Gregorian Chant Notation
If you've ever glimpsed an ancient page of music from the liturgy of masses from ages gone past that appears really different from what you might be accustomed to from your studies of J. S. Bach and Wolfgang Amadeus Mozart, it's probable you've seen Gregorian Chant (hereafter referred to simply as "Chant"). Square notes, fewer lines and spaces--it's all quite different from what you'll be used to. Let's go through a brief overview before I introduce you to the neumes of Chant.
Note!!! ASCII was never meant to describe Chant notation. I've done my best here, but because of the limitations of the form, some may remain hazy. I apologize for this, there's nothing to be done. If you require further description of each of these notes, I can direct you to a variety of websites that preserve Chant manuscripts. Additionally, there are several programs out there that will notate music in Chant form, my favorite of which is called Gregoire, and can be downloaded for free from
http://gregoire.tele.free.fr/index.php. I have found the programmer to be a very kind man, who has answered several questions of mine regarding the program with eagerness and a smile.
On normal music notation, you'll see 5 lines and 4 spaces that are the base boundaries for the notes. In Chant, you'll see 4 lines, 3 spaces. No time signature is given at the front of the music (the point being that the singers are to follow the director), and the key signature is indicated by a single mark on the far left side of the staff, situated on the line on which the note we now call "C" (Do) or "F" (Fa) occurs, depending on which of the above two marks are used.
The most startling difference between modern music notation and Chant neumes is that it would be nearly impossible to list all the modern day iterations available. Imagine, if you will, listing all possible quarter-note-to-quarter-note pairs, from C to C#, from C to D, from C to D#, &c. That, alone, would outnumber the available neumes in Chant. But the unabashed simplicity of Chant means that if you know how a Virga subtripunctus sounds, you can sing that neume wherever it falls on the staff, so long as you start on the right note.
Perhaps Chant's greatest strength is that it is incredibly easy to change the key signature of the music. If your choir doesn't particularly like having a piece start so high and stay in the upper register for its whole length, simply start lower. The key signature noted is a recommendation, set within the bounds of Catholic liturgy, based on historical precedent. But that doesn't mean you cannot change it to suit a given choir. Remember, the basic principle of Chant is the glorification of prayer, and if it sounds terrible for your choir to sing it too high or too low, then the Chant is happy to be changed.
This here, the Punctum ("point"), is the very base of Gregorian chant. When it stands all alone, it can be called the quarter note of the staff. In running lines, where a single tone runs across long phrases, each word/syllable is noted by the Punctum. The Punctum is used by itself and in combination, to create nearly all of the other neumes of Chant, though technically it only exists at the bottom of the Podatus and Clivis, all three parts of the Torculus, etc. When a descender sits on the right of a Punctum, it is then a Virga, at which point additional notes can be tacked on. The Virga will never sit alone--when it is alone, it is a Punctum.
Perhaps that requires a bit more explanation. The Virga acts in long strings of ascending then descending tones as the top of the ascent. That is to say, when you're singing note A followed by note B a step up, then note C a step up again, and then back to note B then A, note C is often notated as a Virga, a visual mark to say "Hey, you're gonna descend after this note!" As you look at the two-, three- and four-note neumes, pick out the Virga, and note that where one exists, it's immediately followed by a note lower than the one you're looking at.
_ _ _
|#| |#|_ |#| 
_| | |#| | _|
|#| |  |#|
Podatus Clivis Cephalicus Epiphonus
The Podatus is the first step into making the chant sound like what you all expect. Though on a staff it looks a bit like a chord (root + third), in chant it serves a very different purpose. Two notes, one on top of the other, simply means sing the bottom and then the top (see Scandicus flexus for the beginnings of the exceptions to this rule). The Podatus comes in any variety you want, though is most commonly the first-third, first-fourth, and first-fifth of any given chord. The Clivis is a simple descending tone, one note followed by the next whole step down.
The second pair of neumes (Cephalicus and Epiphonus) utilize smaller notes on half of the tone. As is logical, this merely means to give that note a shorter value and, generally, a lighter tone quality. In both cases, the Punctum is sung first, and is allowed to be done so in a slightly longer and slightly louder tone, depending on the director. The smaller note can also draw attention to the consonant of the tone, indicating careful enunciation.
Though not technically a neume, when two Punctums occur right next to each other on a single syllable, as the only tones for that syllable, it should be sung as a note of double length. If it occurs as a juxtaposition of two groups, the note is well accented.
_ _ _ _ _ _  _
|#| |\ |#| |#| _|#|_ |#| |#|_| |#|
_| |\\ _| | /\ |#| |#| | | | |#| _`\\
_|#| | \|#| | \//\ _| | |#| `
|#| \/ |#| 
Scandicus Porrectus Climacus Torculus Pinmosa Scandicus Quilisma
Three- and four-note neumes begin to make the reader question Gregorian chant. No doubt you recognize that these structures are all created using the punctum, basically, with a few extra lines and dashes for dramatic purpose. The punctum, like the whole note, is a piece of all structures to follow (that is to say all other notes, such as the quarter note, are based off of the length of the whole note). The Porrectus, for example, is played much like a triplet in modern music, with note A, followed by note B a whole step lower, and back to note A, each tone receiving the same length. The wide slash between the first and second note replaces the punctum that should exist at the front. A Torculus is merely a Porrectus in reverse, note A followed by note B a step higher, and back to note A.
Note that three-note neumes also allow for the half-size punctum, in the Pinmosa and Scandicus liquescens. The natural, unwritten notation is to give the first two notes slightly longer lengths and emphasis. In these cases, it is also often the case the the next neume to follow will likely be either the note you end on, or a half step above or below.
This category also introduces the diamond-shaped neume, called an Apostropha, and is no different from a Punctum, safe for being turned 45 degrees, and is always showing a descending pattern, one whole step at a time, with two or more tones. Sometimes, the Apostropha will occur as three notes, on the same tone, right next to each other, on the same syllable of a word. When this occurs, it indicates a short swelling out of the tone (crescendo) followed by a similar diminishing (decrescendo). If the three-note Apostropha is not on the same syllable of a word, it indicates a simple repetition, with the crescendo and decrescendo.
Though technically not a three-note neume, the Quilisma has been included in this list because it requires at least two notes, and generally is involved with three. It is also my absolute favorite of the neumes in Chant. The note itself, depicted as either a squiggly line the width of a Punctum, or as a Punctum with a crown on top, is sung as a normal length tone. The note preceding it, however, is sung as twice as long as the normal tone. Brilliant, no?
_ _ _ _ _ _ _
_ |#| |\ |#|_ |#| _|#|_|#| |#| |#|
|#|| | |\\ _| |#| | /\ _ |#| |#| | _|/\ |/\
_|| |_ | \|#| | \//\|#| | |#|\//\ |\//\
|#| |#| \/ \/ \//\
Scandicus Porrectus Climacus Torculus Pes Virga
flexus flexus respinus respinus subtripuntis subtripunctus
By now, you're a pro at recognizing the neumes of Chant, so this paragraph will be relatively brief. Obviously, nearly all of these neumes are simple expansions of the three-note varieties, in some cases simply tacking on another note following the pattern of the three-note option, as is the case between the Virga subtripunctus and the Climacus.
The four-note neumes show in the most vivid color that Chant is very easy to learn, and even with the more complex patterns, once you get it the first time, you can sing it on any note, at any time, whenever it comes up. That is the strength of Chant, and its simplicity is its beauty. With relatively little work, a choir can put together a whole sung mass setting in relatively little time if the base neumes are all learned. The congregation can easily join in on Chant masses as well, making it the natural choice for a sung mass (Anglican Chant, on the other hand, is more difficult to learn, and is more rigid in style).