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A dot after a note adds half of its duration. This is called a “dotted note”. I am interested in the history of the dot itself. How is it called, and what is its origin. I’m looking for earliest original sources.

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The formal name is the Dot of Augmentation (or Point of Augmentation, particularly in British sources). This is to distinguish it among the four classes of dots/points that were used in earlier music.

This link gives a good summary. The thing one must understand about dot usage in early music (so-called "mensural notation," the earlier form of Western rhythmic notation) is that there were complex rules revolving around the interpretation of the duration of notes. In our modern notation, note shapes always denote the same relative duration to other note shapes. That was not true in early music, where the same note shape could have various lengths relative to other note shapes, depending on a lot of complicated rules. (The first few pages here attempt to summarize the most common rules for typical renaissance-era notation.) The one essential concept had to do with "perfection" which was generally when a note had a value of three times a smaller note value, versus "imperfection" where that same note shape had a value of two times the smaller note value.

Basically, the four classes of dot in medieval and early renaissance music were:

  1. Dot of Augmentation (punctus augmentationis) - essentially equivalent to our modern dot, it had an effect of adding half the value to the preceding note.
  2. Dot of Perfection (punctus perfectionis) - a dot that restored an imperfect note (which was interpreted as imperfect due to its context) to a perfect note value, often in effect similar to the dot of augmentation.
  3. Dot of Alteration (punctus alterationis) - a dot that was used to create an alteration, which in mensural notation meant that a note was doubled in length to complete a perfection (group of 3). There were rules where alteration happened automatically according to context of the rhythm, but in some cases it might be confusing to keep track of where it occurred. Hence the dot of alteration, which doubled ("altered") the duration of the note that occurred two notes later.
  4. Dot of Division (punctus divisionis) - a dot merely present to function as a sort of "barline" in ambiguous rhythms. It simply showed were one perfection (group of 3) ended and another began.

All of these dots basically look the same, so it can be confusing to those unfamiliar with mensural music when one of the more obscure types occurs. (The last two types sometimes are notated above or below noteheads, rather than following them, but this usage is inconsistent.)

As noted, the Dot of Augmentation and the Dot of Perfection basically had similar effects (though on different rhythmic levels, and sometimes required in different contexts). And that effect of adding 50% of the note duration is equivalent to our modern dot. The latter two types of dots fell out of use with the demise of mensural rhythmic notation in the 17th century, where they were rendered unnecessary as note shapes now always determined relative duration.

As for the origin of the Dot of Augmentation, it appears even in early chant sources predating the use of exact rhythmic notation, so it's hard to give it an exact origin. At that point, it denoted a general lengthening of a note, rather than specifically adding 50% of the length. Once the earliest rhythmic notation develops in the late 1100s (modal rhythmic notation), the Dot of Augmentation was adapted into the Dot of Perfection to show groups of 3 by lengthening a note with duration 2 into 3. However, if I remember correctly, this also created the Dot of Division, as a dot that made a complete perfection (three "beats") by transforming a note of length 2 into 3 also could serve a showing a division point between two perfections.

In any case, the emphasis of the 2 vs. 3 element in modal notation seemed to cement the idea of the Dot of Augmentation/Perfection in a specific 2:3 ratio for notes with the added dot. That ultimately resulted in its application to other note values with a 50% addition in value, hence our modern Dot of Augmentation.

To summarize the earliest history: dots appear in various early chant sources, just indicating some sort of general lengthening of a note. When rhythmic notation first emerged around 1200, it emphasized groups of 2 vs. 3 subdivisions, so the dot was newly interpreted to specifically indicate this 2:3 ratio, as it still does.

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Great question, as far as in know it’s called a dot, or dotted note, no other name I’m aware of. Before the modern day use of the dot which adds 1/2 to a note’s duration it was used in Gregorian Chant but it had a different meaning then. Since specific rhythms were not notated it simply meant a note held for a longer duration. There is a bit of info on it towards the bottom of this web page:

http://www.lphrc.org/Chant/

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