applied to this Credo. In some sources the alternating parts are written out in duplicate or signalled by ut supra markings. Such simplification again makes the signs less necessary, just as co-ordination marks lose their force when a piece has been transcribed into score. The circles, here and elsewhere, are in effect a cautionary restatement of the preceding tempus perfectum, with the stroke serving not to increase tempo but to signal scoring change, again, not on a specifically prescriptive but on a toggle principle.

The matching Gloria 3a (ex.10) has in the cantus [half note] for `Qui tollis' (in Trent 87). In the part here called `subcontra', [half note] follows its `Qui tollis' rests: it enters only at `suscipe'. (Note the text entered without music.) Other sources place the d) not after but before the same number of rests. If [half note] signalled a change of mensuration, it would imply simultaneous application of [whole note] and [half note] The rests support no such change; they are the same-whether they precede or follow the signature, making a vocal scoring indication much more likely than an--erroneous--mensural one. If [half note] was a distinct mensural sign, it would matter whether it stood before or after the rests; if it is merely a vocal scoring toggle, it does not.

[Example 10 OMITTED]

The Grossin Kyrie was tidied up by Reaney to an imagined convention that does not match the signatures in the unique source, Aosta (ex.11; for transcription, see ex.1) In the Kyrie Angelorum by Binchois, two source traditions are out of phase on the indication and out of phase with the Grossin. If [half note] is a tempo indication, then we have to believe that users of one manuscript would have sung the sections slow-fast-slow, while others using another manuscript of the same piece would have sung the same music fast-slow-fast. Remember that the presumed meaning of [half note], to increase tempo is our only evidence that identical textures might have been repeated at different speeds. Now that we must question the assumption that [half note] always increases speed, we must also question the musical aesthetic within which such tempo increases have been accommodated. They seem unlikely. Moreover, in the absence of any consistent tradition for repeated Kyrie performance, and with a pattern different again for the Grossin Kyrie (table 3) this case makes an already dubious practice look even more questionable. The inconsistent signatures make no sense as mensural signs, but good sense as toggles simply giving graphic distinction to adjacent sections, leaving no problem about source inconsistency, and resolving the awkwardness of a tempo interpretation. Such inconsistencies between pieces and between different sources of the same piece belie any consistent performance tradition, whether of slow-fast-slow or fast-slow-fast; and they can be more easily accommodated through a non-mensural interpretation than through a mensural one. Is the same piece, or the same kind of piece, really to be tolerated with the reversed tempo relationships suggested by the diverse order of mensural signs in its different sources?

[Example 11 OMITTED]
Table 3 Mensuration signs in Binchois and
Grossin Kyries

Binchoiis Kyrie Angelorum           Grossin Kyrie
Most sources      Trent 92, 93V

[half note]        [whole note]       [whole note]
[whole note]       [half note]        [half note]
[half note]        [whole note]       [whole note]

[whole note]       [whole note]       [half note]
[half note]        [half note]        [whole note]
[whole note]       [whole note]       [half note]

[half note]        [whole note]       [whole note]
[whole note]       [half note]
[half note]        [whole note]




Cut signatures are rarely used consecutively without an intervening uncut signature; if they were, such use would argue against, and defeat the purpose of, a toggle. When adjacent sections with strokes occur, there turns out to be a special significance. The third Kyrie has separate music in all sources except Trent 92, which is the odd one out on the stroke alternation and marks the final Kyrie to be sung thrice. Trent 87 specially labels the two invocations that share the same music as [Kyrie] 4 and 6, the different (apparently final) one as 5. I believe this is confirmed by the signs; we can now see that two adjacent would in themselves be sufficient indication that the uncut section should come between them. Aosta marks the different final Kyrie as `Kyrie ultimum', but the more precise prescription of Trent '87 seems to disagree with that, both by the numbering and by the adjacence of two [half note] signatures. When adjacent signs are identical but not clarified by numbers, such an explanation should now be considered.

The Agnus 7b by Binchois appears in several sources with slightly different signature indications. It is more common for Agnus 1 and 2 to be sung to the same music, with a different statement for the third Agnus ending `done nobis pacem'. This one is unusual, in that Agnus 2 has the different music, notated in ?? and Agnus 3 repeats the music of Agnus 1 to the words `done nobis pacem'. In one transmission (Trent 82a and Trent 88) this is not signalled verbally, but the repeat of Agnus 1 is signalled by [whole note] and [half note] (whatever else the stroke means). In a second appearance in Trent 92, the signatures for the lower parts are [whole note] and nothing, followed in both cases by ?? for Agnus 2. In the top parts, both the text for `done nobis pacem' and the [half note] are apparently added later. The third appearance in Trent 92 is neatly presented, with [whole note] and [half note] for the first section, and the `done nobis' words. In Aosta there are no signatures at all for the first Agnus, but the repeat is signalled by the addition of the words `done nobis pacem'. I suggest that the stroke through the circle, where present, simply signals the repeat and has no mensural significance. Where it is absent, as in Aosta, the musical effect is exactly the same. In both these cases and in many others, the stroke through the circle functions as a dal segno with no mensural effect. It has a meaning, a terminology, a separability, and may be distinct from the signature with which it is combined.

A final example (ex. 12) illustrates yet another use of the stroke for a dal segno repeat. The Binchois Sanctus 7a uses [whole note] [half note], ??, [whole note]. Here, as in several other Sanctus settings, [half note] is used only for the Osanna. If it is a mensural sign, that would suggest some kind of convention whereby the repeated Osanna would be sung faster, a convention that we miss with respect to alternating trios and duos on the one hand and Kyrie repetitions on the other. The music of the Osanna, in all cases where it is so signed, is repeated after the Benedictus, often signalled by ut supra markings. I believe that the [half note] is used as a place-finder that happens to coincide here with a conventional change of mensuration back to tempus perfectum--a dal segno. The Osanna need therefore be no faster than the opening tempo.

[Example 12 OMITTED]

Let us sum up. [half note] is discussed by no theorist before the 14705. Inescapable use as a proportion occurs in no early manuscript except the two Cordier songs (of uncertain date). Indeed, the sign is more often used non-mensurally as an insertion point or place-finder. The earliest sectional uses with the nonmensural meanings here proposed are coeval with or earlier than the establishment of a 2:1 tradition in simultaneous use. [half note] is unknown as an initial signature until the 14305, and then it is rare.

[whole note] and [half note] mean and have always meant the same thing in mensural organization, i.e. perfect time with minor proration. They never coincide in the same piece except where 2:1 proportional use is intended. EN-en there, [half note] may have been used at first simply as a that warning something unusual happens, not necessarily that the sign itself was yet regarded as a specific proportional prescription. It is already accepted that [half note] cannot or might not mean the same thing in all contexts. Indeed, there is, or comes to be, a tradition in which [half note] signals a 2:1 proportion in simultaneous use. But at first this was only one meaning of a more general-purpose sign, and a meaning that was only weakly established before 1430. In the kinds of pieces affected, the context made it perfectly obvious which meaning was intended, as is the case with other general-purpose signs, such as signa congruentiae. Where present, the strokes are signposts, repeat marks and co-ordination signs. They have nonmensural functions, and the stroke may have no additional effect on tempo or proportion. The circle and stroke are not an inseparable unit but a composite sign, both graphically and in meaning. In [half note] with no simultaneous overlap of signatures the circle is still always a mensuration sign (but not necessarily a mensuration change), while the stroke is usually not a mensural modifier.

Within a few decades the primary meaning of [half note] indeed came to be some kind of acceleration, precise or imprecise, and that must derive from the indisputable proportional meaning. I believe that [half note] must have evolved from a general-purpose usage, sometimes synonymous with ut supra, sometimes synonymous with signa congruentiae, sometimes with unus/chorus markings. There is some redundancy through the period of experimentation. It was not fixed retroactively from Tinctoris as a constant accelerator. Can an understanding of the early stages help us with some anomalies in later manuscripts that might also be residually non-mensural? The implications are of course quite wide. A lot of music will have to be reconsidered both for editorial and performance purposes, particularly most cases where double tempo has been specified or built into the transcription.

Moreover, if sectional signatures may not serve a primarily mensural function, and if our expectations for non-repetition of mensuration signs are very slightly relaxed, as I have suggested, an absent opening signature need not be assumed to have been different from a following section in uncut O. Is it even possible that the restated signatures in Dufay's Vergene bella, to take a much discussed example, are just that, and that they serve as section or paragraph markers, or, for an unusual piece, the rehearsal letters we have so often wished they would provide? In other words, [nothing] / [whole note] / [half note] may simply mark three successive sections, two piece and a sirma, in perfect time in the same tempo.

This is only a start. If we must now accept the stroke as a general-purpose sign that came to have specific meanings, there may be other meanings waiting to be uncovered. The discovery of pieces where the sign cannot function as I have suggested need not in itself invalidate this hypothesis, which is confined in the first instance to the particular classes of pieces set out above, but rather it may extend the range of general meanings. We can bid farewell to most of the unwritten but presumed [half note] signatures added by editors to early 15th-century music, and the tempos that go with them. The case for supplying them editorially with mensural significance to unsigned sections now seems very weak. Editors should reduce note values consistently throughout a piece, making no mensural adjustment for [half note] Singers should be alert for editions that have made such reductions without warning, and undo their effect. They may experiment with a constant semibreve between adjacent sections in triple time, whether the signature is [whole note] or [half note] Performers and scholars alike should be vigilant for suspect relationships, as this hypothesis undergoes further exploration and testing. The good news is that we need no longer be bound to sing faster when it makes no sense to do so.

A first version of this paper (with more detail on the Binchois pieces, to be published separately) was given at the Binchois conference in New York, I 1 November 1995, at the invitation of Dennis Slavin and Andrew Kirkman, a few days after the death of Thomas Walker. I had discussed the paper with Tom by Email within a week of his death; that presentation was, and this paper is, dedicated to the memory of a a great friend and colleague.

(1) Here I sometimes follow a common practice in referring to signatures with and without a stroke es 'cut' end `uncut', although there is little historical justification for this latter terminology. Eunice Schroeder gives, among early words used by theorists for the stroke, virgula, tractus (tractulus), paragraphum, linea, strich, strichlen, in `The stroke comes full circle: [half note] and ?? in in writings on music, ca. 1450-1540', Musica disciplina, xxxvi (1982), pp. 119-66.

(2) Facsimiles can be seen in many places including, of Tout par compas, C. Parrish, The notation of medieval music (New York, 1957), pl. LXII, and of Belle bonne, W. Apel, The notation of polyphonic music, 900-1600 (Cambridge, MA, 1942), facs. 88. The Cordier pieces are edited in Early fifteenth century music, i, ed. G. Reaney, Corpus Mensurabilis Musicae, xi/1 (American Institute of Musicology, 1955). It has been argued by Craig Wright that Cordier might be one Baude Fresnel who died in 1397: `Tapissier and Cordier, new documents and conjectures', Musical quarterly, xlix (1973), pp. 177-89. Even without the further suggestion that these pieces might be autograph, because of their highly individual notation, this dating raises problems. The constant exception that has to be made for the Cordier pieces, and the 30-year gap that would separate an early dating (before 1400) from his other songs in Oxford 213 (14305), leads me increasingly to believe that they may be considerably later than 1400, perhaps in composition as well as in script. Without any firm biographical identification, a date late in the 14105 or even in the 1420s would accord better with their style and usage.

(3) Early fifteenth century music, iii, ed. G. Reaney, Corpus Mensurabilis Musicae, xi/3 (American Institute of Musicology, 1966), Grossin, Kyrie, pp. xiii, 42 (no.19).

(4) Polyphonia sacra, a Continental miscellany of the fifteenth century, ed. C. van den Borren (Burnham, Bucks, 1932; 2/1962), no. 8, p. 53.

(5) See Schroeder, `The stroke comes full circle', and A. M. Busse Berger, Mensuration and proportion signs (Oxford, 1993), who defends a 2:1 proportional reading for [half note].

(6) C. Hamm, A. chronology of the works of Guillaume Dufay based on a study of mensural practice (Princeton, NJ, 1964) prescribes performance a third faster: see pp. 38-42, 62-3. He calls [half note] not a sign of proportion but merely a tempo indication'. Contrary to this distinction, used by several writers, for present purposes I treat any change to the speed at which the notation is to be read (faster or slower) as a general category of tempo change, of which a precise tempo relationship expressed as a proportion is a special subset. For reduction by one-third, see also A. E. Planchart, `The relative speed of tempora in the period of Dufay', RMA research chronicle, xvii (1981), pp. 33-51.

(7) See Schroeder, `The stroke comes full circle', pp. 133-7, and R. C. Wegman, `What is "acceleratio mensurae"?', Music and letters, lxxiii (1992), pp. 515-24.

(8) First pointed out in R. Hoppin, `Notational licences of Guillaume de Machaut', Musica disciplina, xiv (1960), pp. 20-23.

(9) The works of Johannes Ciconia, ed. M. Bent and A. Hallmark, Polyphonic Music of the Fourteenth Century, xxiv (Monaco, 1985), no. 45. Oxford 229 is a leaf from the fragmentary manuscript known as Padua A.

(10) The consequences of the present argument for so-called tempus perfectum diminutum will be explored separately. There is less basis than ever for the widespread practice of supplying editorial [half note] signatures in a period where they do not exist as normal currency, and where the earliest uses of the signature now appear to have carried various other meanings. For an example of an unsignalled shift in the course of a piece, see Old Hall, Gloria no. 24, where all voices are in unsigned ?? until the upper voice shifts to signed [whole note] (bar 93) requiring the new semibreve to be equivalent to the previous and simultaneous minims of major proration. The Old Hall Manuscript ed. A. Hughes and M. Bent, Corpus Mensurabilis Musicae, xlvi, 3 vols. (American Institute of Musicology, 1969-73).

(11) For the last, see M. Bent, `The Yoxford Credo', Essays in musicology: a tribute to Alvin Johnson, ed. L. Lockwood and E. Roesner (American Musicological Society, 1990), pp. 26-51.

(12) Barbara Haggh has also kindly sent me some examples of [half note] as a signe de renvoi from a 13th-century Cambrai Antiphoner that was still in use there at the time the later Cambrai polyphonic manuscripts (Cambrai 6 and 11, mentioned below) were copied.

(13) A. Cappelli, Dizionario di Abbreviature latine ed italiane (Milan, R/1967) does not list [half note] as synonymous with [whole note] except as an abbreviation for obiit (13th century), and for some other 8th-century abbreviations. But it does appear as a 14th-century alternative to 0(zero). Also [half note] for fiorino, [half note] [sup tia] for consequentia (14th century) alternative and for continens (13th century).

(14) Early fifteenth century music, ii, ed. G. Reaney, Corpus Mensurabilis Musicae, Xi/2 (American Institute of Musicology, 1959), G. Legrant, Gloria, pp.xxxi, 53.

(15) E.g. The sacred music of Gilles Binchois, ed. P. Kaye (Oxford, 1992), Credo no. 19.

(16) A. Blachly, Mensuration and tempo in 15th-century music: cut signatures in theory and practice (PhD diss., Columbia U., 1995) briefly considered, and as quickly rejected, the idea that [half note] might be a vocal scoring indicator, on grounds that it is used sometimes for duets, sometimes for tutti passages. Indeed, it does not consistently represent one or the other.

(17) For vocabulary for the stroke see Schroeder, `The stroke comes full circle' and n.1 above. Circumlocutions are always used to describe its application to a mensuration sign.

(18) The sequence [whole note] ?? [half note] remains to be investigated. The earliest uses of ?? are no earlier than these cases of [half note], but it seems to have evolved in a somewhat different way.

(19) Cambrai 6 (alone) pairs the Gloria and Credo printed by Kaye as 1a, 1b. Three other sources outside Cambrai, Oxford 213, Bologna Q15 and Trent '92 pair the Gloria la with the Credo `a versi' printed as no. 19. Liane Curtis argues that the much less widely circulated Credo 1b (otherwise only in Trent 92) represents a revised pairing with a Credo newly provided to match more closely the Gloria 1a. L. Curtis, Music manuscripts and their production in fifteenth-century Cambrai (PhD diss., Chapel Hill, 1991), p. 119.

(20) Binchois 1a and 1b start with duets, the Credo 19 with tutti. In these cases, the first change (i.e. the tutti in 1a and 1b, the first duet in no. 19) are marked [half note].

(21) The Credo in Cambrai 6 also uses a combination of signa and [half note]. The [half note] signs are often squeezed in before the note, while the signa, evidently there earlier, are on it, above or below.

(22) Nos. 3a/3b in in Kaye's edition.

(23) In Cambrai 11 the piece is divided into sections, each of which is completely written before the next. On this opening we see three parts each, but not always the same three, for `Et ex patre', then `Genitum', then `Et incarnatus' ([half note]), joined a 4 for `Ex Maria'. This way of notating it requires almost no rests.

Margaret Bent is a Fellow of All Souls College, Oxford, and a Fellow of the British Academy.
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