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Gregorian square neume ligatures

There is limited support for Gregorian square neumes notation (following the style of the Editio Vaticana). Core ligatures can already be typeset, but essential issues for serious typesetting are still lacking, such as (among others) horizontal alignment of multiple ligatures, lyrics alignment, and proper handling of accidentals.

Note heads can be modified and/or joined.

• The shape of the note head can be modified by prefixing the note name with any of the following commands: \virga, \stropha, \inclinatum, \auctum, \descendens, \ascendens, \oriscus, \quilisma, \deminutum, \cavum, \linea.
• Ligatures, properly speaking (i.e., notes joined together), are produced by placing one of the joining commands \pes or \flexa, for upwards and downwards movement, respectively, between the notes to be joined.

A note name without any qualifiers will produce a punctum. All other neumes, including the single-note neumes with a different shape such as the virga, are in principle considered as ligatures and should therefore be placed between \[…\].

Single-note neumes

• The punctum is the basic note shape (in the Vaticana style: a square with some curvation for typographical finesse). In addition to the regular punctum, there is also the oblique punctum inclinatum, produced with the prefix \inclinatum. The regular punctum can be modified with \cavum, which produces a hollow note, and \linea, which draws vertical lines on either side of the note.
• The virga has a descending stem on the right side. It is produced by the modifier \virga.

Ligatures

Unlike most other neumes notation systems, the typographical appearance of ligatures is not directly dictated by the input commands, but follows certain conventions dependent on musical meaning. For example, a three-note ligature with the musical shape low-high-low, such as \[ a \pes b \flexa g \], produces a Torculus consisting of three Punctum heads, while the shape high-low-high, such as \[ a \flexa g \pes b \], produces a Porrectus with a curved flexa shape and only a single Punctum head. There is no command to explicitly typeset the curved flexa shape; the decision of when to typeset a curved flexa shape is based on the musical input. The idea of this approach is to separate the musical aspects of the input from the notation style of the output. This way, the same input can be reused to typeset the same music in a different style of Gregorian chant notation.

Liquescent neumes

Another main category of notes in Gregorian chant is the so-called liquescent neumes. They are used under certain circumstances at the end of a syllable which ends in a ‘liquescent’ letter, i.e., the sounding consonants that can hold a tone (the nasals, l, r, v, j, and their diphthong equivalents). Thus, the liquescent neumes are never used alone (although some of them can be produced), and they always fall at the end of a ligature.

Liquescent neumes are represented graphically in two different, more or less interchangeable ways: with a smaller note or by ‘twisting’ the main note upwards or downwards. The first is produced by making a regular pes or flexa and modifying the shape of the second note: \[ a \pes \deminutum b \] , the second by modifying the shape of a single-note neume with \auctum and one of the direction markers \descendens or \ascendens, e.g., \[ \auctum \descendens a \] .

Special signs

A third category of signs is made up of a small number of signs with a special meaning (which, incidentally, in most cases is only vaguely known): the quilisma, the oriscus, and the strophicus. These are all produced by prefixing a note name with the corresponding modifier, \quilisma, \oriscus, or \stropha.

Virtually, within the ligature delimiters \[ and \], any number of heads may be accumulated to form a single ligature, and head prefixes like \pes, \flexa, \virga, \inclinatum, etc., may be mixed in as desired. The use of the set of rules that underlies the construction of the ligatures in the above table is accordingly extrapolated. This way, infinitely many different ligatures can be created.

Note that the use of these signs in the music itself follows certain rules, which are not checked by LilyPond. E.g., the quilisma is always the middle note of an ascending ligature, and usually falls on a half-tone step, but it is perfectly possible, although incorrect, to make a single-note quilisma.

In addition to the note signs, LilyPond also defines the commands \versus, \responsum, \ij, \iij, \IJ, and \IIJ, that will produce the corresponding characters, e.g., for use in lyrics, as section markers, etc. These commands use special Unicode characters and will only work if a font is used which supports them.

The following table shows a limited, but still representative pool of Gregorian ligatures, together with the code fragments that produce the ligatures. The table is based on the extended neumes table of the 2nd volume of the Antiphonale Romanum (Liber Hymnarius), published 1983 by the monks of Solesmes. The first column gives the name of the ligature, with the main form in boldface and the liquescent forms in italics. The third column shows the code fragment that produces this ligature, using g, a, and b as example pitches.

Single-note neumes

Basic and Liquescent forms	Output	LilyPond code
Punctum		\[ b \]
		\[ \cavum b \]
		\[ \linea b \]
Punctum Auctum Ascendens		\[ \auctum \ascendens b \]
Punctum Auctum Descendens		\[ \auctum \descendens b \]
Punctum inclinatum		\[ \inclinatum b \]
Punctum Inclinatum Auctum		\[ \inclinatum \auctum b \]
Punctum Inclinatum Parvum		\[ \inclinatum \deminutum b \]
Virga		\[ \virga b' \]

Two-note ligatures

Clivis vel Flexa		\[ b \flexa g \]
Clivis Aucta Descendens		\[ b \flexa \auctum \descendens g \]
Clivis Aucta Ascendens		\[ b \flexa \auctum \ascendens g \]
Cephalicus		\[ b \flexa \deminutum g \]
Podatus/Pes		\[ g \pes b \]
Pes Auctus Descendens		\[ g \pes \auctum \descendens b \]
Pes Auctus Ascendens		\[ g \pes \auctum \ascendens b \]
Epiphonus		\[ g \pes \deminutum b \]
Pes Initio Debilis		\[ \deminutum g \pes b \]
Pes Auctus Descendens Initio Debilis		\[ \deminutum g \pes \auctum \descendens b \]

Multi-note ligatures

Torculus		\[ a \pes b \flexa g \]
Torculus Auctus Descendens		\[ a \pes b \flexa \auctum \descendens g \]
Torculus Deminutus		\[ a \pes b \flexa \deminutum g \]
Torculus Initio Debilis		\[ \deminutum a \pes b \flexa g \]
Torculus Auctus Descendens Initio Debilis		\[ \deminutum a \pes b \flexa \auctum \descendens g \]
Torculus Deminutus Initio Debilis		\[ \deminutum a \pes b \flexa \deminutum g \]
Porrectus		\[ a \flexa g \pes b \]
Porrectus Auctus Descendens		\[ a \flexa g \pes \auctum \descendens b \]
Porrectus Deminutus		\[ a \flexa g \pes \deminutum b \]
Climacus		\[ \virga b \inclinatum a \inclinatum g \]
Climacus Auctus		\[ \virga b \inclinatum a \inclinatum \auctum g \]
Climacus Deminutus		\[ \virga b \inclinatum a \inclinatum \deminutum g \]
Scandicus		\[ g \pes a \virga b \]
Scandicus Auctus Descendens		\[ g \pes a \pes \auctum \descendens b \]
Scandicus Deminutus		\[ g \pes a \pes \deminutum b \]

Special signs

Quilisma		\[ g \pes \quilisma a \pes b \]
Quilisma Pes Auctus Descendens		\[ g \quilisma a \pes \auctum \descendens b \]
Oriscus		\[ \oriscus b \]
Pes Quassus		\[ \oriscus g \pes \virga b \]
Pes Quassus Auctus Descendens		\[ \oriscus g \pes \auctum \descendens b \]
Salicus		\[ g \oriscus a \pes \virga b \]
Salicus Auctus Descendens		\[ g \oriscus a \pes \auctum \descendens b \]
(Apo)stropha		\[ \stropha b \]
Stropha Aucta		\[ \stropha \auctum b \]
Bistropha		\[ \stropha b \stropha b \]
Tristropha		\[ \stropha b \stropha b \stropha b \]
Trigonus		\[ \stropha b \stropha b \stropha a \]

Predefined commands

The following head prefixes are supported: \virga, \stropha, \inclinatum, \auctum, \descendens, \ascendens, \oriscus, \quilisma, \deminutum, \cavum, \linea.

Head prefixes can be accumulated, though restrictions apply. For example, either \descendens or \ascendens can be applied to a head, but not both to the same head.

Two adjacent heads can be tied together with the \pes and \flexa infix commands for a rising and falling line of melody, respectively.

Use the unary music function \augmentum to add augmentum dots.

See also

Music Glossary: ligature.

Notation Reference: Gregorian square neume ligatures, White mensural ligatures, Ligatures.

Known issues and warnings

When an \augmentum dot appears at the end of the last staff within a ligature, it is sometimes vertically placed wrong. As a workaround, add an additional skip note (e.g., s8) as last note of the staff.

\augmentum should be implemented as a head prefix rather than a unary music function, such that \augmentum can be intermixed with head prefixes in arbitrary order.