Accordingly the fundamental principle is that the rise and fall of the melody are expressed by the signs of the accentus acutus () and the accentus gravis (). The acutus, being drawn upwards, from left to right, indicates a rise in the melody, a higher note; the gravis, being drawn downwards, a fall in the melody, a lower note. From the combination of these two signs there result various group signs: (1) , acutus and gravis, a higher note followed by a lower one, a descending group of two notes (clivis); (2) , gravis and acutus, lower and higher notes (pes or podatus); (3) , acutus, gravis, acutus; a group of three notes of which the second is the lowest (porrectus); (4) , gravis, acutus, gravis; a group of three notes of which the second is the highest (torculus); and so on. In these combinations the elements generally preserve their original form pretty clearly, except that the angles are often rounded off, as indicated below. When used singly, the acutus, too, retained its shape fairly accurately and from its shape received the name virga (virgula). The gravis, however, was generally converted into a short horizontal line (), or a dot (), or something similar, and hence received the name of punctum. In this form it is also used in an ascending group of three or more notes (, scandicus) and in a similar descending group (, climacus). More complicated combinations were designated as modifications of the simpler groups. The addition of a lower note to a group ending with a higher note was indicated by the adjective flexus, the addition of a higher note to a group ending with a lower note, by resupinus. Thus even the clivis (more correctly clinis) was at an early period called virga flexa, and the torculus could be considered as a pes flexus. The sign would be a porrectus flexus, the a torculus resupinus, etc. Again the placing of several puncta before a sign is expressed by the term præpunctis, their addition after a sign subpunctis. In accordance with that a scandicus is a virga præpunctis; a climacus, a virga subpunctis; , pes subpunctis; , scandicus subpunctis, or, also compunctis, the last-named adjective indicating the addition of punctis before and after.

A special modification of the neum form is that which is called liquescent or semivocal. It consists generally of a shortening, attenuating, or curling of the last stroke. It occurs only at the transition from one syllable to the next and there only in certain circumstances. It is never found when another neum follows on the same syllable. An analysis of all the cases of liquescence occurring in the manuscript Gradual 339 of St. Gall is made in the second volume of the "Paléographie Musicale" (pp. 41 sqq.), where the subject is treated very fully. This analysis shows that by far the largest number of cases (2450 out of 3504) occur when a vowel is followed by two or more consonants the first of which is one of the "liquids" (l, m, n, r) either within a word (like sanctos) or through the collocation of two words (as in te). A considerable number is found before an explosive dental at the end of a word followed by another word beginning with one or more consonants (317 before t, 48 before d). Forty-nine times it is found before a final s followed by another consonant (e.g. nobis Domine) and six times before s in Israhel; seventy-three times before g, thirty-two times before two consonants the second of which is j (e.g. adjutor), forty-six times before single m, thirty-four times before a single g followed by e or i. One hundred and fifty-nine times on the diphthong au, and two hundred and eighty-eight times before a single j (including one hundred and fifty-three cases on alleluia).

It is clear from what has been said, that this liquescence must be connected with the proper pronunciation of the consonants. But as to what it should mean in the rendering, authors are not agreed. Thus the preface to the Vatican Gradual says: "ipsa cogente syllabarum natura, vox de una ad alteram limpide transiens tunc 'liquescit'; ita ut in ore compressa 'non finiri videatur', et quasi dimidium suæ, non moræ, sed potestatis amittat". This is not easy to translate, but it would seem that the last tone of the liquescent neum should "lose one half, not of its length, but of its strength". The "Paléographie Musicale" on the other hand, says that in the exact pronunciation of certain combinations of consonants an obscure vowel sound enters between them, so that a word like confundantur would sound con^efun^edan^etur and that it is this after-sound which exerts its influence on the tone preceding the first consonant. It is not easy to see why this obscure vowel sound coming after the first consonant should influence the tone preceding it, nor why the consonants should change the dynamic character of the preceding vowel sound. Possibly the nature of the liquid consonants, l, m, n, r, which evidently have given the name to the liquescent neums, would give a more satisfactory explanation. It is well known that these consonants can be sung, that is be prolonged on a definite and varying pitch. It would seem, then, that when one of these consonants follows a vowel, then sometimes the last note on the vowel sound is smoothly fused into the consonantal sound, part of its time value being given to the singing of the liquid or semivocal consonant. This would conveniently apply to the first class of cases mentioned above, which comprise the large majority of all the cases. Also to the case of single m and j (or i), the latter partaking of the nature of the liquid consonants. It would further apply to the case of gn, if we suppose that combination was pronounced ny, and to the case of final s, if that consonant was voiced, when it also could be sung. In the case of the diphthong au the liquescence would consist in the transition from the first vowel to the second. The remaining cases of double consonants should be explained by analogy, the liquescence consisting simply in the shortening of the vowel sound made for the purpose of distinct pronunciation of the group of consonants without loss of time. This explanation would have the further advantage of being in accordance with the practice of the best choirs that nowadays make a peculiar study of Plain Chant.

Some of the liquescent neums have special names. Thus the liquescent podatus is called epiphonus, the liquescent clivis, cephalicus, the liquescent climacus, ancus.

In addition to the neums which are derived from the accents and which form the groundwork of the neumatic system, there is another class which may be taken as indicating special effects. They have, as Wagner has pointed out, as a common feature, the hook form. In the first place we mention the strophicus, having the shape of a comma (). When occurring singly, it is called apostropha, when doubled, distropha; when trebled, tristropha. The apostropha is generally found at the end of another neum, or followed by a distropha at a higher pitch; it is never used as a single note over a syllable. When added to a neum, it is generally represented in the later staff-notation manuscripts at the same pitch as the last note of that neum. But there is reason to believe that originally there was an interval smaller than a semi-tone between those two notes. The distropha and tristropha indicate a quick repetition of the same note, possibly again with a minute difference of pitch between the repeated notes.

Akin to the apostropha is the oriscus, having a shape somewhat like this: . Apostropha and oriscus are sometimes interchanged in different manuscripts. In a few instances the oriscus, however, is found as the single sign over a syllable. The quilisma is generally written as a number of hooks open to the right and joined together (, ). It occurs invariably as the middle note in an ascending group and seems to indicate a glide of the voice, being accompanied by a sustaining of the note or group of notes preceding it. The salicus is a figure like the scandicus, but with the second note in the shape of a hook opening downwards (). It seems to indicate a prologation of the middle note. Sometimes, in staff-notation manuscripts, the first two notes are given at the same pitch. Possibly here again there was a difference of less than a semitone between them. The pressus is a kind of combination of a virga with added oriscus and a punctum (, pressus minor; , pressus major). It is generally understood as equivalent to a clivis with the first note prolonged and rendered sforzato. Finally to be mentioned is the trigon, a combination of three puncta, the middle one being higher than the other two (). From its shape it would seem to be a kind of torculus, but it is often transcribed with the first two notes at the same pitch, suggesting once more a minute interval not expressible in staff notation.

The illustrations which accompany this article are reproduced by kind permission of the editors, from the "Paléographie Musicale". Illustration I ("Pal. Mus.", III, pl. 179) [see printed Text, vol. X, p. 766] represents the type of the Anglo-Saxon neums of the eleventh century. The piece is a trope for the Introit "In medio". The three portions of the Introit itself are merely indicated by the cues In Med., Et impleb., and Stola. The signs for the single notes are the plain virga and the round punctum, the former on the last syllable of iohannis, the second and third syllables of adimplens, etc., the latter on the second syllable of Gratia, the second syllable of Dei, the first of iohannis, etc. In the podatus the gravis is a short horizontal stroke, the acutus a straight virga joining almost at a right angle; see third syllable of Gratia, third of salutifere, third of dogmata, etc. There is also a second form consisting of a disjointed punctum and virga, see third syllable of Gloria (last line on left page), first syllable of xristus (first line of right page), third syllable of æternum (fourth line). This is considered as indicating a long form of the podatus. The liquescent form (epiphonus) is marked by a rounding of the angle; see second syllable of iohannis, third syllable of fluxerunt. The clivis shows the curved angle, as on second syllable of pectus, second and fourth of salutifere. The liquescent form (cephalicus), somewhat shortened, is seen on the third syllable of iohannem (first line on right page). The torculus is seen on the first syllable of adimplens, first syllable of docente (fourth line), etc. On the first syllable of celsa we have the torculus liquescens, the last gravis being shortened. The porrectus is easily recognizable on the first syllable of Sola. A climacus occurs on the second syllable of docente (fourth line) being followed by an epiphonus; a pes subpunctis, on the last syllable of salutifere. The strophicus (on med) has here no distinct sign, but is written with the ordinary virga sign. The oriscus, however, is clearly marked. Thus we have a virga with oriscus (also called franculus) on the first syllable of Gratia, and the full pressus (virga, oriscus, and punctum) on the first syllable of pectus, the first of fluxerunt, etc. The quilisma is shown on the second syllable of celsa, where we first have a punctum, serving as the starting-point, then the triple curve of the quilisma itself, to which the virga stroke, representing the highest note, is attached. We have it again on the second syllable of impleb., where a second virga follows, the whole figure representing the notes f g a b .

A less usual sign is found on the first syllable of carus (last line, right page). The quilisma there is followed by a climacus in which the three signs, acutus and two graves are joined together: .

Illustration II ("Paléogr. Mus.", IV, pl. A) [see Text, X, 766] is from a manuscript written in the monastery of Einsiedeln at the end of the tenth or the beginning of the eleventh century. It belongs to the St. Gall school of notation. The affinity of this school to the Anglo-Saxon is evident. There are, however, a number of peculiarities. First we find a greater variety of signs. Thus the virga appears in two forms, one slightly curved to the right and vanishing at the top, the other straighter and with a thickening at the top. This second variety arises, graphically, from its being drawn downwards, the pen spreading itself a little at the start of the stroke. For the rendering it indicates a longer form of the note. We find the first form on the first syllable of Ostende, the fifth of misericordiam, etc., the second on the second syllable of Ostende (first sign), on the first syllable of tuam (second sign), etc. Similarly we have for the punctum, besides the dot form, that of a short horizontal line. This is also sometimes used for one of the puncta of the climacus (first syllable of tuam, third and sixth neums, etc.) and towards the end of the group neuma on nobis (fifth sign from the end) we see a trigon subpuncte, the last dot of the trigon and the added punctum being drawn out. The odatus appears in three forms: first with rounded corner, as on the third syllable of Alleluia (first sign); second with some pen pressure on the initial stroke and a fairly square angle, as on the fourth syllable of Alleluia (third sign); and third, with a more elaborate gravis, as in the final neuma of nobis (second last sign). The first may be considered as the normal form, the second marks a firmer rendering of the first note, and the third a decided leaning on it. The torculus appears in its plain form (second syllable of Ostende, fourth syllable of misericordiam) and with pen pressure on both graves () marking a prolongation of the whole figure (first syllable of tuum, seventh sign). The two forms of the pressus, minor and major, are found in the final neuma of Alleluia (fourth last and last signs). Of liquescent signs we have a scandicus liquescens on the first syllable of Alleluia, a distropha liquescens of the third, an epiphonus on the last syllable of misericordiam.

A second peculiarity of the St. Gall notation is the occasional addition of a little stroke to the neums, marking a prolongation of the affected note. The "Paléographie Musicale" (IV, pl. 17) has given the name episema to this little addition. Mention has already been made of the thickening of the head of the virga, which often amounts to a distinct stroke. Our illustration gives examples of a similar addition to the last note of the torculus ( instead of ), the last of the porrectus, the first and the second of the clivis. The episematic torculus is seen in the final neuma of nobis (before the first trigon). The first sign in the same neuma is also an episematic torculus followed by another long punctum. On the first syllable of tuum we have an episematic porrectus, followed by two puncta, while the plain porrectus appears on the first syllable of domine (third sign). The clivis with episema to the first note is found on the first syllable of tuam (first sign) and twice towards the end of the neuma on tuum. On the second syllable of nobis, after the torculus subpunctis already mentioned, we have a clivis with the episema attached to the second note, the clivis being preceded by two short puncta and followed by a long one.

Thirdly, we find as a peculiarity of this notation the addition of certain letters. These are often called "Romanian" letters, because a St. Gall writer of the eleventh century attributes their use to a singer named Romanus who, according to him, brought the chant from Rome to St. Gall towards the end of the eighth century (see "Pal. Mus.", IV, pl. 9; Wagner, "Einleitung", II, 114). The litteræ significativæ are of two classes, one referring to rhythm, the other referring to pitch. Of the former class we find in our illustration frequently the c (celeriter) and the t (tenete). At the beginning of the Offertory (last line of illustration), we find also the m (mediocriter) modifying the effect of the preceding c. Of the second class we find the e (equaliter) enjoining the same pitch between domine and misericordiam between the second and third syllables of misericordiam and between tuam and et. To give a clearer idea of the meaning of the neums in this illustration we subjoin the notation of the same piece according to the Vatican edition, [see Text, X, 767] pointing out only the few differences in the two readings. On the first syllable of "Alleluia" the Vatican edition omits the liquescence; similarly on the third syllable of that word and on the final syllable of "misericordiam". It may be mentioned in this connexion that a very frequent use of liquescence is characteristic of the St. Gall school. The strophici on Alleluia and tuam are given as ordinary puncta. Similarly the special sign for the pressus has disappeared and is replaced by a doubling of the first note. The first of these two notes of the same pitch is then sometimes combined with the preceding neum. Thus at the end of the Alleluia neuma it joins the virga to form a clivis, and at the end of the neuma on nobis the podatus of the manuscript is changed into a torculus. These things are in accordance with the general practice of the later Middle Ages. Towards the end of the neuma on tuam (where in the manuscript the neums surmount the second syllable) the staff notation substitutes a pes subbipunctis for a virga and climacus—a mere graphic difference. Similarly on do a porrectus and virga are replaced by a clivis and podatus.

Illustration III [see Text, X, 767], taken from a manuscript of the ninth or the beginning of the tenth century in the library of Laon, which is in course of publication in the "Pal. Mus." (p. 28), shows the Metz notation. On the first two syllables of Gaudeamus we have the familiar punctum dot. On the third we recognize easily a podatus followed by a virga. But on the last we meet the most characteristic sign of this school, the punctum consisting of a short slanting line with a little hook added. Of the clivis form peculiar to this school our illustration contains no example; but on the second syllable of festum and the second and fourth of celebrantes we have the porrectus, which in its first two strokes contains the clivis. There are two forms of the torculus, one with sharp angles, on the first syllable of domino, the second of honore (where it is preceded by a punctum), etc.; the other rounded, on the third syllable of honore and the fourth of passione. Of liquescent neums we find the epiphonus on the second syllable of diem and the third of celebrantes, the cephalicus on the first of omnes, a pes subbipunctis liquescens (the first punctum connected with the pes in the manner of a torculus and the second, liquescent, bent back to the left) on the second syllable of collaudant and a porrectus compunctis liquescens on the last syllable of filium. The oriscus is found after the podatus on agatha and the quilisma, consisting of two hooks, on the second syllable of domino, the second of angeli and the first of dei, in each case a porrectus being joined to it.

Another peculiarity of this school is the frequent use of disjoint neums, all of which indicate a prolongation of the notes. Mention was made of a disjoint podatus in connexion with the first illustration. We find it here on in and the first syllable of celebrantes. A torculus of this kind is shown in the second syllable of martyris. The descending figures are indicated by the puncta placed perpendicularly. Thus we have a clivis on the second syllable of omnes, the second (before the quilisma) and the third of domino, the third of angeli (where the lower one got attached to the l), etc.; a climacus on angeli, preceding the quilisma.

We note further the use of literæ significativæ. Thus we have the c used in the same sense as in the St. Gall school, on agathæ. Similarly a t appears at the bottom of the illustration under the word meu. The a on Gaudeamus stands here for augete and is, therefore, synonymous with the t, whereas in St. Gall it stands for alte. The idea of high pitch is expressed by the f occurring twice on domino. The first time it refers evidently to the rise of the melody to c, the second time it probably enjoins a b natural instead of a b flat.

The comparison with the reading of the Vaticana [Text, X, 768] will show a close resemblance. We only notice that on gaudent and angeli the manuscript adds a liquescent note to the podatus and porrectus subbipunctis, and on celebrantes has twice a porrectus for the strophic clivis, which suggests that the apostropha (oriscus) was sung slightly higher than the last note of the clivis, as mentioned above.

Illustration IV [Text, X, 769] is taken from an eleventh-century manuscript of Silos, written in the Mozarabic notation ("Pal. Mus.", I, pl. II) in order to show that even this is based on the same principles. The usual forms of virga, punctum, podatus, clivis, torculus, porrectus will be recognized easily. The other features will be explained with reference to the modern form of the Vatican Gradual [Text, X, 768]. The piece occurs in the Roman Liturgy as Introit of the Saturday after the fourth Sunday of Lent. On the last syllable of Sitientes the manuscript has a pes subbipunctis, with the puncta joined together, representing the same notes as the staff notation without the pressus. On the first syllable of venite the manuscript has a clivis instead of the single note of the Roman version, on the second, the punctum and torculus (placed one over the other) are only graphically different from the pes and clivis. On the first syllable of equas a tristopha takes the place of the trigon. On the second syllable of dicit the manuscript omits the last note of the print. On the second syllable of dominus the disjoint punctum and clivis correspond to the conjoint torculus. The second figure on non is a liquescent torculus. It begins below with the gravis to which the acutus is attached in the usual manner, but the last, liquescent, gravis is represented by a curve to the left of the acutus. The remaining slight differences are like those already explained.

As has been sufficiently indicated, the neums merely marked the rise or fall of the melody. They gave, in themselves, no clear information as to the exact amount of rise and fall, in other words, they did not mark the intervals. A podatus, e.g., may indicate a second, a third, a fourth or a fifth without change in its form. This may now be accepted as an established fact. The various efforts made from time to time, most recently by Fleischer in his "Neumenstudien", to find interval signification in the neums, have failed completely. It is clear then, that at no time could the melody be read absolutely from the neumatic notation. Rather this served merely as an aid to memory. Nor did the choir sing from the notation. The manuscript was only for the choir-master, or at most for the solo singer. The whole body of the Plain Chant melodies had to be committed to memory in the rehearsing room, and we know from contemporary writers that it took a singer several years to become acquainted with all the melodies. In the course of time, as oral tradition began to grow less reliable, a desire was felt to have also the amount of rise or fall fixed. Accordingly we find even at the date of our earliest manuscripts the use of letters, added to the neums, to warn the singer here and there as to the intervals, as we have mentioned above. These indications, however, were again merely vague and could not finally satisfy. Various efforts which space forbids us to detail here, were then made to supplement the neumatic notation. All of them, however, were destined to disappear before the introduction of a new principle, which was to distinguish the higher or lower pitch of the tones by the higher or lower position of the notes, grading the distances between the notes in strict accordance with the intervals. Attempts in this direction can be noticed even in the class of manuscripts which have been considered up to this. Our example of Metz notation shows pretty clearly an endeavour on the part of the scribe to place the notes according to pitch. The full, systematic carrying out of this idea is found in the tenth century, first in the Lombardic notation, shortly afterwards in the Aquitanian. Illustration V, [Text, X, 769] taken from an eleventh-century Versiculary and Prosary from St. Martial in Limoges ("Pal. Mus.", II, pl. 86) belongs to the latter class, which is further characterized by the almost complete disjoining of the neums. There being no clef, the semi-tones cannot be found from the notation. But apart from that the intervals can be read without difficulty, it being kept in mind that notes placed perpendicularly should be read downwards, as in the Metz notation. A few remarks will suffice to point out the difference between the manuscript and the reading of the Vaticana [Text, X, 768] given above. On palma the manuscript gives a liquescent note, on the first syllable of adnunciandum it has a podatus (a c, or d f, as this notation should be read a fifth lower) instead of a single note; in the last, a podatus instead of an epiphonus. The first group on mane is the same as in the Vaticana, the lowest mark being a mere blot. In the third group the manuscript has a fourth (c g, or f c) instead of a third (b g). After the fifth group there is an omission of the whole passage which in our staff notation example is placed between the two little bars at the end of the second line. Such omissions are not uncommon, it being supposed that the singer knew frequently-occurring long neumata by heart. The omission is indicated in the manuscript by the little perpendicular line. On the first syllable of misericordiam, the first two notes of the Vaticana are omitted. At the end of the line we observe the custos, indicating the pitch of the first note of the second line. On tuam there is again an omission of a whole group indicated as above. On veritatem the fourth dot is an accidental blot. At the end of the second tuam the manuscripts has a third (f d) instead of a fourth (c g). The final neuma is left incomplete.

This procedure solved in principle the problem of diastematic (interval) notation. For greater convenience, however, scribes soon began to draw horizontal lines which helped to facilitate the correct placing and reading of the notes. It was the work of the Benedictine monk Guido of Arezzo (about 1000) to fix the use of these lines finally in such a way that adjacent lines mark the interval of a third, the intervening note being placed between the two lines. Letters were also affixed to the beginning of the staff to give the alphabetical name of one or several places on the staff and thus to indicate the position of the semitones. Soon c and f were used for this purpose by preference and out of them by a graphic transformation, our present C and F (bass) clefs evolved. Later the letter g was employed, which through the addition of an ornamental flourish developed into the modern violin clef. In the beginning, however, the f and c lines were run over with various colours, or if f fell into space, a coloured line was drawn between the e and g lines.

In the staff thus perfected the neums were written according to the forms that had been previously in use in the various localities, such modifications being introduced as were necessary to mark the exact position of the notes, notably the thickening of the head of the acutus. Illustration VI, [Text, X, 770] taken from a twelfth-century Gradual of St. Evroult ("Pal. Mus.", III, pl. 194), shows the process clearly. It has four dry lines drawn on the parchment, of which the one for f was coloured red, that for c green. The other two lines have the clef letters a and e.

From the thirteenth century the notes began to be written larger, so that they might be read by a number of singers at the same time. The thickening of the strokes at the exact place the notes occupy also became more pronounced. Thus gradually in the Latin countries the type shown in the foregoing illustration evolved which is practically the one adopted in our modern chant books.

Illustration VII ("Pal. Mus.", III, pl. 207 B) [Text, X, 771] is taken from a fourteenth-century plenary

Neum

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