Could someone explain a little more about the concept of diminution - as mentioned by Fux. I understand it is a form of "improvisation" where a singer adds intervening notes, but there seems some form of rules for its application that are not apparent to me.

thanks in advance

Zero

I am not familiar with Fux, but I do know that diminution is a technique where a theme is played at twice the rate as usual. A Quarter would be played thus as an eighth.

It is the opposite to the technique of augmentation, where the theme is played at half speed. A quarter is then a half

Augmentation is used more frequently in the fugues of Bach.

I realize that I am giving quite basic information here, so please forgive me if you are talking about something different.

Fux's diminution is related to the normal definition as explained by pianoexcellence, but he uses it in reference to what we might call passing tones. For example, on page 33, Fux shows us the skip of a 5th using two whole notes. Then, he shows us the same thing again, but with the first whole note being subdivided into four quarter notes diatonically leading down to the 2nd whole note. So we have D descending a perfect 5th directly to G, then D desecending to G by diatonic stepwise motion - the same melodic interval but via "diminution."

I hope this helps!

Thanks, passing tones I understand. From what is said I can think of dimunition of substituting passing tones between two counterpoint positions, I presume these must be diatonic of course.
When the diminution tones are substituted - these are treated as part of the counterpoint and subject to the rules - I think?
Sometimes Fux seems to consider diminution as infered - the notes being hidden or implied, I am not sure if he is thinking that this is always the case between all counterpoint tones, or if he is only sometimes considering it.

Yes, the rules would still apply with diminution, which is why Fux brings it up to prove his point about direct motion to a perfect consonance. Fux calls attention to diminution because the possibility of it occurring must be considered when making choices about voice leading (actually, we don't really have to consider it if we just follow the rule; but Fux is giving us a reason for this rule).

Got it - thanks harmosis - again. Today I downloaded "Counterpointer" software which will allow my exercises to be marked - and give aural feedback. I will post when I get it going.
I currently feel like I am learning more about history than music - but I shall persevere