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Neumes are an ancient musical notation used to write down Gregorian plainsong. They are very well suited to this kind of monophonic, melismatic music. As neumes were used during the Middle Ages, a period that covers a millennium, in all regions of Western Europe, they exist naturally in dozens of flavors. The earliest neumes were simply accent marks over the lyrics, showing the outline of the melody, whereas the most sophisticated ones indicate even the smallest nuances of the music, or trace the melismas in an elaborate, almost artistic way.
The major neumatic traditions include:
- Sangallian neumes (Sankt-Gallen, Switzerland)
- Beneventan neumes (Benevent, Italy)
- Mozarabic or hispanic neumes (Spain)
- Messine neumes (Laon, France)
- Aquitanian neumes
- Germanic neumes
- Modern square neumes
Many neumatic notations do not indicate pitch precisely, but rather show the outline of individual pitch groups -- this is called in campo aperto. Later, neumatic systems evolved in which the vertical position had a relation with the pitch -- these are diastematic notations. Later still, horizontal lines were added to clarify the notation further -- these evolved on to our modern staff notation.
Sangallian neumes
The neumes of Sankt-Gallen are a "classic" and easy to learn variety, having a simple form, yet an enormous power due to their ample repertory of expressive markings.
Basic 1-note neumes: (some images missing: approximating with text characters)
- high note:
 (virga "staff")
- low note:
 (punctum "point") or - (tractulus "dash")
Basic 2-note neumes:
- low-high:
 Variants:   (pes or podatus "foot")
- high-low:
 Variants:   (clivis)
Basic 3-note neumes:
- low-high-low: J\ (torculus)
- high-low-high: ∩/ (porrectus)
- three rising notes: ../ (scandicus)
- three falling notes: /.. (climacus)
Basic neumes can be joined to form longer melismas, for example
- low-high-2 falling: J.. (pes subbipunctis "foot with two points underneath")
- low-high-low-high: J\/
- low-high-low-high-low-high-low-high-2 falling: J\∩∩/..
Expressive neumes (having sometimes quite obscure and discutable interpretations):
- ' (apostropha), '' (bistropha), ''' (tristropha)
- ∴ (trigon "triangle")
- ~ (oriscus)
- ~. (pressus minor), /~. (pressus maior)
- .~/
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