Speak about something vs Speak of something vs Speak on something

speak about something—talk about smth.; discuss smth.:

• We don’t speak about that unfortunate period in our family history.

Cf.: speaking about something—(also: speaking of something) used to introduce once again the subject that has just been mentioned:

• The weather affects how we think, move, and feel. Speaking about the weather I have to say, that our natural conditions are very similar to yours.

speak of something—

1. = speak about something:

• The colonel very rarely spoke of his war experiences.

2. (of things or actions) give proof in favor of smth.; be evidence of smth. (also: speak for something ):

• This gift of money speaks of your generosity.

speak on something—speak at greater length on a subject; deliver a talk about smth.:

• I’ve been asked to speak on the future of education for very young children.