This question arose at the end of another discussion, but since nobody gave an answer and I believe it may be important on its own I repeat it here:
Can anyone point me to an explanation of circulus, semi-circulus and reversed semi-circulus accents? These are featured in the ordinary of the Mass chants of Anton Stingl's website Gregor und Taube (together with the [horizontal] episema---I also do not know if its meaning in this context is the same as in the so-called Solesmes method), and are supported by the Gregorio project, but till now I have never seen their use described, or justified from manuscripts.
Just from looking at the examples, it appears that the full circle indicates a syllable on an accented text which has only one note, but is followed by more than one note on the following unaccented syllable; Thus, although you might count it as a 2 or 3, it receives a text accent. The half circle is the opposite: it marks an unaccented syllable which is counted as a 1, but must be unaccented. The half circle is the mark in prosody for a short or unaccented syllable.
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