What do the Symbols ◒ and ◓ Signify In Old Chinese Poetry Books? I recently bought an old manual of how 詞 (classical lyric) are supposed to be "filled".  The pages look like this:



Naturally am curious about the meaning of the circle symbols next to each characters and suspect they are related to classical "平／仄" phonology.  Indeed ◯ seems associated exclusively with 平声 and ● appears to refer to anything but 平声: specifically 去／入／上声.  

However I am baffled about the significance of ◒ and ◓.  Analysis of some 菩薩蠻 lyrics indicates that the half-symbols, intuitively enough, mean that either 平/not-平 is allowable in that position in the lyric. For example, the first line of such a lyric has the pattern:

◒◯◓●◯◯●,

And the following are legal tonal groups (based on a pull of some 词 and conversion of the lyrics to classically defined tonal categories):

平平入入平平入
or
去平平去平平去

In that case what is the difference between ◒ and ◓?  Since baidu-ing "circle things AND classical poetry" has not proven fruitful, so thought I would ask for help here.  What are those "circle things" even called, properly?
Seems to be 清浊音, with ◒、◓ representing 次清、次浊. There are no tones in old Chinese, so it can't be 平／仄, but the way the tones emerged can well be heavily related to the voice of the consonant.