7.7.10.2 Gregorian square neumes 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.

The following table contains the extended neumes table of the 2nd volume of the Antiphonale Romanum (Liber Hymnarius), published 1983 by the monks of Solesmes.

Neuma aut Neumarum Elementa	Figurae Rectae	Figurae Liquescentes Auctae	Figurae Liquescentes Deminutae
1. Punctum
2. Virga
3. Apostropha vel Stropha
4. Oriscus
5. Clivis vel Flexa
6. Podatus vel Pes
7. Pes Quassus
8. Quilisma Pes
9. Podatus Initio Debilis
10. Torculus
11. Torculus Initio Debilis
12. Porrectus
13. Climacus
14. Scandicus
15. Salicus
16. Trigonus

Unlike most other neumes notation systems, the input language for neumes does not reflect the typographical appearance, but is designed to focus on musical meaning. For example, \[ a \pes b \flexa g \] produces a Torculus consisting of three Punctum heads, while \[ a \flexa g \pes b \] 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.

The following table shows the code fragments that produce the ligatures in the above neumes table. The letter in the first column in each line of the below table indicates to which ligature in the above table it refers. The second column gives the name of the ligature. The third column shows the code fragment that produces this ligature, using g, a, and b as example pitches.

#	Name	Input Language
a	Punctum	\[ b \]
b	Punctum Inclinatum	\[ \inclinatum b \]
c	Punctum Auctum Ascendens	\[ \auctum \ascendens b \]
d	Punctum Auctum Descendens	\[ \auctum \descendens b \]
e	Punctum Inclinatum Auctum	\[ \inclinatum \auctum b \]
f	Punctum Inclinatum Parvum	\[ \inclinatum \deminutum b \]
g	Virga	\[ \virga b \]
h	Stropha	\[ \stropha b \]
i	Stropha Aucta	\[ \stropha \auctum b \]
j	Oriscus	\[ \oriscus b \]
k	Clivis vel Flexa	\[ b \flexa g \]
l	Clivis Aucta Descendens	\[ b \flexa \auctum \descendens g \]
m	Clivis Aucta Ascendens	\[ b \flexa \auctum \ascendens g \]
n	Cephalicus	\[ b \flexa \deminutum g \]
o	Podatus vel Pes	\[ g \pes b \]
p	Pes Auctus Descendens	\[ g \pes \auctum \descendens b \]
q	Pes Auctus Ascendens	\[ g \pes \auctum \ascendens b \]
r	Epiphonus	\[ g \pes \deminutum b \]
s	Pes Quassus	\[ \oriscus g \pes \virga b \]
t	Pes Quassus Auctus Descendens	\[ \oriscus g \pes \auctum \descendens b \]
u	Quilisma Pes	\[ \quilisma g \pes b \]
v	Quilisma Pes Auctus Descendens	\[ \quilisma g \pes \auctum \descendens b \]
w	Pes Initio Debilis	\[ \deminutum g \pes b \]
x	Pes Auctus Descendens Initio Debilis	\[ \deminutum g \pes \auctum \descendens b \]
y	Torculus	\[ a \pes b \flexa g \]
z	Torculus Auctus Descendens	\[ a \pes b \flexa \auctum \descendens g \]
A	Torculus Deminutus	\[ a \pes b \flexa \deminutum g \]
B	Torculus Initio Debilis	\[ \deminutum a \pes b \flexa g \]
C	Torculus Auctus Descendens Initio Debilis	\[ \deminutum a \pes b \flexa \auctum \descendens g \]
D	Torculus Deminutus Initio Debilis	\[ \deminutum a \pes b \flexa \deminutum g \]
E	Porrectus	\[ a \flexa g \pes b \]
F	Porrectus Auctus Descendens	\[ a \flexa g \pes \auctum \descendens b \]
G	Porrectus Deminutus	\[ a \flexa g \pes \deminutum b \]
H	Climacus	\[ \virga b \inclinatum a \inclinatum g \]
I	Climacus Auctus	\[ \virga b \inclinatum a \inclinatum \auctum g \]
J	Climacus Deminutus	\[ \virga b \inclinatum a \inclinatum \deminutum g \]
K	Scandicus	\[ g \pes a \virga b \]
L	Scandicus Auctus Descendens	\[ g \pes a \pes \auctum \descendens b \]
M	Scandicus Deminutus	\[ g \pes a \pes \deminutum b \]
N	Salicus	\[ g \oriscus a \pes \virga b \]
O	Salicus Auctus Descendens	\[ g \oriscus a \pes \auctum \descendens b \]
P	Trigonus	\[ \stropha b \stropha b \stropha a \]

The ligatures listed above mainly serve as a limited, but still representative pool of Gregorian ligature examples. 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.

Augmentum dots, also called morae, are added with the music function \augmentum. Note that \augmentum is implemented as a unary music function rather than as head prefix. It applies to the immediately following music expression only. That is, \augmentum \virga c will have no visible effect. Instead, say \virga \augmentum c or \augmentum {\virga c}. Also note that you can say \augmentum {a g} as a shortcut for \augmentum a \augmentum g.

     
     \include "gregorian-init.ly"
     \score {
       \new VaticanaVoice {
         \[ \augmentum a \flexa \augmentum g \]
         \augmentum g
       }
     }

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.

Bugs

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.